diff --git a/-dFLT4oBgHgl3EQfCy73/content/2301.11977v1.pdf b/-dFLT4oBgHgl3EQfCy73/content/2301.11977v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..416eafa98c9e0ee3ffb51d760684b2720806dccb --- /dev/null +++ b/-dFLT4oBgHgl3EQfCy73/content/2301.11977v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d2ce6054b64c91e967c5004671e480b2ecb158e39387dc70a99955c5006ddae1 +size 1125971 diff --git a/-dFLT4oBgHgl3EQfCy73/vector_store/index.faiss b/-dFLT4oBgHgl3EQfCy73/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..a657bad2cc55f7a183b899b6d788419459acab77 --- /dev/null +++ b/-dFLT4oBgHgl3EQfCy73/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ee72983ec499880bb3d7f86b4960609c2598a388bd4d82a47a7752fe562c999d +size 2687021 diff --git a/-tE2T4oBgHgl3EQfmQed/content/tmp_files/load_file.txt b/-tE2T4oBgHgl3EQfmQed/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..16afe2a3a4c428335e787ba9cd1e0cd9e4cf0a7b --- /dev/null +++ b/-tE2T4oBgHgl3EQfmQed/content/tmp_files/load_file.txt @@ -0,0 +1,1881 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf,len=1880 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='03997v1 [math-ph] 10 Jan 2023 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION ALEC COOPER1, BART VLAAR1,2, AND ROBERT WESTON1 Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the algebraic approach to Baxter’s Q-operators for the closed Heisenberg XXZ spin chain, certain infinite-dimensional ‘prefundamental’ representations of the q-deformed Borel subal- gebras play a central role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To extend this formalism to open spin chains, one needs a factorization identity for particular solutions of the reflection equation associated to these representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the case of quantum affine sl2, we derive such an identity using the recent theory of universal K-matrices for quantum affine algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Contents 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Introduction 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quantum affine sl2 and its universal R-matrix 4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The augmented q-Onsager algebra, its twists and its universal K-matrices 10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Borel representations in terms of the q-oscillator algebra 14 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' L-operators and R-operators 19 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' K-matrices 20 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Fusion intertwiners revisited 22 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boundary factorization identity 23 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Discussion 26 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed Pochhammer symbols and exponentials 26 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Explicit expressions for R-operators 29 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' An alternative proof of the main theorem 34 References 37 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Introduction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Background and overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baxter first introduced his Q-operator in [Ba72, Ba73] as an auxiliary tool in the derivation of Bethe Equations for the eigenvalues of the 8-vertex model transfer matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key characters in the story are the transfer matrix T pzq and the Q-operator Qpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A detailed description of the essential properties of T pzq and Qpzq can be found in [BLZ97] (also see [VW20] and references therein);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' the key relation that they satisfy that leads directly to the Bethe equations is of the form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) T pzqQpzq “ α`pzqQpqzq ` α´pzqQpq´1zq, 1Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK 2Beijing Institute for Mathematical Sciences and Applications, 11th Building (Fengye Villa), Yanqi Island, Huairou, Beijing, China E-mail addresses: awc4@hw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='uk,b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='vlaar@bimsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='cn,r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='weston@hw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='uk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Primary 81R10, 81R12, 81R50;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Secondary 16T05, 16T25, 39B42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 2 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION where α˘pzq are meromorphic functions and q P Cˆ is not a root of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the original papers of Baxter, the operator Qpzq was constructed by a brilliant but ad hoc argument;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' the representation-theoretic construction of Qpzq had to wait more than 20 years until the work of Bazhanov, Lukyanov and Zamolodchikov [BLZ96, BLZ97, BLZ99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The main idea of the latter approach is to construct both T pzq and Qpzq as partial traces over different representations of the universal R-matrix R of Uqppsl2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The operator T pzq is a twisted trace over a two-dimensional Uqppsl2q-representation Πz, and Qpzq is a similarly twisted trace over an infinite-dimensional Uqppb`q- representation ρ` z , where Uqppb`q is a Borel subalgebra of Uqppsl2q (the relevant representations are defined in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4 of the current paper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The relation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) for closed spin chains then follows immediately by considering a short exact sequence (SES) of Uqppb`q-representations with Πz b ρ` z as its ‘middle’ object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The extension of this approach to Q-operators for the open XXZ chain was carried out in [VW20] and details and references can be found therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As well as this direct SES route to the equation, there is an alternative strategy which we refer to as the ‘factorization approach’;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' for closed chains see [BS90, De05, DKK06, De07, BJMST09, BLMS10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In fact, this approach was the one taken by Bazhanov, Lukyanov and Zamolodchikov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The work that developed this formalism in language most similar to the current paper, in particular the formulation of the intertwining property of the operator O` (defined in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5 of the current paper), is [KT14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this approach, a second operator Qpzq with similar properties to Qpzq is introduced as a trace of R over another infinite-dimensional representation ¯ρ` z of Uqppb`q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The affinized version υz of the Uqpsl2q-Verma module is also considered as well as an another infinite-dimensional filtered Uqppb`q-module φ` z ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' these two representations depend on a complex parameter µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key connec- tion between all representations is given by Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6, which expresses the fact that particular pairwise tensor products are isomorphic as Uqppb`q-modules by means of an explicit intertwiner O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' At the level of the L-operators this implies (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) O` 12L` ̺ pqµzq13L` ¯̺ pq´µzq23 “ L` υ pzq13L` φ pzq23O` 12, (see Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 of the current paper), which is referred to as factorization of the Verma module L-operator L` υ pzq in terms of the L-operators L` ̺ pzq and L` ¯̺ pzq which can be used to define Qpzq, Qpzq (the additional operator L` φ pzq is triangular and hence the corresponding transfer matrix is diagonal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Defining Tµpzq to be the transfer matrix that is the trace over the µ-dependent representation υz of R in the first space, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 yields a relation of the following form: (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) Tµpzq 9 Qpzq´µ{2q ¯Qpzqµ{2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A consideration of the SES structure associated with υz when µ is an integer then leads to the key relation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The main result of the current paper is the following boundary analogue of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2, which we call the boundary factorization identity: (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) Kυpzq1Rυφpz2qKφpzq2 O` “ O`K̺pqµzq1R̺¯̺pz2qK¯̺pq´µzq2 where z is a formal parameter (which can be specialized to generic complex numbers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The precise statement is given in Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This formula involves the actions of the universal R-matrix of Uqppsl2q in tensor products of the various infinite-dimensional representations introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In addition, the various K-operators are diagonal solutions of reflection equations (boundary Yang- Baxter equations) [Ch84, Sk88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' They arise as actions of the universal K-matrix associated to a A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 3 particular coideal subalgebra of Uqppgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is the augmented q-Onsager algebra, which featured also in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BB13, RSV15, BT18, VW20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It plays the role of ‘boundary quantum group’: it is the subalgebra of quantum symmetries compatible with a particular system of boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, diagonal solutions of the reflection equation with a free parameter, considered by Sklyanin in his 2-boundary version of the algebraic Bethe ansatz, see [Sk88], are intertwiners for this algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) has a natural diagrammatic formulation - see Section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In a subsequent paper the authors will explain how (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) yields relations analogous to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) and hence (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) for open chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The proof of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) and of the well-definedness of the various K-operators is an application of the universal K-matrix formalism developed in [AV22a, AV22b] which is built on the earlier works [BW18, BK16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, it relies on an extension of the theory of K-matrices for finite- dimensional Uqppgq-representations in [AV22b] to level-0 representations of Uqppb`q, which we discuss in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key point is that, for the special case of the augmented q-Onsager algebra there exists a universal element K, centralizing the augmented q-Onsager algebra up to a twist, with three desirable properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (i) The element K lies in (a completion of) the Borel subalgebra Uqppb`q, so that the resulting family of linear maps is itself compatible with Uqppb`q-intertwiners (which play an essential role in the algebraic theory of Baxter Q-operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (ii) The coproduct of K is of a particularly simple form, which is relevant for the proof of the boundary factorization identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (iii) The linear operators accomplishing the action of K in level-0 representations satisfy the untwisted reflection equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Thus we obtain the factorization identity (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) as a natural consequence of the representation theory of Uqppgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The main benefit of this universal approach is that laborious linear-algebraic computations are avoided;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' in particular, explicit expressions for the various components are not necessary at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nevertheless, we do provide these explicit expressions, as we expect them to be useful in further work in this direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We also give an alternative computational proof of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4), to further illustrate the power of the universal approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The above approach is a boundary analogue of the level-0 theory of the universal R-matrix of Uqppsl2q, which underpins e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' the construction in [KT14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As a prelude, in Section 2, we also provide rigorous derivations of properties of the action of the universal R-matrix on tensor prod- ucts of level-0 representations (this section is written for the pertinent quantum affine algebra Uqppsl2q, but the proofs naturally generalize to any quantum untwisted affine algebra).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In par- ticular, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 states that the grading-shifted universal R-matrix has a well-defined action as a linear-operator-valued formal power series on tensor products of any level-0 representations of Uqppb`q and Uqppb´q-modules (this includes, but is not restricted to, finite-dimensional repre- sentations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' often this well-definedness is tacitly assumed, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [VW20, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This result also follows from the Khoroshkin-Tolstoy factorization [TK92] of the universal R-matrix, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BGKNR10, BGKNR13, BGKNR14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Here we give a proof closer in style to the original work by Drinfeld and Jimbo [Dr85, Dr86, Ji86a, Ji86b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The only additional assumption is the use of the principal grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Outline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Section 2 we study the action of the universal R-matrix of quantum affine sl2 on tensor products of level-0 representations of Borel subalgebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Section 3 is a ‘boundary coun- terpart’ to Section 2, where we consider the augmented q-Onsager algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We show that its 4 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION standard universal K-matrix, see [AV22a, AV22b], has a well-defined action on level-0 representa- tions of Uqppb`q, see Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5, and, with a simple correction, satisfies the above three desirable properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Section 4 we discuss the relevant representations of Uqppb`q in terms of (an extension of) the q-oscillator algebra, as well as the Khoroshkin-Tsuboi Uqppb`q-intertwiner O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Section 5 we introduce various solutions of Yang-Baxter equations as actions of the universal R-matrix in tensor products of Borel representations, making use of the results of Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Similarly, in Section 6 we introduce solutions of the reflection equation as a actions of the universal K-matrix in Borel representations, which relies on Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Next, in Section 7 we revisit the SES approach to Baxter’s Q-operators for the open XXZ spin chain in light of the universal K-matrix formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Finally, in Section 8 we give a diagrammatic motivation of the boundary factorization identity (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) for the open XXZ spin chain, and provide a short proof using the level-0 theory developed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Some supplementary material is given in appendices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Namely, Appendix A provides some back- ground material on deformed Pochhammer symbols and exponentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, we derive some commutation relations used in the proof of the key intertwining property of the operator O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The final two appendices provide a proof of the boundary factorization identity which is independent of the universal K-matrix approach (but still requiring some of the level-0 theory of the universal R-matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, Appendix B contains derivations of the explicit expressions of the two R-operators appearing in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Appendix C we provide an alternative proof of the boundary factorization identity (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4), relying on the explicit expressions of all involved factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key tool of this proof is provided by Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1, which consists of two product formulas involving deformed Pochhammer symbols and exponentials (to our best knowledge equation (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) is a new result).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' would like to thank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Appel and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Reshetikhin for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' would like to thank the Galileo Galilei Institute in Florence and the Centre de recherches math´ematiques in Montr´eal for their hospitality in the spring and autumn of 2022 during which some of this work was completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quantum affine sl2 and its universal R-matrix In this section we study the action of the universal R-matrix of the quasitriangular Hopf algebra quantum affine sl2 on tensor products of level-0 representations (including infinite-dimensional representations) of the Borel subalgebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We give a basic survey of the algebras involved, the representations and the quasitriangular structure and show that the universal R-matrix has a well- defined action on tensor products of all level-0 representations of the Borel subalgebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' General overview of finite-dimensional R-matrix theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To formulate a quantum integrable system in terms of an R-matrix, one needs a representation of a suitable quasitriangular Hopf algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To get trigonometric R-matrices, one can proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let g be a finite-dimensional simple Lie algebra and note that the untwisted loop algebra Lg “ g b Crz, z´1s has a central extension pg “ Lg ‘ Cc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In turn, this can be extended by an element d such that rd, Xs “ z d dzX to yield rg “ pg ‘ Cd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For a fixed Cartan subalgebra h Ă g we define ph :“ h ‘ Cc, rh :“ ph ‘ Cd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The Lie algebra rg is a Kac-Moody algebra and hence has a non-degenerate bilinear form p¨, ¨q, which restricts to a non-degenerate bilinear form on rh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' See e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ka90] for more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 5 The universal enveloping algebras Uppgq and Uprgq can be q-deformed, yielding non-cocommutative Hopf algebras (Drinfeld-Jimbo quantum groups) Uqppgq and Uqprgq, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Dr85, Dr86, Ji86a, TK92, Lu94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The nondegenerate bilinear form p¨, ¨q lifts to Uqprgq inducing a pairing between the q-deformed Borel subalgebras and hence a quasitriangular structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' On the other hand, the subalgebra Uqppgq has a rich finite-dimensional representation theory, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [CP94, CP95, KS95, Ch02, HJ12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The grading-shifted universal R-matrix has a well-defined action on tensor products of finite-dimensional representations of Uqppgq as a formal power series, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Dr86, FR92, He19]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We now discuss the extension of this theory to level-0 representations of Borel subalgebras in the case g “ sl2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quantum affine sl2 and its universal R-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Denoting the canonical Cartan generator of sl2 by h1, ph is spanned by h0 “ c ´ h1 and h1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The bilinear form on rh is defined by ph0, h0q “ ph1, h1q “ ´ph0, h1q “ 2, ph0, dq “ 1, ph1, dq “ pd, dq “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Fix ǫ P C such that q “ exppǫq is not a root of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all x P C we will denote exppǫxq by qx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' First, we define Uqpgq as the algebra generated over C by e, f and invertible k subject to the relations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) ke “ q2ek, kf “ q´2fk, re, fs “ k ´ k´1 q ´ q´1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following assignments determine a coproduct ∆ : Uqpgq Ñ Uqpgq b Uqpgq: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) ∆peq “ e b 1 ` k b e, ∆pfq “ f b k´1 ` 1 b f, ∆pk˘1q “ k˘1 b k˘1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It uniquely extends to a Hopf algebra structure on Uqpgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now the main algebra of interest, Uqppgq, arises as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 (Quantum affine sl2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We denote by Uqppgq the Hopf algebra generated by two triples tei, fi, kiu (i P t0, 1u), such that: (i) the following assignments for i P t0, 1u define Hopf algebra embeddings from Uqpgq to Uqppgq: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) e ÞÑ ei, f ÞÑ fi, k ÞÑ ki;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (ii) the following cross relations are satisfied: kikj “ kjki, kiej “ q´2ejki, kifj “ q2fjki, rei, fjs “ 0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) rei, rei, rei, ejsq2s1sq´2 “ rfi, rfi, rfi, fjsq2s1sq´2 “ 0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) for i ‰ j, where we have introduced the notation rx, ysp :“ xy ´ pyx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � Consider the affine Cartan subalgebra ph “ Ch0 ‘ Ch1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that its q-deformation Uqpphq “ xk˘1 0 , k˘1 1 y is isomorphic to the group algebra of the affine co-root lattice (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) pQ_ “ Zh0 ` Zh1 Ă ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To define the quantized Kac-Moody algebra Uqprgq, we need to choose an extension rQ_ of pQ_ (a lattice of rank 3 contained in rh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To explain our choice, note that the nontrivial diagram automorphism Φ of the affine Dynkin diagram, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' the nontrivial permutation of the index set t0, 1u, lifts to a linear automorphism Φ of ph which preserves the lattice pQ_.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Accordingly, it also lifts an involutive Hopf algebra automorphism of Uqppgq, also denoted Φ, via the assignments (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) Φpeiq “ eΦpiq, Φpfiq “ fΦpiq, Φpk˘1 i q “ k¯1 Φpiq for i P t0, 1u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 6 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quantized Kac-Moody algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The standard extension of the affine co-root lattice Zh0` Zh1`Zd is not so convenient for us, since extensions of Φ to rh which are compatible with the pairing between rh and its dual do not preserve this lattice, see also [Ko14, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6] and [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Setting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) dpr :“ ´1 8h0 ` 3 8h1 ` 2d, we obtain pdpr, h0q “ pdpr, h1q “ 1, pdpr, dprq “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now we define the extended affine co-root lattice as rQ_ “ Zh0 ` Zh1 ` Zdpr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now we can set Φpdprq “ dpr and obtain a linear automorphism of rh preserving the lattice rQ_.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The corresponding dual map on rh˚, also denoted by Φ, preserves the extended affine weight lattice (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) rP “ tλ P rh˚ | λp rQ_q Ď Zu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Accordingly, we define Uqprgq as the Hopf algebra obtained by extending Uqppgq by a group-like element1 g satisfying (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) gei “ qeig, gfi “ q´1fig, gki “ kig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence, the assignment Φpgq “ g together with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) defines an involutive Hopf algebra automor- phism of Uqprgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Co-opposite Hopf algebra structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For any C-algebra A, denote by σ the algebra au- tomorphism of A b A which sends a b a1 to a1 b a for all a, a1 P A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If X P A b A we will also write X21 for σpXq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If A is a bialgebra with coproduct ∆, the co-opposite bialgebra, denoted Acop, is the bialgebra with the same underlying algebra structure and counit as A but with ∆ replaced by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) ∆op :“ σ ˝ ∆ (if A is a Hopf algebra with invertible antipode S, then Acop is also a Hopf algebra with antipode S´1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The assignments (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) ωpeiq “ fi, ωpfiq “ ei, ωpk˘1 i q “ k¯1 i for i P t0, 1u, ωpgq “ g´1 define a bialgebra isomorphism from Uqprgq to Uqprgqcop, commuting with Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, we have pω b ωq ˝ ∆ “ ∆op ˝ ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Some elementary representation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We review some basic definitions regarding representations of Uqprgq and, especially, its subalgebra Uqppgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider the commutative subalgebra (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) Uqprhq “ xk˘1 0 , k˘1 1 , g˘1y Ă Uqprgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Call a Uqprhq-module M a Uqprhq-weight module if M “ à λP rP Mλ, Mλ “ tm P M | ki ¨ m “ qλphiqm for i P t0, 1u, g ¨ m “ qλpdprqmu 1It is equal to qdpr if we view Uqprgq as a topological Hopf algebra defined over Crrǫss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 7 and elements of Mλ are said to have weight λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The adjoint action of Uqprhq (with each k˘1 i and g˘1 acting by conjugation) endows Uqprgq itself with a Uqprhq-weight module structure, with elements of Uqprhq of weight 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, the weights of Uqprgq are given by the affine root lattice pQ :“ Zα0 ` Zα1 Ă rP (ei has weight αi, fi has weight ´αi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Furthermore, note that Uqprgq is generated by Uqprhq and the quantum analogues of the standard nilpotent subalgebras (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) Uqppn`q “ xe0, e1y, Uqppn´q “ xf0, f1y and the weights of Uqppn˘q are given by the monoids ˘ pQ`, where pQ` :“ Zě0α0 ` Zě0α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We denote by Uqppn˘qλ the subspace of elements of weight λ P pQ˘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quasitriangularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The universal R-matrix for Uqprgq is an element of a completion of Uqprgq b Uqprgq satisfying R∆puq “ ∆oppuqR for all u P Uqprgq, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) p∆ b idqpRq “ R13R23, pid b ∆qpRq “ R13R12 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) and hence (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) R12R13R23 “ R23R13R12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider the Hopf subalgebras Uqprb˘q “ xUqprhq, Uqppn˘qy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The element R arises as the canonical element of the bialgebra pairing between Uqprb`q and the algebra Uqprb´qop (the bialgebra isomorphic as a coalgebra to Uqprb´q but with the opposite mul- tiplication), see [Dr85, Lu94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, R lies in a completion of Uqprb`q b Uqprb´q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Further, invariance properties of the bialgebra pairing imply pω b ωqpRq “ R21, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) pΦ b ΦqpRq “ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) Moreover, this pairing has a non-degenerate restriction to Uqppn`qλ ˆ Uqppn´q´λ for all λ P pQ`;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' denote the canonical element of this restricted pairing by Θλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then, with our conventions for the coproduct, we have (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) R “ Θ´1 ¨ κ´1, Θ “ ÿ λP pQ` Θλ, A priori, Θ acts naturally on Uqprgq-modules with a locally finite Uqppn`q or Uqppn´q-action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We briefly explain one possible definition2 of the element κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The non-degenerate bilinear form p¨, ¨q on rh induces one on rh˚, which we denote by the same symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If V, V 1 are Uqprhq-weight modules we define a linear map κV : V b V 1 Ñ V b V 1 by stipulating that it acts on Vλ b V 1 λ1 (λ, λ1 P rP) as multiplication by qpλ,λ1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The family of these maps κV , where V runs through all Uqprhq-weight modules, is compatible with Uqprhq-intertwiners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence it gives rise to a well-defined weight-0 element κ of the corresponding completion of Uqprgq b Uqprgq (see [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6]) which we call 2Note that in the topological Hopf algebra setting one simply has κ “ qcbd`dbc`h1bh1{2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 8 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION here weight completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Similarly, one can define weight-0 elements of the weight completion of Uqprgq itself using functions from rP to C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' See also [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8] for more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Level-0 representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider the following subalgebras of Uqppgq: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='21) Uqppb˘q “ xUqpphq, Uqppn˘qy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We are mainly interested in level-0 representations π : Uqppb˘q Ñ EndpV q, possibly infinite- dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' These are weight modules with respect to the rank-1 weight lattice associated to the subalgebra sl2 Ă pg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, we say that a Uqppb˘q-module V is level-0 if it is finitely generated and decomposes as (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='22) V “ à tPCˆ V ptq, V ptq “ tv P V | k0 ¨ v “ t´1v, k1 ¨ v “ tvu with each V ptq finite-dimensional, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [HJ12, Def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If V is a finite-dimensional Uqppgq-module then it is level-0 with the eigenvalues of k1 contained in ˘qZ, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [CP95, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As a consequence of relation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10), level-0 Uqppgq-modules do not extend to Uqprgq-modules, unless they are trivial (direct sums of 1-dimensional representations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The action of R on tensor products of level-0 modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To connect the quasitriangular structure of Uqprgq with the level-0 representation theory of Uqppgq, one needs to make some provi- sions, as first pointed out in [Dr86, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 13] (also see [FR92, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4], [He19, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If we write the action of k1 on an arbitrary level-0 module V as exppǫHV q, then note that κ naturally acts on tensor products V b V 1 of level-0 modules as exppǫHV b HV 1{2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To let Θ act on tensor products of level-0 modules, we replace the field of scalars C over which we defined Uqprgq by the Laurent polynomial ring Crz, z´1s, where z is a formal parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Quite generally, for any C-linear space M (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' a C-algebra) we will denote extension by scalars as follows: Mrz, z´1s “ M bC Crz, z´1s, Mrrzss “ M bC Crrzss, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The action of Θ is particularly well-behaved if we use the principal grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' That is, we define a Hopf algebra automorphism Σz of Uqprgqrz, z´1s such that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='23) Σzpeiq “ zei, Σzpfiq “ z´1fi, Σz|Uqprhq “ id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Straightforwardly one sees that ω ˝ Σz “ Σz´1 ˝ ω, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) Φ ˝ Σz “ Σz ˝ Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='25) Let the height function ht : pQ Ñ Z be defined by htpm0α0 ` m1α1q “ m0 ` m1 for all m0, m1 P Z and note that the number of elements of pQ` of given height is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key observation is that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='26) pΣz b idqpΘq “ pid b Σz´1qpΘq “ ÿ rě0 zr ÿ λP pQ`, htpλq“r Θλ, is a formal power series in z whose coefficients are finite sums and hence lie in Uqppn`q b Uqppn´q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence pΣz b idqpΘq “ pid b Σz´1qpΘq has a well-defined action as a linear-operator-valued formal power series on a tensor product of any Uqppn`q-representation with any Uqppn´q-representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider now the grading-shifted universal R-matrix: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27) Rpzq :“ pΣz b idqpRq “ pid b Σz´1qpRq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that by applying Σz b id to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) we deduce that Rpzq commutes with ∆pk1q “ ∆oppk1q “ k1 b k1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We collect the results obtained thus far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 9 Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal R-matrix Rpzq be defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider a pair of level-0 representations π˘ : Uqppb˘q Ñ EndpV ˘q, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) Rπ`π´pzq :“ pπ` b π´qpRpzqq P EndpV ` b V ´qrrzss is well-defined and commutes with π`pk1q b π´pk1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From now on we will use the standard convention that if π is any level-0 representation then the corresponding grading-shifted representation is denoted by a subscript z: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29) πz :“ π ˝ Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence we may write Rπ`π´pzq “ pπ` z b π´qpRq “ pπ` b π´ 1{zqpRq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider two indeterminates z1, z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying, say, Σz1bidbΣ1{z2, to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17), we obtain a Crrz1, z2ss- version of the universal Yang-Baxter equation which can be evaluated on suitable triple tensor products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal R-matrix Rpzq be defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If π` : Uqppb`q Ñ EndpV `q, π : Uqppgq Ñ EndpV q and π´ : Uqppb´q Ñ EndpV ´q are level-0 represen- tations, then we have the following identity of linear-operator-valued formal power series in two indeterminates: (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30) Rπ`πpz1q12 Rπ`π´pz1z2q13 Rππ´pz2q23 “ Rππ´pz2q23 Rπ`π´pz1z2q13 Rπ`πpz1q12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Given a pair of level-0 representations π˘ : Uqppb˘q Ñ EndpV ˘q it is often convenient to have an explicit expression of Rπ`π´pzq which does not rely on computing the expansion coefficients of Rpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Essentially following Jimbo’s approach from [Ji86b], we may try to solve a linear equation for Rπ`π´pzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To derive such a linear equation, it is convenient to assume that, say, π´ extends to a representation of Uqppgq so that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) Rπ`π´pzq ¨ pπ` z b π´qp∆puqq “ pπ` z b π´qp∆oppuqq ¨ Rπ`π´pzq holds for all u P Uqppb`q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this case3, one directly obtains the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal R-matrix Rpzq be defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If π` is a level-0 Uqppb`q-representation and π´ a level-0 Uqppgq-representation, then (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) holds for all u P Uqppb`q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If the solution space of the linear equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) is 1-dimensional, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4 implies that any solution must be a scalar multiple of Rπ`π´pzq and hence satisfy the Yang-Baxter equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is well-known if both V ˘ extend to finite-dimensional Uqppgq-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this case the existence of the universal R-matrix implies the existence of a solution of the intertwining condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) depending rationally on z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If π` and π´ are both irreducible then it is known, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [KS95, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2] and [Ch02, Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3], that V `ppzqq b V ´ is irreducible as a representation of Uqppgqppzqq (extension of scalars to formal Laurent series);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' hence an application of Schur’s lemma yields the 1-dimensionality of the solution space of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this case, the rational intertwiner is called trigonometric R-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For more background and detail, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [He19] and [AV22b, Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6 & 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3More generally, one can apply π` z bπ´ to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) for any Uqppb˘q-representations π˘, yielding (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) for all u P Uqppgq such that ∆puq and ∆oppuq both lie in Uqppb`q b Uqppb´q, but by applying counits this subalgebra is easily seen to be equal to Uqppb`q X Uqppb´q “ Uqpphq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence, one would just recover the second statement of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 10 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION In the absence of a linear relation such as (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31), one can use the Yang-Baxter equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30) to determine an explicit expression for Rπ`πpzq, Rπ`π´pzq, or Rππ´pzq, provided the other two are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � Note that in this approach the principal grading is essential to deduce Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 without further constraints on the representations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' local nilpotency conditions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For completeness we briefly explain how to extend the results obtained here to arbitrary grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For nonnegative integers s0, s1 such that s :“ s0 ` s1 is nonzero, define a more general Hopf algebra automorphism Σs0,s1 z of Uqprgq b Crz, z´1s by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='32) Σs0,s1 z peiq “ zsiei, Σs0,s1 z pfiq “ z´sifi, Σs0,s1 z |Uqprhq “ id (note that the choice s0 “ 0, s1 “ 1 is used in in [KT14, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Rather than generalizing the theory above to this case, we make the following observation for a cyclic Uqppb`q-module V , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=', V “ Uqppb`q ¨ v0 for some v0 P V , which is level-0 (all modules considered in this paper are cyclic level-0 modules).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Writing the corresponding representation as π : Uqppb`q Ñ EndpV q then the more general grading-shifted representation defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='33) πs0,s1 z :“ π ˝ Σs0,s1 z can be related to the representation shifted by the principal grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Namely, for such modules, there exists t0 P Cˆ such that the nonzero weight spaces V ptq appearing in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='22) have t “ q2mt0 for some m P Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now for any indeterminate y and any integer m, let ymD denote the map on V which acts on V pq2mt0q as scalar multiplication by ym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now adjoin to the ring Crz, z´1s a square root Z of z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then we have (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='34) πs0,s1 z “ Ad ` Zps1´s0qD˘ ˝ πZs, where on the right-hand side Ad stands for ‘conjugation by’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' See [AV22b, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2] for essentially the same point in the context of irreducible finite-dimensional Uqppgq-representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The augmented q-Onsager algebra, its twists and its universal K-matrices In parallel with the previous section, we consider a particular subalgebra of Uqppgq and discuss some recent results on universal K-matrices [AV22a, AV22b] in the context of (possibly infinite- dimensional) level-0 representations of Borel subalgebras of quantum affine sl2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For a related universal approach involving essentially the same subalgebra, tailored to evaluation representations, see [BT18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The twist map ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We consider the following algebra automorphism and coalgebra antiau- tomorphism of Uqprgq (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) ψ :“ ω ˝ Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='25), respectively, we immediately deduce pψ b ψqpRq “ R21, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) ψ ˝ Σz “ Σz´1 ˝ ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) By the following result, P-symmetric R-matrices (Rpzq21 “ Rpzq) naturally arise in tensor products of representations of the upper and lower Borel subalgebras on the same vector space, provided they are related through ψ and the principal grading is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 11 Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal R-matrix Rpzq be defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider a pair of level-0 representations π˘ : Uqppb˘q Ñ EndpV q, respectively, such that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) π´ “ π` ˝ ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then Rπ`π´pzq21 “ Rπ`π´pzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Unpacking the definitions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27), we have Rπ`π´pzq21 “ ´` pπ` b π´q ˝ pΣz b idq ˘ pRq ¯ 21 “ ` pπ´ b π`q ˝ pid b Σzq ˘` R21 ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) we deduce Rπ`π´pzq21 “ ` pπ´ b π`q ˝ pψ b ψq ˝ pid b Σz´1q ˘ pRq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) and using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27) once again, we obtain Rπ`π´pzq as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The augmented q-Onsager algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The map ψ plays an important role in the theory of diagonal matrix solutions with a free parameter of the reflection equation in Uqppgq-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Namely, fix an a parameter ξ P Cˆ consider the following subalgebra of Uqppgq, also called the (embedded) augmented q-Onsager algebra: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) Uqpkq :“ C @ e0 ´ q´1ξ´1k0f1, e1 ´ q´1ξk1f0, k0k´1 1 , k´1 0 k1 D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is a left coideal: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) ∆pUqpkqq Ď Uqppgq b Uqpkq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The automorphism ψ is the trivial q-deformation of a Lie algebra automorphism of pg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If we also call this ψ for convenience, then Uqpkq is the parameter-dependent q-deformation of the universal enveloping algebra of the fixed-point subalgebra k “ pgψ, in the style of [Ko14] but with opposite conventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' See [VW20, Rmk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3] for more background on this subalgebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The definition of Uqpkq in loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' cit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' has a misprint: ξ should be replaced by ξ´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � To connect with the universal K-matrix formalism of [AV22a, AV22b], let rS be the bialgebra isomorphism4 from Uqprgq to Uqprgqop,cop (also known as the unitary antipode) defined by the assign- ments (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) rSpeiq “ ´qk´1 i ei, rSpfiq “ ´q´1fiki, rSpk˘1 i q “ k¯1 i , rSpg˘1q “ g¯1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 0 Note that rS2 “ id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now consider5 the right coideal subalgebra Uqpkq1 “ rSpUqpkqq “ Cxf0 ´ qξ´1e1k´1 0 , f1 ´ qξe0k´1 1 , k0k´1 1 , k´1 0 k1y which is the subalgebra considered in [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7], forming part of a more general family of right coideal subalgebras (quantum symmetric pair subalgebras) of quantum affine algebras as considered in [Ko14, AV22a, AV22b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4In particular, rS, like the antipode S itself, is an algebra antiautomorphism and a coalgebra antiautomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5In general, each element or map in the right coideal setting of [Ko14, AV22a, AV22b] is denoted by a prime on the corresponding object in the current left coideal setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 12 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Universal K-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By [AV22a, Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5], Uqprgq is endowed with a so-called standard universal K-matrix, which is an invertible element in a completion of Uqprb`q satisfying a twisted Uqpkq-intertwining property and a twisted coproduct formula involving the universal R-matrix6 R1 “ R´1 21 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' There is an action of invertible elements of a completion of Uqprgq, gauge-transforming the universal K-matrix and the twisting operator simultaneously, see [AV22b, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For the case under consideration, there exists a gauge transformation (a ‘Cartan correction’, see [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8]) that brings both the intertwining property and the coproduct formula for the universal K-matrix into a particularly nice form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Moreover, the gauge-transformed universal K-matrix still resides in a completion of Uqprb`q and, when shifted by the principal grading, acts as a linear- operator-valued formal power series for all level-0 Uqppb`q-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To make this more precise, let Ω : rP Ñ Cˆ be any group homomorphism such that Ωpα0q “ ´ξ and Ωpα1q “ ´ξ´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now define a function G1 : rP Ñ Cˆ by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) G1pλq “ Ωpλqq´pΦpλq,λq{2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that this is not a group homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Define the corresponding linear operator acting on Uqprhq-weight modules as follows: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) G1 ¨ v “ G1pλqv, v P Vλ, λ P rP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Analogously to our definition of the factor κ of the universal R-matrix, we thus obtain an invertible element G1 of the weight completion of Uqprgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Finally, let δ “ α0 ` α1 be the basic imaginary root of pg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then the following result is a special case of [AV22a, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7], with the coproduct formula a direct consequence of [AV22a, (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='21)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' There exists an invertible element (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) Υ1 “ ÿ λPZě0δ Υ1 λ, Υ1 λ P Uqppn`qλ, such that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) K1 :“ G1 ¨ Υ1 satisfies K1 ¨ u “ ψpuq ¨ K1 for all u P Uqpkq1, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) ∆pK1q “ p1 b K1q ¨ pψ b idqpR1q ¨ pK1 b 1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) Now we transform this formalism [AV22a] for the right coideal subalgebra Uqpkq1, expressed in terms of the universal R-matrix R1, to a formalism for the left coideal subalgebra Uqpkq “ rSpUqpkq1q, expressed in terms of the universal R-matrix R as used in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To do this, note that, when going from a Uqprgq-weight module to its dual, weights transform as λ ÞÑ ´λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This defines the extension of S and rS to a map on the weight completion of Uqprgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Therefore rSpΩq “ Ω´1 but the non-group-like factor of G1 is fixed by rS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We define G : rP Ñ Cˆ by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) Gpλq :“ ΩpλqqpΦpλq,λq{2 6Note that our choice of coproduct is the same as in [AV22a], but our ordering of the tensor product of the two Borel subalgebras is opposite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence the R-matrix in [AV22a], which we denote here by R1, is expressed in terms of R as R´1 21 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 13 so that G “ rSpG1q´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Also, we set (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) Υ :“ rSpΥ1q´1 “ ÿ λPZě0δ Υλ, Υλ P rSpUqppn`qλq and note that rSpUqppn`qλq P Uqpphq ¨ Uqppn`qλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The element (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) K :“ rSpK1q´1 “ G ¨ Υ satisfies K ¨ u “ ψpuq ¨ K for all u P Uqpkq, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) ∆pKq “ pK b 1q ¨ pid b ψqpRq ¨ p1 b Kq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This follows from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Namely, we apply rS to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) and prS b rSq ˝ σ to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13), and use the fact that rS ˝ ψ “ ψ ˝ rS and prS b rSqpRq “ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ Note that Uqppb`q is a bialgebra and, as expected, the right-hand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) lies in a completion of Uqppb`qbUqppb`q, since ψ interchanges the two Borel subalgebras Uqppb˘q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The reflection equation satisfied by the universal element K is as follows: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) R ¨ pK b 1q ¨ pid b ψqpRq ¨ p1 b Kq “ p1 b Kq ¨ pid b ψqpRq ¨ pK b idq ¨ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is a consequence of the linear relation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) for R and the coproduct formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) for K, alongside (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) and ψ2 “ id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The action of the universal K-matrix on level-0 representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To deduce that K has a well-defined action on level-0 representations of, say, Uqppb`q, we can proceed in a similar way to the case of the R-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This builds on the finite-dimensional theory for more general quantum symmetric pair subalgebras in [AV22b, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' First note that if π is a level-0 representation, π and the twisted representation π ˝ψ coincide on Uqpphq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now let z once again be a formal variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) the function G sends the basic imaginary root δ to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence the proof of [AV22b, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 (3)] implies that the corresponding factor G of the universal K-matrix descends to level-0 modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Furthermore, the argument that shows ΣzpΘq is a Uqppn`q b Uqppn´q-valued formal power series can be easily adapted to Υ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' it yields a formal power series with coefficients in rSpUqppn`qq: ΣzpΥq “ ÿ rě0 zr ÿ λPZě0δ, htpλq“r Υλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now consider (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) Kpzq “ ΣzpKq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Noting that the form of Υ implies that K commutes with k1, we arrive at the following main result, which is the boundary analogue of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal K-matrix be defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider a level-0 representation π : Uqppb`q Ñ EndpV q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='21) Kπpzq :“ πpKpzqq P EndpV q b Crrzss is well-defined and commutes with πpk1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 14 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION We also provide boundary counterparts of Propositions 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider two indeterminates z1, z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying Σz1 b Σz2 to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) and using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3), we obtain the following reflection equation for the grading-shifted universal operators: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='22) Rpz1{z2q ¨ pKpz1q b 1q ¨ pid b ψqpRpz1z2qq ¨ p1 b Kpz2qq “ “ p1 b Kpz2qq ¨ pid b ψqpRpz1z2qq ¨ pKpz1q b idq ¨ Rpz1{z2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Recalling that the universal R-matrix R lies in a completion of Uqppb`q b Uqppb´q and applying a tensor product of suitable representations to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='22), one obtains the right reflection equation with multiplicative spectral parameters for P-symmetric R-matrices, as we now state precisely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal K-matrix be defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider level-0 representations π` : Uqppb`q Ñ EndpV `q and π : Uqppgq Ñ EndpV q such that π ˝ ψ “ π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='23) Rπ`πpz1{z2qpKπ`pz1q b IdV qRπ`πpz1z2qpIdV ` b Kπpz2qq “ “ pIdV ` b Kπpz2qqRπ`πpz1z2qpKπ`pz1q b IdV qRπ`πpz1{z2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The use of Uqpkq-intertwining relations to find explicit solutions of reflection equations was pro- posed in [DG02, DM03].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' First note that the intersection of Uqpkq and Uqppb`q is contained in Uqpphq, so that, in the absence of further assumptions, applying a level-0 representation π to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) one just recovers the second part of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To obtain a more powerful statement, as for the R-matrix it is convenient to assume that π extends to a Uqppgq-representation, in which case it restricts to a Uqpkq-representation and we obtain the following result as a consequence of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let the grading-shifted universal K-matrix be defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If π : Uqppgq Ñ EndpV q is a level-0 representation such that π ˝ ψ “ π, then (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) Kπpzq ¨ πzpuq “ π1{zpuq ¨ Kπpzq for all u P Uqpkq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We close this section with some comments parallel to Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If the solution space of the linear equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) is 1-dimensional, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7 implies that any solution must be a scalar multiple of Kpzq and hence automatically satisfy the reflection equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the case that π : Uqppb`q Ñ EndpV q extends to a Uqppgq-representation and V is finite-dimensional, statements analogous to those in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5 (i) can be made (existence of a solution of the intertwining condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) depending rationally on z and 1-dimensionality of the solution space of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) for irreducible representations), see [AV22b, Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5 and 6] for more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In many cases π` : Uqppb`q Ñ EndpV q does not extend to a Uqppgq-representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To explicitly determine Kπ`pzq in those cases, we will use the reflection equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='23), with the other K-matrix Kπpzq determined using Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Borel representations in terms of the q-oscillator algebra 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The infinite-dimensional vector space W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The countably-infinite-dimensional vector space plays a central role in the theory of Baxter’s Q-operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We may define it as the free C-module over a given set twjujPZě0: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) W “ à jě0 Cwj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Given this distinguished basis, elements of EndpWq naturally identify with infinite-by-infinite ma- trices with the property that all but finitely many entries of each column are zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is convenient A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 15 to work with a particular subalgebra of EndpWq depending on the deformation parameter q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, consider the C-linear maps a, a: on W defined by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) a ¨ wj`1 “ wj, a ¨ w0 “ 0, a: ¨ wj “ ` 1 ´ q2pj`1q˘ wj`1 for all j P Zě0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' These operators satisfy the relation ra, a:sq2 “ 1 ´ q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Naturally, we obtain an embedding of an abstract algebra with these generators and this defining relation into EndpWq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Up to rescaling of the generators, this was considered for instance in [AC76, Mf89, Ku91, Bi92] and can be viewed as a q-deformation of the Weyl or oscillator algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that each basis vector wj is an eigenvector of the compositions aa: and a:a with eigenvalues 1 ´ q2pj`1q and 1 ´ q2j, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For the description of L-operators associated to Uqppgq acting on W b C2 (particular solutions of the Yang-Baxter equation), it is convenient to consider a linear operator qD which is a square root of 1 ´ a:a: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) qD ¨ wj “ qjwj for j P Zě0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The definitions of the linear maps imply the following relations: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) aa: “ 1 ´ q2pD`1q, a:a “ 1 ´ q2D, qD`1a “ aqD, qDa: “ a:qD`1, where we have used natural shorthand notations q2D “ pqDq2, qD`1 “ qqD and q2pD`1q “ q2pqDq2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that qD is invertible and we let q´D denote its inverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In many applications, the q-oscillator algebra is defined as the abstract algebra gen- erated by a, a: and q˘D subject to the relations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This version of the q-oscillator algebra appeared in the guise of a topological algebra for instance in [BGKNR10, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3] and with slightly different conventions in [KT14]7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Diagonal operators from functions and an extended q-oscillator algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To accom- modate the action of the universal R and K-matrices on certain level-0 modules, we will need an extension of the above algebra xa, a:, q˘Dy and work over the commutative ring Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Denote by F the commutative algebra of functions from Zě0 to Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let D be the linear operator on W defined by D ¨ wj “ jwj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For any f P F we define fpDq P EndpWq via (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) fpDq ¨ wj “ fpjqwj, thereby recovering (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) as a special case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Thus, we obtain an algebra embedding F Ñ EndpWqrrzss, whose image FpDq is the subalgebra of diagonal operators on W (with respect to the given basis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now we combine this with the maps a, a: to obtain a subalgebra of EndpWqrrzss properly containing (the Crrzss-extension of) the algebra generated by a, a: and q˘D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The (extended) q-oscillator algebra is the subalgebra A Ă EndpWqrrzss generated by a:, a and FpDq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � As can be verified on basis vectors, in A one has the relations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) aa: “ 1 ´ q2pD`1q, a:a “ 1 ´ q2D, afpDq “ fpD ` 1qa, fpDqa: “ a:fpD ` 1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' One straightforwardly verifies that the subalgebras FpDq, Cra:s and Cras are self-centralizing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the operator (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) ¯a: :“ ´q´2Da: P EndpWq 7Note that the two vector spaces W1 and W2 introduced in [KT14, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3] are naturally isomorphic, so that the two algebras Osc1 and Osc2 defined via generators and relations can be identified with the same subalgebra of EndpW1q – EndpW2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 16 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION sends wj to p1 ´ q´2pj`1qqwj`1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Clearly, A is also generated by ¯a:, a and FpDq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The transforma- tion q ÞÑ q´1 defines an algebra automorphism of A, preserving the subalgebra FpDq, fixing the generator a and interchanging the generators a: and ¯a:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Endomorphisms of W bW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Elements of the tensor product AbA naturally act on W bW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the elements a1 :“ a b IdW, a: 1 :“ a: b IdW , a2 :“ IdW b a, a: 2 :“ IdW b a: together with FpD1q Y FpD2q generate A b A over Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will need a larger subalgebra of EndpW b Wq: we will allow all functions of two nonnegative integers as well as formal power series in certain locally nilpotent endomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Denote by Fp2q the commutative algebra of functions from Zě0 ˆ Zě0 to Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Similarly, we denote by D1 and D2 the linear operators on the tensor product W b W defined by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) D1 ¨ pwj b wkq “ jwj b wk, D2 ¨ pwj b wkq “ kwj b wk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For any f P Fp2q we define fpD1, D2q P EndpW b Wqrrzss via (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) fpD1, D2q ¨ pwj b wkq “ fpj, kqwj b wk, yielding an algebra embedding Fp2q Ñ EndpW b Wqrrzss, whose image Fp2qpD1, D2q is the sub- algebra of diagonal operators on W b W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now note that a1a: 2 and a: 1a2 are locally nilpotent endomorphisms of W b W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since elements of Fp2qpD1, D2q preserve each tensor product of basis vectors, series of the form (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) ÿ k,ℓě0 pa: 2qℓgk,ℓpD1, D2qak 1, ÿ k,ℓě0 pa: 1qkhk,ℓpD1, D2qaℓ 2 are well-defined elements of EndpW b Wqrrzss for any gk,ℓ, hk,ℓ P Fp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The subalgebra of EndpW b Wqrrzss generated by the operators (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) is called Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � In fact, it is not hard to see that Ap2q is spanned over Crrzss by the operators (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will later rely on the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The centralizer of the subset ta: 1, ¯a: 2u in Ap2q is equal to Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This centralizer is the intersection of the centralizer Ca: 1pAp2qq of a: 1 and the centralizer C¯a: 2pAp2qq of ¯a: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' One straightforwardly checks that linear operators of the form (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) in fact span Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now the computation of the centralizers is straightforward: we obtain Ca: 1pAp2qq “ " ÿ k,ℓě0 pa:qk 1fk,ℓpD2qaℓ 2 ˇˇˇˇ fk,ℓ P F , C¯a: 2pAp2qq “ " ÿ k,ℓě0 p¯a:qk 2gk,ℓpD1qaℓ 1 ˇˇˇˇ gk,ℓ P F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Clearly their intersection is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 17 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The Borel representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We introduce four cyclic level-0 representations of Uqppb`q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' One of these corresponds to the Uqpsl2q-Verma module and extends to a representation of Uqppgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Namely, let µ P C be a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is straightforward to check that the following assignments define a representation υ of Uqppgq on W: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) υpe0q “ υpf1q “ 1 1 ´ q2 a:, υpk0q “ q´µ`1`2D, υpe1q “ υpf0q “ q2 1 ´ q2 apq´µ ´ qµ´2Dq, υpk1q “ qµ´1´2D, The module structure on W defined by υ is the evaluation Verma module: affinizations of finite- dimensional irreducible Uqpsl2q-modules arise as quotients for positive integer values of µ (also see [KT14, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will in addition consider three Uqppb`q-representations which do not extend to representations of Uqppgq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A reducible representation φ` : Uqppb`q Ñ EndpWq is given by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) φ`pe0q “ 0, φ`pe1q “ q 1 ´ q2 a, φ`pk0q “ qµ`1`2D, φ`pk1q “ q´µ´1´2D which is closely related to the special evaluation homomorphism defined in [KT14, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following representations ̺`, ¯̺` : Uqppb`q Ñ EndpWq play an essential role in the definition of Baxter Q-operators: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) ̺`pe0q “ 1 1 ´ q2 a:, ̺`pe1q “ q2 1 ´ q2 a, ̺`pk0q “ q2D, ̺`pk1q “ q´2D, ¯̺`pe0q “ q2 1 ´ q2 ¯a:, ¯̺`pe1q “ 1 1 ´ q2 a, ¯̺`pk0q “ q2pD`1q, ¯̺`pk1q “ q´2pD`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' They correspond to the representations L˘ 1,a introduced in [HJ12, Def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7] for suitable a P Cˆ (called prefundamental representations in the subsequent paper [FH15] which considers their role in construction of Q-operators for closed chains).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will henceforth repeatedly denote grading-shifted representations by the notation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the grading-shifted representations ̺` z , ¯̺` z correspond to the representations defined by [KT14, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the grading-shifted representation in [VW20, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9)] is related to the ̺` z by a factor of ´1 in the actions of e0 and e1: in other words it is equal to ̺` ´z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since the Baxter Q-operators only depend on z2, see [VW20, Lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5], this does not cause issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The benefit of the current sign convention is its consistency across the level-0 representations under consideration, noting that υ is fixed by its relation to finite-dimensional evaluation representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The Uqppb`q-intertwiner O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The pairs p̺` q´µ{2z, ¯̺` qµ{2zq and pυz, φ` z q of shifted representa- tions are closely related in the following sense: the two induced Uqppb`q-actions on W b W are conjugate by an element in Ap2q which is independent of z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, consider the q-exponential (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) eq2pxq “ 8 ÿ k“0 xk pq2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Appendix A we recall further properties of this deformation of the power series of the exponential function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Being a formal power series in x with nonzero constant term, eq2pxq is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence, 18 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION setting x equal to a scalar multiple of a1¯a: 2 or a: 1a2 we obtain an invertible element of Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We define (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) O` “ eq2pq2a1¯a: 2q´1qµpD1´D2q{2 P Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following statement is [KT14, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4)] and connects to [FH15, Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' for completeness we provide a proof in the present conventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The Uqppb`q-representations ̺` q´µ{2z b ¯̺` qµ{2z and υz b φ` z are intertwined by O`: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) O` ` ̺` q´µ{2z b ¯̺` qµ{2z ˘ p∆puqq “ ` υz b φ` z ˘ p∆puqq O` for all u P Uqppb`q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) we obtain qµpD2´D1q{2eq2pq2a1¯a: 2q¯a: 2 “ ` q´µ{2a: 1 ` q2pD1`1q`µ{2¯a: 2 ˘ qµpD2´D1q{2eq2pq2a1¯a: 2q, qµpD2´D1q{2eq2pq2a1¯a: 2q ` a1pq´2µ ´ q´2D1q ` q´2pD1`1qa2 ˘ “ “ ` a1q´3µ{2 ` q´µ{2´2pD1`1qa2 ˘ qµpD2´D1q{2eq2pq2a1¯a: 2q, qµpD2´D1q{2eq2pq2a1¯a: 2qq2pD1`D2`1q “ q2pD1`D2`1qqµpD2´D1q{2eq2pq2a1¯a: 2q, qµpD2´D1q{2eq2pq2a1¯a: 2qq´2pD1`D2`1q “ q´2pD1`D2`1qqµpD2´D1q{2eq2pq2a1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' These directly imply (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) for u P te0, e1, k0, k1u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Formalism for Uqppb´q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Recall the automorphism ψ defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1), interchanging the two Borel subalgebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that υ : Uqppgq Ñ EndpWq satisfies (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) υ “ υ ˝ ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence, it is natural to define representations of Uqppb´q corresponding to ̺`, ¯̺´ and φ`, as follows: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) ̺´ :“ ̺` ˝ ψ, ¯̺´ :“ ¯̺` ˝ ψ, φ´ :“ φ` ˝ ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3), whereas the grading-shifted representations ̺` z , ¯̺` z , φ` z take values in EndpWq b Crzs, their negative counterparts ̺´ z , ¯̺´ z , φ´ z take values in EndpWq b Crz´1s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Explicitly, we have (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) ̺´pf0q “ q2 1 ´ q2 a, ̺´pf1q “ 1 1 ´ q2 a:, ̺´pk0q “ q2D, ̺´pk1q “ q´2D, ¯̺´pf0q “ 1 1 ´ q2 a, ¯̺´pf1q “ q2 1 ´ q2 ¯a:, ¯̺´pk0q “ q2pD`1q, ¯̺´pk1q “ q´2pD`1q, φ´pf0q “ q 1 ´ q2 a, φ´pf1q “ 0, φ´pk0q “ qµ`1`2D, φ´pk1q “ q´µ´1´2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since ψ is a coalgebra antiautomorphism, using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) we immediately deduce the following char- acterization of the tensorial opposite of O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The linear map (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) O´ :“ O` 21 “ eq2pq2¯a: 1a2q´1qµpD2´D1q{2 P EndpW b Wq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' intertwines the Uqppb´q-representations ¯̺´ q´µ{2z b ̺´ qµ{2z and φ´ z b υz, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='21) O´ ` ¯̺´ q´µ{2z b ̺´ qµ{2z ˘ p∆puqq “ ` φ´ z b υz ˘ p∆puqq O´ for all u P Uqppb´q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 19 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' L-operators and R-operators In order to define L-operators, we define the standard 2-dimensional representation Π : Uqppgq Ñ EndpC2q by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) Πpe0q “ Πpf1q “ ˆ 0 0 1 0 ˙ , Πpk0q “ ˆ q´1 0 0 q ˙ , Πpe1q “ Πpf0q “ ˆ 0 1 0 0 ˙ , Πpk1q “ ˆ q 0 0 q´1 ˙ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In analogy with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17), we have (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) Π “ Π ˝ ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' L-operators for Uqppb`q-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will now obtain explicit formulas for certain scalar multiples of R̺`Πpzq, R¯̺`Πpzq, RυΠpzq and Rφ`Πpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this case both Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 and Proposi- tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4 apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It turns out that the relevant linear equations all have 1-dimensional solution spaces over Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following linear operators are convenient scalar multiples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' L` ̺ pzq “ ˆ qD a:q´D´1z aqD`1z q´D ´ qD`2z2 ˙ , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) L` ¯̺ pzq “ ˆ qD`1 ´ q´D`1z2 ¯a:q´Dz aqDz q´D´1 ˙ , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) L` υ pzq “ ˆ qD ´ q´D`µz2 a:q´D´2`µz aq ` qD´µ ´ q´D`µ˘ z q´D´1`µ ´ qD`1z2 ˙ , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) L` φ pzq “ ˆ qD`1 0 aqD`1z q´D´µ ˙ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We have abused notation by representing the linear operators on EndpW b C2qrrzss as 2 ˆ 2 matrices with coefficients in EndpWq (as opposed to the conventional useage that realizes operators on EndpC2 b Wqrrzss in this way).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � The following result is [KT14, Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The above L-operators satisfy the following relation in EndpW b W b C2qrrzss: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) O` 12L` ̺ pq´µ{2zq13L` ¯̺ pqµ{2zq23 “ L` υ pzq13L` φ pzq23O` 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) one deduces L` ̺ pq´µ{2zq13L` ¯̺ pqµ{2zq23 9 p̺` q´µ{2z b ¯̺` qµ{2z b Πq ` p∆ b idqpRq ˘ , L` υ pzq13L` φ pzq23 9 pυz b φ` z b Πq ` p∆ b idqpRq ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6 implies (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) up to a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By applying both sides to w0 bw0 bp1 0q one observes that the scalar is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' L-operators for Uqppb´q-representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We can repeat the construction of L-operators in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 for the various Uqppb´q-representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' If we combine the relations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) between the representations in terms of ψ with the properties (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='25) of 20 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION the constituent factors of ψ, we straightforwardly obtain the following scalar multiples of RΠ̺´pzq, RΠ̺`pzq, RΠυpzq and RΠφ´pzq, respectively: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) L´ ̺ pzq “ L` ̺ pzq21, L´ ¯̺ pzq “ L` ¯̺ pzq21, L´ υ pzq “ L` υ pzq21, L´ φ pzq “ L` φ pzq21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 immediately yields the following result: Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following relation in EndpC2 b W b Wqrrzss is satisfied: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) O´ 23L´ ̺ pq´µ{2zq13L´ ¯̺ pqµ{2zq12 “ L´ υ pzq13L´ φ pzq12O´ 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Actions of Rpzq on tensor products of infinite-dimensional Borel representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2, the grading-shifted universal R-matrix also acts on the tensor product of the level-0 modules pW, υq and pW, φ´q and on the tensor product of the level-0 modules pW, ̺`q and pW, ¯̺´q as EndpW b Wq-valued formal power series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is convenient for us to use rescaled linear- operator-valued formal power series (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) R̺¯̺pzq, Rυφpzq P EndpW b Wq b Crrzss, uniquely defined by the condition that they fix w0 b w0: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) R̺¯̺pzq 9 p̺` b ¯̺´qpRpzqq, R̺¯̺pzq ¨ pw0 b w0q “ w0 b w0, Rυφpzq 9 pυ b φ´qpRpzqq, Rυφpzq ¨ pw0 b w0q “ w0 b w0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' These power series will appear in the boundary factorization identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In appendix B we obtain explicit expressions for R̺¯̺pzq and Rυφpzq, although we will not need these for the proof of the boundary factorization identity using the universal K-matrix formalism of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' K-matrices In this section we consider solutions of reflection equations associated to the subalgebra Uqpkq, whose existence is guaranteed by the universal K-matrix formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Right K-matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5, applying any of the level-0 Uqppb`q-representations ̺`, ¯̺`, υ, φ` to the grading-shifted universal K-matrix associated to Uqpkq we obtain EndpWq-valued formal power series, satisfying the reflection equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Moreover, since these commute with the action of k1 they act diagonally with respect to the basis twjujě0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will consider the scalar multiples of these linear operators which fix w0: (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) K̺pzq 9 ̺`pKpzqq, K̺pzq ¨ w0 “ w0, K¯̺pzq 9 ¯̺`pKpzqq, K¯̺pzq ¨ w0 “ w0, Kυpzq 9 υpKpzqq, Kυpzq ¨ w0 “ w0, Kφpzq 9 φ`pKpzqq, Kφpzq ¨ w0 “ w0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is convenient to obtain explicit expressions by applying Propositions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The linear operator (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) KΠpzq “ ˆ ξz2 ´ 1 0 0 ξ ´ z2 ˙ P EndpC2qrrzss is, up to a scalar, the unique solution of the Uqpkq-intertwining condition (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) KΠpzq ˝ Πzpuq “ Π1{zpuq ˝ KΠpzq for all u P Uqpkq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5, it is proportional to the action of the grading-shifted universal K-matrix in the representation pΠ, C2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 21 For all π P t̺, ¯̺, υ, φu, consider the right reflection equations (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) L´ π,21py z qKπpyqL` π pyzqKΠpzq “ KΠpzqL´ π,21pyzqKπpyqL` π py z q P EndpW b C2qrry{z, zss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is convenient to consider the linear space (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) REπ :“ tKπpyq P FpDq | (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) is satisfiedu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let π P t̺, ¯̺, υ, φu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then REπ is one-dimensional over Crrzss and the unique element of REπ that fixes w0 P W is given by (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) K̺pzq “ p´q´DξqDpq2ξ´1z2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD, K¯̺pzq “ pqz2q´Dpq2ξ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D , Kυpzq “ z´2D pq2´µξ´1z2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD pq2´µξ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD , Kφpzq “ p´q´µ´D´1 ξqD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We emphasize that the expressions given in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) are well-defined elements of FpDq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For instance, we have, for all γ P C, z´2Dpγz´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D “ p´qD´1γq´D D´1 ź m“0 p1 ´ γ´1q´2mz2q´1, with each factor of the product interpreted as a geometric series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof of Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By a straightforward check, the intertwining condition (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) Kυpzq ˝ υzpuq “ υ1{zpuq ˝ Kυpzq for all u P Uqpkq can be solved to find Kυpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since Kpzq commutes with the action of k1 it follows that Kυpzq “ fpDq for some f P F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now imposing (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) for the generators e0 ´ q´1ξ´1k0f1, e1 ´ q´1ξk1f0 yields the recurrence relation fpD ` 1q fpDq “ 1 ´ q2pD`1q´µξ´1z2 z2 ´ q2pD`1q´µξ´1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Together with the constraint fp0q “ 1 it yields the formula given in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5 and the universal reflection equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) it follows that (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) satisfies (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) (of course, it can be directly checked).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the representation φ is reducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Indeed, one straightforwardly checks that the general solution Kφpzq of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) is of the form p´q´µ´D´1 ξqDp with p in the centralizer of a in A (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' a polynomial in a with coefficients in Crrzss).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The solution given in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) is now observed to be the unique solution in FpDq which fixes w0, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The operator K̺pzq was obtained in [VW20, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4] as the unique element of the 1-dimensional linear space RE̺ which fixes w0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In an analogous way we obtain the explicit expression for K¯̺pzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Left K-matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We now obtain solutions of a reflection equation for the left boundary by using a well-established bijection, see [Sk88, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (14)], between its solution set and the solution set of the right reflection equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For fixed rξ P Cˆ we define (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) rKΠpzq :“ p1 ´ q2rξ´1z2q´1p1 ´ q2rξz2q´1` KΠpqzq´1|ξÞÑrξ´1 ˘ “ ˜ q2rξz2 ´ 1 0 0 rξ ´ q2z2 ¸ P EndpC2qrrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Also, for π P t̺, ¯̺, υ, φu we define (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) rKπpzq :“ Kπpqzq´1|ξÞÑrξ´1 P EndpWqrrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 22 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION Similarly, note that L` π pγzq is invertible in EndpW b C2qrrzss for all γ P C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We define (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) rL˘ π pzq “ L˘ π pq2zq´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all π P t̺, ¯̺, υ, φu the left reflection equation holds: (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) rKπpyq rL´ π pyzq rKΠpzqL´ π py z q “ L` π py z q rKΠpzq rL` π pyzq rKπpyq P EndpW b C2qrry{z, zss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The desired equation (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) can be rewritten as rKΠpzq´1 rL´ π pyzq´1 rKπpyq´1L` π py zq “ L´ π py zq rKπpyq´1 rL`pyzq´1 rKΠpzq´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10), this is equivalent to the right-reflection equation (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) with y ÞÑ qy, z ÞÑ qz and ξ ÞÑ rξ´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ Using the explicit formulas (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) we obtain that the solutions of the left reflection equations (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) are the following EndpWq-valued formal power series in z: (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) rK̺pzq “ p´qDrξqDpq4rξz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D , rK¯̺pzq “ pq3z2qDprξz´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD, rKυpzq “ pqzq2D pq´µrξz´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD pq4´µrξz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD , rKφpzq “ p´qµ`D`1rξqD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Fusion intertwiners revisited In this short intermezzo we explain how the universal K-matrix formalism naturally leads to relations involving K-matrices and Uqpb`q-intertwiners called fusion intertwiners which play a key role in the approach to Baxter’s Q-operator using short exact sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' These intertwiners were discussed in [VW20] and the relevant relations with K-matrices, see [VW20, Lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2], were shown by a linear-algebraic computation relying on the explicit expressions of the various constituent factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In other words, the representation-theoretic origin of these relations was unclear, which we now remedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Level-0 representations of Uqppb`q are amenable to scalar modifications of the action of Uqphq “ xk˘1 1 y, see also [HJ12, Rmk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, for r P Cˆ, define a modified Borel representation ̺` as follows: (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) ̺` r peiq “ ̺`peiq, ̺` r pk0q “ r̺`pk0q, ̺` r pk1q “ r´1̺`pk1q and consider the grading-shifted representation ̺` r,z :“ p̺` r qz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' There exist Uqppb`q-intertwiners ιprq : pW, ̺` qr,qzq Ñ pW b C2, ̺` r,z b Πzq, τprq : pW b C2, ̺` r,z b Πzq Ñ pW, ̺` q´1r,q´1zq, called fusion intertwiners, which take part in the following short exact sequence: (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) 0 pW, ̺` qr,qzq pW b C2, ̺` r,z b πzq pW, ̺` q´1r,q´1zq 0 ιprq τprq Explicitly8, we have (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) ιprq “ ˆ q´Da: ´qD`1r ˙ , τprq “ ` qD, q´Dr´1a:˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 8The sign mismatch with [VW20, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1)] is explained in Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 23 Analogously to Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2, fusion relations for the L-operators L`pr, zq, defined as suitable scalar multiples of p̺` r,zbΠqpRq, now follow from these intertwining properties and the coproduct formulas for R (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16), see [VW20, Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Recalling the universal K-matrix K and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5, we define the corresponding K-operator K̺pr, zq as the unique scalar multiple of ̺` r,zpKq which fixes w0 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [VW20, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' One directly checks from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) that (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) p̺` r,z b Πzqp∆pKqq 9 K̺pr, zq1L`pr, z2qKΠpzq2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since K lies in a completion of Uqppb`q, the intertwining properties of ιprq and τprq now directly yield the following fusion relation for the K-operator: K̺pr, zq1Lpr, z2qKΠpzq2ιprq 9 ιprqK̺pqr, qzq τprqK̺pr, zq1Lpr, z2qKΠpzq2 9 K̺pq´1r, q´1zqτprq, with the scalar factors determined by evaluating on w0, say.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will see that a boundary counterpart of the factorization identity (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) for L-operators can be proved using similar ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We recover, with a much smaller computational burden, the essential result of [VW20, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2] (a similar relation for left K-operators can easily be deduced from this as explained in the last sentence of [VW20, Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the approach to Baxter’s Q-operator using short exact sequences, the fusion relations for L and K-operators induce fusion relations for 2-boundary monodromy operators, see [VW20, Lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2] from which Baxter’s relation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) follows by taking traces, see [VW20, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boundary factorization identity In motivating and presenting the key boundary relations, it is very useful to introduce a graphical representation of spaces and operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let us introduce the following pictures for the different representations introduced in Section 4: ̺` z “ z ¯̺` z “ z , φ` z “ z , ̺´ z “ z ¯̺´ z “ z , φ´ z “ z , υz “ z Πz “ z , For any vector spaces V , V 1, denote by P the linear map from V b V 1 to V 1 b V such that Ppv b v1q “ v1 b v for all v P V , v1 P V 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We then have the following pictures for L-operators and R-operators: PL` ̺ pzq “ z2 z1 PL¯ρpzq` “ z2 z1 PL` υ pzq “ z2 z1 PL` φ pzq “ z2 z1 PL´ ̺ pzq “ z1 z2 PL´ ¯ρ pzq “ z1 z2 PL´ υ pzq “ z1 z2 PL´ φ pzq “ z1 z2 24 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION PR̺¯̺pzq “ z2 z1 PRυφpzq “ z2 z1 where z “ z1 z2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We now make the following definitions9: (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) rRυφpzq :“ Rυφpq2zq´1, rR̺¯̺pzq :“ R̺¯̺pq2zq´1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' and represent these modified R-matrices by the following pictures: rR̺¯̺pzqP “ z2 z1 rRυφpzqP “ z2 z1 where z “ z1 z2 as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The various right-boundary K-matrices are represented as follows: Kρpzq “ z z´1 K¯ρpzq “ z z´1 Kυpzq “ z z´1 Kφpzq “ z z´1 The left-boundary K-matrices defined in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 are represented by the natural analogues of these pictures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For example: rKρpzq “ z z´1 Making use of these pictures, we see that Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 is represented by qµ{2z1 q´µ{2z1 z1 z1 O` z2 “ qµ{2z1 q´µ{2z1 z1 z1 O` z2 and Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3 by z1 z1 q´µ{2z1 qµ{2z1 O´ z2 “ z1 z1 q´µ{2z1 qµ{2z1 O´ z2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For the compatibility with the right boundary we claim that 9These are the modified forms of the R-matrices that appear in the corresponding left reflection equations, see [Sk88, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (13)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 25 qµ{2z q´µ{2z z z´1 z z´1 O` = z´1 z´1 q´µ{2z´1 qµ{2z q´µ{2z qµ{2z´1 O´ which corresponds to the following identity in Ap2q: (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) Kυpzq1Rυφpz2qKφpzq2 O` “ O´ 21K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2, which we call the right boundary factorization identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The diagrams above serve as a motivation for the identity, which we now prove using results from Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all µ P C, all q P Cˆ not a root of unity and all ξ P Cˆ, relation (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It directly follows from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) that (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) is equivalent to (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) Kυpzq1Rυφpz2qKφpzq2 O` “ O`K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2, The proof is analogous to the proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We first note that ` ̺` q´µ{2z b ¯̺` qµ{2z ˘` pid b ψqpRq ˘ “ ` ̺` q´µ{2z b ¯̺´ q´µ{2z´1 ˘ pRq 9 R̺¯̺pz2q, ` υz b φ` z ˘` pid b ψqpRq ˘ “ ` υz b φ´0z´1 ˘ pRq 9 Rυφpz2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Noting the coproduct formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18), we obtain K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2 9 ` ̺` q´µ{2z b ¯̺` qµ{2z ˘ p∆pKqq, Kυpzq1Rυφpz2qKφpzq2 9 ` υz b φ` z ˘ p∆pKqq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6 implies (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) up to a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The fact that all factors fix w0 b w0 shows that the scalar is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ An alternative computational proof of Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 is given in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Compatibility with the left boundary requires that 26 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION z´1 z´1 pO´q´1 qµ{2z q´µ{2z qµ{2z´1 q´µ{2z´1 “ z´1 z´1 z z qµ{2z q´µ{2z pO`q´1 The identity in Ap2q corresponding to this is (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) rK¯̺pqµ{2z, rξq2 rR̺¯̺pz2q rK̺pq´µ{2z, rξq1pO`q´1 “ pO`q´1 rKφpz, rξq2 rRυφpz2q rKυpz, rξq1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Relation (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Given the definitions (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) and (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1), this follows straightforwardly by inverting (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) and replacing pz, ξq ÞÑ pqz, rξ´1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Discussion The main result of this paper is Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 which can be viewed as a boundary analogue of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To establish this result, we needed to first show that all R and K-operators involved in Equation (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) are well-defined actions of the universal elements R and K on the infinite-dimensional Uqppb`q-modules involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The key fact that allows for this is that R and K live in completions of Uqppb`q b Uqppb´q and of Uqppb`q, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is very familiar for R but for K relies on the recent work [AV22a].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Introducing the Uqppb`q-intertwiner O` and the formula for ∆pKq given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18), relation (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) follows immediately from the intertwining property of O`.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The open Q-operator Qpzq of [VW20] is the trace of a product of R and K-operators over the Uqppb`q-module pW, ρ` z q and there is a similar construction of an open Q-operator Qpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In a future paper, the authors will present this construction and the use of Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 in deriving a boundary analogue of the factorization relation Tµpzq 9 Qpzq´µ{2qQpzqµ{2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' They will also develop the analogous theory for different coideal subalgebras, in particular those for which non-diagonal solutions of the reflection equation are intertwiners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed Pochhammer symbols and exponentials This appendix is independent from the main text, but provides identities which are used there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We review some basic theory of deformed Pochhammer symbols and exponentials (as formal power series) with a deformation parameter p P Cˆ, which corresponds to q2 in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed Pochhammer symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let x be a formal variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For n P Z, the (finite) deformed Pochhammer symbol px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqn P Crrxss is defined by (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqn :“ $ ’ ’ ’ ’ & ’ ’ ’ ’ % n´1 ź m“0 p1 ´ xpmq if n ě 0, ´1 ź m“n p1 ´ xpmq´1 if n ă 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 27 For all p P Cˆ and n P Zě0 we have the following basic identity, see [GR90, (I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2), (I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3)]: (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´n “ pp´nx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 n “ px{p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q´1 n “ p´xq´npnpn`1q{2pp{x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The infinite deformed Pochhammer symbol (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq8 :“ 8 ź m“0 p1 ´ xpmq is an invertible formal power series with well-defined coefficients in C if |p| ă 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following identity holds in Crrxss, see [GR90, (I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5)]: (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqn “ px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq8 ppnx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed exponentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From now on we assume that p is not a root of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, pp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqk ‰ 0 for all k P Zě0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The deformed exponential is the invertible formal power series (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) eppxq :“ 1φ0p0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' ´;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p, xq “ 8 ÿ k“0 xk pp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The ordinary exponential formal power series arises as the termwise limit lim pÑ1 eppp1 ´ pqxq “ ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This series satisfies the functional relation (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) epppxq “ p1 ´ xqeppxq, see [GR90, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3], and by inspecting the constant coefficients we obtain (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) eppxq “ 1 px;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq8 if |p| ă 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Similarly we consider the invertible formal power series (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) Eppxq :“ 0φ0p´;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' ´;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p, ´xq “ 8 ÿ k“0 pkpk´1q{2xk pp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then Epp´xq´1 also satisfies (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As before we deduce (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) eppxq´1 “ Epp´xq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2), the right-hand side of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) can be re-written as ep´1p´p´1xq and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) implies (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) eppxq´1 “ ep´1pp´1xq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The above identities are all in Crrxss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' General product formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The deformed exponentials satisfy various identities in partic- ular quotients of the free algebra on two symbols, and completions thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In any algebra generated by the symbols x and y such that yx “ γxy for γ P C, from the definition one immediately sees (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) yeppxq “ eppγxqy as an identity of formal power series;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' we will repeatedly use this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For a survey of product formulas analogous to exppxq exppyq “ exppx ` yq, see [Ko97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will need the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 28 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let x, y be elements of an algebra such that yx “ pxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The following identities hold as formal power series in x, y: eppxqeppyq “ eppx ` yq, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) eppyqeppxq “ ep ` xp1 ´ yq ˘ eppyq “ eppxqepp´xyqeppyq “ eppxqep ` p1 ´ xqy ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) is a direct consequence of the well-known q-binomial formula, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Sc53] or [GR90, Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) see [Ko97, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed exponentials as linear maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Deformed exponentials give rise to two different types of (formal power series whose coefficients are) linear maps on W “ ‘jě0Cwj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (i) If f P F, then we define eppfpDqq P EndpWqrrzss by the condition that, for all j ě 0, eppfpDqqpwjq “ eppfpjqqwj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (ii) Suppose x is a locally nilpotent linear map on W, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' for all j ě 0 there exists oj P Zą0 such that xoj ¨ wj “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then eppxq is a well-defined linear map on V : for all j ě 0, eppxqpwjq “ oj´1 ÿ k“0 1 pp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqk xkpwjq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Recall the subalgebra Ap2q Ă EndpWqrrzss with q2 abbreviated by p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will be particularly interested in the centralizer (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) Ap2q 0 :“ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X P Ap2q ˇˇˇ “ X, qD1`D2‰ “ 0 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Straightforwardly one verifies that Ap2q 0 is generated by elements of the form (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) ÿ kě0 p¯a: 2qkfkpD1, D2qak 1, ÿ kě0 pa: 1qkfkpD1, D2qak 2, fk P Fp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that elements of Ap2q 0 commute with all elements of the form fpD1 ` D2q (f P F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In particular, Ap2q 0 contains epp¯a: 2fpD1, D2qa1q and eppa: 1fpD1, D2qa2q for all f P Fp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We have the following commutation relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let γ P Crzs be arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In EndpW b Wqrrzss the following identities hold: (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) “ eppγa1¯a: 2q, fpD1 ` D2q ‰ “ “ eppγa1¯a: 2q, a1 ‰ “ “ eppγa1¯a: 2q, ¯a: 2 ‰ “ 0 for all f P F and “ eppγa1¯a: 2q, a: 1 ‰ “ γpD1¯a: 2eppγa1¯a: 2q, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) “ eppγa1¯a: 2q, p´D1a2 ‰ “ γeppγa1¯a: 2qa1p´D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) follows directly from the definition of the deformed exponential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A straight- forward inductive argument using (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) yields rak`1, a:s “ p1 ´ pk`1qpDak, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) rp¯a:qk`1, aspk`1 “ p1 ´ pk`1qp¯a:qk, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) for all k P Zě0, which imply (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 29 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Explicit expressions for R-operators In this appendix we derive explicit formulas for R̺¯̺pzq and Rυφpzq, defined by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) as images of the universal R-matrix R fixing w0 b w0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We expect that these formulas will be useful in further studies of Baxter’s Q-operators for the open XXZ spin chain;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' for now they will allow us to give a proof of the boundary factorization identity which does not rely on the universal K-matrix formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' First we note that, by the second part of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2, R̺¯̺pzq and Rυφpzq lie in Ap2q 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We keep using the shorthand notation p “ q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The automorphism χ and the q-oscillator subalgebra r A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A useful automorphism χ can be defined, but not naturally on all of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We need to define a subalgebra r A and a completion of its tensorial square.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Consider the subalgebra rFpDq Ă FpDq generated by p˘DpD`1q{2, γD, ppδ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq˘1 D , ppγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD, p´γz2q´Dppγ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D for all γ P Cˆ and δ P CˆzpZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that elements of GpDq, unlike general elements of FpDq, have the pleasant property that they naturally identify with formal Laurent series (for the functions defined in terms of q-Pochhammer symbols, by means of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Accordingly, we define an involutive automorphism χ of rFpDq accomplishing the formal replacement D ÞÑ ´D ´ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To be more precise, we set (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) χ ` p˘DpD`1q{2˘ “ p˘DpD`1q{2, χ ` γD˘ “ γ´D´1, χ ` ppδ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq˘1 D ˘ “ p1 ´ δq¯1p˘DpD`1q{2p´δq¯Dppδ´1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq¯1 D , χ ` ppγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD ˘ “ p1 ´ γz2q´1pDpD`1q{2p´γz2q´Dppγ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D , χ ` p´γz2q´Dppγ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D ˘ “ p1 ´ γz2qp´DpD`1q{2ppγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Definition B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The subalgebra of EndpWq generated by a:, a and GpDq is denoted r A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � It is straightforward to check that χ extends to a (non-involutive) algebra automorphism of r A by means of the assignments (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) χpaq “ ¯a:, χpa:q “ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Set J :“ ˆ 0 1 1 0 ˙ and let Ad denote ‘conjugation by’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) ` AdpJq b χ ˘` L` ̺ pzq ˘ “ L` ¯̺ pzq, AdpJq ` KΠpzq ˘ “ ´ξ ` KΠpzq|ξÞÑξ´1 ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Subsequently applying χ b AdpJq to the reflection equation (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) with π “ ̺` and inverting ξ we see that K̺pzq ÞÑ χpK̺pzq|ξÞÑξ´1q defines a bijection: RE̺ Ñ RE¯̺.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Indeed, we have K¯̺pzq “ qpz2 ´ ξ´1q χpK̺pzq|ξÞÑξ´1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � Now we can complete the tensor product r A b r A as we did for A b A and obtain an algebra r Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, we consider the subalgebra rFp2q of Fp2q generated by the subsets rFpD1q, rFpD2q and the special elements p˘D1pD2`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 30 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION Definition B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The completed tensorial square of r A is defined to be the subalgebra r Ap2q is of EndpW b Wq generated by the elements (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) with gk,ℓ, hk,ℓ P rFp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the automorphism (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) χp2q :“ σ ˝ pχ b χ´1q of r A b r A naturally extends to an automorphism of r Ap2q, fixing pointwise p˘D1pD2`1q and acting termwise on series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Remark B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the boundary factorization identity (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) is an identity in the subalgebra r Ap2q Ă EndpW b Wqrrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � There are two more identities similar to those in Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2 which we will need later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let γ P Crzs be arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In EndpW b Wq the following identities hold: r¯a: 2, eppγa: 1a2qs “ γeppγa: 1a2qa: 1p´D2´1, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) r¯a: 1a2, eppγa1¯a: 2qs “ γ ` eppγa1¯a: 2qp´D1´1 ´ p´D2´1eppγa1¯a: 2q ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To prove (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5), first we apply χp2q to (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17), obtaining (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) reppγa1¯a: 2q, a2s “ γa1p´D2´1eppγa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now consider the unique involutive algebra anti-automorphism η : A Ñ A which exchanges a and a: and fixes fpDq for all f P F and the unique involutive algebra anti-automorphism η : A Ñ A which exchanges a and ¯a: and fixes fpDq for all f P F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then ηp2q :“ ηbη is an algebra antiautomorphism of A b A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It extends in a natural way to an algebra antiautomorphism of Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By applying ηp2q to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) we obtain (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Finally, to prove (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6), upon right-multiplying (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) by pD1`D2`1 we obtain (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) reppγa1¯a: 2q, a1pD2s “ γeppγa1¯a: 2qa1pD2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) it follows that (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) reppγa1¯a: 2q, a: 1a2pD2s “ γ¯a: 2pD1eppγa1¯a: 2qa2pD2 ` γa: 1eppγa1¯a: 2qa1pD2 “ γ ´ pD1eppγa1¯a: 2q ` pD2 ´ 1 ˘ ` ` 1 ´ pD1˘ eppγa1¯a: 2qpD2 ¯ “ γ ` eppγa1¯a: 2qpD2 ´ pD1eppγa1¯a: 2q ˘ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) follows as the χp2q-image of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Explicit expression for Rυφpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We are now ready to give the explicit expression for Rυφpzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all z P C we have (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) Rυφpzq “ eppza: 1a2qqpµ´1qpD2´D1q´2D1pD2`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4 we deduce that Rυφpzq is a solution of the linear relation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) Xpυz b φ´qp∆puqq “ pυz b φ´qp∆oppuqqX for all u P Uqppb´q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' First of all, note that the element in the right-hand side of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) satisfies (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) with u P tk0, k1u and so it suffices to prove that the vector space (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) X “ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X P Ap2q 0 ˇˇˇ X satisfies (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) for u P tf0, f1u ) A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 31 is spanned by eppz2a: 1a2qqpµ´1qpD2´D1q´2D1pD2`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Using the explicit formulas (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19), we obtain that (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) is equivalent to the system X ´ z´1a1pq´µ ´ qµ´2D1qq´µ´2D2´1 ` q´1a2 ¯ “ ´ z´1a1pq´µ ´ qµ´2D1q ` qµ´2pD1`1qa2 ¯ X, Xa: 1qµ`1`2D2 “ a: 1X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Without loss of generality we may write X “ r Xqpµ´1qpD2´D1q´2D1pD2`1q with r X P Ap2q 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) is equivalent to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) z´1r r X, a1p1 ´ pµ´D1qs “ pµ´D1´1a2 r X ´ r XpD1a2, r r X, a: 1s “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is straightforward to check that the centralizer in Ap2q 0 of a: 1 is the subalgebra generated by elements of the form ř kě0pa: 1qkfkpD2qak 2 with fk P F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It follows that r X “ ÿ kě0 pa: 1qkfkpD2qak 2 for some fk P F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Therefore (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) is equivalent to the single equation ÿ kě0 “ pa: 1qk, a1p1 ´ pµ´D1q ‰ fkpD2qak 2 “ z ÿ kě0 pa: 1qk` pµ´D1´k´1fkpD2 ` 1q ´ pD1fkpD2q ˘ ak`1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the commutator vanishes if k “ 0, and for k ą 0 we have “ pa:qk, ap1 ´ pµ´Dq ‰ “ pa:qk´1` p1 ´ pDqp1 ´ pµ´Dq ´ p1 ´ pD`kqp1 ´ pµ´D´kq ˘ “ pa:qk´1p1 ´ pkqppµ´D´k ´ pDq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) is equivalent to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) ÿ kě0 pa: 1qkp1 ´ pk`1qppµ´D1´k´1 ´ pD1qfk`1pD2qak`1 2 “ “ z ÿ kě0 pa: 1qk` pµ´D1´k´1fkpD2 ` 1q ´ pD1fkpD2q ˘ ak`1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' which is equivalent to the recurrence relation p1 ´ pk`1q ` pµ´D1´k´1 ´ pD1˘ fk`1pD2q “ z ` pµ´D1´k´1fkpD2 ` 1q ´ pD1fkpD2q ˘ which, since fkpD2q does not depend on D1, is equivalent to the system p1 ´ pk`1qfk`1pDq “ zfkpD ` 1q, fkpD ` 1q “ fkpDq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This is in turn equivalent to fkpDq P pp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 k zkC for k P Zą0, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Explicit expression for R̺¯̺pzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the representations ̺` and ¯̺` satisfy ¯̺` z “ χ ˝ ̺` z ˝ Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Furthermore, we observe that the linear maps L˘ π pzq actually lie in the subalgebra EndpC2q b r A for all π P t̺, ¯̺, υ, φu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Recall the centralizer Ap2q 0 defined in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='14) and consider the subalgebra r Ap2q 0 “ r Ap2q X Ap2q 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that the automorphism χp2q of r Ap2q defined in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) preserves r Ap2q 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The element R̺¯̺pzq is a r Ap2q 0 -valued formal power series whose coefficients are fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 32 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It is clear from the formulas (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) that ̺` b ¯̺´ takes values in r A b r A Ă r Ap2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now recall (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) and note that the factor κ acts as pD1pD2`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Furthermore, noting the form of pΣz b idqpΘq given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='26) with the components Θλ lying in Uqppn`qλ b Uqppn`q´λ (λ P pQ`), we obtain that the action of Rpzq on pW b W, ̺` b ¯̺´q is by an element of r Ap2q 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For the second part, note that χp2q ˝ p̺` b ¯̺´q “ pχ´1 b χq ˝ p¯̺´ b ̺`q ˝ σ “ p̺` b ¯̺´q ˝ pω b ωq ˝ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying this to Rpzq, making use of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18), we obtain χp2qpR̺¯̺pzqq “ R̺¯̺pzq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ Now we are ready to state and prove a formula for R̺¯̺pzq in terms of q-exponentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all z we have (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15) R̺¯̺pzq “ eq2pq3za1¯a: 2qeq2pq´1za: 1a2qq´2D1pD2`1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Clearly, w0 b w0 is fixed by the expression on the right-hand side of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the following we initially work over the ring Crrz, z2ss for some new indeterminate z2 and write z1 “ zz2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By applying ̺` z1 b Π1 b ¯̺´ z2 to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) and left and right-multiplying by L´ ¯̺,23pz´1 2 q´1 we obtain (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16) R̺¯̺pzq12L` ̺ pz1q13L´ ¯̺ pz´1 2 q´1 32 “ L´ ¯̺ pz´1 2 q´1 32 L` ̺ pz1q13R̺¯̺pzq12 an equation in p r Ap2q b EndpC2qqrrz2ss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By a direct computation we obtain (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) L´ ¯̺ pz´1 2 q´1 “ 1 z2 2 ´ 1 ˆ q´D´1z2 2 ¯a:q´D´1z2 aqD´1z2 qD`1z2 2 ´ q´D´1 ˙ P EndpC2q b r A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now we consider the equation (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) pz2 2 ´ 1qX12L` ̺ pz1q13L´ ¯̺ pz´1 2 q´1 32 “ pz2 2 ´ 1qL´ ¯̺ pz´1 2 q´1 32 L` ̺ pz1q13X12 in p r Ap2q b EndpC2qqrrz2ss, for some X P r Ap2q 0 such that χp2qpXq “ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It suffices to prove that the vector space (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='19) X “ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X P r Ap2q 0 ˇˇˇ X satisfies (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) and is fixed by χp2q) , which by Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7 contains p̺` z b ¯̺´qpRq, is spanned by the element given in the right-hand side of (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By considering explicit expressions for pz2 2´1qL` ̺ pz1q13L´ ¯̺ pz´1 2 q´1 32 and pz2 2´1qL´ ¯̺ pz´1 2 q´1 32 L` ̺ pz1q13, we obtain that (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='18) amounts to the system X ` qD1´D2´1 ´ a: 1a2q´D1`D2´2z ˘ “ ` qD1´D2´1 ´ a1¯a: 2qD1´D2z ˘ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X ´` ¯a: 2qD1´D2´1 ` a: 1q´D1´D2´2z ˘ ´ a: 1q´D1`D2zz2 2 ¯ “ “ ´ ¯a: 2q´D1´D2´1 ´ ` a: 1q´D1´D2´2 ` ¯a: 2qD1´D2`1z ˘ zz2 2 ¯ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X ´ a2q´D1`D2´1 ´ ` a1qD1´D2 ` a2qD1`D2`1z ˘ zz2 2 ¯ “ “ ´` a2qD1`D2´1 ` a1qD1´D2z ˘ ´ a1qD1`D2`2zz2 2 ¯ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' X ´ q´D1`D2`1 ` qD1´D2`1z2 ´ a1¯a: 2qD1´D2z ¯ “ ´ q´D1`D2`1 ` qD1´D2`1z2 ´ a: 1a2q´D1`D2´2z ¯ X A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 33 for X P r Ap2q 0 fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Since Crrz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' z2ss – Crrzssrrz2ss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' considering expansion coefficients with respect to z2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' we see that the above system is equivalent to Xa2q´D1`D2 “ ` a2qD1`D2 ` a1qD1´D2`1z ˘ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' a1qD1`D2`2X “ X ` a1qD1´D2 ` a2qD1`D2`1z ˘ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Xa: 1q´D1`D2 “ ` a: 1q´D1´D2´2 ` ¯a: 2qD1´D2`1z ˘ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' ¯a: 2q´D1´D2X “ X ` ¯a: 2qD1´D2 ` a: 1q´D1´D2´1z ˘ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' “ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' qD1´D2´1‰ “ ` Xa: 1a2q´D1`D2´2 ´ a1¯a: 2qD1´D2X ˘ z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' “ X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q´D1`D2`1 ` qD1´D2`1z2‰ “ ` Xa1¯a: 2qD1´D2 ´ a: 1a2q´D1`D2´2X ˘ z for X P r Ap2q 0 fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Using the fact that X commutes with qD1`D2, we obtain this is equivalent to the system Xa2q´2D1 “ ` a2 ` a1q´2D2`1z ˘ X, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20) a1X “ X ` a1q´2pD2`1q ` q´1a2z ˘ , (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='21) Xa: 1q2pD2`1q “ ` a: 1 ` ¯a: 2q2D1`3z ˘ X, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='22) ¯a: 2X “ X ` ¯a: 2q2D1 ` q´1a: 1z ˘ , (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='23) “ X, q2D1‰ “ ` Xa: 1a2q2D2´1 ´ a1¯a: 2q2D1`1X ˘ z, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='24) “ X, q2D2 ` q2D1z2‰ “ ` Xa1¯a: 2q2D1´1 ´ a: 1a2q2D2´3X ˘ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='25) Note that q´2D1pD2`1q P r Ap2q 0 is fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence without loss of generality we may write (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='26) X “ r Xq´2D1pD2`1q, for some r X P r Ap2q 0 fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The system (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='20-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='25) is equivalent to r r X, a2s “ q´2D2`1a1 r Xz, ra1, r Xs “ r Xq2D1´1a2z, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27) r r X, a: 1s “ ¯a: 2q2D1`3 r Xz, r¯a: 2, r Xs “ r Xa: 1q´2D2´3z, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) “ r X, q2D1‰ “ ` r Xa: 1a2q2D1´1 ´ a1¯a: 2q2D1`1 r X ˘ z, (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29) “ r X, q2D2 ` q2D1z2‰ “ ` r Xa1¯a: 2q2D2`3 ´ a: 1a2q2D2´3 r X ˘ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30) We now show that the system (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) implies the system (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Indeed, assuming the former, since r r X, q2D1s “ ra: 1a1, r Xs we have r r X, q2D1s ` a1¯a: 2q2D1`1 r Xz ´ r Xa: 1a2q2D1´1z “ “ a1¯a: 2q2D1`1 r Xz ´ r r X, a: 2sa1 ` a: 1ra1, r Xs ´ r Xa: 1a2q2D1´1z “ ` ¯a: 2q2D1`3ra1, r Xs ´ r r X, a: 1sa2q2D1´1˘ z, which vanishes, thereby recovering (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying χp2q to (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='29) we obtain r r X, q´2D2s “ ` r Xa: 1a2q´2D2´1 ´ a1¯a: 2q´2D2`1 r X ˘ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Left-and-right multiplying this by q2D2 we arrive at r r X, q2D2s “ ` a1¯a: 2 r Xq2D2`3 ´ q2D2´1 r Xa: 1a2 ˘ z 34 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION which using (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) we can re-write as (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) r r X, q2D2s “ ` ¯a: 2 r Xa1q2D2`3 ´ q2D2´1a: 1 r Xa2 ˘ z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Finally, using (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='31) and again (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28), we derive that r r X, q2D2 ` q2D1z2s ´ r Xa1¯a: 2q2D2`3z ` a: 1a2q2D2´3 r Xz “ “ ¯a: 2 r Xa1q2D2`3z ´ q2D2´1a: 1 r Xa2z ` r r X, q2D1sz2` ´ p¯a: 2 r X ´ r Xa: 1q´2D2´3zqa1q2D2`3z ` a: 1q2D2´1p r Xa2 ´ a1q´2D2`1 r Xzqz “ ` r Xa: 1a1 ` a: 1a1 r X ` r r X, 1 ´ a: 1a1s ˘ z2 which vanishes, thereby proving (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Furthermore, since χp2q fixes r X, the equations in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27) and the equations in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) are pairwise equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We deduce that the system (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='27-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='30) is equivalent to the system (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Now without loss of generality set r X “ Y eq2pq3za1¯a: 2qeq2pq´1za: 1a2q for some Y P r Ap2q 0 fixed by χp2q, noting that eq2pq3za1¯a: 2q and eq2pq´1za: 1a2q lie in r Ap2q 0 and are fixed by χp2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The theorem now follows from the following claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Claim: (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) is satisfied if and only if Y P Crrzss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In the special case Y “ 1, indeed (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='28) is indeed satisfied: r r X, a: 1s ´ ¯a: 2q2D1`3z r X “ ´ req2pq3za1¯a: 2q, a: 1s ´ ¯a: 2q2D1`3zeq2pq3za1¯a: 2q ¯ eq2pq´1za: 1a2q, r¯a: 2, r Xs ´ r Xa: 1q´2D2´3z “ eq2pq3za1¯a: 2q ´ r¯a: 2, eq2pq´1za: 1a2qs ´ eq2pq´1za: 1a2qa: 1q´2D2´3z ¯ , with the expressions in parentheses vanishing by virtue of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='17) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For general Y we therefore have r r X, a: 1s ´ ¯a: 2q2D1`3z r X “ rY, a: 1seq2pq3za1¯a: 2qeq2pq´1za: 1a2q, r¯a: 2, r Xs ´ r Xa: 1q´2D2´3z “ r¯a: 2, Y seq2pq3za1¯a: 2qeq2pq´1za: 1a2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Both right-hand sides vanish if and only if Y lies in the centralizer in r Ap2q of ta: 1, ¯a: 2u, which is trivial by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' This proves the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' An alternative proof of the main theorem In this part of the appendix we give a proof of the boundary factorization identity (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) indepen- dent of the universal K-matrix formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Throughout, p is a nonzero complex number unequal to a root of unity (corresponding to q2 in the main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Let γ, δ P C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Ap2q 0 we have the identities epppa1¯a: 2qpγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD1 “ pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD1epp´a1¯a: 2pD1γz2qepppa1¯a: 2q (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) epppa1¯a: 2qpp1´D1δz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D1epppδz2¯a: 1a2q “ epppδz2¯a: 1a2qpp1´D2δz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D2epppa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 35 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that W b W “ à mPZě0 pW b Wqm, pW b Wqm :“ à j,kě0 j`k“m Cwj b wk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Because each factor in (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) preserves each finite-dimensional subspace pW bWqm, it suffices to prove the restrictions of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) to pW bWqm, where m P Zě0 is fixed but arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that on pW b Wqm the operators appearing as arguments of the deformed exponentials are nilpotent of or- der m`1 and therefore, taking into account the appearance of the parameters, rational functions of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hence it suffices to prove these restricted equations for countably many values of each parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As for (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1), we will in fact prove its restriction to pW b Wqm for all p P C such that |p| ă 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As for (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1), using (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) with x replaced by pDγz2 we obtain pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD “ epppDγz2q eppγz2q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' As a consequence, (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1) is equivalent to (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='3) epppa1¯a: 2qepppD1γz2q “ epppD1γz2qepp´a1¯a: 2pD1γz2qepppa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' But this equation follows directly from (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='13) and the observation pa1¯a: 2qppD1γz2q “ pppD1γz2qpa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Similarly, we will prove the restricted version of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) for all p P Cˆ such that |p| ą 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In this case, for all j P Zě0 we have pp1´jδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 j “ pδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q´1 j “ pp´jδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q8 pδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that pp´jδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q8 is a well-defined element of Crrzss for all j P Zě0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' By (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) we obtain pp´jδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q8 “ ep´1pp´jδz2q´1 “ eppp1´jδz2q as an identity of formal power series in z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Putting it all together, we obtain the following identity in EndpWqrrzss: pp1´Dδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D “ pδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' p´1q´1 8 eppp1´Dδz2q We obtain that (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) is equivalent to (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4) epppa1¯a: 2qeppp1´D1δz2qepppδz2¯a: 1a2q “ epppδz2¯a: 1a2qeppp1´D2δz2qepppa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' To prove this, note that (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) with γ “ p can be rewritten as epppa1¯a: 2q ` p´D1 ` ¯a: 1a2 ˘ “ ` p´D2 ` ¯a: 1a2 ˘ epppa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' It follows that (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5) epppa1¯a: 2qep ` p1´D1δz2 ` pδz2¯a: 1a2 ˘ “ ep ` p1´D2δz2 ` pδz2¯a: 1a2 ˘ epppa1¯a: 2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Note that p¯a: 1a2qp1´D1 “ p p1´D1p¯a: 1a2q and p1´D2p¯a: 1a2q “ p p¯a: 1a2qp1´D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Applying (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12), we obtain (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4), as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ Remark C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We will need (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) with |p| ă 1, but in this case it is not clear how to prove (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We reiterate that the rational dependence of the matrix entries of the two sides of the restriction of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) to pW b Wqm means that our proof for all values of p outside the unit circle is sufficient to deduce the result for all values of p where the two sides of the restricted equation are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' � 36 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION Recall that the statement of Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1 is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' For all µ P C and q, ξ P Cˆ such that q is not a root of unity, the following identity holds in EndpW b Wqrrzss: (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) Kυpzq1Rυφpz2qKφpzq2 O` “ O`K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2, Alternative proof of Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We set γ “ q2´µξ´1 P Cˆ, δ “ qµ´2ξ P Cˆ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Owing to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='15), the desired identity (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6) is equivalent to (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) eq2pq2a1¯a: 2qKυpzq1Rυφpz2qKφpzq2eq2pq2a1¯a: 2q´1 “ “ qµpD1´D2q{2K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2qµpD2´D1q{2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' From (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) we deduce that (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='8) pδ´1z´2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 j “ pjp1´jq{2p´δz2qjpp1´jδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 j for all j P Zě0 and hence (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='9) Kυpzq “ ` ´ q1´Dδ ˘Dpγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qDpq2p1´Dqδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D , K¯̺pq´µzq “ ` ´ q´µ´Dδ ˘Dpq2p1´Dqδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The strategy of the proof is to show that by straightforward identities involving q-exponentials, various simple factors in Fp2qpD1, D2q can be moved to the right in both sides of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7), thus bringing them to a similar form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Then an application of more advanced product formulas involving q-exponentials and finite q-Pochhammer symbols yields the desired equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' More precisely, making use of the identities q´D2a: “ a:q´2D´1q´D2 “ ´q¯a:q´D2, q´D2a “ aq2D´1q´D2 in A, we obtain, for the left-hand side of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7), (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10) eq2pq2a1¯a: 2qKυpzq1Rυφpz2qKφpzq2eq2pq2a1¯a: 2q´1 “ “ eq2pq2a1¯a: 2q ` ´ δq1´D1˘D1pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD1pq2p1´D1qδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D1eq2pz2a: 1a2q¨ ¨ qp2µ´1qD1´2D2´2D1D2´D2 2p´ξqD2eq2pq2a1¯a: 2q´1 “ eq2pq2a1¯a: 2qpγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD1pq2p1´D1qδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D1eq2pq2δz2¯a: 1a2qp´q´D1´D2´2ξqD1`D2eq2pq2a1¯a: 2q´1 “ eq2pq2a1¯a: 2qpγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD1pq2p1´D1qδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D1eq2pq2δz2¯a: 1a2qeq2pq2a1¯a: 2q´1p´q´D1´D2´2ξqD1`D2 and similarly, for the right-hand side of (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7), (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='11) qµpD1´D2q{2K̺pq´µ{2zq1R̺¯̺pz2qK¯̺pqµ{2zq2qµpD2´D1q{2 “ “ pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD1qµpD1´D2q{2´D2 1p´ξqD1eq2pq3z2a1¯a: 2qeq2pq´1z2a: 1a2q¨ ¨ pq2p1´D2qδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D2qµpD2´D1q{2´2pD1`D2q´2D1D2´D2 2p´ξqD2 “ “ pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2qD1eq2p´a1¯a: 2q2D1γz2qeq2pq2δz2¯a: 1a2qpq2p1´D2qδz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' q2q´1 D2p´q´D1´D2´2ξqD1`D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' We obtain that (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='7) is equivalent to (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) epppa1¯a: 2qpγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD1pp1´D1δz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D1epppδz2¯a: 1a2qepppa1¯a: 2q´1 “ “ pγz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pqD1epp´a1¯a: 2pD1γz2qepppδz2¯a: 1a2qpp1´D2δz2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' pq´1 D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION 37 Applying the identities (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='2) for deformed exponentials we deduce (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='12) as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' □ References [AC76] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Arik, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Coon, Hilbert spaces of analytic functions and generalized coherent states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 17 (1976) 524.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [AV22a] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Appel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Vlaar, Universal K-matrices for quantum Kac-Moody algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theory 26 (2022), 764–824.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [AV22b] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Appel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Vlaar, Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Preprint at arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='16503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ba72] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baxter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Partition function of the eight-vertex lattice model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' of Physics, 70, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (1972), 193–228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ba73] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baxter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Some fundamental eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' of Physics, 76, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (1973), 1–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BB13] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baseilhac, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Belliard, The half-infinite XXZ chain in Onsager’s approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' B 873, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3 (2013), 550–584.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:0906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BGKNR10] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' G¨ohmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kl¨umper, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nirov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Razumov, Exercises with the universal R-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 41 (2010): 415208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BGKNR13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' G¨ohmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kl¨umper, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nirov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Razumov, Universal integrability objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 174, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (2013): 21–39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='4399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BGKNR14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' G¨ohmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kl¨umper, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nirov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Razumov, Universal R-matrix and functional relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 6 (2014), 1430005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Bi92] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Biedenharn, The quantum group SUq(2) and a q-analogue of the boson operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 22 (1992) L873.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BJMST09] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Boos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Jimbo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Miwa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Smirnov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Takeyama, Hidden Grassmann structure in the XXZ model II: creation operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 286, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3 (2009), 875–932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:0801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BK16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Balagovi´c, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kolb, Universal K-matrix for quantum symmetric pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Journal f¨ur die reine und angewandte Mathematik (Crelles Journal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='06276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BLMS10] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bazhanov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' �Lukowski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Meneghelli and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Staudacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A Shortcut to the Q-operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' : Theory Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 11 (2010), P11002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BLZ96] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bazhanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lukyanov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Zamolodchikov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Integrable structure of conformal field theory, quan- tum KdV theory and thermodynamic Bethe ansatz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 177, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2 (1996), 381–398.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BLZ97] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bazhanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lukyanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Zamolodchikov, Integrable Structure of Conformal Field Theory II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Q- operator and DDV equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 190 (1997), 247–278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BLZ99] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bazhanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lukyanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Zamolodchikov, Integrable Structure of Conformal Field Theory III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' The Yang-Baxter relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 200, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2 (1999), 297–324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BS90] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bazhanov, Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Stroganov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Chiral Potts model as a descendant of the six-vertex model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3 (1990), 799-817.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BT18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baseilhac, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Tsuboi, Asymptotic representations of augmented q-Onsager algebra and boundary K- operators related to Baxter Q-operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' B 929 (2018), 397–437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [BW18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Bao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Wang, A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Paris: Soci´et´e math´ematique de France (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ch02] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Chari, Braid group actions and tensor products, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (2002), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 7, 357–382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ch84] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Cherednik, Factorizing particles on a half-line and root systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' and Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 61, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (1984), 977–983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [CP94] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Chari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Pressley, Quantum affine algebras and their representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Representation theory of groups (Banff, AB, 1994), CMS Conference Proceedings, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 16, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (1994), 59–78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [CP95] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Chari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Pressley, A guide to quantum groups, Cambridge University Press, Cambridge, 1995, Corrected reprint of the 1994 original.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [De05] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Derkachov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Factorization of R-matrix and Baxter’s Q-operator (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Preprint at arXiv:math/0507252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [De07] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Derkachov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Factorization of the R-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' of Mathematical Sciences, 143, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (2007), 2773– 2790.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [DG02] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Delius, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' George, Quantum affine reflection algebras of type dp1q n and reflection matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 62 (2002), 211–217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:math/0208043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [DKK06] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Derkachov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Karakhanyan, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kirschner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Baxter Q-operators of the XXZ chain and R-matrix factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' B, 738, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3 (2006), 368–390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [DM03] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Delius, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Mackay, Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 233 (2003), 173–190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:hep-th/0112023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 38 A Q-OPERATOR FOR OPEN SPIN CHAINS II: BOUNDARY FACTORIZATION [Dr85] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Drinfeld, Hopf algebras and the quantum Yang-Baxter equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Soviet Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Dokl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 32 (1985), 254– 258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Dr86] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Drinfeld, Quantum groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Cong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=', Berkeley (1986), A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Gleason (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' ), 798–820.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=', Providence, RI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [FH15] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Frenkel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hernandez, Baxter’s Relations and Spectra of Quantum Integrable Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 164, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 12 (2015), 2407–2460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [FR92] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Frenkel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Reshetikhin, Quantum affine algebras and holonomic difference equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 146, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1 (1992), 1–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [GR90] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Gasper and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Rahman, Basic hypergeometric series, Encyclopedia of mathematics and its applica- tions 35 (1990), Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [He19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hernandez, Avanc´ees concernant les R-matrices et leurs applications [d’apr`es Maulik-Okounkov, Kang-Kashiwara-Kim-Oh, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='] (2019), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 407, S´eminaire Bourbaki, 69`eme ann´ee, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 2016-2017, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 1129, 297–331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [HJ12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Hernandez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Jimbo, Asymptotic representations and Drinfeld rational fractions, Compositio Math- ematica 148, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 5 (2012), 1593–1623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='1891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ji86a] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Jimbo, A q-analogue of UpglpN ` 1qq, Hecke algebra, and the Yang-Baxter equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3 (1986), 247–252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ji86b] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Jimbo, Quantum R Matrix for the Generalized Toda System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 102 (1986), 537– 547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ka90] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kac, Infinite-dimensional Lie algebras, third ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=', Cambridge University Press, Cambridge (1990) [Ko14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kolb, Quantum symmetric Kac-Moody pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 267 (2014), 395–469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='6036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ko97] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Koornwinder, Special functions and q-commuting variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' In Special Functions, q-Series and Related Topics, Fields Institute Communications 14, American Mathematical Society (1997), 131–166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [KS95] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kazhdan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Soibelman, Representations of quantum affine algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=') 1 (1995), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 3, 537–595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [KT14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Khoroshkin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Tsuboi, The universal R-matrix and factorization of the L-operators related to the Baxter Q-operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 47 (no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 19) (2014), 192003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Ku91] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Kulish, Contraction of quantum algebras and q-oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' and Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Physics 86 (1991) 108–110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Lu94] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Lusztig, Introduction to quantum groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Birkh¨auser, Boston, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Mf89] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Macfarlane, On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 22 (1989) 4581-4588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [RSV15] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Reshetikhin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Stokman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Vlaar, Boundary quantum Knizhnik-Zamolodchikov equations and fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Annales Henri Poincar´e (2015), 1–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:1404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='5492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Sc53] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Sch¨utzenberger, Une interpr´etation de certaines solutions de l’´equation fonctionelle: Fpx ` yq “ FpxqFpyq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Paris 236 (1953), 352–353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [Sk88] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Sklyanin, Boundary conditions for integrable quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 21 (1988), 2375–2389.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [TK92] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Tolstoy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Khoroshkin, The universal R-matrix for quantum untwisted affine Lie algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 26 (1992), 69–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' [VW20] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Vlaar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Weston, A Q-operator for open spin chains I: Baxter’s TQ relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 53 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' 24 (2020): 245202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content=' arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} +page_content='10760.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-tE2T4oBgHgl3EQfmQed/content/2301.03997v1.pdf'} diff --git a/.gitattributes b/.gitattributes index 86b5c4c9aaff4e42d49ff79207a1efc5ab571b2c..1d2df47d68aa3aa8c69fc0da650c839a635fe822 100644 --- a/.gitattributes +++ b/.gitattributes @@ -8015,3 +8015,64 @@ UdAzT4oBgHgl3EQf0_6m/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -tex KdAzT4oBgHgl3EQfVfys/content/2301.01286v1.pdf filter=lfs diff=lfs merge=lfs -text OdAyT4oBgHgl3EQfg_gX/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text E9FLT4oBgHgl3EQfFi_K/content/2301.11988v1.pdf filter=lfs diff=lfs merge=lfs -text +3dE1T4oBgHgl3EQf5wXA/content/2301.03516v1.pdf filter=lfs diff=lfs merge=lfs -text +H9AyT4oBgHgl3EQf5vo1/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +K9A0T4oBgHgl3EQfC_82/content/2301.01996v1.pdf filter=lfs diff=lfs merge=lfs -text +HtAyT4oBgHgl3EQfS_fv/content/2301.00099v1.pdf filter=lfs diff=lfs merge=lfs -text +F9E0T4oBgHgl3EQfhQEq/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +yNE0T4oBgHgl3EQftQGw/content/2301.02590v1.pdf filter=lfs diff=lfs merge=lfs -text +XtFRT4oBgHgl3EQfNzdw/content/2301.13511v1.pdf filter=lfs diff=lfs merge=lfs -text +qNE5T4oBgHgl3EQflA99/content/2301.05667v1.pdf filter=lfs diff=lfs merge=lfs -text +6tE0T4oBgHgl3EQfwAE6/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +fdE_T4oBgHgl3EQf2RwE/content/2301.08339v1.pdf filter=lfs diff=lfs merge=lfs -text +KNE0T4oBgHgl3EQfSQBx/content/2301.02219v1.pdf filter=lfs diff=lfs merge=lfs -text +jNAzT4oBgHgl3EQf4_5S/content/2301.01852v1.pdf filter=lfs diff=lfs merge=lfs -text +5NFKT4oBgHgl3EQfSS3g/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ydE1T4oBgHgl3EQf4AWL/content/2301.03496v1.pdf filter=lfs diff=lfs merge=lfs -text +Q9E4T4oBgHgl3EQfKgxv/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +zNE0T4oBgHgl3EQf_AJ2/content/2301.02821v1.pdf filter=lfs diff=lfs merge=lfs -text +ntAyT4oBgHgl3EQfy_ls/content/2301.00694v1.pdf filter=lfs diff=lfs merge=lfs -text +ntAyT4oBgHgl3EQfy_ls/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +6tAyT4oBgHgl3EQfQfaP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +-dFLT4oBgHgl3EQfCy73/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +xtE3T4oBgHgl3EQflwoI/content/2301.04609v1.pdf filter=lfs diff=lfs merge=lfs -text +q9AyT4oBgHgl3EQfzvm4/content/2301.00707v1.pdf filter=lfs diff=lfs merge=lfs -text +DNE4T4oBgHgl3EQfew0W/content/2301.05101v1.pdf filter=lfs diff=lfs merge=lfs -text +XtE4T4oBgHgl3EQfNgyO/content/2301.04957v1.pdf filter=lfs diff=lfs merge=lfs -text +MNFPT4oBgHgl3EQfkjUi/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +-dFLT4oBgHgl3EQfCy73/content/2301.11977v1.pdf filter=lfs diff=lfs merge=lfs -text +FNE0T4oBgHgl3EQfhAFe/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +XtFRT4oBgHgl3EQfNzdw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +CdE1T4oBgHgl3EQfWAQw/content/2301.03108v1.pdf filter=lfs diff=lfs merge=lfs -text +ydE1T4oBgHgl3EQf4AWL/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +W9FLT4oBgHgl3EQfTS_4/content/2301.12045v1.pdf filter=lfs diff=lfs merge=lfs -text +ptE4T4oBgHgl3EQfUQxX/content/2301.05014v1.pdf filter=lfs diff=lfs merge=lfs -text +TtAzT4oBgHgl3EQf0v7t/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +TdAyT4oBgHgl3EQfuflV/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +mdE2T4oBgHgl3EQfJQZR/content/2301.03689v1.pdf filter=lfs diff=lfs merge=lfs -text +vtFAT4oBgHgl3EQfih2j/content/2301.08600v1.pdf filter=lfs diff=lfs merge=lfs -text +P9AyT4oBgHgl3EQfUve2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +e9E1T4oBgHgl3EQfegRi/content/2301.03207v1.pdf filter=lfs diff=lfs merge=lfs -text +O9E2T4oBgHgl3EQfVQdj/content/2301.03821v1.pdf filter=lfs diff=lfs merge=lfs -text +TtAzT4oBgHgl3EQf0v7t/content/2301.01790v1.pdf filter=lfs diff=lfs merge=lfs -text +CdE1T4oBgHgl3EQfWAQw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +KNE0T4oBgHgl3EQfSQBx/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +UNAyT4oBgHgl3EQf8fqv/content/2301.00858v1.pdf filter=lfs diff=lfs merge=lfs -text +AdE4T4oBgHgl3EQf4w7g/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +59E2T4oBgHgl3EQfOwac/content/2301.03752v1.pdf filter=lfs diff=lfs merge=lfs -text +MNFPT4oBgHgl3EQfkjUi/content/2301.13118v1.pdf filter=lfs diff=lfs merge=lfs -text +GdFIT4oBgHgl3EQfWysJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +zNE0T4oBgHgl3EQf_AJ2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +FNE2T4oBgHgl3EQfSwf4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +w9FQT4oBgHgl3EQfwTaN/content/2301.13401v1.pdf filter=lfs diff=lfs merge=lfs -text +MNE3T4oBgHgl3EQfwQsY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +MNE3T4oBgHgl3EQfBAmd/content/2301.04263v1.pdf filter=lfs diff=lfs merge=lfs -text +5tE0T4oBgHgl3EQfvwEb/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +xtE3T4oBgHgl3EQflwoI/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +UdE1T4oBgHgl3EQfuwU5/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +5NE2T4oBgHgl3EQfOgaA/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +vtAzT4oBgHgl3EQfB_rN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +WtE1T4oBgHgl3EQfJAP_/content/2301.02948v1.pdf filter=lfs diff=lfs merge=lfs -text +adE1T4oBgHgl3EQfwwXB/content/2301.03415v1.pdf filter=lfs diff=lfs merge=lfs -text +qNAyT4oBgHgl3EQfzfnr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +UdE1T4oBgHgl3EQfuwU5/content/2301.03391v1.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/2301.03509v1.pdf.txt b/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/2301.03509v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..3054d1cfac38e07a6cbbb884f7073812c9bed72c --- /dev/null +++ b/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/2301.03509v1.pdf.txt @@ -0,0 +1,1001 @@ +IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION. ACCEPTED DECEMBER, 2022 +1 +Learning-based Design and Control for +Quadrupedal Robots with Parallel-Elastic Actuators +Filip Bjelonic1,2, Joonho Lee1, Philip Arm1, Dhionis Sako1, Davide Tateo2, Jan Peters2, Marco Hutter1 +Abstract—Parallel-elastic joints can improve the efficiency and +strength of robots by assisting the actuators with additional +torques. For these benefits to be realized, a spring needs to be +carefully designed. However, designing robots is an iterative and +tedious process, often relying on intuition and heuristics. We +introduce a design optimization framework that allows us to co- +optimize a parallel elastic knee joint and locomotion controller +for quadrupedal robots with minimal human intuition. We design +a parallel elastic joint and optimize its parameters with respect to +the efficiency in a model-free fashion. In the first step, we train a +design-conditioned policy using model-free Reinforcement Learn- +ing, capable of controlling the quadruped in the predefined range +of design parameters. Afterwards, we use Bayesian Optimization +to find the best design using the policy. We use this framework to +optimize the parallel-elastic spring parameters for the knee of our +quadrupedal robot ANYmal together with the optimal controller. +We evaluate the optimized design and controller in real-world +experiments over various terrains. Our results show that the new +system improves the torque-square efficiency of the robot by 33 % +compared to the baseline and reduces maximum joint torque by +30 % without compromising tracking performance. The improved +design resulted in 11 % longer operation time on flat terrain. +Index Terms—Legged Robots, Reinforcement Learning, Com- +pliant Joints and Mechanisms, Mechanism Design +I. INTRODUCTION +T +HE quest of creating a single versatile, efficient and +strong robotic platform has driven research in legged +robotics for many years. While controllers are getting more +robust and intelligent, locomotion performance is limited by +the available joint speed and joint torque. Better performance +can be achieved by creating more efficient and powerful actu- +ators. Adding elastic elements has the promise of supporting +the actuators with additional torque [1]. +In this letter, we explore the effect of the elastic component +on energy efficiency during locomotion by attaching a parallel +spring mechanism on the knee joints of the ANYmal robot +(Fig. 1). This system is used to experiment and verify the +benefit of the parallel elasticity. +A. Robots with elastic actuators +One of the first approaches in this direction was the Series +Elastic Actuator (SEA) by Gill Pratt [2] which incorporates +a series-elastic element between the actuator and the load. +This design makes the joint positioning error-tolerant, reduces +Manuscript received: August 27, 2022; Revised November 21, 2022; +Accepted December 16, 2022. +This paper was recommended for publication by Editor Abderrahmane A. +Kheddar upon evaluation of the Associate Editor and Reviewers’ comments. +This work was supported by a fellowship within the IFI program of the +German Academic Exchange Service (DAAD). +1 Authors are with ETH Zurich; Robotic Systems Lab; Leonhardstrasse 21, +8092 Zurich, Switzerland. +2 Authors are with TU Darmstadt; Intelligent Autonomous Systems Lab; +Hochschulstrasse 10, 64289 Darmstadt, Germany +Digital Object Identifier (DOI): see top of this page. +Fig. 1. +The ANYmal robot with parallel-elastically actuated knee joints. +ANYmal is walking upstairs at the central station of Zurich, which is used +as one of the experimental sites during this work. +impact loads, and, most importantly, allows for precise torque +measurement. The ANYmal quadrupedal robot [3] integrates +into its ANYdrive actuator a serial elastic spring. More exam- +ples are ATRIAS [4], a biped that has serial elastic springs +at the actuator level and Cassie [1] with a 6-bar linkage +with 2 springs in series. HyQ [5] has a serial elastic spring +between the knee and the foot of the robot, which reduces foot +chattering during touch-down. +Another approach is the Parallel Elastic Actuator (PEA). In +this setup, the actuator and the spring are in parallel. While +this approach has been studied in robotic manipulation for +gravity compensation [6], for pick-and-place [7] and efficient +oscillation [8], there is no comparative evaluation of walking +robots with PEA outside of controlled lab environments. One +example of a legged robot with PEAs is SpaceBok [9]. In a +lab experiment with simulated moon gravity, PEAs reduced +the energy required for a jump by a factor of two on this +robot [10]. Another, more recent example of using PEA is +BirdBot [11], which has a parallel elastic spring clutching +mechanism, spanning multiple joints. The avian-inspired leg +design shows self-stable and robust bipedal locomotion while +requiring 10 % of the knee-flexing torque compared to a non- +clutching parallel spring setup. Another example is STEPPR +[12]. This bipedal robot has a parallel-elastic spring at the hip +and the ankle. Using only the hip springs during walking, the +robot consumes 31 % less joint electrical power and reduces +power consumption overall by 13 %. +All of the previous works mention the possibility of saving +energy with the carefully designed springs. Unfortunately, +most of them are designed based on heuristic and cannot +exploit the full potential of elastic elements. +Building upon intuitive design, a common approach starts +with mimicking nature’s counterparts [13]. Atrias [4] and +arXiv:2301.03509v1 [cs.RO] 9 Jan 2023 + +2 +IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION. ACCEPTED DECEMBER, 2022 +BirdBot [11] for instance are inspired by ostriches and the +emu. The problem with bio-inspired design is the high amount +of variables that need to be taken into account to fully +model the targeted animal accurately. Nevertheless, there is +no systematic way of designing robots in general. +B. Computational design +Computational robot design can be divided into gradient- +based methods that work well with deterministic differentiable +objective functions, gradient-free algorithms with smooth ob- +jectives (e.g. trust-region methods), meta-heuristic methods +that are nature inspired (e.g. simulated annealing, genetic al- +gorithms), and surrogate methods (e.g. Bayesian Optimization +(BO)) [14]. Meta-heuristic and surrogate methods have been +successfully used in black-box optimization problems, where +the properties of the objective function are not known in +advance [15] [16]. +A work related to the goal in this work has been done +by Scalera et al. [7] where the design optimization of elastic +elements was carried out for a four Degrees of Freedom (DoF) +parallel robotic arm. Here, the robot achieved an efficiency +gain of 67 % on a predefined trajectory by defining a non- +linear optimization problem for finding energy optimal spring +parameters. This approach is unsuitable for legged locomotion +since it optimizes over a fixed trajectory that is by no means +guaranteed to be optimal. +The approach from De Vincenti et. al. [17] uses a differ- +entiable trajectory tracking controller such that the overall +leg design optimization becomes control-aware. Effectively, +the gradient computation takes the control formulation into +account in each step. Nevertheless, the trajectory is still fixed +for all the tasks. +A co-optimization approach is developed by Dinev et. al. +[18] for leg lengths, joint positions, trunk shape, and weight +distribution. Here, motion planning is recomputed in every +evaluation of the design process. Using finite differences, the +design optimization increases the energy efficiency of the Solo +robot by a factor of 3 and shows faster convergence than using +an evolutionary optimizer (CMA-ES). Using finite differences +on rough terrain may result in an unstable solver, making this +approach hard to incorporate into our goals. +In general, these methods incorporate a design optimization +that is wrapped around the robot control and planning loop. +While the approaches incorporate gradient-based or gradient- +free solvers for the outer loop, the inner loop can be either +fixed [7] [19], or efficiently re-optimized in every performance +evaluation [18] [17] [20] [21]. +An interesting simultaneous approach from Chen et al. [22] +defines a hardware policy besides the control policy, that is +jointly optimized over the training process with model-free +Reinforcement Learning (RL). The optimized weights of the +hardware policy define the hardware parameters and, together +with the control policy, create the output of the algorithm. +While this is a fully integrated approach, defining the hardware +policy as a computational graph is not possible in many cases +[22]. +Another method by Schaff et al. [23] optimizes an RL policy +and distribution of design parameters at the same time. The +agent is able to observe design parameters while the design +space slowly shrinks toward high-performing designs. This +approach has been successfully applied on a soft robot crawler +Shank +Thigh +Spring +Disc +(a) Design +Shank +Thigh +(b) Elliptic Cam +Fig. 2. Fig. 2a illustrates a generic two-segment leg with potentially nonlinear +parallel elastic knee joints. The conceptual implementation of the rotatory +spring stiffness k in this work is visualized in Fig. 2a. The linear elastic spring- +wire mechanism connects the thigh with the shank. This creates a spring +torque τs on the knee. Parts with the same color are physically connected. +[24] and outperformed a baseline design from an expert with +the optimal design walking more than 2× as fast. +Inspired by the co-optimization approach from Dinev et. al. +[18] and the learning-based approach by Chen et al. [22], the +following section briefly introduces our design optimization +framework as well as our main contributions. +C. Contribution +We present a systematic approach to designing elastic mech- +anisms for legged robots by incorporating design-conditioned +controllers in the optimization. In particular, we present: +• Co-optimization of the design parameters and the loco- +motion controller for the PEA-driven legged robot using +model-free RL and BO. +• Integration of the optimized design onto the physical +system and sim-to-real transfer of the learned control +policy. +• Real-world experiments to demonstrate the feasibility and +robustness of our approach followed by the quantitative +evaluation. +We would like to emphasize the last contribution because, to +the authors’ knowledge, this paper provides the first evaluation +of PEAs on walking robots outside of lab environments. +II. METHOD +In this section, we first present our PEA design and then +present our framework to co-optimize the controller as well as +design parameters. For any equation, vectors and matrices are +marked in bold text. Further, we refer to specific legs by their +position with respect to the base in the anterior and lateral +direction with the left front (LF), right front (RF), left hind +(LH), and right hind (RH) leg. +A. Parallel Elastic Knee +We design a PEA knee joint for quadrupedal robots seen +in Fig. 2a. Particularly, a parameterization d ∈ D of the joint +stiffness k is necessary. We design and implement a spring- +wire mechanism (Fig. 2a). The wire connects the thigh and +shank over a generic disc that defines the lever arm for the +spring force. The disc is attached to the shank of the robot. +The torque on the knee that is generated by this design can +be calculated in general by + +BJELONIC et al.: LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS +3 +Fig. 3. The non-linear trajectory of the spring force’s lever arm ˆlr over on full +rotation is plotted in pink. The radius of the major and minor axis is 3 and 1 +respectively, while the spring force is assumed to always point upwards. The +length, as well as the angle of the lever arm, changes dynamically, depending +on the angle of the knee. +τs(q) = Fs × ˆlr(θ) +(1) +with Fs being the force created by the linear spring, θ ∈ +[0, 2π) defines the boundary of the cam and ˆlr(θ) is the spring +force’s lever arm. The amplitude of the spring force can be +calculated by Hooke’s law as fs = ||Fs|| = ks∆ls, with +ks being the spring stiffness. The spring elongation ∆ls is +influenced by the length of wire which is wrapped around +the cam and the position of the lever arm. With this setup, +the first parameter d1 is the equilibrium position ¯qKFE of +the linear spring, which is defined as the knee angle where +Fs = 0. Further parameters are added through the definition +of the cam. Since the wire is always assumed to be in contact +with the cam, the lever arm can be calculated by finding the +point on the cam that is tangent to the spring force. This can +be formalized by the following equation +0 = Fs × ∂ˆlr +∂θ . +(2) +We select an elliptic cam as a trade-off between simplicity +and degrees of freedom of parameterization. In this case, this +equation has always two solutions depending on the side at +which the spring force acts. In our case, the left side of the +lever arm respects the inequality +� +Fs, ˆlr(θ) +� +≥ 0. +(3) +Following, we describe the elliptic cam attached to the +shank of the robot. +1) Elliptic Cam: Elliptic cam is defined by +lr(θ) = Rφ +� +a · cos(θ) +b · sin(θ) +� +(4) +Rφ = +� +cos(φ) +−sin(φ) +sin(φ) +cos(φ) +� +φ = φ0 + qKFE, +where θ ∈ [0, 2π) and φ0 being the initial angle of the ellipse +with respect to the shank’s longitudinal axis at qKFE = 0 rad, +a and b are the radius of the major and minor axis respectively, +seen in Fig. 2b. Now, the lever arm ˆlr is not stationary and +changes during the rotation of the knee. An example trajectory +of the contact point over one full rotation of 360° for an ellipse +with a = 3 and b = 1 is illustrated in Fig. 3. +The contact point ˆlr can be calculated using (2) and (3). +Fig. 4. The trajectories τ are collected with the trained design-conditioned +policy in simulation. Afterward, the robot’s performance for a specific design +choice is measured by a custom objective function f(D) and sent to the BO. +Using this value, the algorithm builds a surrogate function (blue + cyan color +in the left plot) and samples new points with respect to its acquisition function +(green color in the right plot). The blue dots refer to already sampled points +and the green dots to the next design set to be rolled out. +Similarly, based on equations (1) - (4), we can compute the +spring displacement by numerically solving an elliptic integral. +We skip the derivations for the sake of space. The resulting +torque is non-linear if a ̸= b +τs(d) = ψ(qKFE, d) +(5) +with the design space d = [¯qKFE, a, b, φ0]T +∈ R4. An +animation of the design space is included in the supplementary +video. +B. Design Optimization +Here we present our framework for optimizing the design +parameters d. The general approach of our design optimization +strategy is pictured in Fig. 4. We roll out trajectories with the +design-conditioned policy (explained in section II-C) in the +environment with each given set of design parameters. We +define the objective function f for the design optimization +by the Monte Carlo estimate over a large number of sam- +ples collected in the simulation. By doing so, we evaluate +the general performance of a design instance across many +different scenarios with different initial states, disturbances, +and commands. +1) Design Objective: The main objective of our design op- +timization problem is energy efficiency. Accurately simulating +the efficiency of a robot is a difficult task due to various +sources of energy consumption, e.g., mechanical energy at the +actuators, power used to run computers and sensors, etc. We +assume that the power loss of the system can be approximated +by the joule heating of the individual actuators. There are +other factors like transmission loss and electronics loss that are +neglected. Joule heating is one of the major terms for energetic +losses in electric motors and is proportional to the square of the +actuator torque. Similar to the Cost of Transportation (CoT), +we define the Cost of Torque (CoTr) as +CoT ∝ CoTr = +� +τ 2dt +mg∆s +(6) +with m being the total mass of the robot, g = 9.81 m/s2 the +gravitational acceleration and ∆s the traveled distance by the +robot. By normalizing with m, which depends on the design, + +2 +1 +F +S +0 +9 +-1 +Ellipse +-2 +-3 +-2 +-1 +0 +1 +2 +C4 +IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION. ACCEPTED DECEMBER, 2022 +and ∆s, this metric allows for the comparison of different +designs and walking speeds. +2) Optimization: The aim of the design optimization step is +to find optimal design parameters d ∈ D for a specific task t ∈ +T with respect to an objective function f(d|t, π) : T ×D → R, +given the pre-trained policy π. The objective f evaluates d for +a fixed task t, which is velocity tracking on rough terrain in +our setup, and outputs a performance measure. +A task t defines the specific problem the policy solves. +These parameters could be for example terrain property (rough +terrain, stairs, etc.) as well as command amplitude and direc- +tion. The task parameters are randomly sampled during policy +training and design optimization. +The objective f is defined by the physical quantities we +are optimizing the design, e.g., joint torques or tracking per- +formance (our setup), which are often not differentiable with +respect to d. In our setup, we assume f is not differentiable +because legged locomotion entails many discrete changes in +dynamics due to foot contact. Thereby we use a black-box +optimization method. +The optimization problem can then be mathematically for- +malized as +d∗ = arg min Ed∈D,t∈T [f(d|t, π)] +(7) +s.t. +0 ≤ c(d). +We use the Heteroscedastic Evolutionary Bayesian Optimi- +sation (HEBO) algorithm [25]. This BO algorithm won the +NeurIPS2020 black-box optimization challenge [26]. The out- +come of this challenge is the reason why we chose a surrogate +method over a meta-heuristic method (compare Sec. I-B). +C. Design-conditioned Policy +It is important to have an optimal controller for each +design instance to evaluate each design instance at its best +performance. We assume that we can achieve near-optimal +performance with a neural network policy conditioned on +design parameters. A recent work by Won et al. [27] showed +that it is possible to train a shape-conditioned policy for a +bipedal robot through RL that can maintain a stable gait while +the shape of its body is dynamically changing. +Our policy training follows the approach, and we addition- +ally adapt the privileged learning method by Lee et. al. [28] +for sim-to-real transfer. +We train two types of policies: +• Design-conditioned policy (teacher): This policy directly +observes design parameters and other environmental pa- +rameters (e.g., terrain shape and friction coefficient), +which we call privileged information, from simulation. +The policy is used in the design optimization loop (see +Fig. 4). +• Deployment policy (student): This policy is deployed on +the robot with noisy measurements as observation. This +policy does not have access to privileged observations +and observes the history of noisy proprioceptive measure- +ments and exteroceptive measurements. The deployment +policy is explained in section II-D. +The design-conditioned policy is trained via RL in simulation +and the student policy is trained via imitation learning with +simulated sensor noises. Using temporally extended observa- +tions, e.g., history of proprioceptive measurements [28] or +noisy exteroception [29], the student policy can estimate the +Teacher (Reinforcement Learning) +Learning Environment +Policy +Update +Fig. 5. +The learning pipeline is adapted from the teacher-student approach +[28]. The most important change is that the teacher directly observes the +design parameter in the privileged observation. +Fig. 6. We performed several tests with AoPS on rough terrain, showing its +robustness. The policy was extensively tested in the mountains, the forests, +and the City of Zurich. +privileged information and adapt to the sim-to-real discrep- +ancy. +1) Reinforcement Learning: The design-conditioned policy +is trained using RL. We model the RL problem as a Markov +Decision Process (MDP), where the design-conditioned policy +πθ defines the distribution of at ∈ A conditioned on the ob- +servation ot ∈ O. The environment updates the robots state in +each step according to a transition function p(st+1|st, at) and +gives a reward rt(st, st+1, at). The objective is to maximize +πθ∗(at|ot) → max E +� +� +∞ +� +˜t=t +γ˜t−tr(a˜t, s˜t) +� +� +(8) +with γ ∈ [0, 1] being the discount factor. +An MDP is defined by the 4-tuple of O, A, r, p. The state +transition (p) follows rigid body dynamics in simulation. Each +other component is explained below. +We use the Proximal Policy Optimization (PPO) Algorithm +[30] to update and train our policy. +ot (∈ R133) contains the base target velocity commands, +base orientation, base linear and angular velocity, parameters +for the leg motion primitive (Foot Trajectory Generator (FTG) +by [28]), a short history of joint positions and joint velocities, +and the last two joint position targets. The privileged informa- +tion in R46 includes contact friction, state and force at each +foot, external forces and torques applied to the base, the design +parameters, and the robot’s link masses. +During the policy training, the design parameters are ran- +domly sampled from D (compare Sec. II-B) per episode. In +order to avoid tedious design calibration, we provide observa- + +contact states +contact forces +terrain profile +contact friction +disturbancesPolicyaesign params. o +Encoder BJELONIC et al.: LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS +5 +(a) Assembled Spring Setup +(b) Hip +(c) Ellipse +(d) Wire +(e) Spring +Fig. 7. +These images of the robot as well as the individual parts show +the spring-wire setup developed in this work. The green letters in Fig. 7a +correspond to the 4 pictures on the right. +tions of the equilibrium positions of the PEAs separately for +each leg. +2) Action: The agent controls the robot through at ∈ R16 +(compare Fig. 5), with the first 4 actions setting the frequency +of the FTG [28] and 12 additional joint position deltas. +The FTG outputs vertical foot trajectories with predefined +clearance that are mapped to desired joint positions using +inverse kinematics. +3) Reward: The reward function includes a metric for +following linear base commands in the x and y directions +as well as the rotation along the yaw axis. Furthermore, +we punish undesired movement in the base (z velocity, roll, +and pitch angular velocity). For smooth and realistic torque +commands, we penalize the acceleration with which the joint +position targets change over time. For the agent to find optimal +and efficient behavior, we penalize the L2 norm of the actuator +torques. Lastly, we penalize joint velocities that exceed the +actuator limits and foot slippage, which reduces foot strain +due to sliding. +4) Architecture: The design-conditioned policy is modeled +as a Multi Layer Perceptron (MLP) and an auto-encoder +network. The encoder network takes the privileged information +and outputs an embedding vector ¯lt. Finally, the proprioceptive +observations and this vector ¯lt are used as the input to the +policy network (compare Fig. 5). +D. Deployment Policy +The deployed policy does not have access to privileged +information. Instead, it uses a sequence of past observations +to infer the unobserved state of the environment [29]. The +student policy is constructed by a Recurrent Neural Network +(RNN) [31] to effectively handle the sequential data. Similarly +to Lee et al. [28], the training is done by imitation learning +with an additional reconstruction loss for the embedding of +the privileged information (¯lt). +The observation of the deployed policy consists of pro- +prioceptive measurements from the IMU and joint encoders +and exteroceptive measurements from depth sensors. Both +modalities are simulated with noise during the training, which +is not added to the design-conditioned policy’s observation. +The action space of the deployment policy is the same as the +design-conditioned policy. +An important factor for the sim-to-real transfer is to account +for the model mismatch of the springs. During the student +policy training, the design parameters are perturbed by 10 % +from the optimized parameter to emulate limited manufactur- +ing precision (see Sec. III-A). The design-conditioned policy +observes the exact values as privileged information while +the student policy does not have direct access to the design +parameter. +III. EXPERIMENTS +We report the results of five different experiments to +quantify the effectiveness of our approach as well as the +performance gained by our new parallel elastic knee. The first +experiment in Sec. III-B shows that our design optimization +framework can find optimal parameters with respect to our +design-conditioned policy in various tasks and with high +repeatability. Experiments 2 and 3, in Sec. III-C and Sec. III-D +respectively, are hardware experiments on flat terrain, showing +that the parallel-elastic robot is more efficient than the baseline +and requires less torque in forward walking as well as tracking +random commands. The fourth experiment in Sec. III-E shows +that the novel design can traverse difficult terrain. Lastly, Sec. +III-F reports the last experiment, using the robot on a running +track, which shows that the newly designed robot can operate +longer with the same battery charge. +A. Setup +The task t for which the robot is optimized is forward +walking at 1 m s−1 in an environment with stepping stones, +flat terrain, and rough terrain with base perturbations of up to +50 N force and 50 N m torque. The contact friction that the +robot experiences is in the range µ = [0.5, 2]. The objective +function f is chosen as the average reward +f = 1 +N +N +� +i=0 +r(ati, sti). +(9) +We use 1000 different episodes to estimate the expectation of +the objective. +We optimize the design parameters (II-A1) and build the +elliptic cam in Fig. 2b for the hardware experiments. The +physical parts that we created are illustrated in Fig. 7. Our +final design consists of a linear spring with stiffness ks = +4154 N m−1 and the four optimal design parameters, namely +the radius of the major axis a = 8.1 cm and minor axis +b = 6.0 cm, initial angle φ0 = 0.0 rad and the equilibrium +position of ¯qKFE = 0.36 rad. The wires in Fig. 7d define +the equilibrium position ¯qKFE of each leg and are due to +manufacturing constraints not equally long. We randomize +these values separately for each leg during the student training +to account for unsymmetrical spring parameters. The policies +use the spring exclusively in the pulling direction. Thus, we +can implement the design with one tension spring per knee. +After training the design-conditioned agent, we create two +student policies. For the distillation, we fix our design pa- +rameters in the demonstrations from the design-conditioned +policy to the optimal design (parallel-elastic knee joint) and +to a = 0 cm and b = 0 cm (rigid baseline). This allows us to +create a comparative evaluation of having parallel elastically + +AAwmal6 +IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION. ACCEPTED DECEMBER, 2022 +Fig. 8. +This figure illustrates a contour plot of the design space in the +case of a linear characteristic (using a circular shape). The objective is the +Average Learning Reward. Additionally, we report 25 iterations of our design +optimization framework progressing from blue dots to pink dots. The green +line shows the first-principles design which is derived from a conventional +design approach. The yellow star indicates the optimal design and the green +star is the optimal first-principles design. +actuated knee joints with respect to the baseline. The baseline +is referred to as ANYmal and the optimal design as AoPS with +a total mass of 51.3 kg and 52.5 kg respectively. +B. Simulation-based Results +This simulation-based experiment shows that our design +optimization framework can find optimal design parameters +within a given interval for PEAs. In order to visualize the +result, we optimize the elliptic cam from Fig. 2b and set +a = b = r. Therefore, since the design is point symmetric with +the origin, this design has only 2 parameters d = [¯q, r]T ∈ R2. +The plot in Fig. 8 shows a contour plot of the average learning +reward in the design space D. The contour is obtained by +sampling 40 points for each design parameter and 200 robots +per design (320.000 simulated trajectories). Additionally, we +report 25 iterations of our design optimization framework in +Fig. 8. From the contour of the objective, it is observable that +the optimal value lies around ¯q ≈ 0.0 rad and r ≈ 6.0 cm +(yellow star). Within the first iterations, the framework is +already close to the optimal value and still explores the design +space for other optimal parameters. +The green first-principles design curve in Fig. 8 is defined by +a conventional design approach. This design compensates the +gravity of the robot at the average joint configuration while +walking with normal ANYmal, which is 1.3 rad. We would +like to minimize the torque in the flight phase (q > 1.3) which +results in ¯q being as small as possible. The optimal design +(green star) is ¯q = 0.0 rad and r = 9.02 cm. +The x-axis, where r = 0 cm, corresponds to our baseline +since the torque is zero due to a zero lever arm. While the +average reward differs in about 1 %, the optimal parameter +reduces the CoTr by 33 % in comparison to the baseline. +In contrast, the first-principles design reduces the CoTr by +only 8 %. This shows that our design optimization effectively +finds the best design parameters given the conditioned control +policy. In this case, the highest average reward results in the +lowest CoTr. Please note that the CoTr is a subset of the +average reward CoTr ⊂ AverageReward (compare Sec. II-C). +Using the full design space, we trained policies with 5 +different random seeds and optimized the parameters for +forward walking at 1 m s−1 on flat terrain (see Fig. 9d). The +standard deviation is below 3 ◦ for the angles (¯qKFE, φ0) +and below 1 mm for the radii (a, b). This shows that our +(a) Standing +(b) Payload +(c) Stairs +(d) Flat +(e) Rough +Fig. 9. On the top row, 5 different environments are shown for which each +design is trained and optimized. From left to right, the task is standing on +flat terrain, carrying 20 kg payload on flat terrain, walking on stairs, flat- +and rough terrain. The bottom row shows each optimal design found by +our framework in the equilibrium position of the spring. For the hardware +experiments, we built the design in 9e +Fig. 10. +This bar plot illustrates the efficiency gain by adding springs on +AoPS (purple bars) compared to ANYmal (red bars). The former can reduce +the needed torques to travel 15m by 32.8 % compared to the latter. +design optimization method is repeatable and does not produce +random designs over multiple runs. +Finally, we optimize the design of the robot for 5 different +tasks shown in Fig. 9 The walking experiments are optimized +for 1 m s−1. The resulting designs in the bottom row show the +knee configurations at the equilibrium positions and optimized +cam shapes. This result shows the effectiveness of our method +for finding different optimal designs depending on different +scenarios. +C. Forward Walking +In this first hardware experiment, we compare the per- +formance difference of ANYmal and AoPS on flat terrain, +walking 16 m forwards and backward in a straight line (see +supplementary video). Each robot walks 3× forward and 3× +backward. +The CoTr is visualized as a bar plot in Fig. 10. Both +robots have only little variance in each test, with ANYmal +experiencing a CoTr ≈ 12 N m s while AoPS drives the cost +down to 8 N m s. On average, AoPS is 33 % more efficient +with respect to CoTr than the baseline ANYmal. +As shown by Fig. 10, our optimized design does not +sacrifice the tracking performance for efficiency. Both AoPS +and ANYmal could track the target velocity with an error +less than 0.25m s−1. The figure shows slightly better tracking +for AoPS, but the difference is negligible considering the +confidence intervals (error bars). +D. Random Command Tracking +In our second hardware experiment, we test how the per- +formance translates to a more versatile task. We send 10 + +25 +10 +0.92 +Iteration in BO +cm +Radius r in +6 +0.91 +2 +First-principles design +0.90 +0.0 +0.5 +1.0 +Equilibrium a in rad12 +ANYmal +AoPS +ms +8 +9 +4 +2 +0 - +Forwards +BackwardsBJELONIC et al.: LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS +7 +Fig. 11. This figure compares the command tracking performance of ANYmal +(red) and AoPS (purple) for the forward walking experiment. The dashed lines +show the desired velocity in the x and y direction and around the yaw axis +respectively. +(a) ANYmal +(b) AoPS +Fig. 12. +These two graphs show box plots of the torques needed for each +joint separately in one experiment where the robots are tracking the 10 random +commands. For readability reasons, only the LF leg is presented. Furthermore, +the distribution for each joint torque is indicated by colored violin plots. This +plot transfers similarly to the other legs as well. +random commands for 3s each to the robots while the com- +mands change dynamically (see supplementary video). The +commands are randomly sampled between [−1.2, 1.2]m s−1 +in x direction, [−0.6, 0.6]m s−1 in the y direction, and +[−1.2, 1.2]rad s−1 around the yaw axis and the same for +both robots. The efficiency gain for the execution of all the +commands is again around 30 % for AoPS while the tracking +performance was similar to ANYmal. +Additionally, Fig. 12 reports the joint torques for the left +front leg of the robots as a boxplot with an overlaying violin +plot. Regarding the KFE joint (knee), the average torque is +around 26 N m for ANYmal in Fig. 12a while AoPS is around +7 N m. Basically, the whole distribution shifts down thanks to +the parallel elastic spring, which reduces the CoTr notably. As +a result, the maximum absolute torque that AoPS needs for the +same task is 52 N m, which is only 71 % of ANYmal (73 N m). +Furthermore, the HFE joint average torque for AoPS is closer +to 0 N m than ANYmal, while at the same time requiring less +variance. This also drives down the CoTr. Expectedly, the +HAA joint is unaffected by the parallel elastic spring, and +for both systems mostly the same. +E. Rough Terrain +For the fourth and fifth tests, we adapted the perceptive +learning from Miki et. al. [29] and included exteroceptive +observations during the student distillation. Using this adapted +policy, we performed several outdoor experiments with our +parallel-elastic robot. We climbed several inclinations, tra- +versed different types of stairs, went through confined spaces, +walked over forest ground, inclined gravel paths, etc. A few +snapshots are presented in Fig. 6 and videos in the supplemen- +tary material. The robot did not fall once during the tests and +reports the robustness of the controller and the novel design. +Fig. 13. +The state of charge for ANYmal (Red) and AoPS (Purple) over +time during the experiment in Sec. III-E shows that our optimized design can +achieve higher operating times with the same battery. +TABLE I +RUNNING TRACK PERFORMANCE +AoPS +ANYmal +Number of Rounds +7.5 +6.6 +Traveled distance [m] +3000 +2640 +Initial Charge [%] +92 +89 +Final Charge [%] +11 +10 +Operation Time [min] +68 +59 +Average Velocity [m/s] +0.735 +0.740 +Efficiency [%] +111 +100 +Outside Temperature [°C] +31 +26 +This shows that adding parallel elastic springs does not affect +the robustness negatively. +F. Battery Life +Finally, we used both robots sequentially on a running +track of 400 m length and let the robots walk with the same +battery until the battery was fully depleted. The battery was +as much as possible fully charged before and after the first +run with AoPS to ensure a fair evaluation. Both robots were +commanded 1 m s−1 and carefully steered to stay in the inner +path of the track. The performance of each robot is reported +in Tab. I. This experiment shows that the overall traveled +distance of our quadrupedal robot can be increased by at least +11 % from 2640 m to 3000 m. We introduce the following +efficiency metric as the quotient in covered distance scaled +by the mismatch in battery charge (2 %). +Efficiency = 3000 m +2640 m ∗ 0.89 − 0.10 +0.92 − 0.11 = 1.11. +(10) +We also report the state of the charge over time in Fig. 13. +Besides the faster drop for ANYmal, this shows that the battery +that we used is internally calibrated and the linear scaling in +(10) can compensate for the 2 % difference in charge. +IV. CONCLUSION +This paper shows that, with the co-optimization of the de- +sign and controller, parallel springs on the knee of quadrupedal +robots can increase locomotion efficiency without compromis- +ing the command tracking performance and robustness. While +it is well studied that gravity compensation with PEAs is +energetically beneficial for static tasks [6], the PEA’s contri- +bution during the dynamic locomotion is relatively unstudied. +The effect of PEA is nontrivial during the locomotion since +the actuators have to repeatedly work against the spring. A +key takeaway of our work is that PEAs can also increase the +performance during dynamic locomotion. +We co-optimized design parameters and locomotion con- +trollers that act optimally for a given set of design parameters + +- Command +1.00 +1.00 +S +ANYmal +S +Linear Velocity in m/ +AoPS +0.75 +0.75 +0.50 +0.50 +0.25 +0.25 +0.00 +0.00 +-0.25 +-0.25 +Velocity Velocity y Velocity :ANYmal +80 +AoPS +% +.≤ +Charge +60 +JO +40 +State +20 +0 +10 +20 +30 +40 +50 +60 +Time in min8 +IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION. ACCEPTED DECEMBER, 2022 +and task. With a parallel elastic knee actuator designed by +our approach, we could reduce the required joint torques, +which yields a higher operation time for our quadrupedal robot +ANYmal during locomotion. +An important thing to note from our hardware experiments +is the robustness of our controller to the model uncertainty, +which shows the practical benefit of the RL-based control +method. Trained by the privileged learning method [28] with +randomized spring parameters, our controller tolerates possible +model mismatches on the physical system without accurate +spring calibration procedures, thus, removing the need to run +any complex system identification routine. +As we showed the potential of PEAs in legged robotics, +further investigations in this direction have to follow. Firstly, +the physical system’s energy consumption must be better +modeled. This work assumes that the CoTr measurement is +proportional to the battery life of the robot. Nevertheless, +during the experiments in Sec. III-C and Sec. III-F, we found +a discrepancy. There are unmodeled factors such as electrical +and mechanical losses which we did not identify in this work. +Secondly, the design-conditioned policy cannot be guaranteed +to be as performant as a policy trained for each design +parameter. The discrepancy was negligible in the setup covered +in this paper. A previous study on this topic was conducted by +us [32]. Lastly, a more elaborate design should be introduced. +Our current design limits the workspace of the knee joint +and the implementation of the cable-spring mechanism can be +inaccurate. Additionally, research will be devoted to including +other parameters in the design process like link masses or leg +lengths. +ACKNOWLEDGMENT +The authors would like to thank the RSL Design Team for +their insightful discussions and Marko Bjelonic for his great +support on the Cluster and for helping with the state estimation +on AoPS. +REFERENCES +[1] A. M. Abate, “Mechanical design for robot locomotion,” Ph.D. disser- +tation, Oregon State University, 2018. +[2] G. A. Pratt and M. M. Williamson, “Series elastic actuators,” in +Proceedings IEEE/RSJ International Conference on Intelligent Robots +and Systems. Human Robot Interaction and Cooperative Robots, vol. 1, +1995, pp. 399–406. +[3] M. Hutter, et al., “Anymal-a highly mobile and dynamic quadrupedal +robot,” in IEEE/RSJ International conference on intelligent robots and +systems (IROS), 2016, pp. 38–44. +[4] C. Hubicki, et al., “Atrias: Design and validation of a tether-free +3d-capable spring-mass bipedal robot,” The International Journal of +Robotics Research, vol. 35, no. 12, pp. 1497–1521, 2016. +[5] C. Semini, N. G. Tsagarakis, E. Guglielmino, M. Focchi, F. Cannella, +and D. G. Caldwell, “Design of hyq–a hydraulically and electrically +actuated quadruped robot,” Proceedings of the Institution of Mechanical +Engineers, Part I: Journal of Systems and Control Engineering, vol. +225, no. 6, pp. 831–849, 2011. +[6] N. Kashiri, et al., “An overview on principles for energy efficient robot +locomotion,” Frontiers in Robotics and AI, vol. 5, p. 129, 2018. +[7] L. Scalera, G. Carabin, R. Vidoni, and T. Wongratanaphisan, “Energy +efficiency in a 4-dof parallel robot featuring compliant elements,” Int. +J. Mech. Control, vol. 20, no. 02, pp. 49–57, 2019. +[8] F. Bjelonic, A. Sachtler, A. Albu-Sch¨affer, and C. Della Santina, +“Experimental closed-loop excitation of nonlinear normal modes on an +elastic industrial robot,” IEEE Robotics and Automation Letters, vol. 7, +no. 2, pp. 1689–1696, 2022. +[9] P. Arm, et al., “Spacebok: A dynamic legged robot for space explo- +ration,” in IEEE/RSJ International conference on robotics and automa- +tion (ICRA), 2019, pp. 6288–6294. +[10] H. Kolvenbach, E. Hampp, P. Barton, R. Zenkl, and M. Hutter, “Towards +jumping locomotion for quadruped robots on the moon,” in IEEE/RSJ +International Conference on Intelligent Robots and Systems (IROS), +2019, pp. 5459–5466. +[11] A. Badri-Spr¨owitz, A. Aghamaleki Sarvestani, M. Sitti, and M. A. Daley, +“Birdbot achieves energy-efficient gait with minimal control using avian- +inspired leg clutching,” Science Robotics, vol. 7, no. 64, p. eabg4055, +2022. +[12] A. Mazumdar, et al., “Parallel elastic elements improve energy efficiency +on the steppr bipedal walking robot,” IEEE/ASME Transactions on +mechatronics, vol. 22, no. 2, pp. 898–908, 2016. +[13] M. F. Silva and J. T. Machado, “A literature review on the optimization +of legged robots,” Journal of Vibration and Control, vol. 18, no. 12, pp. +1753–1767, 2012. +[14] S. Koziel and X.-S. Yang, Computational optimization, methods and +algorithms. +Springer, 2011, vol. 356. +[15] R. Turner, et al., “Bayesian optimization is superior to random search +for machine learning hyperparameter tuning: Analysis of the black- +box optimization challenge 2020,” in NeurIPS 2020 Competition and +Demonstration Track. +PMLR, 2021, pp. 3–26. +[16] P. I. Frazier, “A tutorial on bayesian optimization,” arXiv preprint +arXiv:1807.02811, 2018. +[17] F. De Vincenti, D. Kang, and S. Coros, “Control-aware design opti- +mization for bio-inspired quadruped robots,” in IEEE/RSJ International +Conference on Intelligent Robots and Systems (IROS), 2021, pp. 1354– +1361. +[18] T. Dinev, C. Mastalli, V. Ivan, S. Tonneau, and S. Vijayakumar, “A +versatile co-design approach for dynamic legged robots,” in IEEE/RSJ +International Conference on Intelligent Robots and Systems (IROS), +2022. +[19] M. Chadwick, H. Kolvenbach, F. Dubois, H. F. Lau, and M. Hutter, +“Vitruvio: An open-source leg design optimization toolbox for walking +robots,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6318– +6325, 2020. +[20] A. Zhao, et al., “Robogrammar: graph grammar for terrain-optimized +robot design,” ACM Transactions on Graphics (TOG), vol. 39, no. 6, +pp. 1–16, 2020. +[21] S. Ha, S. Coros, A. Alspach, J. Kim, and K. Yamane, “Joint optimization +of robot design and motion parameters using the implicit function +theorem.” in Robotics: Science and systems, vol. 8, 2017. +[22] T. Chen, Z. He, and M. Ciocarlie, “Hardware as policy: Mechanical and +computational co-optimization using deep reinforcement learning,” in +Proceedings of the 2020 Conference on Robot Learning, ser. Proceedings +of Machine Learning Research, vol. 155. +PMLR, 16–18 Nov 2021, pp. +1158–1173. +[23] C. Schaff, D. Yunis, A. Chakrabarti, and M. R. Walter, “Jointly learning +to construct and control agents using deep reinforcement learning,” +in IEEE/RSJ International Conference on Robotics and Automation +(ICRA), 2019, pp. 9798–9805. +[24] C. Schaff, A. Sedal, and M. R. Walter, “Soft robots learn to crawl: +Jointly optimizing design and control with sim-to-real transfer,” arXiv +preprint arXiv:2202.04575, 2022. +[25] A. I. Cowen-Rivers, et al., “Hebo: Pushing the limits of sample- +efficient hyper-parameter optimisation,” Journal of Artificial Intelligence +Research, vol. 74, pp. 1269–1349, 2022. +[26] R. Turner, et al., “Bayesian optimization is superior to random search +for machine learning hyperparameter tuning: Analysis of the black- +box optimization challenge 2020,” in Proceedings of the NeurIPS 2020 +Competition and Demonstration Track, ser. Proceedings of Machine +Learning Research, vol. 133. +PMLR, 06–12 Dec 2021, pp. 3–26. +[27] J. Won and J. Lee, “Learning body shape variation in physics-based +characters,” ACM Transactions on Graphics (TOG), vol. 38, no. 6, pp. +1–12, 2019. +[28] J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter, “Learning +quadrupedal locomotion over challenging terrain,” Science robotics, +vol. 5, no. 47, p. eabc5986, 2020. +[29] T. Miki, J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter, +“Learning robust perceptive locomotion for quadrupedal robots in the +wild,” Science Robotics, vol. 7, no. 62, p. eabk2822, 2022. +[30] J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Prox- +imal policy optimization algorithms,” arXiv preprint arXiv:1707.06347, +2017. +[31] K. +Cho, +et +al., +“Learning +phrase +representations +using +rnn +encoder-decoder for statistical machine translation,” arXiv preprint +arXiv:1406.1078, 2014. +[32] +´A. Belmonte-Baeza, J. Lee, G. Valsecchi, and M. Hutter, “Meta rein- +forcement learning for optimal design of legged robots,” IEEE Robotics +and Automation Letters, vol. 7, no. 4, pp. 12 134–12 141, 2022. + diff --git a/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/load_file.txt b/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6b5d4b0d133d42430f1912608ccad18dc94d4bc3 --- /dev/null +++ b/1tE1T4oBgHgl3EQf5QU9/content/tmp_files/load_file.txt @@ -0,0 +1,704 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf,len=703 +page_content='IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACCEPTED DECEMBER, 2022 1 Learning-based Design and Control for Quadrupedal Robots with Parallel-Elastic Actuators Filip Bjelonic1,2, Joonho Lee1, Philip Arm1, Dhionis Sako1, Davide Tateo2, Jan Peters2, Marco Hutter1 Abstract—Parallel-elastic joints can improve the efficiency and strength of robots by assisting the actuators with additional torques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For these benefits to be realized, a spring needs to be carefully designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' However, designing robots is an iterative and tedious process, often relying on intuition and heuristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We introduce a design optimization framework that allows us to co- optimize a parallel elastic knee joint and locomotion controller for quadrupedal robots with minimal human intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We design a parallel elastic joint and optimize its parameters with respect to the efficiency in a model-free fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In the first step, we train a design-conditioned policy using model-free Reinforcement Learn- ing, capable of controlling the quadruped in the predefined range of design parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Afterwards, we use Bayesian Optimization to find the best design using the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We use this framework to optimize the parallel-elastic spring parameters for the knee of our quadrupedal robot ANYmal together with the optimal controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We evaluate the optimized design and controller in real-world experiments over various terrains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Our results show that the new system improves the torque-square efficiency of the robot by 33 % compared to the baseline and reduces maximum joint torque by 30 % without compromising tracking performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The improved design resulted in 11 % longer operation time on flat terrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Index Terms—Legged Robots, Reinforcement Learning, Com- pliant Joints and Mechanisms, Mechanism Design I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' INTRODUCTION T HE quest of creating a single versatile, efficient and strong robotic platform has driven research in legged robotics for many years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While controllers are getting more robust and intelligent, locomotion performance is limited by the available joint speed and joint torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Better performance can be achieved by creating more efficient and powerful actu- ators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Adding elastic elements has the promise of supporting the actuators with additional torque [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In this letter, we explore the effect of the elastic component on energy efficiency during locomotion by attaching a parallel spring mechanism on the knee joints of the ANYmal robot (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This system is used to experiment and verify the benefit of the parallel elasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Robots with elastic actuators One of the first approaches in this direction was the Series Elastic Actuator (SEA) by Gill Pratt [2] which incorporates a series-elastic element between the actuator and the load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This design makes the joint positioning error-tolerant, reduces Manuscript received: August 27, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Revised November 21, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Accepted December 16, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This paper was recommended for publication by Editor Abderrahmane A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kheddar upon evaluation of the Associate Editor and Reviewers’ comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This work was supported by a fellowship within the IFI program of the German Academic Exchange Service (DAAD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1 Authors are with ETH Zurich;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Robotic Systems Lab;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Leonhardstrasse 21, 8092 Zurich, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2 Authors are with TU Darmstadt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Intelligent Autonomous Systems Lab;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hochschulstrasse 10, 64289 Darmstadt, Germany Digital Object Identifier (DOI): see top of this page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The ANYmal robot with parallel-elastically actuated knee joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ANYmal is walking upstairs at the central station of Zurich, which is used as one of the experimental sites during this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' impact loads, and, most importantly, allows for precise torque measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The ANYmal quadrupedal robot [3] integrates into its ANYdrive actuator a serial elastic spring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' More exam- ples are ATRIAS [4], a biped that has serial elastic springs at the actuator level and Cassie [1] with a 6-bar linkage with 2 springs in series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' HyQ [5] has a serial elastic spring between the knee and the foot of the robot, which reduces foot chattering during touch-down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Another approach is the Parallel Elastic Actuator (PEA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In this setup, the actuator and the spring are in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While this approach has been studied in robotic manipulation for gravity compensation [6], for pick-and-place [7] and efficient oscillation [8], there is no comparative evaluation of walking robots with PEA outside of controlled lab environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' One example of a legged robot with PEAs is SpaceBok [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In a lab experiment with simulated moon gravity, PEAs reduced the energy required for a jump by a factor of two on this robot [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Another, more recent example of using PEA is BirdBot [11], which has a parallel elastic spring clutching mechanism, spanning multiple joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The avian-inspired leg design shows self-stable and robust bipedal locomotion while requiring 10 % of the knee-flexing torque compared to a non- clutching parallel spring setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Another example is STEPPR [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This bipedal robot has a parallel-elastic spring at the hip and the ankle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using only the hip springs during walking, the robot consumes 31 % less joint electrical power and reduces power consumption overall by 13 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' All of the previous works mention the possibility of saving energy with the carefully designed springs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Unfortunately, most of them are designed based on heuristic and cannot exploit the full potential of elastic elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Building upon intuitive design, a common approach starts with mimicking nature’s counterparts [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Atrias [4] and arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='03509v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='RO] 9 Jan 2023 2 IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACCEPTED DECEMBER, 2022 BirdBot [11] for instance are inspired by ostriches and the emu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The problem with bio-inspired design is the high amount of variables that need to be taken into account to fully model the targeted animal accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Nevertheless, there is no systematic way of designing robots in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Computational design Computational robot design can be divided into gradient- based methods that work well with deterministic differentiable objective functions, gradient-free algorithms with smooth ob- jectives (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' trust-region methods), meta-heuristic methods that are nature inspired (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' simulated annealing, genetic al- gorithms), and surrogate methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Bayesian Optimization (BO)) [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Meta-heuristic and surrogate methods have been successfully used in black-box optimization problems, where the properties of the objective function are not known in advance [15] [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A work related to the goal in this work has been done by Scalera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [7] where the design optimization of elastic elements was carried out for a four Degrees of Freedom (DoF) parallel robotic arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Here, the robot achieved an efficiency gain of 67 % on a predefined trajectory by defining a non- linear optimization problem for finding energy optimal spring parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This approach is unsuitable for legged locomotion since it optimizes over a fixed trajectory that is by no means guaranteed to be optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The approach from De Vincenti et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [17] uses a differ- entiable trajectory tracking controller such that the overall leg design optimization becomes control-aware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Effectively, the gradient computation takes the control formulation into account in each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Nevertheless, the trajectory is still fixed for all the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A co-optimization approach is developed by Dinev et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [18] for leg lengths, joint positions, trunk shape, and weight distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Here, motion planning is recomputed in every evaluation of the design process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using finite differences, the design optimization increases the energy efficiency of the Solo robot by a factor of 3 and shows faster convergence than using an evolutionary optimizer (CMA-ES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using finite differences on rough terrain may result in an unstable solver, making this approach hard to incorporate into our goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In general, these methods incorporate a design optimization that is wrapped around the robot control and planning loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While the approaches incorporate gradient-based or gradient- free solvers for the outer loop, the inner loop can be either fixed [7] [19], or efficiently re-optimized in every performance evaluation [18] [17] [20] [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An interesting simultaneous approach from Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [22] defines a hardware policy besides the control policy, that is jointly optimized over the training process with model-free Reinforcement Learning (RL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The optimized weights of the hardware policy define the hardware parameters and, together with the control policy, create the output of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While this is a fully integrated approach, defining the hardware policy as a computational graph is not possible in many cases [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Another method by Schaff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [23] optimizes an RL policy and distribution of design parameters at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The agent is able to observe design parameters while the design space slowly shrinks toward high-performing designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This approach has been successfully applied on a soft robot crawler Shank Thigh Spring Disc (a) Design Shank Thigh (b) Elliptic Cam Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2a illustrates a generic two-segment leg with potentially nonlinear parallel elastic knee joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The conceptual implementation of the rotatory spring stiffness k in this work is visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The linear elastic spring- wire mechanism connects the thigh with the shank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This creates a spring torque τs on the knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Parts with the same color are physically connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [24] and outperformed a baseline design from an expert with the optimal design walking more than 2× as fast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Inspired by the co-optimization approach from Dinev et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [18] and the learning-based approach by Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [22], the following section briefly introduces our design optimization framework as well as our main contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Contribution We present a systematic approach to designing elastic mech- anisms for legged robots by incorporating design-conditioned controllers in the optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In particular, we present: Co-optimization of the design parameters and the loco- motion controller for the PEA-driven legged robot using model-free RL and BO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Integration of the optimized design onto the physical system and sim-to-real transfer of the learned control policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Real-world experiments to demonstrate the feasibility and robustness of our approach followed by the quantitative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We would like to emphasize the last contribution because, to the authors’ knowledge, this paper provides the first evaluation of PEAs on walking robots outside of lab environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' METHOD In this section, we first present our PEA design and then present our framework to co-optimize the controller as well as design parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For any equation, vectors and matrices are marked in bold text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Further, we refer to specific legs by their position with respect to the base in the anterior and lateral direction with the left front (LF), right front (RF), left hind (LH), and right hind (RH) leg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Parallel Elastic Knee We design a PEA knee joint for quadrupedal robots seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Particularly, a parameterization d ∈ D of the joint stiffness k is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We design and implement a spring- wire mechanism (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The wire connects the thigh and shank over a generic disc that defines the lever arm for the spring force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The disc is attached to the shank of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The torque on the knee that is generated by this design can be calculated in general by BJELONIC et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' : LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS 3 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The non-linear trajectory of the spring force’s lever arm ˆlr over on full rotation is plotted in pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The radius of the major and minor axis is 3 and 1 respectively, while the spring force is assumed to always point upwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The length, as well as the angle of the lever arm, changes dynamically, depending on the angle of the knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' τs(q) = Fs × ˆlr(θ) (1) with Fs being the force created by the linear spring, θ ∈ [0, 2π) defines the boundary of the cam and ˆlr(θ) is the spring force’s lever arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The amplitude of the spring force can be calculated by Hooke’s law as fs = ||Fs|| = ks∆ls, with ks being the spring stiffness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The spring elongation ∆ls is influenced by the length of wire which is wrapped around the cam and the position of the lever arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' With this setup, the first parameter d1 is the equilibrium position ¯qKFE of the linear spring, which is defined as the knee angle where Fs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Further parameters are added through the definition of the cam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Since the wire is always assumed to be in contact with the cam, the lever arm can be calculated by finding the point on the cam that is tangent to the spring force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This can be formalized by the following equation 0 = Fs × ∂ˆlr ∂θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' (2) We select an elliptic cam as a trade-off between simplicity and degrees of freedom of parameterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In this case, this equation has always two solutions depending on the side at which the spring force acts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In our case, the left side of the lever arm respects the inequality � Fs, ˆlr(θ) � ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' (3) Following, we describe the elliptic cam attached to the shank of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1) Elliptic Cam: Elliptic cam is defined by lr(θ) = Rφ � a · cos(θ) b · sin(θ) � (4) Rφ = � cos(φ) −sin(φ) sin(φ) cos(φ) � φ = φ0 + qKFE, where θ ∈ [0, 2π) and φ0 being the initial angle of the ellipse with respect to the shank’s longitudinal axis at qKFE = 0 rad, a and b are the radius of the major and minor axis respectively, seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Now, the lever arm ˆlr is not stationary and changes during the rotation of the knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An example trajectory of the contact point over one full rotation of 360° for an ellipse with a = 3 and b = 1 is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The contact point ˆlr can be calculated using (2) and (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The trajectories τ are collected with the trained design-conditioned policy in simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Afterward, the robot’s performance for a specific design choice is measured by a custom objective function f(D) and sent to the BO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using this value, the algorithm builds a surrogate function (blue + cyan color in the left plot) and samples new points with respect to its acquisition function (green color in the right plot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The blue dots refer to already sampled points and the green dots to the next design set to be rolled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Similarly, based on equations (1) - (4), we can compute the spring displacement by numerically solving an elliptic integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We skip the derivations for the sake of space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The resulting torque is non-linear if a ̸= b τs(d) = ψ(qKFE, d) (5) with the design space d = [¯qKFE, a, b, φ0]T ∈ R4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An animation of the design space is included in the supplementary video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Design Optimization Here we present our framework for optimizing the design parameters d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The general approach of our design optimization strategy is pictured in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We roll out trajectories with the design-conditioned policy (explained in section II-C) in the environment with each given set of design parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We define the objective function f for the design optimization by the Monte Carlo estimate over a large number of sam- ples collected in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' By doing so, we evaluate the general performance of a design instance across many different scenarios with different initial states, disturbances, and commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1) Design Objective: The main objective of our design op- timization problem is energy efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Accurately simulating the efficiency of a robot is a difficult task due to various sources of energy consumption, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', mechanical energy at the actuators, power used to run computers and sensors, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We assume that the power loss of the system can be approximated by the joule heating of the individual actuators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' There are other factors like transmission loss and electronics loss that are neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Joule heating is one of the major terms for energetic losses in electric motors and is proportional to the square of the actuator torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Similar to the Cost of Transportation (CoT), we define the Cost of Torque (CoTr) as CoT ∝ CoTr = � τ 2dt mg∆s (6) with m being the total mass of the robot, g = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='81 m/s2 the gravitational acceleration and ∆s the traveled distance by the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' By normalizing with m, which depends on the design, 2 1 F S 0 9 1 Ellipse 2 3 2 1 0 1 2 C4 IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACCEPTED DECEMBER, 2022 and ∆s, this metric allows for the comparison of different designs and walking speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2) Optimization: The aim of the design optimization step is to find optimal design parameters d ∈ D for a specific task t ∈ T with respect to an objective function f(d|t, π) : T ×D → R, given the pre-trained policy π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The objective f evaluates d for a fixed task t, which is velocity tracking on rough terrain in our setup, and outputs a performance measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A task t defines the specific problem the policy solves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' These parameters could be for example terrain property (rough terrain, stairs, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=') as well as command amplitude and direc- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The task parameters are randomly sampled during policy training and design optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The objective f is defined by the physical quantities we are optimizing the design, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', joint torques or tracking per- formance (our setup), which are often not differentiable with respect to d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In our setup, we assume f is not differentiable because legged locomotion entails many discrete changes in dynamics due to foot contact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Thereby we use a black-box optimization method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The optimization problem can then be mathematically for- malized as d∗ = arg min Ed∈D,t∈T [f(d|t, π)] (7) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 0 ≤ c(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We use the Heteroscedastic Evolutionary Bayesian Optimi- sation (HEBO) algorithm [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This BO algorithm won the NeurIPS2020 black-box optimization challenge [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The out- come of this challenge is the reason why we chose a surrogate method over a meta-heuristic method (compare Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' I-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Design-conditioned Policy It is important to have an optimal controller for each design instance to evaluate each design instance at its best performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We assume that we can achieve near-optimal performance with a neural network policy conditioned on design parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A recent work by Won et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [27] showed that it is possible to train a shape-conditioned policy for a bipedal robot through RL that can maintain a stable gait while the shape of its body is dynamically changing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Our policy training follows the approach, and we addition- ally adapt the privileged learning method by Lee et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [28] for sim-to-real transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We train two types of policies: Design-conditioned policy (teacher): This policy directly observes design parameters and other environmental pa- rameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', terrain shape and friction coefficient), which we call privileged information, from simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The policy is used in the design optimization loop (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Deployment policy (student): This policy is deployed on the robot with noisy measurements as observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This policy does not have access to privileged observations and observes the history of noisy proprioceptive measure- ments and exteroceptive measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The deployment policy is explained in section II-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The design-conditioned policy is trained via RL in simulation and the student policy is trained via imitation learning with simulated sensor noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using temporally extended observa- tions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', history of proprioceptive measurements [28] or noisy exteroception [29], the student policy can estimate the Teacher (Reinforcement Learning) Learning Environment Policy Update Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The learning pipeline is adapted from the teacher-student approach [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The most important change is that the teacher directly observes the design parameter in the privileged observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We performed several tests with AoPS on rough terrain, showing its robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The policy was extensively tested in the mountains, the forests, and the City of Zurich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' privileged information and adapt to the sim-to-real discrep- ancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1) Reinforcement Learning: The design-conditioned policy is trained using RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We model the RL problem as a Markov Decision Process (MDP), where the design-conditioned policy πθ defines the distribution of at ∈ A conditioned on the ob- servation ot ∈ O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The environment updates the robots state in each step according to a transition function p(st+1|st, at) and gives a reward rt(st, st+1, at).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The objective is to maximize πθ∗(at|ot) → max E � � ∞ � ˜t=t γ˜t−tr(a˜t, s˜t) � � (8) with γ ∈ [0, 1] being the discount factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An MDP is defined by the 4-tuple of O, A, r, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The state transition (p) follows rigid body dynamics in simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Each other component is explained below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We use the Proximal Policy Optimization (PPO) Algorithm [30] to update and train our policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ot (∈ R133) contains the base target velocity commands, base orientation, base linear and angular velocity, parameters for the leg motion primitive (Foot Trajectory Generator (FTG) by [28]), a short history of joint positions and joint velocities, and the last two joint position targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The privileged informa- tion in R46 includes contact friction, state and force at each foot, external forces and torques applied to the base, the design parameters, and the robot’s link masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' During the policy training, the design parameters are ran- domly sampled from D (compare Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' II-B) per episode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In order to avoid tedious design calibration, we provide observa- contact states contact forces terrain profile contact friction disturbancesPolicyaesign params.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' o Encoder BJELONIC et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' : LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS 5 (a) Assembled Spring Setup (b) Hip (c) Ellipse (d) Wire (e) Spring Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' These images of the robot as well as the individual parts show the spring-wire setup developed in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The green letters in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7a correspond to the 4 pictures on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' tions of the equilibrium positions of the PEAs separately for each leg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2) Action: The agent controls the robot through at ∈ R16 (compare Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5), with the first 4 actions setting the frequency of the FTG [28] and 12 additional joint position deltas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The FTG outputs vertical foot trajectories with predefined clearance that are mapped to desired joint positions using inverse kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 3) Reward: The reward function includes a metric for following linear base commands in the x and y directions as well as the rotation along the yaw axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Furthermore, we punish undesired movement in the base (z velocity, roll, and pitch angular velocity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For smooth and realistic torque commands, we penalize the acceleration with which the joint position targets change over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For the agent to find optimal and efficient behavior, we penalize the L2 norm of the actuator torques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lastly, we penalize joint velocities that exceed the actuator limits and foot slippage, which reduces foot strain due to sliding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4) Architecture: The design-conditioned policy is modeled as a Multi Layer Perceptron (MLP) and an auto-encoder network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The encoder network takes the privileged information and outputs an embedding vector ¯lt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Finally, the proprioceptive observations and this vector ¯lt are used as the input to the policy network (compare Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Deployment Policy The deployed policy does not have access to privileged information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Instead, it uses a sequence of past observations to infer the unobserved state of the environment [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The student policy is constructed by a Recurrent Neural Network (RNN) [31] to effectively handle the sequential data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Similarly to Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [28], the training is done by imitation learning with an additional reconstruction loss for the embedding of the privileged information (¯lt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The observation of the deployed policy consists of pro- prioceptive measurements from the IMU and joint encoders and exteroceptive measurements from depth sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Both modalities are simulated with noise during the training, which is not added to the design-conditioned policy’s observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The action space of the deployment policy is the same as the design-conditioned policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An important factor for the sim-to-real transfer is to account for the model mismatch of the springs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' During the student policy training, the design parameters are perturbed by 10 % from the optimized parameter to emulate limited manufactur- ing precision (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The design-conditioned policy observes the exact values as privileged information while the student policy does not have direct access to the design parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' EXPERIMENTS We report the results of five different experiments to quantify the effectiveness of our approach as well as the performance gained by our new parallel elastic knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The first experiment in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-B shows that our design optimization framework can find optimal parameters with respect to our design-conditioned policy in various tasks and with high repeatability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Experiments 2 and 3, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-C and Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-D respectively, are hardware experiments on flat terrain, showing that the parallel-elastic robot is more efficient than the baseline and requires less torque in forward walking as well as tracking random commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The fourth experiment in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-E shows that the novel design can traverse difficult terrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lastly, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-F reports the last experiment, using the robot on a running track, which shows that the newly designed robot can operate longer with the same battery charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Setup The task t for which the robot is optimized is forward walking at 1 m s−1 in an environment with stepping stones, flat terrain, and rough terrain with base perturbations of up to 50 N force and 50 N m torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The contact friction that the robot experiences is in the range µ = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='5, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The objective function f is chosen as the average reward f = 1 N N � i=0 r(ati, sti).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' (9) We use 1000 different episodes to estimate the expectation of the objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We optimize the design parameters (II-A1) and build the elliptic cam in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2b for the hardware experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The physical parts that we created are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Our final design consists of a linear spring with stiffness ks = 4154 N m−1 and the four optimal design parameters, namely the radius of the major axis a = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='1 cm and minor axis b = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 cm, initial angle φ0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 rad and the equilibrium position of ¯qKFE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='36 rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The wires in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7d define the equilibrium position ¯qKFE of each leg and are due to manufacturing constraints not equally long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We randomize these values separately for each leg during the student training to account for unsymmetrical spring parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The policies use the spring exclusively in the pulling direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Thus, we can implement the design with one tension spring per knee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' After training the design-conditioned agent, we create two student policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For the distillation, we fix our design pa- rameters in the demonstrations from the design-conditioned policy to the optimal design (parallel-elastic knee joint) and to a = 0 cm and b = 0 cm (rigid baseline).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This allows us to create a comparative evaluation of having parallel elastically AAwmal6 IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACCEPTED DECEMBER, 2022 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This figure illustrates a contour plot of the design space in the case of a linear characteristic (using a circular shape).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The objective is the Average Learning Reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Additionally, we report 25 iterations of our design optimization framework progressing from blue dots to pink dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The green line shows the first-principles design which is derived from a conventional design approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The yellow star indicates the optimal design and the green star is the optimal first-principles design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' actuated knee joints with respect to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The baseline is referred to as ANYmal and the optimal design as AoPS with a total mass of 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='3 kg and 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='5 kg respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Simulation-based Results This simulation-based experiment shows that our design optimization framework can find optimal design parameters within a given interval for PEAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In order to visualize the result, we optimize the elliptic cam from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2b and set a = b = r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Therefore, since the design is point symmetric with the origin, this design has only 2 parameters d = [¯q, r]T ∈ R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 8 shows a contour plot of the average learning reward in the design space D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The contour is obtained by sampling 40 points for each design parameter and 200 robots per design (320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='000 simulated trajectories).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Additionally, we report 25 iterations of our design optimization framework in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' From the contour of the objective, it is observable that the optimal value lies around ¯q ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 rad and r ≈ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 cm (yellow star).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Within the first iterations, the framework is already close to the optimal value and still explores the design space for other optimal parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The green first-principles design curve in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 8 is defined by a conventional design approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This design compensates the gravity of the robot at the average joint configuration while walking with normal ANYmal, which is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='3 rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We would like to minimize the torque in the flight phase (q > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='3) which results in ¯q being as small as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The optimal design (green star) is ¯q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 rad and r = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='02 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The x-axis, where r = 0 cm, corresponds to our baseline since the torque is zero due to a zero lever arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While the average reward differs in about 1 %, the optimal parameter reduces the CoTr by 33 % in comparison to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In contrast, the first-principles design reduces the CoTr by only 8 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This shows that our design optimization effectively finds the best design parameters given the conditioned control policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' In this case, the highest average reward results in the lowest CoTr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Please note that the CoTr is a subset of the average reward CoTr ⊂ AverageReward (compare Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' II-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using the full design space, we trained policies with 5 different random seeds and optimized the parameters for forward walking at 1 m s−1 on flat terrain (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 9d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The standard deviation is below 3 ◦ for the angles (¯qKFE, φ0) and below 1 mm for the radii (a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This shows that our (a) Standing (b) Payload (c) Stairs (d) Flat (e) Rough Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' On the top row, 5 different environments are shown for which each design is trained and optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' From left to right, the task is standing on flat terrain, carrying 20 kg payload on flat terrain, walking on stairs, flat- and rough terrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The bottom row shows each optimal design found by our framework in the equilibrium position of the spring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For the hardware experiments, we built the design in 9e Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This bar plot illustrates the efficiency gain by adding springs on AoPS (purple bars) compared to ANYmal (red bars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The former can reduce the needed torques to travel 15m by 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='8 % compared to the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' design optimization method is repeatable and does not produce random designs over multiple runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Finally, we optimize the design of the robot for 5 different tasks shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 9 The walking experiments are optimized for 1 m s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The resulting designs in the bottom row show the knee configurations at the equilibrium positions and optimized cam shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This result shows the effectiveness of our method for finding different optimal designs depending on different scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Forward Walking In this first hardware experiment, we compare the per- formance difference of ANYmal and AoPS on flat terrain, walking 16 m forwards and backward in a straight line (see supplementary video).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Each robot walks 3× forward and 3× backward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The CoTr is visualized as a bar plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Both robots have only little variance in each test, with ANYmal experiencing a CoTr ≈ 12 N m s while AoPS drives the cost down to 8 N m s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' On average, AoPS is 33 % more efficient with respect to CoTr than the baseline ANYmal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' As shown by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 10, our optimized design does not sacrifice the tracking performance for efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Both AoPS and ANYmal could track the target velocity with an error less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='25m s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The figure shows slightly better tracking for AoPS, but the difference is negligible considering the confidence intervals (error bars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Random Command Tracking In our second hardware experiment, we test how the per- formance translates to a more versatile task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We send 10 25 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='92 Iteration in BO cm Radius r in 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='91 2 First-principles design 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='0 Equilibrium a in rad12 ANYmal AoPS ms 8 9 4 2 0 - Forwards BackwardsBJELONIC et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' : LEARNING-BASED DESIGN AND CONTROL FOR QUADRUPEDAL ROBOTS 7 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This figure compares the command tracking performance of ANYmal (red) and AoPS (purple) for the forward walking experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The dashed lines show the desired velocity in the x and y direction and around the yaw axis respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' (a) ANYmal (b) AoPS Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' These two graphs show box plots of the torques needed for each joint separately in one experiment where the robots are tracking the 10 random commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' For readability reasons, only the LF leg is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Furthermore, the distribution for each joint torque is indicated by colored violin plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This plot transfers similarly to the other legs as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' random commands for 3s each to the robots while the com- mands change dynamically (see supplementary video).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The commands are randomly sampled between [−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='2]m s−1 in x direction, [−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='6]m s−1 in the y direction, and [−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='2]rad s−1 around the yaw axis and the same for both robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The efficiency gain for the execution of all the commands is again around 30 % for AoPS while the tracking performance was similar to ANYmal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Additionally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12 reports the joint torques for the left front leg of the robots as a boxplot with an overlaying violin plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Regarding the KFE joint (knee), the average torque is around 26 N m for ANYmal in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12a while AoPS is around 7 N m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Basically, the whole distribution shifts down thanks to the parallel elastic spring, which reduces the CoTr notably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' As a result, the maximum absolute torque that AoPS needs for the same task is 52 N m, which is only 71 % of ANYmal (73 N m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Furthermore, the HFE joint average torque for AoPS is closer to 0 N m than ANYmal, while at the same time requiring less variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This also drives down the CoTr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Expectedly, the HAA joint is unaffected by the parallel elastic spring, and for both systems mostly the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Rough Terrain For the fourth and fifth tests, we adapted the perceptive learning from Miki et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [29] and included exteroceptive observations during the student distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Using this adapted policy, we performed several outdoor experiments with our parallel-elastic robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We climbed several inclinations, tra- versed different types of stairs, went through confined spaces, walked over forest ground, inclined gravel paths, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A few snapshots are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6 and videos in the supplemen- tary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The robot did not fall once during the tests and reports the robustness of the controller and the novel design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The state of charge for ANYmal (Red) and AoPS (Purple) over time during the experiment in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-E shows that our optimized design can achieve higher operating times with the same battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' TABLE I RUNNING TRACK PERFORMANCE AoPS ANYmal Number of Rounds 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='6 Traveled distance [m] 3000 2640 Initial Charge [%] 92 89 Final Charge [%] 11 10 Operation Time [min] 68 59 Average Velocity [m/s] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='735 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='740 Efficiency [%] 111 100 Outside Temperature [°C] 31 26 This shows that adding parallel elastic springs does not affect the robustness negatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Battery Life Finally, we used both robots sequentially on a running track of 400 m length and let the robots walk with the same battery until the battery was fully depleted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The battery was as much as possible fully charged before and after the first run with AoPS to ensure a fair evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Both robots were commanded 1 m s−1 and carefully steered to stay in the inner path of the track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The performance of each robot is reported in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This experiment shows that the overall traveled distance of our quadrupedal robot can be increased by at least 11 % from 2640 m to 3000 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We introduce the following efficiency metric as the quotient in covered distance scaled by the mismatch in battery charge (2 %).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Efficiency = 3000 m 2640 m ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='89 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='92 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='11 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' (10) We also report the state of the charge over time in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Besides the faster drop for ANYmal, this shows that the battery that we used is internally calibrated and the linear scaling in (10) can compensate for the 2 % difference in charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' CONCLUSION This paper shows that, with the co-optimization of the de- sign and controller, parallel springs on the knee of quadrupedal robots can increase locomotion efficiency without compromis- ing the command tracking performance and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' While it is well studied that gravity compensation with PEAs is energetically beneficial for static tasks [6], the PEA’s contri- bution during the dynamic locomotion is relatively unstudied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The effect of PEA is nontrivial during the locomotion since the actuators have to repeatedly work against the spring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A key takeaway of our work is that PEAs can also increase the performance during dynamic locomotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' We co-optimized design parameters and locomotion con- trollers that act optimally for a given set of design parameters Command 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='00 S ANYmal S Linear Velocity in m/ AoPS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='25 Velocity Velocity y Velocity :ANYmal 80 AoPS % .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='≤ Charge 60 JO 40 State 20 0 10 20 30 40 50 60 Time in min8 IEEE ROBOTICS AND AUTOMATION LETTERS, PREPRINT VERSION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACCEPTED DECEMBER, 2022 and task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' With a parallel elastic knee actuator designed by our approach, we could reduce the required joint torques, which yields a higher operation time for our quadrupedal robot ANYmal during locomotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' An important thing to note from our hardware experiments is the robustness of our controller to the model uncertainty, which shows the practical benefit of the RL-based control method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Trained by the privileged learning method [28] with randomized spring parameters, our controller tolerates possible model mismatches on the physical system without accurate spring calibration procedures, thus, removing the need to run any complex system identification routine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' As we showed the potential of PEAs in legged robotics, further investigations in this direction have to follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Firstly, the physical system’s energy consumption must be better modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' This work assumes that the CoTr measurement is proportional to the battery life of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Nevertheless, during the experiments in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-C and Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' III-F, we found a discrepancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' There are unmodeled factors such as electrical and mechanical losses which we did not identify in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Secondly, the design-conditioned policy cannot be guaranteed to be as performant as a policy trained for each design parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' The discrepancy was negligible in the setup covered in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A previous study on this topic was conducted by us [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lastly, a more elaborate design should be introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Our current design limits the workspace of the knee joint and the implementation of the cable-spring mechanism can be inaccurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Additionally, research will be devoted to including other parameters in the design process like link masses or leg lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' ACKNOWLEDGMENT The authors would like to thank the RSL Design Team for their insightful discussions and Marko Bjelonic for his great support on the Cluster and for helping with the state estimation on AoPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' REFERENCES [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Abate, “Mechanical design for robot locomotion,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' disser- tation, Oregon State University, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Pratt and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Williamson, “Series elastic actuators,” in Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Human Robot Interaction and Cooperative Robots, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1, 1995, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 399–406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Anymal-a highly mobile and dynamic quadrupedal robot,” in IEEE/RSJ International conference on intelligent robots and systems (IROS), 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 38–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hubicki, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Atrias: Design and validation of a tether-free 3d-capable spring-mass bipedal robot,” The International Journal of Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1497–1521, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Semini, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Tsagarakis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Guglielmino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Focchi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Cannella, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Caldwell, “Design of hyq–a hydraulically and electrically actuated quadruped robot,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 225, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 831–849, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [6] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kashiri, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “An overview on principles for energy efficient robot locomotion,” Frontiers in Robotics and AI, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 129, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [7] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Scalera, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Carabin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Vidoni, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Wongratanaphisan, “Energy efficiency in a 4-dof parallel robot featuring compliant elements,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 02, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 49–57, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [8] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Bjelonic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Sachtler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Albu-Sch¨affer, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Della Santina, “Experimental closed-loop excitation of nonlinear normal modes on an elastic industrial robot,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1689–1696, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [9] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Arm, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Spacebok: A dynamic legged robot for space explo- ration,” in IEEE/RSJ International conference on robotics and automa- tion (ICRA), 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6288–6294.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [10] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kolvenbach, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hampp, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Barton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Zenkl, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, “Towards jumping locomotion for quadruped robots on the moon,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5459–5466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Badri-Spr¨owitz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Aghamaleki Sarvestani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Sitti, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Daley, “Birdbot achieves energy-efficient gait with minimal control using avian- inspired leg clutching,” Science Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 64, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' eabg4055, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Mazumdar, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Parallel elastic elements improve energy efficiency on the steppr bipedal walking robot,” IEEE/ASME Transactions on mechatronics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 898–908, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Silva and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Machado, “A literature review on the optimization of legged robots,” Journal of Vibration and Control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1753–1767, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Koziel and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Yang, Computational optimization, methods and algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Springer, 2011, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 356.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [15] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Turner, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Bayesian optimization is superior to random search for machine learning hyperparameter tuning: Analysis of the black- box optimization challenge 2020,” in NeurIPS 2020 Competition and Demonstration Track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' PMLR, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 3–26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Frazier, “A tutorial on bayesian optimization,” arXiv preprint arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='02811, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [17] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' De Vincenti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Coros, “Control-aware design opti- mization for bio-inspired quadruped robots,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1354– 1361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Dinev, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Mastalli, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Ivan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Tonneau, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Vijayakumar, “A versatile co-design approach for dynamic legged robots,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Chadwick, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kolvenbach, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Dubois, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lau, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, “Vitruvio: An open-source leg design optimization toolbox for walking robots,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6318– 6325, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Zhao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Robogrammar: graph grammar for terrain-optimized robot design,” ACM Transactions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1–16, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Ha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Coros, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Alspach, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Kim, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Yamane, “Joint optimization of robot design and motion parameters using the implicit function theorem.” in Robotics: Science and systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 8, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [22] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' He, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Ciocarlie, “Hardware as policy: Mechanical and computational co-optimization using deep reinforcement learning,” in Proceedings of the 2020 Conference on Robot Learning, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Proceedings of Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' PMLR, 16–18 Nov 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1158–1173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Schaff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Yunis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Chakrabarti, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Walter, “Jointly learning to construct and control agents using deep reinforcement learning,” in IEEE/RSJ International Conference on Robotics and Automation (ICRA), 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 9798–9805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [24] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Schaff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Sedal, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Walter, “Soft robots learn to crawl: Jointly optimizing design and control with sim-to-real transfer,” arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='04575, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Cowen-Rivers, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Hebo: Pushing the limits of sample- efficient hyper-parameter optimisation,” Journal of Artificial Intelligence Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 74, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1269–1349, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Turner, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Bayesian optimization is superior to random search for machine learning hyperparameter tuning: Analysis of the black- box optimization challenge 2020,” in Proceedings of the NeurIPS 2020 Competition and Demonstration Track, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Proceedings of Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' PMLR, 06–12 Dec 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 3–26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Won and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lee, “Learning body shape variation in physics-based characters,” ACM Transactions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 1–12, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hwangbo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Wellhausen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Koltun, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, “Learning quadrupedal locomotion over challenging terrain,” Science robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 47, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' eabc5986, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [29] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Miki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hwangbo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Wellhausen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Koltun, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, “Learning robust perceptive locomotion for quadrupedal robots in the wild,” Science Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 62, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' eabk2822, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Schulman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Wolski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Dhariwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Radford, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Klimov, “Prox- imal policy optimization algorithms,” arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='06347, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [31] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Cho, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=', “Learning phrase representations using rnn encoder-decoder for statistical machine translation,” arXiv preprint arXiv:1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content='1078, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' [32] ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Belmonte-Baeza, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Valsecchi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' Hutter, “Meta rein- forcement learning for optimal design of legged robots,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} +page_content=' 12 134–12 141, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQf5QU9/content/2301.03509v1.pdf'} diff --git a/2tE0T4oBgHgl3EQfdwDZ/vector_store/index.pkl b/2tE0T4oBgHgl3EQfdwDZ/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..c3047a5a461102ddffb1c8fb91fcec49cb60a844 --- /dev/null +++ b/2tE0T4oBgHgl3EQfdwDZ/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4644bfcb0e8cf4f34dcf1f66541f51540f890d31a48e2bc565cd0dd98240d2fd +size 106977 diff --git a/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/2301.00033v1.pdf.txt b/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/2301.00033v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9967e42a794af651dc2dea6ab4b6b987f5d63193 --- /dev/null +++ b/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/2301.00033v1.pdf.txt @@ -0,0 +1,858 @@ +Are high-energy photoemission final states +free-electron-like? +V.N. Strocov,1 L.L. Lev,1,2 F. Alarab,1 P. Constantinou,1 T. Schmitt,1 +T. J. Z. Stock,3 L. Nicolaï,4 J. Očenášek4 & J. Minár4 +1Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland +2Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russia +3London Centre for Nanotechnology, University College London, London WC1H 0AH, UK +4University of West Bohemia, New Technologies Research Centre, 301 00 Plzeň, Czech Republic +Abstract +Three-dimensional (3D) electronic band structure is fundamental for understanding a vast diversity of +physical phenomena in solid-state systems, including topological phases, interlayer interactions in van +der Waals materials, dimensionality-driven phase transitions, etc. Interpretation of ARPES data in terms +of 3D electron dispersions is commonly based on the free-electron approximation for the photoemission +final states. Our soft-X-ray ARPES data on Ag metal reveals, however, that even at high excitation +energies the final states can be a way more complex, incorporating several Bloch waves with different +out-of-plane momenta. Such multiband final states manifest themselves as a complex structure and +excessive broadening of the spectral peaks from 3D electron states. We analyse the origins of this +phenomenon, and trace it to other materials such as Si and GaN. Our findings are essential for accurate +determination of the 3D band structure over a wide range of materials and excitation energies in the +ARPES experiment. + +Introduction +Knowledge of electronic band structure resolved in three-dimensional (3D) electron momentum (k) is +fundamental for understanding a vast diversity of physical phenomena in crystalline solid-state systems. +Recently, the interest in 3D band structure has been boosted due to its essential role in topological +phases such as Weyl semimetals characterised by 3D cones of linear electron dispersion (see, for +example, refs. 1,2) as well as their generalisation to high-fold chiral fermions3,4 and high-dimensional +degeneracies such as the Hopf links and nodal lines, chains and knots in 3D k-space (see the reviews5–8 +and the references therein). Less straightforward but equally important implications of the 3D band +structure include, for example, interlayer interaction and 3D charge-density waves in van der Waals +materials9–11, formation of quantum-well states at interfaces and heterostructures12–16 as well as +minibands in semiconductor superlattices17, k-dependent electron-phonon interactions18, +dimensionality-driven phase transitions19,20, 3D quantum Hall effect21, and many more properties of +solid-state systems. +High-energy angle-resolved photoelectron spectroscopy (ARPES), operating in the soft- and hard-X-ray +photon energy (hv) regions, has pushed the k-resolving spectroscopic abilities of this technique from the +conventional surface science to the intrinsic electronic structure deep in the bulk, buried interfaces and +heterostructures, and diluted impurity systems (see the recent reviews22–26 and the references therein). +The main advantage of high photoelectron energies is an increase of the photoelectron mean free path +(λPE) to a few nanometres and more27. Crucial for the experimental determination of 3D band structure, +the increase of λPE translates, via the Heisenberg uncertainty principle, to sharpening of the intrinsic +resolution of the ARPES experiment in the out-of-plane momentum (kz) which is defined as Δkz = λPE +-1 28. +The sharp resolution in kz underlies the applications of high-energy ARPES for accurate determination of +the electronic band structure resolved in 3D k-space as illustrated by many of the works cited above. +In contrast to the in-plane momentum k// = (kx,ky), conserved in the photoemission process because of +the in-plane periodicity of the system, the kz component is distorted upon the photoelectron escape from +the crystal to vacuum. It can however be reconstructed based on its conservation in the photoexcitation +process in the bulk (corrected for the photon momentum phv) if the final-state kz is known. Conventionally, +the final-sate dispersion is modelled within the free-electron (FE) approximation, where kz is found as +, with Ek and K// being the photoelectron kinetic energy and in-plane +𝑘𝑧 = +2𝑚 +ħ +𝐸𝑘 − +ħ +2 +2𝑚 𝐾// +2 − 𝑉0 +momentum, respectively, m the free-electron mass, and V0 the inner potential. Somewhat stretching this +formula, an energy dependence of the dynamic exchange-correlation29,30 can be accommodated via an +energy-dependent V0. Importantly, the FE approximation implies that the final-state wavefunction is a +plane wave, where the finite λPE is described by an imaginary part of kz. It has since long been realised +that at low excitation energies used in the conventional VUV-ARPES the FE approximation may in many +cases fail even for metals31–34 and all the more for semiconductors35 and more complex materials, for +example, transition metal dichalcogenides36–38. For high-energy ARPES, however, the relevance of this +approximation is commonly taken for granted. Being quintessential for 3D band mapping with +high-energy ARPES, this assumption is based on a physically appealing argument that at high excitation +energies Ek of photoelectrons much exceeds modulations of the crystal potential V(r), and they can be +considered as free particles. +Here, we analyse soft-X-ray ARPES data on Ag the metal and demonstrate that even at high excitation +energies the complexity of the final states can go far beyond the FE picture. In particular, they can be +composed of multiple Bloch waves having different kzs which manifest themselves as complex structure +of the spectral peaks or their excessive broadening. This analysis extends to GaN and Si the +semiconductors. We theoretically demonstrate the origin of these non-trivial effects as resulting from + +hybridization of plane waves on the crystal potential, and elucidate how they should be taken into +account for accurate determination of 3D valence-band dispersions in the high-energy ARPES +experiment. +Results +Fig. 1 presents the Brillouin zone (BZ) of the fcc Ag (a) and the experimental out-of-plane cross-section +of the Fermi surface (FS) in the ГXW symmetry plane measured under variation of hv (b). The indicated +kzs, running through a sequence of the Г and X points, were rendered from the hv values assuming FE +final states with V0 = 10 eV. In-plane cross-sections measured at two hv values, bringing kz to the Г and +X points, are presented in the two panels (c). In general, the experimental out-of-plane FS follows a +pattern of repeating rounded contours characteristic of the states near the Fermi level (EF) formed by the +sp-band of Ag. This pattern is reproduced by our one-step ARPES calculations (e) where FE-like final +states were used. Surprisingly, however, a closer look at the experimental FS reveals significant +deviations: (1) Multiple FS contours, offset in kz, can be resolved in some (E,k) regions such as those +marked by magenta arrows. The corresponding multiple dispersions coming from the sp-band are +apparent, for example, in the ARPES image measured at hv = 997 eV (d, top) and the corresponding +momentum-distribution curve as a function of kx at EF (kx-MDC, yellow line). This multiple-dispersion +pattern contrasts to the clean dispersions at hv = 894 eV (d, bottom). As we discuss in more detail below, +such replica spectral structures demonstrate that the final states incorporate multiple bands with different +kzs – hereinafter called multiband final states (MBFSs) – which is a phenomenon beyond the +conventional picture of FE-like final states implying one single band with one kz. In our case the +separation of the kzs in these MBFSs is larger than the intrinsic Δkz (according to the λPE values from the +TPP-2M formula, varying from ~0.15 Å-1 at 300 eV to 0.056 Å-1 at 1300 eV); (2) The second type of +deviations from the FE final states, seen in the out-of-plane FS (b), is a notable spectral intensity +spreading into the X points where the sp-band is unoccupied. Furthermore, broadening of the FS +contours in kz irregularly varies through k-space, and in some (E,k) regions (such as those marked by +yellow arrows) can be excessively large. These two effects are also caused by the MBFSs, but in this +case the kzs are separated less than Δkz. We note that in the extremes of the E(kz) dispersion (dkx/dkz=0 +in the out-of-plane FS) the MBFSs have only a second-order effect on the ARPES structure; however, +even in this situation a large enough kz separation within the MBFSs can cause multiple FS contours, as +seen in the in-plane FS map measured at hv = 712 eV (c, magenta arrow). Obviously, the MBFS effects +are not reproduced by the ARPES calculations (e) employing FE final states. Although presently on a +qualitative level, these effects are reproduced by our one-step ARPES calculations (Supplemental +Material) where the final states are treated within the multiple-scattering formalism, naturally +incorporating the non-FE effects including the MBFSs. + +Fig. 1. FS cross-sections for Ag(100): Theoretical FS (a), its experimental out-of-plane cross-section (b), +and two in-plane cross-sections (c) measured at the indicated hv values, bringing kz to the Г and X points +(lower and upper panels, respectively). Replicas and broadening of the FS contours in certain (E,k) +regions (such as those marked by magenta and yellow arrows, respectively) manifest MBFSs. These +effects are particularly clear in the ARPES image and kx-MDC at hv = 997 eV (d, top) in contrast to those +at hv = 894 eV (bottom). These effects are beyond the one-step ARPES calculations with FE-like final +states (e). +In Fig. 2, the theoretical E(k) along the ГX direction (a) is compared with the experimental out-of-plane +band dispersions E(kz) at kx=0 (b) and the in-plane E(k//) images (c) measured at kz running through the +successive Г points (energies as binding energies Eb relative to EF). Again, the gross structures of the +experimental E(kz) follow the expected periodic pattern with the sp-band crossing EF as reproduced by +our one-step ARPES calculations in (e) with the FE-like final states. We see, however, replicas and +anomalous broadening of the sp-band (such as marked by magenta arrows) as well as significant +spectral intensity around the X point. These anomalies appear most clearly in the zoom-in of the sp-band +and the kz-MDC at EF (d, yellow line) where we observe a complex multi-peak structure of the spectral +intensity around the X point. Again, these effects are manifestations of the MBFSs, with the ARPES +dispersions originating from the individual final-state bands marked by the magenta arrows. Again, they +are absent in the ARPES calculations employing FE final states (e) but are qualitatively reproduced upon +inclusion of multiple-scattering final states (Supplemental Material). The MBFS effects could not be +observed in the first soft-X-ray study on Ag(100) focused on the 3d states39 because the smaller kz +dispersion of these states compared to the sp ones could not provide sufficient separation of the spectral +peaks from the different bands in the MBFS. We note in passing that the experimental 3d states appear +in ~1 eV below the LDA-DFT energies; such an energy shift, already noticed for Cu, is a pronounced +self-energy effect due to non-local exchange interaction of the 3d electrons strongly localized in the core +region40. + +b +(d) +a +1200 +997 eV +800 +894eV +600 +572 eV +400Fig. 2. Band dispersions along the ГX direction for Ag(100): Theoretical E(k) (a) compared with the +experimental out-of-plane ARPES dispersions at kx=0 (b, the spectral intensity represented in +logarithmic scale) and (c) in-plane dispersions for the indicated hv values, bringing kz to the successive +Г point. A zoom-in of the sp-band (d) shows its replicas and excessive broadening (such as marked by +magenta arrows) most evident in the kz-MDC at EF (yellow line) as multiple and broadened spectral +peaks, manifesting the MBFSs. These effects are beyond the one-step calculations of the ARPES +intensity and kz-MDC with FE-like final states (e). +Discussion +Origin of the MBFSs +By definition, a FE-like final state in the crystal is one single plane wave ei(k+G)r which matches the +outgoing photoelectron plane wave. In the whole multitude of bands, formally available under Ek and K// +conservation, this plane wave corresponds to one single band that we will refer to as primary, relaying +Mahan's primary photoemission cones 41. All other bands in the multitude give strictly zero contribution to +the photocurrent. We will be calling them secondary, relaying Mahan's secondary cones. The MBFS +effects, observed in our ARPES data, indicate that the corresponding final states may include, for given +Ek and K//, several bands with different kzs giving comparable contributions to the ARPES intensity. +These effects obviously fall beyond the FE-like picture. As the first-principles calculations can not yet +exhaustively describe our experimental results, we will analyse the MBFS effects based on insightful +model calculations. +The non-FE effects in the final states, in particular their multiband composition, is certainly a +phenomenon not new for low-energy ARPES. They have been studied experimentally and theoretically +for 3D bulk band dispersions in various materials including Cu31,32, Mg34 and even Al the paradigm FE +metal14,42, semiconductors35, various transition metal dichalcogenides36–38 as well as surface states, in +particular for the Al(100) and (111) surfaces33. However, it is intriguing to observe such effects in our +soft-X-ray energy range. Why do they appear in spite of the fact that the photoelectron Ek is +overwhelmingly large compared to the V(r) modulations? + +(b) +(d) +(e) +894eV +1268 eV +310eV +572eVWe will now build a physically appealing picture of the non-FE effects in the photoemission final states +using their standard treatment as the time-reversed LEED states43. They are superpositions of damped +Bloch waves фk(r) with complex kz, whose imaginary part Imkz represents the (1) inelastic electron +scattering, described by a constant optical potential Vi (imaginary part of the self-energy), and (2) elastic +scattering off the crystal potential44–47. The amplitudes Ak of these фk(r), determining their contribution to +the total ARPES signal, were determined within the matching approach of the dynamic theory of +LEED17,38,44,45,48,49 where the electron wavefunction in the vacuum half-space (superposition of the +incident plane wave eiK0r and all diffracted ones ei(K+g)r, g being the surface reciprocal vectors) is matched, +at the crystal surface, to that in the crystal half-space (superposition of фk(r) satisfying the +surface-parallel momentum conservation k//=K//+g). The underlying complex bandstructure calculations +utilised the empirical-pseudopotential scheme, where фk(r) are formed by hybridization of plane waves +ei(k+G)r, G being 3D reciprocal-lattice vectors. The Fourier components VΔK = of the +local pseudopotential V(r) were adjustable parameters. +We start from the ideal FE case, where V(r) is constant and equal to V0 (so-called empty lattice). The +corresponding calculations are plotted in Fig. 3 (a) as the E(Rekz) bands (the corresponding E(Imkz) +bands are not shown here for brevity). Due to the absence of hybridization between the plane waves in +the empty-lattice case, each фk(r) contains one single plane wave corresponding to a certain G vector. +Typical of high energies, we observe a dense multitude of bands brought in by an immense number of all +G vectors falling into our energy region. Starting from the ultimate V0 = 0 case, when the vacuum +half-space is identical to the crystal one, it is obvious that only one band will couple to the photoelectron +plane wave in vacuum eiKr and thus be effective in the ARPES final state, specifically, only the primary +band whose plane wave – in the context of LEED often called conducting plane wave – has k+G equal to +the photoelectron K. The whole multitude of the secondary bands, whose plane wave's k+G is different +from K, will give no contribution to the photocurrent. In our more general case V(r) = V0, the kz +component of the photoelectron distorts upon its escape to vacuum, and the above momentum-equality +condition to identify the conducting plane wave should be cast in terms of the in-plane components as k// ++ G// = K//. In a formal language, these intuitive considerations can be expressed through the partial +contributions of each фk(r) into the total current absorbed in the sample in the LEED process, which are +the so-called partial absorbed currents Tk ∝ Vi⋅ +, with the integration extending from the +0 +∞ +∫ 𝐴𝑘ϕ𝑘(𝑧) +| +| +2𝑑𝑧 +crystal surface into its depth31,32,37. Importantly in the ARPES context, the Tk values multiplied by the +photoemission matrix elements define the partial photocurrents emanating from the individual фk(r) in the +MBFS31. In Fig. 3(a) the calculated Tk are marked in blue colorscale. As expected for the empty-lattice +case, Tk is equal to 1 for the primary (in the LEED context often called conducting) band and strictly zero +for all other ones, realising the ideal FE final state containing one single plane wave. In Mahan's +language, only the primary-cone photoemission is active in our ideal FE case. +We will now introduce spatial modulations of V(r) as expressed by VΔK for non-zero ΔK. The plane waves +start to hybridise through the VΔK matrix elements, and each фk(r) becomes a superposition of a few +plane waves as фk(r) = ΣGCGei(k+G)r. In this case not only one but several фk(r) can acquire a certain +admixture of the k// + G// = K// conducting plane wave – in the formal language, their Tk becomes +non-zero – and give a certain contribution to the total photocurrent. Our model calculations for this case +are sketched in Fig. 3 (b). The ARPES final state appears multiband in a sense that it consists of several +фk(r) with different kzs (typically alongside the primary band) which give comparable contributions to the +total ARPES signal as quantified by the corresponding Tk. In Mahan's language, the qualitative +distinction between the primary- and secondary-cone photoemission dissolves. Correspondingly, the +ARPES spectra will show up several peaks corresponding to different kz or, if the separation of these kzs +is smaller than the intrinsic Δkz, excessive broadening of the spectral peaks. This is exactly what we +have just seen in our ARPES data on Ag(100). We note in passing that on the qualitative level the bands + +contributing to the photocurrent can be easily identified based on the Fourier expansion of their фk(r) +which should have a substantial weight of the k// + G// = K// conducting plane wave50. +Whereas for the sake of physical insight we have intentionally simplified the above picture, the exact +treatment of the MBFSs based on the matching approach of LEED has been developed in a series of +previous works albeit limited to relatively low final-state energies31,34,37,38. Finally, we note that the MBFS +phenomenon can also be understood within the simplified three-step model of photoemission, where the +whole quantum-mechanical photoemission process is splitted into the photoexcitation of a photoelectron, +its transport out of the crystal, and escape to vacuum. In this framework, the MBFSs can be viewed as +resulting from multiple scattering of photoelectrons on their way out of the crystal that creates multiple +Bloch-wave modes of the scattered wavefield. +Fig. 3. Band structure of the final-state Bloch waves E(Rekz) in a model fcc crystal along the ГX +direction (a) in the empty-lattice case V(r) = V0 and (b) with a more realistic spatially modulated +pseudopotential, sketched in the insert. The dense multitude of bands is formed by an immense +number of G vectors falling into our high-energy region.The contributions of each band into the total +photocurrent are quantified by Tk (blue colorscale). Whereas in the first case the photocurrent +emanates from one single FE band (marked with the corresponding G vectors), in the second case it +may distribute over a few bands alongside the FE dispersion, which form a MBFS incorporating a few +kzs. +Whereas the effects of MBFSs have already been established at low excitation energies, their survival in +high-energy ARPES might seem puzzling. In a naive way of thinking, photoelectrons with energies much +higher than the modulations of V(r) should not feel them, recovering the FE case with one single фk(r). +However, VΔK as the strength of hybridization between two plane waves depends, somewhat +counter-intuitively, not on energy but rather on ΔK between them. As sketched in the insert in Fig. 3 (b), +VΔK typically has its maximal negative value at ΔK = 0 (which is the V0), and with increase of ΔK sharply +rises and then asymptotically vanishes. Importantly, however high the energy is, the multitude of the +plane waves always contains pairs of those whose ΔK is small. The corresponding bands can be +identified by close dispersions. For such pairs VΔK is large, giving rise to their strong hybridization. +Importantly, all bands hybridising with the k// + G// = K// plane wave will receive non-zero Tk and thus + +1200 +(a) +G00-6 +(b) +VAK +1100 +△K +1000 +G005 +900 +800 +k +0.5 +E +700 +G004 +600 +500 +400 +Rekz +Rekzcontribute to the total photocurrent, as shown in Fig. 3 (b). This forms the MBFSs that should survive +even at high energies. +Effect of MBFSs on the spectral structure +We will now follow in more detail how the MBFSs affect the ARPES spectra. As an example, we will +analyse the experimental kz-MDC from Fig. 2(d) in the region of the X point at hv ~ 1100 eV, reproduced +in Fig. 4 (with the linear background subtracted). Within the FE approximation, we might expect to +observe here two Lorentzian peaks, placed symmetrically around the X point and broadened by the +same intrinsic Δkz. However, the kz-MDC shows three distinct peaks A-C, with the peak B coming from a +final-state band falling beyond the FE approximation. Moreover, Lorentzian fitting of the peaks finds that +whereas the peak C has a relatively small width of 0.11 Å-1, the widths of the peaks A and B are more +than twice larger, 0.30 and 0.32 Å-1, respectively. The picture of MBFSs neatly explains this observation, +suggesting that whereas the peak C is formed by a final state having one dominant kz contribution, and +the peaks A and B by final states incorporating a multitude of kzs separated less than Δkz. Whereas it is +generally believed that the intrinsic broadening of the ARPES peaks in kz is determined exclusively by +finite λPE the photoelectron mean free path, our example demonstrates that the multiband final-state +composition may not only create additional spectral peaks but also be an important factor of their +broadening additional to λPE. +Fig. 4. kz-MDC at EF from Fig. 2(d) in the hv region around 1100 eV (vicinity of the X point) decomposed in three +Lorentzians. The presence of the peak B and the larger broadening of the peaks A and B compared to C are +caused by MBFSs. +Intriguingly, however, we note that even the narrowest peak C is almost twice broader than Δkz ~ 0.065 +Å-1 expected from λPE ~ 15.5 Å suggested by the TPP-2M formula 51 well-established in XPS and Auger +electron spectroscopy. One explanation might be that already the peak C would incorporate multiple +final-state bands with smaller kz separation compared to other two peaks. Another explanation would +trace back to quasielastic electron-electron or electron-phonon scattering, which would increase with +energy owing to the increase of the phase-space volume available for such scattering. Altering k of +photoelectrons, it should destroy the coherence of photoelectrons and thus reduce λPE as reflected in the +observed Δkz. At the same time, the quasielastic scattering should have only a little effect on attenuation +of the k-integrated signal of the core-level or intrinsically incoherent Auger electrons. In other words, the +effective λPE in ARPES should be smaller than that in XPS/Auger spectroscopy, described by the +TPP-2M and related formalism. Such intriguing fundamental physics certainly deserves further +investigation. + +15 +15.5 +16 +16.5 +17 +17.5 +18 +18.5MBFS phenomena through various materials +The phenomenon of MBFSs surviving at high excitation energies is certainly not restricted to Ag only +and, strengthening with the strength of V(r) modulations, should be fairly general over various materials. +Even for Al the paradigm FE metal, astonishingly, such MBFSs can be detected at least up to excitation +energies of a few hundreds of eV14,42. Quite commonly the MBFS effects at high energies are observed +in van-der-Waals materials such as MoTe2 +52, which should be connected with a large modulation of V(r) +across the van-der-Waals gap. +Another vivid example of the MBFS effects is the soft-X-ray ARPES data for GaN presented in Fig. 5, +compiled from the previously published results on AlN/GaN(1000) heterostructures13. The panel (a) +shows the ARPES spectral structure plot expected from the DFT valence bands and FE final states with +V0 = 5 eV. With the non-symmorphic space group of bulk GaN, the ARPES dispersions allowed by the +dipole selection rules (though in our case somewhat relaxed due to the band bending in GaN) are +marked bold. The panels (b,c) present the experimental out-of-plane ARPES dispersions measured at kx +in two formally equivalent +points of the surface BZ, +0 in the first and +1 in the second zone. As +Г +Г +Г +expected because of weaker electron screening of the atomic potential and thus sharper modulations of +V(r) in the covalent GaN compared to the metallic Ag, the deviations of experimental dispersions from +the predictions of the FE approximation are much stronger than for Ag. One can clearly see the MBFSs +where the individual bands (marked by arrows at their top) are separated in kz more than the intrinsic Δkz +broadening. In the multitude of the experimental ARPES dispersions, one can identify the one which can +be associated with the primary-cone photoemission (bold arrows) although in the +0 data this band +Г +cannot be traced below 1000 eV. Remarkably, for the same initial-state E(k) the ARPES dispersions +measured at the +0 and +1 points appear completely different, identifying different final-state bands +Г +Г +selected from the continuum of all unoccupied states available for given final-state energy and K//. These +bands are identified by their leading plane-wave component to have k// + G// = K//, where K// of the +photoelectron changes between the surface BZs32. +Fig. 5. Out-of-plane ARPES dispersions for GaN(1000): (a) Expected from the DFT valence bands and +FE final states with V0 = 5 eV. With the non-symmorphic space group of bulk GaN, the dispersions +allowed by the dipole selection rules are shown bold; (b,c) Measured at kx = 0 projecting onto the Г0 +and Г1 points over two BZs. The experiment clearly resolves individual final-state bands (marked by +arrows) whose separation in kz is larger than the intrinsic Δkz broadening. + +(b) +(a +(c) +A +A +-10The high-energy final states in Si are a counter-example though. Fig. 6 presents soft-X-ray ARPES data +on a few-nm thick layer of Si(100) n-doped with As53 as the out-of-plane band dispersions (b) and iso-EB +contours (c), respectively. The panel (a) shows the ARPES spectral structure plot expected from the +DFT-GGA calculated valence bands and FE final states with V0 = 10 eV, with the bold lines indicating the +dispersions allowed by the selection rules (for in-depth discussion see Ref. 54). Because of the covalent +character of Si, one might again expect that the non-FE effects here would be comparable to those for +GaN and in any case stronger than for the metallic Ag. Contrary to such expectations, however, the +experimental data in (b,c) does not show any clear signatures of the MBFSs in Si in the shown (Ek,k) +region, although at low excitation energies they are profound35. At the moment we can not decipher any +simple arguments that would relate the strength of the non-FE effects in the high-energy electron states +to any obvious electronic-structure parameters of various materials. +Fig. 6. Out-of-plane ARPES data for Si(100): (a) ARPES dispersions expected from the DFT valence +bands and FE final states with V0 = 10 eV, with dispersions allowed by the selection rules shown bold; +(b) Experimental band dispersions and (c) iso-EB contours in 2 eV below the valence-band maximum. +No clear signatures of the MBFSs can be identified in these data. +Non-FE effects beyond ARPES +The non-FE effects in high-energy electron states such as MBFS manifest themselves not only in the +ARPES dispersions. Another manifestation will be the circular dichroism in the angular distribution of +photoelectrons (CDAD) that necessitates that the final-state wavefunctions deviate from the free-electron +plane waves55,56. The CDAD has indeed been observed already in the early soft-X-ray ARPES study on +Ag(100)39. Another example is the orbital tomography of adsorbed molecules (see, for example, Refs. +57–59) which takes advantage of the Fourier relation between the angle distribution of photoelectrons +and electron density of the valence electron orbitals. The non-FE effects introduce additional plane-wave +components in the final states, calling for refinement of the straightforward Fourier-transform processing +of the experimental data59. Beyond ARPES, the very fact of electron diffraction at crystalline surfaces +identifies non-FE effects in the electron states in the crystal, because otherwise the incident electrons +would upon entering the crystal follow the same FE wavefunction and thus would not reflect. The +Reflection High-Energy Electron Diffraction (RHEED) evidences that the non-FE effects survive even in +the energy range of a few tens of keV, when ΔK between the incident and diffracted plane waves is small + +(a) +(b)and thus the corresponding VΔK large. These considerations suggest that the MBFSs should survive +even in hard-X-ray ARPES, waiting for a direct experimental observation. +Finally, we should point out that the coherent photoemission process underlying the ARPES experiment +discussed above (as well as the orbital tomography) is fundamentally different to the essentially +incoherent process of X-ray photoelectron diffraction (XPD) (see, for example, the reviews60–62. In the first +case, all photoelectron emitters (atoms) throughout the crystal surface region within the depth λPE are +coherent – or entangled, in the modern quantum mechanics discourse – and emit a coherent +photoelectron wavefield characterised by a well-defined k. The resulting ARPES intensity as a function of +Ek and θ bears sharp structures reflecting, through the momentum conservation, the k-resolved band +structure of the valence states. In the XPD, other way around, the coherence between the emitters +throughout the surface region is lost. This takes place, for example, for isolated impurity atoms or +adsorbed molecules, localised core levels, where the initial-state wavefunctions at different atoms are +decoupled from each other, or when the coherence of photoelectrons is broken by thermal or defect +scattering, or when the signal from certain valence-band states, like d-states, is integrated in energy63,64. +The result is that each photoelectron emitter creates scattered waves within a sphere of the radius λPE, +which interfere with each other incoherently with the waves emanating from another emitter. Typical of +diffraction with a few interfering rays, the resulting XPD intensity distribution as a function of Ek and θ is +fairly smooth, and reflects the local atomic structure. With Ek increasing into the hard-X-ray energy +range, λPE and thereby the number of coherently scattered waves increases. This forms sharp +Kikuchi-like structures in the XPD angular distribution, reflecting the long-range atomic structure62. In any +case, the XPD stays incoherent between the emitters. This fundamental difference between the coherent +photoemission and incoherent XPD processes is stressed, for example, by the fact that in the first case +the photoelectron angular distribution follows pph, shifting with hv, and in the second case it is insensitive +to pph +19. +Conclusion +Our analysis of extensive soft-X-ray ARPES data on the Ag metal has demonstrated that even at high +excitation energies the photoemission final states may, intriguingly, in some energy and k-space regions +feature pronounced multiband composition beyond the conventional FE approximation. The +corresponding Bloch waves have different kz momenta, typically alongside the FE dispersion, and give +comparable contribution to the ARPES spectra. Using empirical-pseudopotential simulation of the final +states, where these contributions were quantified as proportional to the partial current in each Bloch +wave determined within the wavefunction-matching formalism of LEED, we have demonstrated that the +MBFSs appear due to hybridization of plane waves through low-K components of the crystal potential. +Depending on the kz separation of the individual Bloch waves, the MBFSs give rise to multiple ARPES +peaks from 3D valence-band dispersions or become an important factor of their broadening in addition to +the intrinsic Δkz broadening due to the finite λPE. From the first principles, these effects can be described +by one-step ARPES calculations with the final states treated within the multiple-scattering or Bloch-wave +approaches. Although our KKR-based calculations on Ag were able to qualitatively describe the +experimental results, further theoretical effort is required to achieve a quantitative agreement at high +excitation energies. Besides Ag, the MBFS phenomena are observed, for example, in previous soft-X-ray +data on the covalent GaN and even Al, the paradigm FE metal. They are surprisingly weak, however, for +the covalent Si. The MBFS phenomenon, typically strengthening with the sharpness of the +crystal-potential modulations, should be fairly general over a wide range of materials and excitation +energies even into the hard-X-ray range. + +Methods +Experiment +The experiments were performed at the soft-X-ray ARPES facility65 installed at the high-resolution +ADRESS beamline66 of the Swiss Light Source, Paul Scherrer Institute, Switzerland. X-rays irradiated the +sample with a flux of ~1013 photons/s at a grazing-incidence angle of 20o. A single crystal of Ag(100) +(MaTecK) was cleaned by a few cycles of Ar ion sputtering/annealing. The sample was cooled down to +~12K in order to quench relaxation of k-conservation due to thermal motion of the atoms67, with the +coherent spectral fraction enhanced by subtracting the angle-integrated spectrum scaled under the +condition of non-negativity of the remaining spectral weight. The measurements were performed with +p-polarised X-rays at a combined energy resolution varying from ~50 to 180 meV when going from hv = +300 to 1300 eV, which is about twice better than in the first soft-X-ray ARPES study on Ag(100) 39. The +FS maps were integrated over an EB window from -75 to 25 meV relative to EF. Angular resolution of the +analyzer PHOIBOS-150 was ~0.1o. Other relevant experimental details, including the conversion of Ek +and emission angle θ to k, corrected for pph, can be found elsewhere65. The data on GaN and Si from the +previous ARPES works, discussed below, were taken under the same experimental conditions, but with +the energy resolution relaxed to ~80 to 250 meV in the same hv range. +Calculations +In our simulations of the photoemission final states, the use of an empirical local pseudopotential has +allowed reduction of the secular equation on complex kz to an eigenvalue problem for a complex +non-Hermitian matrix17,45. For the energy range of our simulation extending to 1200 eV, the basis set +included all plane waves below an energy cutoff of 1800 eV. The inner potential V0 was set to 10 eV, all +VΔK to 5 eV for ΔK2 < 48 and to zero for larger ΔK2, and Vi to 5 eV. The accuracy of the calculations was +controlled via the current conservation generalised for non-zero Vi on the crystal side. For our qualitative +analysis of the final states, no attempt has been made to fit these parameters to our particular case. +Details of the calculations can be found elsewhere32. +The first-principles ARPES calculations were performed using the SPR-KKR package68 relying on the +multiple scattering theory using the Korringa-Kohn-Rostoker (KKR) method. The ground-state properties +of the Ag(001) surface were derived from density-functional-theory (DFT) calculations within the +local-density approximation (LDA) carried out with full potential. The ARPES spectra were calculated +within the one-step model of photoemission in the spin-density-matrix formulation69 taking into account all +aspects of the photoemission process for the actual experiment including pph, matrix elements and final +states constructed as the time-reversed LEED states. Taking into advantage the predominance of +forward scattering at Ek above ~400 eV70 the calculations used the single-site scattering approximation. +The final-state damping was described via constant Vi = 3 eV set to reproduce λPE = 10.2 Å at Ek = 600 +eV given by the TPP-2M formula51. For further computational details see Supplemental Material. The +main paper presents the results obtained with FE final states, and the effects of multiple-scattering final +states and various computational approximations are discussed in Supplemental Material. +Data availability +The raw and derived data presented are available from the corresponding authors upon a reasonable +request. + +References +1. +Weng, H., Fang, C., Fang, Z., Andrei Bernevig, B. & Dai, X. Weyl Semimetal Phase in +Noncentrosymmetric Transition-Metal Monophosphides. Physical Review X 5, 011029 (2015). +2. +Lv, B. Q. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724 (2015). +3. +Schröter, N. B. M. et al. Chiral topological semimetal with multifold band crossings and long Fermi +arcs. Nat. Phys. 15, 759 (2019). +4. +Schröter, N. B. M. et al. Observation and control of maximal Chern numbers in a chiral topological +semimetal. Science 369, 179 (2020). +5. +Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional +solids. Rev. Mod. Phys. 90, 015001 (2018). +6. +Yan, B. & Felser, C. Topological Materials: Weyl Semimetals. Annu. Rev. Condens. Matter Phys. 8, +337 (2017). +7. +Lv, B., Qian, T. & Ding, H. Angle-resolved photoemission spectroscopy and its application to +topological materials. Nature Reviews Physics 1, 609 (2019). +8. +Hasan, M. Z. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nature +Reviews Materials 6, 784 (2021). +9. +Strocov, V. N. et al. Three-dimensional electron realm in VSe2 by soft-x-ray photoelectron +spectroscopy: Origin of charge-density waves. Phys. Rev. Lett. 109, 086401 (2012). +10. Weber, F. et al. Three-dimensional Fermi surface of 2H−NbSe2 : Implications for the mechanism of +charge density waves. Physical Review B 97 235122 (2018). +11. Wang, Z. et al. Three-dimensional charge density wave observed by angle-resolved photoemission +spectroscopy in 1T-VSe2. Phys. Rev. B Condens. Matter 104, 155134 (2021). +12. King, P. D. C. et al. Surface band-gap narrowing in quantized electron accumulation layers. Phys. +Rev. Lett. 104, 256803 (2010). +13. Lev, L. L. et al. k-space imaging of anisotropic 2D electron gas in GaN/GaAlN high-electron-mobility +transistor heterostructures. Nature Communications 9, 2653 (2018). +14. Strocov, V. N. Photoemission response of 2D electron states. Journal of Electron Spectroscopy and +Related Phenomena vol. 229, 100 (2018). +15. Moser, S. et al. How to extract the surface potential profile from the ARPES signature of a 2DEG. J. +Electron Spectrosc. Relat. Phenom. 225, 16 (2018). +16. Schuwalow, S. et al. Band structure extraction at hybrid narrow-gap semiconductor-metal interfaces. +Adv. Sci. 8, 2003087 (2021). +17. Smith, D. L. & Mailhiot, C. Theory of semiconductor superlattice electronic structure. Reviews of +Modern Physics vol. 62, 173 (1990). +18. Husanu, M.-A. et al. Electron-polaron dichotomy of charge carriers in perovskite oxides. +Communications Physics 3, 62 (2020). +19. Berner, G. et al. Dimensionality-tuned electronic structure of nickelate superlattices explored by +soft-x-ray angle-resolved photoelectron spectroscopy. Physical Review B 92, 125130 (2015). + +20. Schütz, P. et al. Dimensionality-driven metal-insulator transition in spin-orbit-coupled SrIrO3. Phys. +Rev. Lett. 119, 256404 (2017). +21. Tang, F. et al. Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5. Nature +569, 537 (2019). +22. Suga, S. & Tusche, C. Photoelectron spectroscopy in a wide hν region from 6eV to 8keV with full +momentum and spin resolution. Journal of Electron Spectroscopy and Related Phenomena 200, 119 +(2015). +23. Fadley, C. S. Looking Deeper: Angle-Resolved Photoemission with Soft and Hard X-rays. +Synchrotron Radiation News 25, 26 (2012). +24. Gray, A. X. et al. Bulk electronic structure of the dilute magnetic semiconductor Ga1−xMnxAs +through hard X-ray angle-resolved photoemission. Nature Materials 11, 957 (2012). +25. Strocov, V. N. et al. Soft-X-ray ARPES at the Swiss Light Source: From 3D Materials to Buried +Interfaces and Impurities. Synchrotron Radiation News 27, 31 (2014). +26. Strocov, V. N. et al. k-resolved electronic structure of buried heterostructure and impurity systems by +soft-X-ray ARPES. Journal of Electron Spectroscopy and Related Phenomena 236, 1 (2019). +27. Powell, C. J. & Jablonski, A. Surface Sensitivity of Auger-Electron Spectroscopy and X-ray +Photoelectron Spectroscopy. Journal of Surface Analysis 17, 170 (2011). +28. Strocov, V. N. Intrinsic accuracy in 3-dimensional photoemission band mapping. Journal of Electron +Spectroscopy and Related Phenomena 130, 65 (2003). +29. Lindgren, S. Å., Walldén, L., Rundgren, J., Westrin, P. & Neve, J. Structure of Cu(111)p(2×2)Cs +determined by low-energy electron diffraction. Physical Review B 28, 6707 (1983). +30. Rundgren, J. Optimized surface-slab excited-state muffin-tin potential and surface core level shifts. +Physical Review B 68, 125405 (2003). +31. Strocov, V. N., Starnberg, H. I. & Nilsson, P. O. Excited-state bands of Cu determined by VLEED +band fitting and their implications for photoemission. Physical Review B 56, 1717 (1997). +32. Strocov, V. N. et al. Three-dimensional band mapping by angle-dependent very-low-energy electron +diffraction and photoemission: Methodology and application to Cu. Physical Review B 63, 205108 +(2001). +33. Krasovskii, E. E. et al. Photoemission from Al(100) and (111): Experiment and ab initio theory. +Physical Review B 78, 165406 (2008). +34. Krasovskii, E. E. Character of the outgoing wave in soft x-ray photoemission. Physical Review B +102, 245139 (2020). +35. Strocov, V. N. et al. Very-low-energy electron diffraction on the H-terminated Si(111) surface: Ab +initio pseudopotential analysis. Phys. Rev. B Condens. Matter 59, R5296 (1999). +36. Strocov, V. N., Starnberg, H. I., Nilsson, P. O., Brauer, H. E. & Holleboom, L. J. New Method for +Absolute Band Structure Determination by Combining Photoemission with Very-Low-Energy +Electron Diffraction: Application to Layered VSe2. Physical Review Letters 79, 467 (1997). +37. Strocov, V. N. et al. Three-dimensional band structure of layered TiTe2: Photoemission final-state +effects. Physical Review B 74, 195125 (2006). + +38. Krasovskii, E. E. et al. Band mapping in the one-step photoemission theory: Multi-Bloch-wave +structure of final states and interference effects. Physical Review B 75, 045432 (2007). +39. Venturini, F., Minár, J., Braun, J., Ebert, H. & Brookes, N. B. Soft x-ray angle-resolved photoemission +spectroscopy on Ag(001): Band mapping, photon momentum effects, and circular dichroism. +Physical Review B 77, 045126 (2008). +40. Strocov, V. N., Claessen, R., Aryasetiawan, F., Blaha, P. & Nilsson, P. O. Band- and k-dependent +self-energy effects in the unoccupied and occupied quasiparticle band structure of Cu. Physical +Review B 66, 195104 (2002). +41. Mahan, G. D. Theory of Photoemission in Simple Metals. Physical Review B 2, 4334 (1970). +42. Hofmann, P. et al. Unexpected surface sensitivity at high energies in angle-resolved photoemission. +Physical Review B 66, 245422 (2002). +43. Feibelman, P. J. & Eastman, D. E. Photoemission spectroscopy—Correspondence between +quantum theory and experimental phenomenology. Physical Review B 10, 4932 (1974). +44. Capart, G. Band structure calculations of low energy electron diffraction at crystal surfaces. Surface +Science 13, 361 (1969). +45. Pendry, J. B. The application of pseudopotentials to low-energy electron diffraction III: The +simplifying effect of inelastic scattering. Journal of Physics C: Solid State Physics 2, 2283 (1969). +46. Dederichs, P. H. Dynamical Diffraction Theory by Optical Potential Methods. Solid State Physics 27 +(1972) eds. H. Ehrenreich, F. Seitz & D. Turnbull (New York: Academic) p. 136. +47. Barrett, N., Krasovskii, E. E., Themlin, J.-M. & Strocov, V. N. Elastic scattering effects in the electron +mean free path in a graphite overlayer studied by photoelectron spectroscopy and LEED. Physical +Review B 71, 035427 (2005). +48. Krasovskii, E. E. & Schattke, W. Angle-Resolved Photoemission from Surface States. Physical +Review Letters 93, 027601 (2004). +49. Heine, V. On the General Theory of Surface States and Scattering of Electrons in Solids. +Proceedings of the Physical Society 81, 300 (1963). +50. Strocov, V. N. On qualitative analysis of the upper band effects in very-low-energy electron +diffraction and photoemission. Solid State Communications 106, 101 (1998). +51. Tanuma, S., Powell, C. J. & Penn, D. R. Proposed formula for electron inelastic mean free paths +based on calculations for 31 materials. Surface Science 192, L849 (1987). +52. J. Krieger et al. Unpublished (2020) +53. Stock, T. J. Z. et al. Atomic-Scale Patterning of Arsenic in Silicon by Scanning Tunneling +Microscopy. ACS Nano 14, 3316 (2020). +54. P. Constantinou et al. Unpublished (2020) +55. Moser, S. An experimentalist’s guide to the matrix element in angle resolved photoemission. Journal +of Electron Spectroscopy and Related Phenomena 214, 29 (2017). +56. Fedchenko, O. et al. 4D texture of circular dichroism in soft-x-ray photoemission from tungsten. New +Journal of Physics 21, 013017 (2019). +57. Puschnig, P. et al. Reconstruction of Molecular Orbital Densities from Photoemission Data. Science + +326, 702 (2009). +58. Kliuiev, P. et al. Combined orbital tomography study of multi-configurational molecular adsorbate +systems. Nature Communications 10, 5255 (2019). +59. Bradshaw, A. M. & Woodruff, D. P. Molecular orbital tomography for adsorbed molecules: is a +correct description of the final state really unimportant? New Journal of Physics 17, 013033 (2015). +60. Fadley, C. S., Van Hove, M. A., Hussain, Z. & Kaduwela, A. P. Photoelectron diffraction: new +dimensions in space, time, and spin. Journal of Electron Spectroscopy and Related Phenomena 75, +273 (1995). +61. Woodruff, D. Adsorbate structure determination using photoelectron diffraction: Methods and +applications. Surface Science Reports 62, 1 (2007). +62. Fedchenko, O., Winkelmann, A. & Schönhense, G. Structure Analysis Using Time-of-Flight +Momentum Microscopy with Hard X-rays: Status and Prospects. Journal of the Physical Society of +Japan 91, 091006 (2022). +63. Osterwalder, J., Greber, T., Hüfner, S. & Schlapbach, L. X-ray photoelectron diffraction from a +free-electron-metal valence band: Evidence for hole-state localization. Physical Review Letters 64, +2683 (1990). +64. Osterwalder, J., Greber, T., Aebi, P., Fasel, R. & Schlapbach, L. Final-state scattering in +angle-resolved ultraviolet photoemission from copper. Physical Review B 53,10209 (1996). +65. Strocov, V. N. et al. Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, +technical realisation and scientific applications. Journal of Synchrotron Radiation 21, 32 (2014). +66. Strocov, V. N. et al. High-resolution soft X-ray beamline ADRESS at the Swiss Light Source for +resonant inelastic X-ray scattering and angle-resolved photoelectron spectroscopies. Journal of +Synchrotron Radiation 17, 631 (2010). +67. Braun, J. et al. Exploring the XPS limit in soft and hard x-ray angle-resolved photoemission using a +temperature-dependent one-step theory. Physical Review B 88, 205409 (2013). +68. Ebert, H., Ködderitzsch, D. & Minár, J. Calculating condensed matter properties using the +KKR-Green’s function method—recent developments and applications. Reports on Progress in +Physics 74, 096501 (2011). +69. Braun, J., Minár, J. & Ebert, H. Correlation, temperature and disorder: Recent developments in the +one-step description of angle-resolved photoemission. Physics Reports 740, 1 (2018). +70. Sébilleau, D., Tricot S. & Koide, A. Unpublished (2022) +Acknowledgements +V.N.S. thanks E.E. Krasovskii for illuminating discussions and critical reading of the manuscript, and J. H. +Dil for valuable exchange on physics of XPD. J.M. is grateful to D. Sébilleau, S. Tricot and A. Koide for +sharing their scattering-amplitude calculations. The authors thank N.J. Curson and S.R. Schofield for +giving access to Si samples prepared at University College London. J.M. and L.N. acknowledge the +support of the Czech Ministry of Education, Youth and Sports via the grant CEDAMNF +CZ.02.1.01/0.0/0.0/15_003/0000358 and the support from GACR Project No. 2018725S. L.L.L. +acknowledges the financial support from the Ministry of Science and Higher Education of the Russian +Federation, grant #075-11-2021-086. T.J.Z.S. acknowledges the financial support of the Engineering and + +Physical Sciences Research Council (grants nos. EP/R034540/1, EP/W000520/1), and Innovate UK +(grant no. 75574). +Author contributions +V.N.S. and J.M. conceived the SX-ARPES experiment at the Swiss Light Source. V.N.S., L.L.L., F.A. and +L.N. performed the experiment supported by T.S. T.J.Z.S. fabricated the thin-film Si samples. V.N.S. +processed and interpreted the data, and performed computational simulation of the final states supported +by P.C. J.M. performed the first-principles ARPES calculations. V.N.S. wrote the manuscript with +contributions from J.M., L.L.L., P.C., T.J.Z.S. and J.O. All authors discussed the results, +interpretations, and scientific concepts. +Competing interests +The authors declare no competing interests. + +Supplemental Material: KKR calculations with +multiple-scattering final states +Computational scheme +In the first step of our theoretical investigations, we performed self-consistent electronic structure +calculations within the ab-initio framework of the spin-density functional theory in order to generate the +self-consistent-field (SCF) potential for further photoemission calculations. The LDA potential of Vosko et +al. was used1. The electronic structure of semi-infinite crystal was calculated within the relativistic +multiple scattering approach using the Green's function Korringa-Kohn-Rostoker (KKR) formalism in the +tight binding mode2. The experimental lattice constant (a = 4.09 Å) was used. In order to achieve precise +description of the most subtle details of the SCF potential, important for photoemission at high excitation +energies, the multipole expansion of the Green’s function employed an unusually large +angular-momentum cutoff lmax of 5. In addition, a large number of k-points (36x36x36) in the first surface +BZ was used. The self-consistent calculations have been performed in two modi, within the so-called +atomic sphere approximation (ASA) and in the full potential (FP) mode. +The obtained SCF potential was used for the photoemission calculations within the one-step model. The +final states (the time-reversed LEED state) were treated using the so-called layer KKR technique3, +allowing accurate description of these states in a wide hv range starting from 6 eV up to several keV. To +ensure the convergence of the multiple scattering between the layers, our calculations used a +plane-wave basis where the number of the surface reciprocal lattice vectors g was increased to 147 +instead of the default value 372. Another important ingredient of the multiple-scattering calculations is an +accurate description of the kinematic and dynamic effects in both initial and final states. For the latter, the +dynamic effects are taken into account via the X-matrix4 which represents the energy-dependent multiple +scattering within a single layer. Whereas in VUV-ARPES the kinematic and dynamic effects are +comparable, in the soft- and hard-X-ray regime the dynamic effects weaken, whereby the X-matrix +approaches zero, leading to the so-called single-site scattering approximation. Another important +parameter in the description of multiple scattering is connected with the expansion of all physical +quantities in terms of angular momentum l, i.e. using the Bauer’s identity to represent plane waves +(scattering between the layers) and spherical waves (inside the layer). These expansions involve a +summation over l that must be truncated at a certain value lmax. In this context, the increase of lmax should +be viewed rather as an extension of the basis set for accurate description of the multiple scattering than +physically meaningful l-channels in the scattering process. A simple assessment of lmax can be obtained +from the radial Schrödinger equation where, in order to scatter on the spherical potential, the electron +must first overcome the centrifugal barrier l(l+1)/a2 (a is the atomic radius). This implies only the partial +waves, whose l satisfies the inequality k2 > l(l+1)/a2, should be included into the l-expansion. The higher +Ek, the larger lmax needs to be used (for the detailed explanation see Ref. 5). For Ek in the range +300-1300eV, considered here, lmax falls between 4 and 5. The calculations have been performed for a +finite temperature of 20K leading to an additional final-state k-broadening, increasing with hv6. + +Effect of various approximations for the multiple-scattering process +We have made an effort to elaborate our ARPES calculations towards their quantitative agreement with +the experiment in a few successive steps: +– Fig. S1 shows the results obtained with multiple-scattering final states, as opposed to the FE final +states used for the calculations in Figs. 1 and 2 in the main text, under successive refinements of the +computational approximations: +– The results in Fig. S1(a) were obtained within the ASA and lmax = 3. Due to the non-FE effects +described by the multiple-scattering final states, they already show spectral structures due to the MBFSs +(such as where marked by magenta arrows) although mostly on the low-energy end of our hv range and +not exactly in the same k-space regions compared to the experiment; +– The inclusion of warping of the potential in the interstitial and surface regions within the FP scheme7, +Fig. S1(b), does not result in any significant improvement in our case of Ag. Nevertheless, we anticipate +that the accurate FP will be crucial for more open crystal structures, covalent materials, van-der-Waals +materials, etc. where the potential modulations are sharper7. As we have seen in the present work, their +accurate description should be particularly important at high Ek where the final states are highly sensitive +to the high-frequency modulations of V(r) and thus to the accurate representation of its real-space +variations; +– Another step, the inclusion of the full X-matrix compared to the single-site approximation, presented in +Fig. S1(c), considerably improves the description of the relative intensity variations in the hv interval +between 400 and 500 eV (magenta arrow, for example) but does not notably affect the spectral intensity +at higher energies. This observation can be understood from analysis of scattering amplitude fk(θ), giving +more insight into the scattering process. The calculations of fk(θ) for Ag by Sébilleau et al.8, reproduced +in Fig. S2, demonstrate that for Ek above ~400 eV it is strongly dominated by forward scattering. In +practice, this means that for these energies the electrons scatter essentially along the rows of atoms, +justifying the single-site approximation for the multiple scattering; +– Finally, at the last step of our computational refinement presented in the Fig. S1(d), we increased lmax +from 3 to 5. As expected, not only has this returned a vivid pattern of the MBFS-induced replica bands +and excessive spectral broadening at low Ek (such as where marked by magenta and yellow arrows, +respectively) but also pushed these effects to yet higher hv up to 700 eV (magenta arrow). Further +increase of lmax would inflate the computational time beyond presently realistic. +Although these successive refinements of the computational scheme do move towards a better +description of the experiment, the achieved agreement with the experimental results can only be +considered as qualitative. We conjecture that the remnant deviation may trace back to quite small +sensitivity of the total energy to high-frequency components of the crystal potential. Therefore, the +total-energy minimization used to generate the self-consistent potential in the DFT calculations may not +ensure sufficient accuracy of its high-frequency components which critically affect the hybridization and +thus non-FE effects in the final states at high energies. The accuracy of the final states used in the +ARPES calculations can in principle be verified independently from the initial states by calculating the +LEED spectra and their fitting to the experiment using the methodology previously developed for very low +energies (see Refs. 9–11 and the references therein). In any case, including the subtle details of V(r) +within the FP approach and the use of sufficiently large lmax give the best possible single-particle +description of the photoemission final state. + +Fig. S1. One-step ARPES calculations as in Fig. 1(d) but using multiple-scattering final states under +successive refinements of their treatment: (a) standard spherical-wave expansion and single-site +scattering approximation; (b) adding full potential; (c) the full X-matrix beyond the single-site scattering; +(d) increasing the angular momentum expansion to lmax = 5. The calculations reproduce the multiple +spectral peaks (magenta arrows) and the excessive spectral broadening (yellow) induced by the +MBFSs. +Fig. S2. Scattering amplitude fk(θ) for Ag as a function of Ek (left panels) and the total forward and +backward scattering contributions (right panel). + +hv (eV) +(a) +(b) +(c) +(d) +1200 +1000 +800 +600 +400 +0Ag Scattering Factor @ E = 50.00 eV +Ag Scattering Factor @ E = 500.00 eV +90* +90° +[0)] +135° +(9(e) ++SET +((e) +3([6)) +(e))C +180° +180° +Ag Forward and Backward scattering amplitudes +225* +225* +315 +Forward +270* +270* +Backward +Ag Scattering Factor @ E = 100.00 eV +Ag Scattering Factor @ E = 700.00 eV +90° +135* +[0]] +g((e) +135* +s((e) +([(0) +3(6)) +180° +180* +2 +225* +225* +315 +270* +270* +200 +400 +600 +800 +1000 +Ag Scattering Factor @ E = 300.00 eV +Ag Scattering Factor @ E = 900.00 eV +90° +Kinetic Energy [eV] +135* +[0]] +[6]] +135* +3(R0) +3((6)) +180* +225 +225* +/315 +270* +270*References +1. S. H. Vosko, L. Wilk, and M. Nusair, Accurate Spin-Dependent Electron Liquid Correlation Energies for +Local Spin Density Calculations: A Critical Analysis, Canadian J. Phys. 58 (1980) 1200 +2. H. Ebert, D. Ködderitzsch, and J. Minár, Calculating Condensed Matter Properties Using the +KKR-Green’s Function Method – Recent Developments and Applications, Rep. Prog. Phys. 74 (2011) +096501. +3. J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, Layer Korringa-Kohn-Rostoker +Technique for Surface and Interface Electronic Properties, Phys. Rev. B 40 (1989) 12164 +4. J. Braun, J. Minár, and H. Ebert, Correlation, Temperature and Disorder: Recent Developments in the +One-Step Description of Angle-Resolved Photoemission, Phys. Rep. 740 (2018) 1. +5. Multiple Scattering Theory for Spectroscopies, eds. D. Sébilleau, K. Hatada and H. Ebert. Springer +Proc. Phys. 204 (2018). +6. J. Braun, The theory of angle-resolved ultraviolet photoemission and its applications to ordered +materials. Rep. Prog. Phys. 59 (1996) 1267. +7. J. Braun, J. Minár, S. Mankovsky, V. N. Strocov, N. B. Brookes, L. Plucinski, C. M. Schneider, C. S. +Fadley, and H. Ebert, Exploring the XPS Limit in Soft and Hard X-Ray Angle-Resolved Photoemission +Using a Temperature-Dependent One-Step Theory, Phys. Rev. B 88 (2013) 205409 +8. D. Sébilleau, S. Tricot, and A. Koide, unpublished (2022). +9. V. N. Strocov, H. Starnberg & P. O. Nilsson. Excited-state bands of Cu determined by VLEED band +fitting & their implications for photoemission, Phys. Rev. B 56 (1997) 1717. +10. V. N. Strocov, R. Claessen, G. Nicolay, S Hüfner, A Kimura, A. Harasawa, S. Shin, A. Kakizaki, P.O. +Nilsson, H.I. Starnberg & P. Blaha. Three-dimensional band mapping by angle-dependent +very-low-energy electron diffraction and photoemission: Methodology and application to Cu. Phys. +Rev. B 63 (2001) 20510. +11. V. N. Strocov, E.E. Krasovskii, W. Schattke, N. Barrett, H. Berger, D. Schrupp & R. Claessen. +Three-dimensional band structure of layered TiTe2: Photoemission final-state effects. Phys. Rev. B 74 +(2006) 195125. + diff --git a/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/load_file.txt b/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee00c4fee27ecf7d553e93086524412cbbe56ad5 --- /dev/null +++ b/3NAyT4oBgHgl3EQfP_YA/content/tmp_files/load_file.txt @@ -0,0 +1,1019 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf,len=1018 +page_content='Are high-energy photoemission final states free-electron-like?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov,1 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lev,1,2 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Alarab,1 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Constantinou,1 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schmitt,1 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Stock,3 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nicolaï,4 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Očenášek4 & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Minár4 1Swiss Light Source,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Paul Scherrer Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' CH-5232 Villigen-PSI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Switzerland 2Moscow Institute of Physics and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dolgoprudny,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Moscow Region 141701,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Russia 3London Centre for Nanotechnology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' University College London,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' London WC1H 0AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' UK 4University of West Bohemia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' New Technologies Research Centre,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 301 00 Plzeň,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Czech Republic Abstract Three-dimensional (3D) electronic band structure is fundamental for understanding a vast diversity of physical phenomena in solid-state systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' including topological phases,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' interlayer interactions in van der Waals materials,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' dimensionality-driven phase transitions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Interpretation of ARPES data in terms of 3D electron dispersions is commonly based on the free-electron approximation for the photoemission final states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Our soft-X-ray ARPES data on Ag metal reveals, however, that even at high excitation energies the final states can be a way more complex, incorporating several Bloch waves with different out-of-plane momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Such multiband final states manifest themselves as a complex structure and excessive broadening of the spectral peaks from 3D electron states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We analyse the origins of this phenomenon, and trace it to other materials such as Si and GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Our findings are essential for accurate determination of the 3D band structure over a wide range of materials and excitation energies in the ARPES experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Introduction Knowledge of electronic band structure resolved in three-dimensional (3D) electron momentum (k) is fundamental for understanding a vast diversity of physical phenomena in crystalline solid-state systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Recently, the interest in 3D band structure has been boosted due to its essential role in topological phases such as Weyl semimetals characterised by 3D cones of linear electron dispersion (see, for example, refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 1,2) as well as their generalisation to high-fold chiral fermions3,4 and high-dimensional degeneracies such as the Hopf links and nodal lines, chains and knots in 3D k-space (see the reviews5–8 and the references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Less straightforward but equally important implications of the 3D band structure include, for example, interlayer interaction and 3D charge-density waves in van der Waals materials9–11, formation of quantum-well states at interfaces and heterostructures12–16 as well as minibands in semiconductor superlattices17, k-dependent electron-phonon interactions18, dimensionality-driven phase transitions19,20, 3D quantum Hall effect21, and many more properties of solid-state systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' High-energy angle-resolved photoelectron spectroscopy (ARPES), operating in the soft- and hard-X-ray photon energy (hv) regions, has pushed the k-resolving spectroscopic abilities of this technique from the conventional surface science to the intrinsic electronic structure deep in the bulk, buried interfaces and heterostructures, and diluted impurity systems (see the recent reviews22–26 and the references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The main advantage of high photoelectron energies is an increase of the photoelectron mean free path (λPE) to a few nanometres and more27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Crucial for the experimental determination of 3D band structure, the increase of λPE translates, via the Heisenberg uncertainty principle, to sharpening of the intrinsic resolution of the ARPES experiment in the out-of-plane momentum (kz) which is defined as Δkz = λPE 1 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The sharp resolution in kz underlies the applications of high-energy ARPES for accurate determination of the electronic band structure resolved in 3D k-space as illustrated by many of the works cited above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In contrast to the in-plane momentum k// = (kx,ky), conserved in the photoemission process because of the in-plane periodicity of the system, the kz component is distorted upon the photoelectron escape from the crystal to vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' It can however be reconstructed based on its conservation in the photoexcitation process in the bulk (corrected for the photon momentum phv) if the final-state kz is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Conventionally, the final-sate dispersion is modelled within the free-electron (FE) approximation, where kz is found as , with Ek and K// being the photoelectron kinetic energy and in-plane 𝑘𝑧 = 2𝑚 ħ 𝐸𝑘 − ħ 2 2𝑚 𝐾// 2 − 𝑉0 momentum, respectively, m the free-electron mass, and V0 the inner potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Somewhat stretching this formula, an energy dependence of the dynamic exchange-correlation29,30 can be accommodated via an energy-dependent V0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Importantly, the FE approximation implies that the final-state wavefunction is a plane wave, where the finite λPE is described by an imaginary part of kz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' It has since long been realised that at low excitation energies used in the conventional VUV-ARPES the FE approximation may in many cases fail even for metals31–34 and all the more for semiconductors35 and more complex materials, for example, transition metal dichalcogenides36–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For high-energy ARPES, however, the relevance of this approximation is commonly taken for granted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Being quintessential for 3D band mapping with high-energy ARPES, this assumption is based on a physically appealing argument that at high excitation energies Ek of photoelectrons much exceeds modulations of the crystal potential V(r), and they can be considered as free particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Here, we analyse soft-X-ray ARPES data on Ag the metal and demonstrate that even at high excitation energies the complexity of the final states can go far beyond the FE picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In particular, they can be composed of multiple Bloch waves having different kzs which manifest themselves as complex structure of the spectral peaks or their excessive broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This analysis extends to GaN and Si the semiconductors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We theoretically demonstrate the origin of these non-trivial effects as resulting from hybridization of plane waves on the crystal potential, and elucidate how they should be taken into account for accurate determination of 3D valence-band dispersions in the high-energy ARPES experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Results Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 1 presents the Brillouin zone (BZ) of the fcc Ag (a) and the experimental out-of-plane cross-section of the Fermi surface (FS) in the ГXW symmetry plane measured under variation of hv (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The indicated kzs, running through a sequence of the Г and X points, were rendered from the hv values assuming FE final states with V0 = 10 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In-plane cross-sections measured at two hv values, bringing kz to the Г and X points, are presented in the two panels (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In general, the experimental out-of-plane FS follows a pattern of repeating rounded contours characteristic of the states near the Fermi level (EF) formed by the sp-band of Ag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This pattern is reproduced by our one-step ARPES calculations (e) where FE-like final states were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surprisingly, however, a closer look at the experimental FS reveals significant deviations: (1) Multiple FS contours, offset in kz, can be resolved in some (E,k) regions such as those marked by magenta arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The corresponding multiple dispersions coming from the sp-band are apparent, for example, in the ARPES image measured at hv = 997 eV (d, top) and the corresponding momentum-distribution curve as a function of kx at EF (kx-MDC, yellow line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This multiple-dispersion pattern contrasts to the clean dispersions at hv = 894 eV (d, bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As we discuss in more detail below, such replica spectral structures demonstrate that the final states incorporate multiple bands with different kzs – hereinafter called multiband final states (MBFSs) – which is a phenomenon beyond the conventional picture of FE-like final states implying one single band with one kz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In our case the separation of the kzs in these MBFSs is larger than the intrinsic Δkz (according to the λPE values from the TPP-2M formula, varying from ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='15 Å-1 at 300 eV to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='056 Å-1 at 1300 eV);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (2) The second type of deviations from the FE final states, seen in the out-of-plane FS (b), is a notable spectral intensity spreading into the X points where the sp-band is unoccupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Furthermore, broadening of the FS contours in kz irregularly varies through k-space, and in some (E,k) regions (such as those marked by yellow arrows) can be excessively large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These two effects are also caused by the MBFSs, but in this case the kzs are separated less than Δkz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We note that in the extremes of the E(kz) dispersion (dkx/dkz=0 in the out-of-plane FS) the MBFSs have only a second-order effect on the ARPES structure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' however, even in this situation a large enough kz separation within the MBFSs can cause multiple FS contours, as seen in the in-plane FS map measured at hv = 712 eV (c, magenta arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Obviously, the MBFS effects are not reproduced by the ARPES calculations (e) employing FE final states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Although presently on a qualitative level, these effects are reproduced by our one-step ARPES calculations (Supplemental Material) where the final states are treated within the multiple-scattering formalism, naturally incorporating the non-FE effects including the MBFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' FS cross-sections for Ag(100): Theoretical FS (a), its experimental out-of-plane cross-section (b), and two in-plane cross-sections (c) measured at the indicated hv values, bringing kz to the Г and X points (lower and upper panels, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Replicas and broadening of the FS contours in certain (E,k) regions (such as those marked by magenta and yellow arrows, respectively) manifest MBFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These effects are particularly clear in the ARPES image and kx-MDC at hv = 997 eV (d, top) in contrast to those at hv = 894 eV (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These effects are beyond the one-step ARPES calculations with FE-like final states (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2, the theoretical E(k) along the ГX direction (a) is compared with the experimental out-of-plane band dispersions E(kz) at kx=0 (b) and the in-plane E(k//) images (c) measured at kz running through the successive Г points (energies as binding energies Eb relative to EF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Again, the gross structures of the experimental E(kz) follow the expected periodic pattern with the sp-band crossing EF as reproduced by our one-step ARPES calculations in (e) with the FE-like final states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We see, however, replicas and anomalous broadening of the sp-band (such as marked by magenta arrows) as well as significant spectral intensity around the X point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These anomalies appear most clearly in the zoom-in of the sp-band and the kz-MDC at EF (d, yellow line) where we observe a complex multi-peak structure of the spectral intensity around the X point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Again, these effects are manifestations of the MBFSs, with the ARPES dispersions originating from the individual final-state bands marked by the magenta arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Again, they are absent in the ARPES calculations employing FE final states (e) but are qualitatively reproduced upon inclusion of multiple-scattering final states (Supplemental Material).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The MBFS effects could not be observed in the first soft-X-ray study on Ag(100) focused on the 3d states39 because the smaller kz dispersion of these states compared to the sp ones could not provide sufficient separation of the spectral peaks from the different bands in the MBFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We note in passing that the experimental 3d states appear in ~1 eV below the LDA-DFT energies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' such an energy shift, already noticed for Cu, is a pronounced self-energy effect due to non-local exchange interaction of the 3d electrons strongly localized in the core region40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' b (d) a 1200 997 eV 800 894eV 600 572 eV 400Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band dispersions along the ГX direction for Ag(100): Theoretical E(k) (a) compared with the experimental out-of-plane ARPES dispersions at kx=0 (b, the spectral intensity represented in logarithmic scale) and (c) in-plane dispersions for the indicated hv values, bringing kz to the successive Г point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' A zoom-in of the sp-band (d) shows its replicas and excessive broadening (such as marked by magenta arrows) most evident in the kz-MDC at EF (yellow line) as multiple and broadened spectral peaks, manifesting the MBFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These effects are beyond the one-step calculations of the ARPES intensity and kz-MDC with FE-like final states (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Discussion Origin of the MBFSs By definition, a FE-like final state in the crystal is one single plane wave ei(k+G)r which matches the outgoing photoelectron plane wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" In the whole multitude of bands, formally available under Ek and K// conservation, this plane wave corresponds to one single band that we will refer to as primary, relaying Mahan's primary photoemission cones 41." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' All other bands in the multitude give strictly zero contribution to the photocurrent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" We will be calling them secondary, relaying Mahan's secondary cones." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The MBFS effects, observed in our ARPES data, indicate that the corresponding final states may include, for given Ek and K//, several bands with different kzs giving comparable contributions to the ARPES intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These effects obviously fall beyond the FE-like picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As the first-principles calculations can not yet exhaustively describe our experimental results, we will analyse the MBFS effects based on insightful model calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The non-FE effects in the final states, in particular their multiband composition, is certainly a phenomenon not new for low-energy ARPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' They have been studied experimentally and theoretically for 3D bulk band dispersions in various materials including Cu31,32, Mg34 and even Al the paradigm FE metal14,42, semiconductors35, various transition metal dichalcogenides36–38 as well as surface states, in particular for the Al(100) and (111) surfaces33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' However, it is intriguing to observe such effects in our soft-X-ray energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Why do they appear in spite of the fact that the photoelectron Ek is overwhelmingly large compared to the V(r) modulations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (b) (d) (e) 894eV 1268 eV 310eV 572eVWe will now build a physically appealing picture of the non-FE effects in the photoemission final states using their standard treatment as the time-reversed LEED states43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' They are superpositions of damped Bloch waves фk(r) with complex kz, whose imaginary part Imkz represents the (1) inelastic electron scattering, described by a constant optical potential Vi (imaginary part of the self-energy), and (2) elastic scattering off the crystal potential44–47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The amplitudes Ak of these фk(r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' determining their contribution to the total ARPES signal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' were determined within the matching approach of the dynamic theory of LEED17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='38,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='44,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='45,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='48,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='49 where the electron wavefunction in the vacuum half-space (superposition of the incident plane wave eiK0r and all diffracted ones ei(K+g)r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' g being the surface reciprocal vectors) is matched,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' at the crystal surface,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' to that in the crystal half-space (superposition of фk(r) satisfying the surface-parallel momentum conservation k//=K//+g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The underlying complex bandstructure calculations utilised the empirical-pseudopotential scheme, where фk(r) are formed by hybridization of plane waves ei(k+G)r, G being 3D reciprocal-lattice vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" The Fourier components VΔK = of the local pseudopotential V(r) were adjustable parameters." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We start from the ideal FE case, where V(r) is constant and equal to V0 (so-called empty lattice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The corresponding calculations are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3 (a) as the E(Rekz) bands (the corresponding E(Imkz) bands are not shown here for brevity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Due to the absence of hybridization between the plane waves in the empty-lattice case, each фk(r) contains one single plane wave corresponding to a certain G vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Typical of high energies, we observe a dense multitude of bands brought in by an immense number of all G vectors falling into our energy region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Starting from the ultimate V0 = 0 case, when the vacuum half-space is identical to the crystal one, it is obvious that only one band will couple to the photoelectron plane wave in vacuum eiKr and thus be effective in the ARPES final state, specifically, only the primary band whose plane wave – in the context of LEED often called conducting plane wave – has k+G equal to the photoelectron K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" The whole multitude of the secondary bands, whose plane wave's k+G is different from K, will give no contribution to the photocurrent." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In our more general case V(r) = V0, the kz component of the photoelectron distorts upon its escape to vacuum, and the above momentum-equality condition to identify the conducting plane wave should be cast in terms of the in-plane components as k// + G// = K//.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In a formal language, these intuitive considerations can be expressed through the partial contributions of each фk(r) into the total current absorbed in the sample in the LEED process, which are the so-called partial absorbed currents Tk ∝ Vi⋅ , with the integration extending from the 0 ∞ ∫ 𝐴𝑘ϕ𝑘(𝑧) | | 2𝑑𝑧 crystal surface into its depth31,32,37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Importantly in the ARPES context, the Tk values multiplied by the photoemission matrix elements define the partial photocurrents emanating from the individual фk(r) in the MBFS31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3(a) the calculated Tk are marked in blue colorscale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As expected for the empty-lattice case, Tk is equal to 1 for the primary (in the LEED context often called conducting) band and strictly zero for all other ones, realising the ideal FE final state containing one single plane wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" In Mahan's language, only the primary-cone photoemission is active in our ideal FE case." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We will now introduce spatial modulations of V(r) as expressed by VΔK for non-zero ΔK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The plane waves start to hybridise through the VΔK matrix elements, and each фk(r) becomes a superposition of a few plane waves as фk(r) = ΣGCGei(k+G)r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In this case not only one but several фk(r) can acquire a certain admixture of the k// + G// = K// conducting plane wave – in the formal language, their Tk becomes non-zero – and give a certain contribution to the total photocurrent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Our model calculations for this case are sketched in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The ARPES final state appears multiband in a sense that it consists of several фk(r) with different kzs (typically alongside the primary band) which give comparable contributions to the total ARPES signal as quantified by the corresponding Tk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" In Mahan's language, the qualitative distinction between the primary- and secondary-cone photoemission dissolves." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Correspondingly, the ARPES spectra will show up several peaks corresponding to different kz or, if the separation of these kzs is smaller than the intrinsic Δkz, excessive broadening of the spectral peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This is exactly what we have just seen in our ARPES data on Ag(100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We note in passing that on the qualitative level the bands contributing to the photocurrent can be easily identified based on the Fourier expansion of their фk(r) which should have a substantial weight of the k// + G// = K// conducting plane wave50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Whereas for the sake of physical insight we have intentionally simplified the above picture, the exact treatment of the MBFSs based on the matching approach of LEED has been developed in a series of previous works albeit limited to relatively low final-state energies31,34,37,38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Finally, we note that the MBFS phenomenon can also be understood within the simplified three-step model of photoemission, where the whole quantum-mechanical photoemission process is splitted into the photoexcitation of a photoelectron, its transport out of the crystal, and escape to vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In this framework, the MBFSs can be viewed as resulting from multiple scattering of photoelectrons on their way out of the crystal that creates multiple Bloch-wave modes of the scattered wavefield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band structure of the final-state Bloch waves E(Rekz) in a model fcc crystal along the ГX direction (a) in the empty-lattice case V(r) = V0 and (b) with a more realistic spatially modulated pseudopotential, sketched in the insert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The dense multitude of bands is formed by an immense number of G vectors falling into our high-energy region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='The contributions of each band into the total photocurrent are quantified by Tk (blue colorscale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Whereas in the first case the photocurrent emanates from one single FE band (marked with the corresponding G vectors), in the second case it may distribute over a few bands alongside the FE dispersion, which form a MBFS incorporating a few kzs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Whereas the effects of MBFSs have already been established at low excitation energies, their survival in high-energy ARPES might seem puzzling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In a naive way of thinking, photoelectrons with energies much higher than the modulations of V(r) should not feel them, recovering the FE case with one single фk(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' However, VΔK as the strength of hybridization between two plane waves depends, somewhat counter-intuitively, not on energy but rather on ΔK between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As sketched in the insert in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3 (b), VΔK typically has its maximal negative value at ΔK = 0 (which is the V0), and with increase of ΔK sharply rises and then asymptotically vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Importantly, however high the energy is, the multitude of the plane waves always contains pairs of those whose ΔK is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The corresponding bands can be identified by close dispersions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For such pairs VΔK is large, giving rise to their strong hybridization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Importantly, all bands hybridising with the k// + G// = K// plane wave will receive non-zero Tk and thus 1200 (a) G00-6 (b) VAK 1100 △K 1000 G005 900 800 k 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5 E 700 G004 600 500 400 Rekz Rekzcontribute to the total photocurrent, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This forms the MBFSs that should survive even at high energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Effect of MBFSs on the spectral structure We will now follow in more detail how the MBFSs affect the ARPES spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As an example, we will analyse the experimental kz-MDC from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2(d) in the region of the X point at hv ~ 1100 eV, reproduced in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 4 (with the linear background subtracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Within the FE approximation, we might expect to observe here two Lorentzian peaks, placed symmetrically around the X point and broadened by the same intrinsic Δkz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' However, the kz-MDC shows three distinct peaks A-C, with the peak B coming from a final-state band falling beyond the FE approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Moreover, Lorentzian fitting of the peaks finds that whereas the peak C has a relatively small width of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='11 Å-1, the widths of the peaks A and B are more than twice larger, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='30 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='32 Å-1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The picture of MBFSs neatly explains this observation, suggesting that whereas the peak C is formed by a final state having one dominant kz contribution, and the peaks A and B by final states incorporating a multitude of kzs separated less than Δkz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Whereas it is generally believed that the intrinsic broadening of the ARPES peaks in kz is determined exclusively by finite λPE the photoelectron mean free path, our example demonstrates that the multiband final-state composition may not only create additional spectral peaks but also be an important factor of their broadening additional to λPE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' kz-MDC at EF from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2(d) in the hv region around 1100 eV (vicinity of the X point) decomposed in three Lorentzians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The presence of the peak B and the larger broadening of the peaks A and B compared to C are caused by MBFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Intriguingly, however, we note that even the narrowest peak C is almost twice broader than Δkz ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='065 Å-1 expected from λPE ~ 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5 Å suggested by the TPP-2M formula 51 well-established in XPS and Auger electron spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' One explanation might be that already the peak C would incorporate multiple final-state bands with smaller kz separation compared to other two peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another explanation would trace back to quasielastic electron-electron or electron-phonon scattering, which would increase with energy owing to the increase of the phase-space volume available for such scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Altering k of photoelectrons, it should destroy the coherence of photoelectrons and thus reduce λPE as reflected in the observed Δkz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' At the same time, the quasielastic scattering should have only a little effect on attenuation of the k-integrated signal of the core-level or intrinsically incoherent Auger electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In other words, the effective λPE in ARPES should be smaller than that in XPS/Auger spectroscopy, described by the TPP-2M and related formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Such intriguing fundamental physics certainly deserves further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 15 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5 16 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5 17 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5 18 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='5MBFS phenomena through various materials The phenomenon of MBFSs surviving at high excitation energies is certainly not restricted to Ag only and, strengthening with the strength of V(r) modulations, should be fairly general over various materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Even for Al the paradigm FE metal, astonishingly, such MBFSs can be detected at least up to excitation energies of a few hundreds of eV14,42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Quite commonly the MBFS effects at high energies are observed in van-der-Waals materials such as MoTe2 52, which should be connected with a large modulation of V(r) across the van-der-Waals gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another vivid example of the MBFS effects is the soft-X-ray ARPES data for GaN presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 5, compiled from the previously published results on AlN/GaN(1000) heterostructures13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The panel (a) shows the ARPES spectral structure plot expected from the DFT valence bands and FE final states with V0 = 5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' With the non-symmorphic space group of bulk GaN, the ARPES dispersions allowed by the dipole selection rules (though in our case somewhat relaxed due to the band bending in GaN) are marked bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The panels (b,c) present the experimental out-of-plane ARPES dispersions measured at kx in two formally equivalent points of the surface BZ, 0 in the first and 1 in the second zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As Г Г Г expected because of weaker electron screening of the atomic potential and thus sharper modulations of V(r) in the covalent GaN compared to the metallic Ag, the deviations of experimental dispersions from the predictions of the FE approximation are much stronger than for Ag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' One can clearly see the MBFSs where the individual bands (marked by arrows at their top) are separated in kz more than the intrinsic Δkz broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In the multitude of the experimental ARPES dispersions, one can identify the one which can be associated with the primary-cone photoemission (bold arrows) although in the 0 data this band Г cannot be traced below 1000 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Remarkably, for the same initial-state E(k) the ARPES dispersions measured at the 0 and 1 points appear completely different, identifying different final-state bands Г Г selected from the continuum of all unoccupied states available for given final-state energy and K//.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These bands are identified by their leading plane-wave component to have k// + G// = K//, where K// of the photoelectron changes between the surface BZs32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Out-of-plane ARPES dispersions for GaN(1000): (a) Expected from the DFT valence bands and FE final states with V0 = 5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' With the non-symmorphic space group of bulk GaN, the dispersions allowed by the dipole selection rules are shown bold;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (b,c) Measured at kx = 0 projecting onto the Г0 and Г1 points over two BZs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The experiment clearly resolves individual final-state bands (marked by arrows) whose separation in kz is larger than the intrinsic Δkz broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (b) (a (c) A A 10The high-energy final states in Si are a counter-example though.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 6 presents soft-X-ray ARPES data on a few-nm thick layer of Si(100) n-doped with As53 as the out-of-plane band dispersions (b) and iso-EB contours (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The panel (a) shows the ARPES spectral structure plot expected from the DFT-GGA calculated valence bands and FE final states with V0 = 10 eV, with the bold lines indicating the dispersions allowed by the selection rules (for in-depth discussion see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 54).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Because of the covalent character of Si, one might again expect that the non-FE effects here would be comparable to those for GaN and in any case stronger than for the metallic Ag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Contrary to such expectations, however, the experimental data in (b,c) does not show any clear signatures of the MBFSs in Si in the shown (Ek,k) region, although at low excitation energies they are profound35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' At the moment we can not decipher any simple arguments that would relate the strength of the non-FE effects in the high-energy electron states to any obvious electronic-structure parameters of various materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Out-of-plane ARPES data for Si(100): (a) ARPES dispersions expected from the DFT valence bands and FE final states with V0 = 10 eV, with dispersions allowed by the selection rules shown bold;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (b) Experimental band dispersions and (c) iso-EB contours in 2 eV below the valence-band maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' No clear signatures of the MBFSs can be identified in these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Non-FE effects beyond ARPES The non-FE effects in high-energy electron states such as MBFS manifest themselves not only in the ARPES dispersions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another manifestation will be the circular dichroism in the angular distribution of photoelectrons (CDAD) that necessitates that the final-state wavefunctions deviate from the free-electron plane waves55,56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The CDAD has indeed been observed already in the early soft-X-ray ARPES study on Ag(100)39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another example is the orbital tomography of adsorbed molecules (see, for example, Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 57–59) which takes advantage of the Fourier relation between the angle distribution of photoelectrons and electron density of the valence electron orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The non-FE effects introduce additional plane-wave components in the final states, calling for refinement of the straightforward Fourier-transform processing of the experimental data59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Beyond ARPES, the very fact of electron diffraction at crystalline surfaces identifies non-FE effects in the electron states in the crystal, because otherwise the incident electrons would upon entering the crystal follow the same FE wavefunction and thus would not reflect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The Reflection High-Energy Electron Diffraction (RHEED) evidences that the non-FE effects survive even in the energy range of a few tens of keV, when ΔK between the incident and diffracted plane waves is small (a) (b)and thus the corresponding VΔK large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These considerations suggest that the MBFSs should survive even in hard-X-ray ARPES, waiting for a direct experimental observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Finally, we should point out that the coherent photoemission process underlying the ARPES experiment discussed above (as well as the orbital tomography) is fundamentally different to the essentially incoherent process of X-ray photoelectron diffraction (XPD) (see, for example, the reviews60–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In the first case, all photoelectron emitters (atoms) throughout the crystal surface region within the depth λPE are coherent – or entangled, in the modern quantum mechanics discourse – and emit a coherent photoelectron wavefield characterised by a well-defined k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The resulting ARPES intensity as a function of Ek and θ bears sharp structures reflecting, through the momentum conservation, the k-resolved band structure of the valence states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In the XPD, other way around, the coherence between the emitters throughout the surface region is lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This takes place, for example, for isolated impurity atoms or adsorbed molecules, localised core levels, where the initial-state wavefunctions at different atoms are decoupled from each other, or when the coherence of photoelectrons is broken by thermal or defect scattering, or when the signal from certain valence-band states, like d-states, is integrated in energy63,64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The result is that each photoelectron emitter creates scattered waves within a sphere of the radius λPE, which interfere with each other incoherently with the waves emanating from another emitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Typical of diffraction with a few interfering rays, the resulting XPD intensity distribution as a function of Ek and θ is fairly smooth, and reflects the local atomic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' With Ek increasing into the hard-X-ray energy range, λPE and thereby the number of coherently scattered waves increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This forms sharp Kikuchi-like structures in the XPD angular distribution, reflecting the long-range atomic structure62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In any case, the XPD stays incoherent between the emitters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This fundamental difference between the coherent photoemission and incoherent XPD processes is stressed, for example, by the fact that in the first case the photoelectron angular distribution follows pph, shifting with hv, and in the second case it is insensitive to pph 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Conclusion Our analysis of extensive soft-X-ray ARPES data on the Ag metal has demonstrated that even at high excitation energies the photoemission final states may, intriguingly, in some energy and k-space regions feature pronounced multiband composition beyond the conventional FE approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The corresponding Bloch waves have different kz momenta, typically alongside the FE dispersion, and give comparable contribution to the ARPES spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Using empirical-pseudopotential simulation of the final states, where these contributions were quantified as proportional to the partial current in each Bloch wave determined within the wavefunction-matching formalism of LEED, we have demonstrated that the MBFSs appear due to hybridization of plane waves through low-K components of the crystal potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Depending on the kz separation of the individual Bloch waves, the MBFSs give rise to multiple ARPES peaks from 3D valence-band dispersions or become an important factor of their broadening in addition to the intrinsic Δkz broadening due to the finite λPE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' From the first principles, these effects can be described by one-step ARPES calculations with the final states treated within the multiple-scattering or Bloch-wave approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Although our KKR-based calculations on Ag were able to qualitatively describe the experimental results, further theoretical effort is required to achieve a quantitative agreement at high excitation energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Besides Ag, the MBFS phenomena are observed, for example, in previous soft-X-ray data on the covalent GaN and even Al, the paradigm FE metal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' They are surprisingly weak, however, for the covalent Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The MBFS phenomenon, typically strengthening with the sharpness of the crystal-potential modulations, should be fairly general over a wide range of materials and excitation energies even into the hard-X-ray range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Methods Experiment The experiments were performed at the soft-X-ray ARPES facility65 installed at the high-resolution ADRESS beamline66 of the Swiss Light Source, Paul Scherrer Institute, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' X-rays irradiated the sample with a flux of ~1013 photons/s at a grazing-incidence angle of 20o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' A single crystal of Ag(100) (MaTecK) was cleaned by a few cycles of Ar ion sputtering/annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The sample was cooled down to ~12K in order to quench relaxation of k-conservation due to thermal motion of the atoms67, with the coherent spectral fraction enhanced by subtracting the angle-integrated spectrum scaled under the condition of non-negativity of the remaining spectral weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The measurements were performed with p-polarised X-rays at a combined energy resolution varying from ~50 to 180 meV when going from hv = 300 to 1300 eV, which is about twice better than in the first soft-X-ray ARPES study on Ag(100) 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The FS maps were integrated over an EB window from -75 to 25 meV relative to EF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Angular resolution of the analyzer PHOIBOS-150 was ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='1o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Other relevant experimental details, including the conversion of Ek and emission angle θ to k, corrected for pph, can be found elsewhere65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The data on GaN and Si from the previous ARPES works, discussed below, were taken under the same experimental conditions, but with the energy resolution relaxed to ~80 to 250 meV in the same hv range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Calculations In our simulations of the photoemission final states, the use of an empirical local pseudopotential has allowed reduction of the secular equation on complex kz to an eigenvalue problem for a complex non-Hermitian matrix17,45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For the energy range of our simulation extending to 1200 eV, the basis set included all plane waves below an energy cutoff of 1800 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The inner potential V0 was set to 10 eV, all VΔK to 5 eV for ΔK2 < 48 and to zero for larger ΔK2, and Vi to 5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The accuracy of the calculations was controlled via the current conservation generalised for non-zero Vi on the crystal side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For our qualitative analysis of the final states, no attempt has been made to fit these parameters to our particular case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Details of the calculations can be found elsewhere32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The first-principles ARPES calculations were performed using the SPR-KKR package68 relying on the multiple scattering theory using the Korringa-Kohn-Rostoker (KKR) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The ground-state properties of the Ag(001) surface were derived from density-functional-theory (DFT) calculations within the local-density approximation (LDA) carried out with full potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The ARPES spectra were calculated within the one-step model of photoemission in the spin-density-matrix formulation69 taking into account all aspects of the photoemission process for the actual experiment including pph, matrix elements and final states constructed as the time-reversed LEED states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Taking into advantage the predominance of forward scattering at Ek above ~400 eV70 the calculations used the single-site scattering approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The final-state damping was described via constant Vi = 3 eV set to reproduce λPE = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='2 Å at Ek = 600 eV given by the TPP-2M formula51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For further computational details see Supplemental Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The main paper presents the results obtained with FE final states, and the effects of multiple-scattering final states and various computational approximations are discussed in Supplemental Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Data availability The raw and derived data presented are available from the corresponding authors upon a reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Weng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Fang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Fang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Andrei Bernevig, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Dai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review X 5, 011029 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lv, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Observation of Weyl nodes in TaAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 11, 724 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schröter, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Chiral topological semimetal with multifold band crossings and long Fermi arcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 15, 759 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schröter, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Observation and control of maximal Chern numbers in a chiral topological semimetal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Science 369, 179 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Armitage, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Mele, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Vishwanath, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Weyl and Dirac semimetals in three-dimensional solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 90, 015001 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Yan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Felser, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Topological Materials: Weyl Semimetals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 8, 337 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lv, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Qian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Ding, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Angle-resolved photoemission spectroscopy and its application to topological materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature Reviews Physics 1, 609 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Hasan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Weyl, Dirac and high-fold chiral fermions in topological quantum matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature Reviews Materials 6, 784 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional electron realm in VSe2 by soft-x-ray photoelectron spectroscopy: Origin of charge-density waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 109, 086401 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Weber, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional Fermi surface of 2H−NbSe2 : Implications for the mechanism of charge density waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 97 235122 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional charge density wave observed by angle-resolved photoemission spectroscopy in 1T-VSe2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Matter 104, 155134 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' King, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surface band-gap narrowing in quantized electron accumulation layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 104, 256803 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lev, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' k-space imaging of anisotropic 2D electron gas in GaN/GaAlN high-electron-mobility transistor heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature Communications 9, 2653 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Photoemission response of 2D electron states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 229, 100 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Moser, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' How to extract the surface potential profile from the ARPES signature of a 2DEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Electron Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Relat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phenom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 225, 16 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schuwalow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band structure extraction at hybrid narrow-gap semiconductor-metal interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 8, 2003087 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Smith, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Mailhiot, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Theory of semiconductor superlattice electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Reviews of Modern Physics vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 62, 173 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Husanu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Electron-polaron dichotomy of charge carriers in perovskite oxides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Communications Physics 3, 62 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Berner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dimensionality-tuned electronic structure of nickelate superlattices explored by soft-x-ray angle-resolved photoelectron spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 92, 125130 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schütz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dimensionality-driven metal-insulator transition in spin-orbit-coupled SrIrO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 119, 256404 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Tang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature 569, 537 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Suga, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Tusche, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Photoelectron spectroscopy in a wide hν region from 6eV to 8keV with full momentum and spin resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena 200, 119 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fadley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Looking Deeper: Angle-Resolved Photoemission with Soft and Hard X-rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Synchrotron Radiation News 25, 26 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Gray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Bulk electronic structure of the dilute magnetic semiconductor Ga1−xMnxAs through hard X-ray angle-resolved photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature Materials 11, 957 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Soft-X-ray ARPES at the Swiss Light Source: From 3D Materials to Buried Interfaces and Impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Synchrotron Radiation News 27, 31 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' k-resolved electronic structure of buried heterostructure and impurity systems by soft-X-ray ARPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena 236, 1 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Powell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Jablonski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surface Sensitivity of Auger-Electron Spectroscopy and X-ray Photoelectron Spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Surface Analysis 17, 170 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Intrinsic accuracy in 3-dimensional photoemission band mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena 130, 65 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Lindgren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Walldén, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Rundgren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Westrin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Neve, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Structure of Cu(111)p(2×2)Cs determined by low-energy electron diffraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 28, 6707 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rundgren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Optimized surface-slab excited-state muffin-tin potential and surface core level shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 68, 125405 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Starnberg, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Nilsson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Excited-state bands of Cu determined by VLEED band fitting and their implications for photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 56, 1717 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional band mapping by angle-dependent very-low-energy electron diffraction and photoemission: Methodology and application to Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 63, 205108 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Photoemission from Al(100) and (111): Experiment and ab initio theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 78, 165406 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Character of the outgoing wave in soft x-ray photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 102, 245139 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Very-low-energy electron diffraction on the H-terminated Si(111) surface: Ab initio pseudopotential analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Matter 59, R5296 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Starnberg, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Nilsson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Brauer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Holleboom, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' New Method for Absolute Band Structure Determination by Combining Photoemission with Very-Low-Energy Electron Diffraction: Application to Layered VSe2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review Letters 79, 467 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional band structure of layered TiTe2: Photoemission final-state effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 74, 195125 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band mapping in the one-step photoemission theory: Multi-Bloch-wave structure of final states and interference effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 75, 045432 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Venturini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Minár, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Ebert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Brookes, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Soft x-ray angle-resolved photoemission spectroscopy on Ag(001): Band mapping, photon momentum effects, and circular dichroism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 77, 045126 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Claessen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Aryasetiawan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Blaha, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Nilsson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band- and k-dependent self-energy effects in the unoccupied and occupied quasiparticle band structure of Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 66, 195104 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Mahan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Theory of Photoemission in Simple Metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 2, 4334 (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Hofmann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Unexpected surface sensitivity at high energies in angle-resolved photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 66, 245422 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Feibelman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Eastman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Photoemission spectroscopy—Correspondence between quantum theory and experimental phenomenology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 10, 4932 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Capart, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Band structure calculations of low energy electron diffraction at crystal surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surface Science 13, 361 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Pendry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The application of pseudopotentials to low-energy electron diffraction III: The simplifying effect of inelastic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Physics C: Solid State Physics 2, 2283 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dederichs, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dynamical Diffraction Theory by Optical Potential Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Solid State Physics 27 (1972) eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ehrenreich, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Seitz & D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Turnbull (New York: Academic) p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Barrett, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Krasovskii, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Themlin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Elastic scattering effects in the electron mean free path in a graphite overlayer studied by photoelectron spectroscopy and LEED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 71, 035427 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Schattke, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Angle-Resolved Photoemission from Surface States.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review Letters 93, 027601 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Heine, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' On the General Theory of Surface States and Scattering of Electrons in Solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Proceedings of the Physical Society 81, 300 (1963).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' On qualitative analysis of the upper band effects in very-low-energy electron diffraction and photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Solid State Communications 106, 101 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Tanuma, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Powell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Penn, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Proposed formula for electron inelastic mean free paths based on calculations for 31 materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surface Science 192, L849 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krieger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Unpublished (2020) 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Stock, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Atomic-Scale Patterning of Arsenic in Silicon by Scanning Tunneling Microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' ACS Nano 14, 3316 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Constantinou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Unpublished (2020) 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Moser, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' An experimentalist’s guide to the matrix element in angle resolved photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena 214, 29 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fedchenko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 4D texture of circular dichroism in soft-x-ray photoemission from tungsten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' New Journal of Physics 21, 013017 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Puschnig, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Reconstruction of Molecular Orbital Densities from Photoemission Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Science 326, 702 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Kliuiev, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Combined orbital tomography study of multi-configurational molecular adsorbate systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nature Communications 10, 5255 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Bradshaw, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Woodruff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Molecular orbital tomography for adsorbed molecules: is a correct description of the final state really unimportant?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' New Journal of Physics 17, 013033 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fadley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Van Hove, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Hussain, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Kaduwela, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Photoelectron diffraction: new dimensions in space, time, and spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Electron Spectroscopy and Related Phenomena 75, 273 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Woodruff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Adsorbate structure determination using photoelectron diffraction: Methods and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Surface Science Reports 62, 1 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fedchenko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Winkelmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Schönhense, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Structure Analysis Using Time-of-Flight Momentum Microscopy with Hard X-rays: Status and Prospects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of the Physical Society of Japan 91, 091006 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Osterwalder, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Greber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Hüfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Schlapbach, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' X-ray photoelectron diffraction from a free-electron-metal valence band: Evidence for hole-state localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review Letters 64, 2683 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Osterwalder, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Greber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Aebi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Fasel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Schlapbach, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Final-state scattering in angle-resolved ultraviolet photoemission from copper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 53,10209 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, technical realisation and scientific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Synchrotron Radiation 21, 32 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' High-resolution soft X-ray beamline ADRESS at the Swiss Light Source for resonant inelastic X-ray scattering and angle-resolved photoelectron spectroscopies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Journal of Synchrotron Radiation 17, 631 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Exploring the XPS limit in soft and hard x-ray angle-resolved photoemission using a temperature-dependent one-step theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physical Review B 88, 205409 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ebert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Ködderitzsch, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Minár, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Calculating condensed matter properties using the KKR-Green’s function method—recent developments and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Reports on Progress in Physics 74, 096501 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Minár, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Ebert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Correlation, temperature and disorder: Recent developments in the one-step description of angle-resolved photoemission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Physics Reports 740, 1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Sébilleau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', Tricot S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' & Koide, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Unpublished (2022) Acknowledgements V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' thanks E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii for illuminating discussions and critical reading of the manuscript, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Dil for valuable exchange on physics of XPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' is grateful to D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Sébilleau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Tricot and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Koide for sharing their scattering-amplitude calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The authors thank N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Curson and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schofield for giving access to Si samples prepared at University College London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' acknowledge the support of the Czech Ministry of Education, Youth and Sports via the grant CEDAMNF CZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='01/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='0/15_003/0000358 and the support from GACR Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 2018725S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' acknowledges the financial support from the Ministry of Science and Higher Education of the Russian Federation, grant #075-11-2021-086.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' acknowledges the financial support of the Engineering and Physical Sciences Research Council (grants nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' EP/R034540/1, EP/W000520/1), and Innovate UK (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 75574).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Author contributions V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' conceived the SX-ARPES experiment at the Swiss Light Source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' performed the experiment supported by T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' fabricated the thin-film Si samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' processed and interpreted the data, and performed computational simulation of the final states supported by P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' performed the first-principles ARPES calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' wrote the manuscript with contributions from J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' All authors discussed the results, interpretations, and scientific concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Competing interests The authors declare no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Supplemental Material: KKR calculations with multiple-scattering final states Computational scheme In the first step of our theoretical investigations, we performed self-consistent electronic structure calculations within the ab-initio framework of the spin-density functional theory in order to generate the self-consistent-field (SCF) potential for further photoemission calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The LDA potential of Vosko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' was used1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=" The electronic structure of semi-infinite crystal was calculated within the relativistic multiple scattering approach using the Green's function Korringa-Kohn-Rostoker (KKR) formalism in the tight binding mode2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The experimental lattice constant (a = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='09 Å) was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In order to achieve precise description of the most subtle details of the SCF potential, important for photoemission at high excitation energies, the multipole expansion of the Green’s function employed an unusually large angular-momentum cutoff lmax of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In addition, a large number of k-points (36x36x36) in the first surface BZ was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The self-consistent calculations have been performed in two modi, within the so-called atomic sphere approximation (ASA) and in the full potential (FP) mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The obtained SCF potential was used for the photoemission calculations within the one-step model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The final states (the time-reversed LEED state) were treated using the so-called layer KKR technique3, allowing accurate description of these states in a wide hv range starting from 6 eV up to several keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' To ensure the convergence of the multiple scattering between the layers, our calculations used a plane-wave basis where the number of the surface reciprocal lattice vectors g was increased to 147 instead of the default value 372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another important ingredient of the multiple-scattering calculations is an accurate description of the kinematic and dynamic effects in both initial and final states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For the latter, the dynamic effects are taken into account via the X-matrix4 which represents the energy-dependent multiple scattering within a single layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Whereas in VUV-ARPES the kinematic and dynamic effects are comparable, in the soft- and hard-X-ray regime the dynamic effects weaken, whereby the X-matrix approaches zero, leading to the so-called single-site scattering approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Another important parameter in the description of multiple scattering is connected with the expansion of all physical quantities in terms of angular momentum l, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' using the Bauer’s identity to represent plane waves (scattering between the layers) and spherical waves (inside the layer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' These expansions involve a summation over l that must be truncated at a certain value lmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In this context, the increase of lmax should be viewed rather as an extension of the basis set for accurate description of the multiple scattering than physically meaningful l-channels in the scattering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' A simple assessment of lmax can be obtained from the radial Schrödinger equation where, in order to scatter on the spherical potential, the electron must first overcome the centrifugal barrier l(l+1)/a2 (a is the atomic radius).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This implies only the partial waves, whose l satisfies the inequality k2 > l(l+1)/a2, should be included into the l-expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The higher Ek, the larger lmax needs to be used (for the detailed explanation see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' For Ek in the range 300-1300eV, considered here, lmax falls between 4 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The calculations have been performed for a finite temperature of 20K leading to an additional final-state k-broadening, increasing with hv6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Effect of various approximations for the multiple-scattering process We have made an effort to elaborate our ARPES calculations towards their quantitative agreement with the experiment in a few successive steps: – Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1 shows the results obtained with multiple-scattering final states, as opposed to the FE final states used for the calculations in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 1 and 2 in the main text, under successive refinements of the computational approximations: – The results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1(a) were obtained within the ASA and lmax = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Due to the non-FE effects described by the multiple-scattering final states, they already show spectral structures due to the MBFSs (such as where marked by magenta arrows) although mostly on the low-energy end of our hv range and not exactly in the same k-space regions compared to the experiment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' – The inclusion of warping of the potential in the interstitial and surface regions within the FP scheme7, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1(b), does not result in any significant improvement in our case of Ag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nevertheless, we anticipate that the accurate FP will be crucial for more open crystal structures, covalent materials, van-der-Waals materials, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' where the potential modulations are sharper7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As we have seen in the present work, their accurate description should be particularly important at high Ek where the final states are highly sensitive to the high-frequency modulations of V(r) and thus to the accurate representation of its real-space variations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' – Another step, the inclusion of the full X-matrix compared to the single-site approximation, presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1(c), considerably improves the description of the relative intensity variations in the hv interval between 400 and 500 eV (magenta arrow, for example) but does not notably affect the spectral intensity at higher energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' This observation can be understood from analysis of scattering amplitude fk(θ), giving more insight into the scattering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The calculations of fk(θ) for Ag by Sébilleau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='8, reproduced in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S2, demonstrate that for Ek above ~400 eV it is strongly dominated by forward scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In practice, this means that for these energies the electrons scatter essentially along the rows of atoms, justifying the single-site approximation for the multiple scattering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' – Finally, at the last step of our computational refinement presented in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1(d), we increased lmax from 3 to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' As expected, not only has this returned a vivid pattern of the MBFS-induced replica bands and excessive spectral broadening at low Ek (such as where marked by magenta and yellow arrows, respectively) but also pushed these effects to yet higher hv up to 700 eV (magenta arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Further increase of lmax would inflate the computational time beyond presently realistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Although these successive refinements of the computational scheme do move towards a better description of the experiment, the achieved agreement with the experimental results can only be considered as qualitative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' We conjecture that the remnant deviation may trace back to quite small sensitivity of the total energy to high-frequency components of the crystal potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Therefore, the total-energy minimization used to generate the self-consistent potential in the DFT calculations may not ensure sufficient accuracy of its high-frequency components which critically affect the hybridization and thus non-FE effects in the final states at high energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The accuracy of the final states used in the ARPES calculations can in principle be verified independently from the initial states by calculating the LEED spectra and their fitting to the experiment using the methodology previously developed for very low energies (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 9–11 and the references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' In any case, including the subtle details of V(r) within the FP approach and the use of sufficiently large lmax give the best possible single-particle description of the photoemission final state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' One-step ARPES calculations as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 1(d) but using multiple-scattering final states under successive refinements of their treatment: (a) standard spherical-wave expansion and single-site scattering approximation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (b) adding full potential;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (c) the full X-matrix beyond the single-site scattering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' (d) increasing the angular momentum expansion to lmax = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' The calculations reproduce the multiple spectral peaks (magenta arrows) and the excessive spectral broadening (yellow) induced by the MBFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Scattering amplitude fk(θ) for Ag as a function of Ek (left panels) and the total forward and backward scattering contributions (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' hv (eV) (a) (b) (c) (d) 1200 1000 800 600 400 0Ag Scattering Factor @ E = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV Ag Scattering Factor @ E = 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV 90* 90° [0)] 135° (9(e) +SET ((e) 3([6)) (e))C 180° 180° Ag Forward and Backward scattering amplitudes 225* 225* 315 Forward 270* 270* Backward Ag Scattering Factor @ E = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV Ag Scattering Factor @ E = 700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV 90° 135* [0]] g((e) 135* s((e) ([(0) 3(6)) 180° 180* 2 225* 225* 315 270* 270* 200 400 600 800 1000 Ag Scattering Factor @ E = 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV Ag Scattering Factor @ E = 900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='00 eV 90° Kinetic Energy [eV] 135* [0]] [6]] 135* 3(R0) 3((6)) 180* 225 225* /315 270* 270*References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Vosko, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Wilk, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nusair, Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis, Canadian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 58 (1980) 1200 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ebert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ködderitzsch, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Minár, Calculating Condensed Matter Properties Using the KKR-Green’s Function Method – Recent Developments and Applications, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 74 (2011) 096501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' MacLaren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Crampin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Vvedensky, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Pendry, Layer Korringa-Kohn-Rostoker Technique for Surface and Interface Electronic Properties, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B 40 (1989) 12164 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Minár, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ebert, Correlation, Temperature and Disorder: Recent Developments in the One-Step Description of Angle-Resolved Photoemission, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 740 (2018) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Multiple Scattering Theory for Spectroscopies, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Sébilleau, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Hatada and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ebert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Springer Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 204 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Braun, The theory of angle-resolved ultraviolet photoemission and its applications to ordered materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 59 (1996) 1267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Minár, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Mankovsky, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Brookes, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Plucinski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schneider, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Fadley, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Ebert, Exploring the XPS Limit in Soft and Hard X-Ray Angle-Resolved Photoemission Using a Temperature-Dependent One-Step Theory, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B 88 (2013) 205409 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Sébilleau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Tricot, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Koide, unpublished (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Starnberg & P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nilsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Excited-state bands of Cu determined by VLEED band fitting & their implications for photoemission, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B 56 (1997) 1717.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Claessen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nicolay, S Hüfner, A Kimura, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Harasawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Shin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Kakizaki, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Nilsson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Starnberg & P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Blaha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional band mapping by angle-dependent very-low-energy electron diffraction and photoemission: Methodology and application to Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B 63 (2001) 20510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Strocov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Krasovskii, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schattke, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Barrett, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Berger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Schrupp & R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Claessen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Three-dimensional band structure of layered TiTe2: Photoemission final-state effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} +page_content=' B 74 (2006) 195125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAyT4oBgHgl3EQfP_YA/content/2301.00033v1.pdf'} diff --git a/3dE1T4oBgHgl3EQf5wXA/content/2301.03516v1.pdf b/3dE1T4oBgHgl3EQf5wXA/content/2301.03516v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8ab75ae7f467446cd986af65be1fa7f6be72df66 --- /dev/null +++ b/3dE1T4oBgHgl3EQf5wXA/content/2301.03516v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0578e5e57d100e2eaf03ee9c55736db160f87d0211f58d3d85a79c07a28109d9 +size 11199323 diff --git a/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/2301.03068v1.pdf.txt b/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/2301.03068v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..442f9f7b783490bc8d581f71bdb751e19a64eb93 --- /dev/null +++ b/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/2301.03068v1.pdf.txt @@ -0,0 +1,917 @@ +Research in Astronomy and Astrophysics manuscript no. +(LATEX: ms2022-0349.tex; printed on January 10, 2023; 1:43) +Limiting Magnitudes of the Wide Field Survey Telescope (WFST) +Lei Lei (雷磊)1,2, Qing-Feng Zhu (朱青峰)1,3, Xu Kong (孔旭)1,3, Ting-Gui Wang (王挺贵)1,3, +Xian-Zhong Zheng (郑宪忠)1,2, Dong-Dong Shi (师冬冬)2, Lu-Lu Fan (范璐璐)1,3 and Wei Liu +(刘伟)2 +1 School of Astronomy and Space Science, University of Science and Technology of China, Hefei +230026, China; zhuqf@ustc.edu.cn +2 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China; +3 Deep Space Exploration Laboratory / Department of Astronomy, University of Science and Technology +of China, Hefei 230026, China; +Received 20xx month day; accepted 20xx month day +Abstract Expected to be of the highest survey power telescope in the northern hemisphere, +the Wide Field Survey Telescope (WFST) will begin its routine observations of the northern +sky since 2023. WFST will produce a lot of scientific data to support the researches of time- +domain astronomy, asteroids and the solar system, galaxy formation and cosmology and so +on. We estimated that the 5 σ limiting magnitudes of WFST with 30 second exposure are +u = 22.31 mag, g = 23.42 mag, r = 22.95 mag, i = 22.43 mag, z = 21.50 mag, w = 23.61 +mag. The above values are calculated for the conditions of airmass = 1.2, seeing = 0.75 +arcsec, precipitable water vapour (PWV) = 2.5 mm and Moon-object separation = 45◦ at +the darkest New Moon night of the Lenghu site (V=22.30 mag, Moon phase θ = 0◦). The +limiting magnitudes in different Moon phase conditions are also calculated. The calculations +are based on the empirical transmittance data of WFST optics, the vendor provided CCD +quantum efficiency, the atmospherical model transmittance and spectrum of the site. In the +absence of measurement data such as sky transmittance and spectrum, we use model data. +Key words: techniques: photometric — surveys — telescopes +1 INTRODUCTION +The Wide Field Survey Telescope (WFST; Lou et al. 2016; Shi et al. 2018; Lou et al. 2020; Lin et al. 2022) is +an optical telescope to be installed at the Lenghu site, located on Saishiteng mountain near Lenghu Town in +Qinghai Province on the Tibetan Plateau, China in 2023. The WFST has a 2.5-m diameter primary mirror +and a 5-lens corrector to form a prime-focus optics (Wang et al. 2016;Lou et al. 2016; Lou et al. 2020). +The detector of WFST consists of nine 9K×9K CCD chips and has 0.9 Giga pixels. The entire system is +arXiv:2301.03068v1 [astro-ph.IM] 8 Jan 2023 + +2 +Lei et al. +optimized for the wavelength range from 3200 ˚A to 9600 ˚A (Lou et al. 2016; Chen et al. 2019). With the aid +of an active optics system and an ADC (atmospheric dispersion compensator), WFST can achieve an image +quality of 0.4 arcsec 80% energy enclosed across a field of view of 3 degree diameter and ∼7 deg2 area. +WFST is able to survey ∼ 2 × 104 deg2 northern sky in ugrizw six bands. As a powerful survey telescope, +its scientific data will greatly support researches of time-domain astronomy, asteroids and the solar system, +the Milky Way and its satellite dwarf galaxies, galaxy formation and cosmology and so on. +In recent years, many large ground-based optical survey telescopes have been built or planned all over +the world. SDSS (Kent 1994; Fukugita et al. 1996), Pan-STARRS (Jedicke & Pan-STARRS 2007; Chambers +& Pan-STARRS Team 2016), SkyMapper (Schmidt et al. 2005; Rakich et al. 2006), ZTF (Bellm 2014; +Bellm et al. 2019; Graham et al. 2019) and other built telescopes have produced a large amount of observa- +tion data, which has greatly promoted astronomical researches and solved many scientific problems. Soon +new, survey telescopes such as LSST (Hlozek et al. 2019), Mephisto (Liu 2019; Lei et al. 2021; Yuan et al. +2020) and WFST will join their peers and conduct deeper multi-band surveys to provide crucial data to +astrophysical researches. Combined with China Space Station Telescope (CSST; Zhao et al. 2016; Yuan +et al. 2021) and other space telescopes, WFST will greatly improve human understanding of the universe +and promote more important scientific discoveries. +The parameters of a survey telescope, such as the diameter of the primary mirror, quantum efficiency +(QE) of CCD, band transmittance, etc., determine the throughput of the telescope. The site conditions of an +astronomical observatory, such as atmospheric transmittance, altitude, seeing and sky background bright- +ness, affect the depth of a survey program.. The limiting magnitude of a survey telescope is an important +guide for planning research objectives and project scopes. It is also the key for designing exposure time +plans and survey strategies. Therefore, an accurate estimation of the limiting magnitudes are needed for the +successful commission of a new telescope. +In this work, we introduce the estimation of the limiting magnitudes of WFST. In Sect. 2 we describe +the method we adopt. In Sect. 3 we show our results of limiting magnitudes of the WFST. +2 LIMITING MAGNITUDES +2.1 Throughput of WFST +The throughput of an astronomical observation (Ttot) is limited by the atmospheric transmittance (Tatmo), +the transmittance of optics (Topt), the transmittance of the filters Tband) and the quantum efficiency of CCD +(QECCD). +Ttot = Tatmo · Topt · Tband · QECCD +(1) +The optical system of WFST consists of a 2.5 meter diameter primary mirror with a 760 mm diameter +central hole, five corrector lenses, a ADC made with two glass wedges and ugrizw six switchable filters +(Lou et al., 2016). Among five correcting lenses, only one is made of the N-BK7HT glass. The others and +ADCs are made of the fused quartz. Since the transmittance of a fused quartz blank can be neglected, we +simulate the total transmittance of the five-lens corrector and the ADC with the product of the transmittance +of a 35 mm thick N-BK7 glass blank and the transmittance of 14 layers of anti-reflection (AR) coatings. + +Limiting Magnitudes of WFST +3 +The transmittance of the N-BK7 glass is obtained from SCHOTT1 and the transmittance of the AR coating +is from Institute of Optics and Electronics (IOE) ’s measurements. Because of the oversized Primary Focus +Assembly (PFA), the actual aperture obscuration is 1 m diameter. +Because we don’t have atmospheric transmitance and spectrum measurements at the site, we adopt +SkyCalc2 (Version 2.0.9) to obtain model curves. SkyCalc is developed by astronomers in ESO based on +the Cerro Paranal Advanced Sky Model (Noll et al. 2012; Jones et al. 2013; Moehler et al. 2014). The +atmospheric transmittance is affected by altitude, humidity, dust, precipitable water vapour (PWV), among +which the altitude is the most important factor. SkyCalc only provides the atmospheric transmittance at +three astronomical sites: Paranal (2400 m), La Silla (2600 m) and Extremely Large Telescope (ELT) site +(3060 m). Figure 1 shows the three transmittance curves of the sites. We can see that three curves have +same features that they are scaled according to different altitudes of three sites. This is reasonable because +the geographic features of the three sites are very similar. The Paranal Observatory is on the Cerro Paranal +mountain, which is in the Atacama Desert of northern Chile. The La Silla Observatory is located on the +outskirts of the Chilean Atacama Desert. The 40-metre-class ELT is on the Cerro Armazones mountain in +the central part of the Atacama Desert. WFST is on the Saishiteng mountain in the Gobi desert area on +the Tibetan Plateau. We consider that the geographic features of the area are more similar to those of sites +in the high-altitude Atacama desert than those of oceanic mountain areas, such as Mauna Kea in Hawaii. +It is a reasonable choice to obtain the atmospheric transmittance of the WFST site by using the spectra +from SkyCalc. So we get the atmospheric transmittance curve of the WFST site at an altitude of 4200 m +by scaling the atmospheric transmittance curves of paranal, lasilla and ELT sites. In our simulations, we +assume that airmass = 1.0 and precipitable water vapour (PWV) = 2.5 mm. Figure 1 also shows the result +of scaling. +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +11000 +wavelength(Å) +0.1 +1.0 +Transmission +10550 +10560 +10570 +10580 +10590 +10600 +10610 +0.974 +0.976 +0.978 +0.980 +3060 m +2640 m +2400 m +4200 m +Fig. 1: The atmospheric transmittance curves of Paranal Observatory (2400 m), La Silla Observatory (2600 +m) and the Extremely Large Telescope site (3060 m), the scaled transmittance curve of the WFST site (4200 +m). We assume the WFST site has the same geographic features (i.e. high altitude Mountain and dry air) as +the three ESO sites. +1 https://refractiveindex.info/?shelf=glass&book=BK7&page=SCHOTT +2 https://www.eso.org/observing/etc/bin/gen/form?INS.MODE=swspectr+INS.NAME=SKYCALC + +4 +Lei et al. +As shown in Figure 2(a), combined system throughput, individual transmittance curves of the atmo- +sphere and the corrector, the reflectivity of the primary mirror and the quantum efficiency of the CCD are +plotted respectively. We also plot the original estimate of the system throughput for WFST by Shi et al. +(2018). We can see that the updated system throughput is higher than the early expectation in most wave- +lengths (Shi et al., 2018). The major reason is that the transmittances of ADC and optical lenses are higher +than the early estimate. In order to obtain high efficiency in short wavelengths, WFST selects e2v standard +Si back-illuminated CCD detectors with the astro multi-2 coating. The QE of the CCDs is also increased. +Figure 2(b) shows the transmittance of the filters and the total throughput of WFST in six bands, which +is calculated by using Equation 1. +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +wavelength (Å) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Efficiency +a) +Atmosphere +Primary Mirror +Lenses +CCD +Atmosphere + Primary Mirror + Lenses + CCD. Shi et al. 2018 +Atmosphere + Primary Mirror + Lenses + CCD. This work +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +wavelength (Å) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +b) +u +g +r +i +z +w +Fig. 2: (a) The transmittance curves of the atmosphere (blue dot-dashed line), the optics including lenses +and the ADC (green line), the reflectivity of the primary mirror (yellow line) and the quantum efficiency of +the CCDs (cyan dot-dashed line). The combined efficiency of the atmosphere, the optics and the CCDs is +in purple. The red line shows the total efficiency of Shi et al.(2018); (b) The transmittance of each filter and +the total efficiency in each WFST filter transmittance. +2.2 Noise of WFST +Noise in astronomical CCD images mainly consists of the contributions from the artificial light on the +ground, astrophysical sources, sky background, CCD dark current, and CCD readout noise. The site of +WFST is on Saishiteng mountain on the Tibetan Plateau, where the nearest residential area is Lenghu town +which is ∼ 50 km from the observatory site and has a population of 200. There is no industrial activity and +the ground light pollution. The Haixi Mongolian and Tibetan Autonomous Prefecture of Qinghai Province +has announced the 17800 square kilometres area of Lenghu as a dark night protecting region in the local law. +It protects the good observational conditions of the Lenghu astronomical site. Deng et al. (2021) studied +long-term astronomical conditions of the Lenghu site and pointed out that the sky background of a New +Moon night can reach 22.3 mag arcsec−2 in the V band and the average night-sky brightness is around 22.0 +mag arcsec−2 when the Moon is below the horizon. We adopt AB magnitude system in this work. +The sky background spectrum of the Lenghu site is also calculated by the software SkyCalc (Noll et al. +2012; Jones et al. 2013; Moehler et al. 2014). The monthly averaged solar radio flux is equal to 130.00 +sfu, that is the solar 10.7 cm radio flux in the Sun median active level (Sparavigna 2008; Petrova et al. +2021). Because the solar activities will affect the sky background brightness, it is necessary to take the + +Limiting Magnitudes of WFST +5 +solar activities into account when we estimate the sky background. We adopt the median values obtained +from long-term solar monitoring programs as the baseline solar brightness. The spectral flux of one sky +region is related to the Moon-Target separation and the Moon phase. We designate the Moon phase with the +Moon phase angle (θ) 0◦ (New Moon), 45◦ (Waxing), 90◦ (Half Moon Waxing), 135◦ (Waxing), 180◦ (Full +Moon) respectively. We assume the separation of the Moon and a target is always 45◦ in our calculation. +So the spectral flux of one region is only dependent on the altitude and the Moon phase. We get the sky +background spectra towards the Zenith under different Moon phase conditions at the Lenghu Observatory +site by scaling the spectra of three ESO sites provided by SkyCalc. Figure 3(a) shows the sky background +spectrum at the altitude of 4200 m (θ = 180◦, here we just plot the spectra at a full Moon night because +it is easier to see their difference.), and the spectra of the three ESO sites at Full Moon night. Figure 3(b) +shows the sky spectra at Lenghu site under six different Moon phase conditions. As shown in the detail part +of Figure 3(b), the sky background spectrum at a New Moon night (θ = 0◦) and the sky spectrum at a Dark +night have almost the same flux. +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +11000 +wavelength(Å) +0.01 +0.10 +1.00 +10.00 +flux (photons s +1 Å +1 arcsec +2 m +2) +a) += 180 +5175 +5200 +5225 +5250 +5275 +5300 +5325 +0.450 +0.475 +0.500 +0.525 +0.550 +0.575 +0.600 +4200 m +3060 m +2640 m +2400 m +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +11000 +wavelength(Å) +0.00 +0.01 +0.10 +1.00 +10.00 +flux (photons s +1 Å +1 arcsec +2 m +2) +b) +4500 +4600 +4700 +4800 +4900 +0.012 +0.014 +Dark night += 0 += 45 += 90 += 135 += 180 +Fig. 3: (a) The sky background spectrum (purple) at Zenith at the altitude of 4200 m in the Full Moon +condition, and the spectra of three ESO sites when the Moon phase is θ = 180◦. (b) The Zenith sky spectra +of the 4200 m site in different Moon phase conditions. The sky background spectrum of Moon phase +θ = 180◦ and the spectrum of a dark night (when the Moon is under the horizon) have almost the same +flux. +We can get the magnitude mV by integrating the sky background spectrum multiplied by the V band +filter transmission curve: +mV = −2.5 × +� +log10 +� ∞ +0 +fλTband,λdλ +� ∞ +0 +Tband,λdλ +� +− 21.1 +(2) +where fλ is sky background spectral flux, Tband is the Johnson V band transmission curve (Bessell, 1990), +ZP = −21.1 is the zero point (Bessell & Murphy 2012). The modeled sky emission radiance flux from +SkyCalc is in units of photon/s/m2/micron/arcsec2. The Johnson V band sky background magnitude +of a New Moon night with the SkyCalc model spectrum at an altitude of 4200 m is 21.74 mag arcsec−2. +We scale the 4200 m sky background spectrum so that the resulting spectrum has a V-band magnitude +of 22.3 or 22.0 mag arcsec−2, corresponding to the best and the average sky brightness conditions at the +Lenghu site. As shown in Figure 3(b), there are differences among the sky spectra under different Moon + +6 +Lei et al. +phase conditions. We scale these sky spectra at different Moon phases use the the same scaling factor +in the new moon case, where we scale the spectrum from V θ=0◦ = 21.74 to 22.30 mag arcsec−2, so +that differences among spectra at different Moon phases are not changed. The estimated V band Zenith +sky background magnitudes at the Lenghu site with different Moon phases are: V θ=0◦, V θ=45◦, V θ=90◦, +V θ=135◦, V θ=180◦=22.30, 22.10, 21.29, 20.28, 18.90 mag arcsec−2. +The Lenghu sky background spectrum is calculated for airmass = 1.0. It can be scaled to another +airmass by multiplying a factor a (Krisciunas & Schaefer 1991). +a = 10−0.172 (X−1)X +2.5 +(3) +when airmass = 1.2, X is +X = +1 +� +(1 − 0.96 × sin (arccos ( +1 +airmass))2) +≈ 1.18958 +(4) +Based on the sky background spectrum of the Lenghu site, we estimate the magnitudes of the sky +background in each band mAB +band: +mAB +band = −2.5 × log10 +�Skyband +ZPband +� +(5) +where +ZPband = +� ∞ +0 +fluxABTband,λdλ +(6) +where fluxAB = 3631Jy for all frequencies, and Tband,λ is the transmittance curve of a particular band. +Skyband = +� ∞ +0 +fλTband,λdλ +(7) +where fλ is sky background spectral flux. The Table 1 shows the sky background magnitudes mAB in +WFST six bands. +Table 1: The sky background brightness mAB of WFST six bands in units of mag arcsec−2. +Moon Phases +u +g +r +i +z +w +0◦ +23.27 +22.82 +21.80 +20.99 +20.05 +21.78 +45◦ +23.02 +22.49 +21.66 +20.93 +20.03 +21.64 +90◦ +22.00 +21.37 +20.99 +20.61 +19.90 +21.01 +135◦ +20.86 +20.21 +20.08 +20.01 +19.61 +20.12 +180◦ +19.30 +18.73 +18.78 +18.97 +18.92 +18.80 +Note: The sky spectra is calculated by SkyCalc when airmass = 1.0, PWV = 2.5 mm. We calculated the sky +background brightness mAB when airmass = 1.2. +2.3 Limiting Magnitudes of WFST +Assuming the signal to noise ratio of WFST in all bands for a point source is S/N, we can write the formula +of the S/N as : +S +N = +S · A · τ +� +S · A · τ + 2 · npix · [(Sky · A · αpix + D) · τ + R2] +(8) +where S is the source signal with a constant spectral flux, τ is the standard exposure time (30 s), A is +the effective area of the primary mirror (∼ 4.12 × 104 cm2), αpix = 0.111 arcsec2 is the area of one + +Limiting Magnitudes of WFST +7 +pixel, D is the dark current of the CCD (D = 0.005 e−/pixel/s, @−100◦C), R2 is the readout noise of +the CCD (R = 8 e− rms), npix is the total pixel number in the point spread function (PSF), the usage +of a factor 2 is because we assume the calculation is performed on sky subtracted images. An optimal +PSF aperture of 1.18 times of the full width at half maximum (FWHM) is adopted for a non-Adaptive +Optics case according to the Integration Time Calculator (ITC) of Gemini3. And the FWHM of the seeing +degrades with the airmass and the wavelength as (airmass)0.6 × λ−0.2 +eff . Here λeff takes the value of +356.17, 476.34, 620.57, 753.07, 870.45, 612.15 nm in the six bands ugrizw given by the Equation 9. +λeff = +� ∞ +0 +λTband dλ +� ∞ +0 +Tband dλ +(9) +With the seeing = 0.75 arcsec measured by Deng et al. (2021) at 500 nm (Tokovinin et al., 2003), we +estimated the seeing values in different bands and airmass conditions. +The sky signal actually lands on the detector is: +Sky = +� ∞ +0 +fλToptTbandQECCD dλ +(10) +where Topt is the throughput of the optics (including the primary mirror, ADC and the 5 corrector lenses), +QECCD is the quantum efficiency of the CCD. +We can solve the Equation 8 to obtain the signal of an astronomical object required at the detection limit +of S/N = 5 and find the corresponding limiting magnitude mlim: +mlim = −2.5 × log10 +� +S +0.61 · ZPlim +� +(11) +A factor 0.61 is used because according to the description of ITC, the 1.18 FWHM sized aperture will +contain 61% energy of a point source. The ZPlim is the system zero point flux: +ZPlim = +� ∞ +0 +fluxABTatmoToptTbandqeCCD dλ +(12) +Table 2 lists the calculated limiting magnitudes of ugrizw six bands. We calculated the limiting mag- +nitudes of WFST at different Moon phases when the sky background brightness is V=22.0 mag and 22.3 +mag, respectively. The results of a single exposure of 30 s and of coadded 100 frames with a total integration +time of 100 × 30 s are listed. It shows that WFST can reach 23.42 (25.95) mag in the g band with a 30 s +(100 × 30 s) exposure under the conditions with the sky background brightness V=22.3 mag, seeing =0.75 +arcseconds, airmass = 1.2 and PWV=2.5 mm. If the sky background is V=22.0 mag, the above values are +23.32 (25.85) mag for 30 s (100 × 30 s). +3 DISCUSSION AND CONCLUSIONS +In the current work, by considering the observational conditions of WFST, including throughput, quantum +efficiency, the noise, the area of the primary mirror and the sky background brightness, we compute the +limiting magnitudes of WFST. We get the sky background magnitudes in AB magnitude system in the +Lenghu site at the New Moon night when airmass = 1.2: u, g, r, i, z, w=23.27, 22.82, 21.80, 20.99, 20.05, +21.78 mag arcsec−2. For the Lenghu darkest night condition (V=22.3 mag arcsec−2) and a exposure time +3 https://www.gemini.edu/observing/resources/itc/itc-help + +8 +Lei et al. +Table 2: 5σ limiting magnitudes of WFST when airmass=1.2, seeing = 0.75 arcsec, precipitable water +vapour (PWV) = 2.5 mm and Moon-object separation is 45◦. +Exposure time +Moon Phase +V band sky +u +g +r +i +z +w +30 s +0◦ +22.30 +22.31 +23.42 +22.95 +22.43 +21.50 +23.61 +30 s +45◦ +22.10 +22.27 +23.30 +22.89 +22.40 +21.49 +23.54 +30 s +90◦ +21.29 +22.04 +22.86 +22.62 +22.26 +21.43 +23.23 +30 s +135◦ +20.28 +21.64 +22.34 +22.21 +21.99 +21.31 +22.79 +30 s +180◦ +18.90 +20.97 +21.62 +21.58 +21.49 +21.00 +22.13 +100 × 30 s +0◦ +22.30 +24.86 +25.95 +25.48 +24.96 +24.03 +26.13 +100 × 30 s +45◦ +22.10 +24.82 +25.84 +25.42 +24.93 +24.02 +26.06 +30 × 100 s +90◦ +21.29 +24.58 +25.38 +25.14 +24.78 +23.96 +25.74 +100 × 30 s +135◦ +20.28 +24.17 +24.85 +24.72 +24.51 +23.83 +25.30 +100 × 30 s +180◦ +18.90 +23.48 +24.12 +24.09 +24.01 +23.51 +24.64 +30 s +0◦ +22.00 +22.26 +23.32 +22.83 +22.30 +21.37 +23.47 +30 s +45◦ +21.80 +22.21 +23.19 +22.77 +22.28 +21.37 +23.40 +30 s +90◦ +20.99 +21.95 +22.74 +22.48 +22.12 +21.29 +23.09 +30 s +135◦ +19.98 +21.52 +22.19 +22.07 +21.85 +21.18 +22.64 +30 s +180◦ +18.60 +20.83 +21.47 +21.44 +21.35 +20.86 +21.99 +100 × 30 s +0◦ +22.00 +24.81 +25.85 +25.36 +24.83 +23.90 +25.99 +100 × 30 s +45◦ +21.80 +24.76 +25.72 +25.30 +24.80 +23.89 +25.92 +100 × 30 s +90◦ +20.99 +24.48 +25.25 +25.01 +24.65 +23.83 +25.60 +100 × 30 s +135◦ +19.98 +24.05 +24.71 +24.58 +24.37 +23.70 +25.15 +100 × 30 s +180◦ +18.60 +23.34 +23.98 +23.95 +23.86 +23.38 +24.49 +Note: The V-band sky brightness is the Zenith sky background magnitudes. +of 30 s, the 5σ limiting magnitudes of WFST are: ulim, glim, rlim, ilim, zlim, wlim = 22.31, 23.42, 22.95, +22.43, 21.50, 23.61 mag. The current estimates of limiting magnitudes are deeper than those in Shi et al. +(2018). This is because the current total throughput of WFST is higher than previous value, especially +the throughput increases by ∼ 50% from ∼ 0.4 to ∼ 0.6 in gri bands (see Figure 2(a)), and the current +Dark night sky background is lower than the previous estimation. Figure 4 compares the sky spectrum of +New Moon night of the Lenghu site and the atmospheric transmittance curve between this work and Shi +et al. (2018). We used SkyCalc to estimate the sky background spectrum and atmospheric transmittance, +while Shi et al. (2018) used the software MODTRAN4 for estimating the atmospheric transmittance at the +5130 m Ali area and used a Hawaii sky background spectrum as a sky background spectral template. The +Hawaii sky brightness in ugz bands is brighter than the current model when we scaled both of them into +the same conditions of mV = 22.3 mag arcsec−2 and airmass = 1.2 (see Figure 4 (a)), Shi et al. (2018) +assumed the V band sky brightness is mV = 21.50 mag arcsec−2. There is little difference between the +current atmospheric transmittance model and the spectrum in Shi et al. (2018) (see Figure 4(b)). Our scaled +atmospheric transmittance is close to the model of MODTRAN. +We also obtain the limiting magnitudes of WFST under various conditions (Figure 5). In Figure 5, the +panel (a) shows the WFST limiting magnitudes of different signal-to-noise ratio when the exposure time +equals to 30 s and 100 × 30 s respectively, the panel (b) shows the limiting magnitudes of different seeing +4 http://modtran.spectral.com/ + +Limiting Magnitudes of WFST +9 +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +11000 +wavelength (Å) +10 +3 +10 +2 +10 +1 +10 +0 +10 +1 +flux (photons s +1 Å +1 arcsec +2 m +2) +a) +Shi et al.(2018) +This work +3000 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +11000 +wavelength (Å) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Atmospheric Transmission +b) +Shi et al.(2018) +This work +Fig. 4: (a) The red line shows the sky background spectrum of Lenghu site at New Moon night (Moon +phase θ = 0◦), mV = 22.3 mag, airmass = 1.2. The black dashed line shows the Hawaii sky background +spectrum scaled into mV = 22.3 mag and airmass = 1.2 in Shi et al. (2018); (b) The red line shows the +atmospheric transmittance curve of Lenghu site estimated by SkyCalc in this work. The black dashed line +shows the atmospheric transmittance curve of Shiquanhe astronomical site at an altitude of 5130 m at the +Ali Area on the Tibetan Plateau estimated by the software MODTRAN. +conditions when signal-to-noise ratio = 5 and the exposure time = 30 s, 100 × 30 s respectively, and the +panel (c) shows the 5σ limiting magnitudes of different exposure times. These results are calculated with +the sky spectrum scaled into airmass = 1.2 condition at a New Moon night (Moon phase θ = 0◦). +2.5 +5.0 +7.5 +10.0 +12.5 +15.0 +S/N +19 +20 +21 +22 +23 +24 +25 +26 +27 +mag +a) +exposure time = 30 s +exposure time = 100 × 30 s +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +seeing (arcsec) +20 +21 +22 +23 +24 +25 +26 +mag +b) +exposure time = 30 s +exposure time = 100 × 30 s +50 +100 +150 +200 +exposure time (s) +20.0 +20.5 +21.0 +21.5 +22.0 +22.5 +23.0 +mag +c) +u g r +i z w +Fig. 5: (a) The limiting magnitudes of different S/N values when the exposure time is 30 s (dot-dashed +line) and 100 × 30 s (solid line); (b) The 5σ limiting magnitudes of different seeing conditions when the +exposure time is 30 s (dot-dashed line) and 100 × 30 s (solid line); (c) The 5σ limiting magnitudes of +different exposure times when the seeing is 0.75 arcsec. The conditions for a New Moon night (θ = 0◦) and +airmass = 1.2. Note: The limiting magnitude curves of the g band (blue) and the w band (red) are so close +that we can not distinguish the two curves easily. +The WFST survey data will cover the entire northern sky. Its stacked scientific image data can be used +to study asteroids, solar system, galaxies and cosmology. Its light curves can be used to discover variable +objects. The estimated WFST limiting redshift of Type Ia supernovae (SNe Ia) can reach z∼0.64 (luminosity +distance ∼ 6.3 × 103 Mpc) and z∼1.67 (∼ 1.2 × 104 Mpc) when the exposure time is 30 s and 100 × 30 s. +SNe Ia can be used to constrain the dark energy in the universe (Riess et al., 1998) and directly measure the +Hubble constant (Riess et al., 2022). By simulating observations of the SNe Ia with the WFST at the Lenghu +site, Hu et al. (2022) estimate that above 104 pre-maximum SNe Ia will be discovered in one-year during the + +10 +Lei et al. +wide or deep observations, which suggests that WFST will be a powerful facility in revealing the physics of +SNe Ia. Lin et al. (2022) computed the prospects of finding Tidal Disruption Events (TDEs) with the WFST. +Their mock observations on 440 deg2 field (CosmoDC2 catalogue) show that ∼ 30 TDEs can be found per +year if observed at ugrizw bands with 30 s exposures every 10 days. According to Gao et al. (2022), the +event rate for galaxy-lensed orphan afterglows of γ-ray bursts (GRBs) is to be less than 0.7 yr−1 for the +whole sky survey of the WFST. Yu et al. (2021) estimated the multi-messenger detection rate of Binary +Neutron Star Mergers is about 300-3500 yr−1 with a GECAM-like detector for γ-ray emissions and an +LSST/WFST detector for optical afterglows. Zhu et al. (2021) and Zhu et al. (2022) showed that the optimal +detection rates of the KN-dominated and AG-dominated GRB afterglows events are ∼0.2/0.5/0.8/20 yr−1 +and ∼500/300/600/3000 yr−1 for ZTF/Mephisto/WFST/LSST, respectively. There are also some studies +looking forward to detecting Active galactic nucleus (AGN) and researching AGN physics using WFST +survey data (Xu-Fan Hu et al. in preparation; Su et al. in preparation). +There are large sky survey telescopes that have been built around the world, and a number of large sky +survey telescopes are being built. These projects have produced or will generate a large amount survey data +and have an important impact in all fields of astronomy. Among them, the WFST will be completed in 2023. +In the future, WFST (Lin et al. 2022; Shi et al. 2018), together with Mephisto (Lei et al. 2021; Lei et al. +2022; Chen et al. in preparation), Pan-STARRS (Jedicke & Pan-STARRS 2007; Chambers & Pan-STARRS +Team 2016), SkyMapper (Schmidt et al. 2005; Rakich et al. 2006), ZTF (Bellm et al. 2019; Graham et al. +2019) and other telescopes will be able to carry out relay observations of the entire sky with large percentage +time coverage, which will greatly enhance the development of the time-domain astronomy. +Acknowledgements This work is supported by the Strategic Priority Research Program of Chinese +Academy of Sciences (Grant No. XDB 41000000, XDB 41010105), the National Science Foundation of +China (NSFC, Grant No. 12233008, 12173037, 11973038), the China Manned Space Project (No. CMS- +CSST-2021-A07) and the Cyrus Chun Ying Tang Foundations. We thank Fredrik T Rantakyrand Rodolfo +Angeloni from Gemini Observatory for their patient elaboration on the Hawaii sky spectrum model and sky +brightness measurements. +References +Bellm, E. 2014, in The Third Hot-wiring the Transient Universe Workshop, ed. P. R. Wozniak, M. J. +Graham, A. A. Mahabal, & R. Seaman, 27 +Bellm, E. C., Kulkarni, S. R., Barlow, T., et al. 2019, PASP, 131, 068003 +Bessell, M., & Murphy, S. 2012, PASP, 124, 140 +Bessell, M. S. 1990, PASP, 102, 1181 +Chambers, K. C., & Pan-STARRS Team. 2016, in American Astronomical Society Meeting Abstracts, Vol. +227, American Astronomical Society Meeting Abstracts #227, 324.07 +Chen, J., Zhang, H.-f., Wang, J., Chen, J.-t., & Zhang, J. 2019, in Society of Photo-Optical Instrumentation +Engineers (SPIE) Conference Series, Vol. 11101, Material Technologies and Applications to Optics, +Structures, Components, and Sub-Systems IV, 111010D +Deng, L., Yang, F., Chen, X., et al. 2021, Nature, 596, 353 + +Limiting Magnitudes of WFST +11 +Fukugita, M., Ichikawa, T., Gunn, J. E., et al. 1996, AJ, 111, 1748 +Gao, H.-X., Geng, J.-J., Hu, L., et al. 2022, MNRAS +Graham, M. J., Kulkarni, S. R., Bellm, E. C., et al. 2019, PASP, 131, 078001 +Hlozek, R., Albert, J., Balogh, M., et al. 2019, in Canadian Long Range Plan for Astronomy and +Astrophysics White Papers, Vol. 2020, 51 +Hu, M., Hu, L., Jiang, J.-a., et al. 2022, Universe, 9, 7 +Jedicke, R., & Pan-STARRS. 2007, in AAS/Division for Planetary Sciences Meeting Abstracts, Vol. 39, +AAS/Division for Planetary Sciences Meeting Abstracts #39, 8.02 +Jones, A., Noll, S., Kausch, W., Szyszka, C., & Kimeswenger, S. 2013, A&A, 560, A91 +Kent, S. M. 1994, Ap&SS, 217, 27 +Krisciunas, K., & Schaefer, B. E. 1991, PASP, 103, 1033 +Lei, L., Chen, B.-Q., Li, J.-D., et al. 2022, Research in Astronomy and Astrophysics, 22, 025004 +Lei, L., Li, J. D., Wu, J. T., Jiang, S. Y., & Chen, B. Q. 2021, Astronomical Research & Technology, 18, +115121 +Lin, Z., Jiang, N., & Kong, X. 2022, MNRAS, 513, 2422 +Liu, X. 2019, in Galactic Archaeology in the Gaia Era, 14 +Lou, Z., Liang, M., Zheng, X. Z., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) +Conference Series, Vol. 11445, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference +Series, 114454A +Lou, Z., Liang, M., Yao, D., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) +Conference Series, Vol. 10154, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference +Series, 101542A +Moehler, S., Modigliani, A., Freudling, W., et al. 2014, A&A, 568, A9 +Noll, S., Kausch, W., Barden, M., et al. 2012, A&A, 543, A92 +Petrova, E., Podladchikova, T., Veronig, A. M., et al. 2021, ApJS, 254, 9 +Rakich, A., Blundell, M., Pentland, G., et al. 2006, in Society of Photo-Optical Instrumentation Engineers +(SPIE) Conference Series, Vol. 6267, Society of Photo-Optical Instrumentation Engineers (SPIE) +Conference Series, ed. L. M. Stepp, 62670E +Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, AJ, 116, 1009 +Riess, A. G., Yuan, W., Macri, L. M., et al. 2022, ApJ, 934, L7 +Schmidt, B. P., Keller, S. C., Francis, P. J., & Bessell, M. S. 2005, in American Astronomical Society +Meeting Abstracts, Vol. 206, American Astronomical Society Meeting Abstracts #206, 15.09 +Shi, D. D., Zheng, X. Z., Zhao, H. B., et al. 2018, Acta Astronomica Sinica, 59, 22 +Sparavigna, A. 2008, arXiv e-prints, arXiv:0804.1941 +Tokovinin, A., Baumont, S., & Vasquez, J. 2003, MNRAS, 340, 52 +Wang, H., Lou, Z., Qian, Y., Zheng, X., & Zuo, Y. 2016, Optical Engineering, 55, 035105 +Yu, J., Song, H., Ai, S., et al. 2021, ApJ, 916, 54 +Yuan, H.-B., Deng, D.-S., & Sun, Y. 2021, Research in Astronomy and Astrophysics, 21, 074 +Yuan, X., Li, Z., Liu, X., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) + +12 +Lei et al. +Conference Series, Vol. 11445, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference +Series, 114457M +Zhao, H., Li, Y., & Zhang, C. 2016, IEEE Geoscience and Remote Sensing Letters, 13, 1139 +Zhu, J.-P., Wu, S., Yang, Y.-P., et al. 2021, arXiv e-prints, arXiv:2110.10469 +Zhu, J.-P., Yang, Y.-P., Zhang, B., Gao, H., & Yu, Y.-W. 2022, ApJ, 938, 147 + diff --git a/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/load_file.txt b/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..269e9384d204fd87df4a04cadeabf27ac2be9096 --- /dev/null +++ b/4dE1T4oBgHgl3EQfSgPo/content/tmp_files/load_file.txt @@ -0,0 +1,834 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf,len=833 +page_content='Research in Astronomy and Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (LATEX: ms2022-0349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='tex;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' printed on January 10, 2023;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1:43) Limiting Magnitudes of the Wide Field Survey Telescope (WFST) Lei Lei (雷磊)1,2, Qing-Feng Zhu (朱青峰)1,3, Xu Kong (孔旭)1,3, Ting-Gui Wang (王挺贵)1,3, Xian-Zhong Zheng (郑宪忠)1,2, Dong-Dong Shi (师冬冬)2, Lu-Lu Fan (范璐璐)1,3 and Wei Liu (刘伟)2 1 School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' zhuqf@ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='cn 2 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3 Deep Space Exploration Laboratory / Department of Astronomy, University of Science and Technology of China, Hefei 230026, China;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Received 20xx month day;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' accepted 20xx month day Abstract Expected to be of the highest survey power telescope in the northern hemisphere, the Wide Field Survey Telescope (WFST) will begin its routine observations of the northern sky since 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' WFST will produce a lot of scientific data to support the researches of time- domain astronomy, asteroids and the solar system, galaxy formation and cosmology and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We estimated that the 5 σ limiting magnitudes of WFST with 30 second exposure are u = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='31 mag, g = 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='42 mag, r = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95 mag, i = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='43 mag, z = 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50 mag, w = 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The above values are calculated for the conditions of airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2, seeing = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 arcsec, precipitable water vapour (PWV) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 mm and Moon-object separation = 45◦ at the darkest New Moon night of the Lenghu site (V=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 mag, Moon phase θ = 0◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The limiting magnitudes in different Moon phase conditions are also calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The calculations are based on the empirical transmittance data of WFST optics, the vendor provided CCD quantum efficiency, the atmospherical model transmittance and spectrum of the site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In the absence of measurement data such as sky transmittance and spectrum, we use model data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Key words: techniques: photometric — surveys — telescopes 1 INTRODUCTION The Wide Field Survey Telescope (WFST;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022) is an optical telescope to be installed at the Lenghu site, located on Saishiteng mountain near Lenghu Town in Qinghai Province on the Tibetan Plateau, China in 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The WFST has a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5-m diameter primary mirror and a 5-lens corrector to form a prime-focus optics (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The detector of WFST consists of nine 9K×9K CCD chips and has 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='9 Giga pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The entire system is arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='03068v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='IM] 8 Jan 2023 2 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' optimized for the wavelength range from 3200 ˚A to 9600 ˚A (Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' With the aid of an active optics system and an ADC (atmospheric dispersion compensator), WFST can achieve an image quality of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='4 arcsec 80% energy enclosed across a field of view of 3 degree diameter and ∼7 deg2 area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' WFST is able to survey ∼ 2 × 104 deg2 northern sky in ugrizw six bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' As a powerful survey telescope, its scientific data will greatly support researches of time-domain astronomy, asteroids and the solar system, the Milky Way and its satellite dwarf galaxies, galaxy formation and cosmology and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In recent years, many large ground-based optical survey telescopes have been built or planned all over the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' SDSS (Kent 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Fukugita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1996), Pan-STARRS (Jedicke & Pan-STARRS 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Chambers & Pan-STARRS Team 2016), SkyMapper (Schmidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Rakich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2006), ZTF (Bellm 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Bellm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019) and other built telescopes have produced a large amount of observa- tion data, which has greatly promoted astronomical researches and solved many scientific problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Soon new, survey telescopes such as LSST (Hlozek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019), Mephisto (Liu 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020) and WFST will join their peers and conduct deeper multi-band surveys to provide crucial data to astrophysical researches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Combined with China Space Station Telescope (CSST;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021) and other space telescopes, WFST will greatly improve human understanding of the universe and promote more important scientific discoveries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The parameters of a survey telescope, such as the diameter of the primary mirror, quantum efficiency (QE) of CCD, band transmittance, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', determine the throughput of the telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The site conditions of an astronomical observatory, such as atmospheric transmittance, altitude, seeing and sky background bright- ness, affect the depth of a survey program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='. The limiting magnitude of a survey telescope is an important guide for planning research objectives and project scopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' It is also the key for designing exposure time plans and survey strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Therefore, an accurate estimation of the limiting magnitudes are needed for the successful commission of a new telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In this work, we introduce the estimation of the limiting magnitudes of WFST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2 we describe the method we adopt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3 we show our results of limiting magnitudes of the WFST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2 LIMITING MAGNITUDES 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='1 Throughput of WFST The throughput of an astronomical observation (Ttot) is limited by the atmospheric transmittance (Tatmo), the transmittance of optics (Topt), the transmittance of the filters Tband) and the quantum efficiency of CCD (QECCD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Ttot = Tatmo · Topt · Tband · QECCD (1) The optical system of WFST consists of a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 meter diameter primary mirror with a 760 mm diameter central hole, five corrector lenses, a ADC made with two glass wedges and ugrizw six switchable filters (Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Among five correcting lenses, only one is made of the N-BK7HT glass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The others and ADCs are made of the fused quartz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Since the transmittance of a fused quartz blank can be neglected, we simulate the total transmittance of the five-lens corrector and the ADC with the product of the transmittance of a 35 mm thick N-BK7 glass blank and the transmittance of 14 layers of anti-reflection (AR) coatings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Limiting Magnitudes of WFST 3 The transmittance of the N-BK7 glass is obtained from SCHOTT1 and the transmittance of the AR coating is from Institute of Optics and Electronics (IOE) ’s measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Because of the oversized Primary Focus Assembly (PFA), the actual aperture obscuration is 1 m diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Because we don’t have atmospheric transmitance and spectrum measurements at the site, we adopt SkyCalc2 (Version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='9) to obtain model curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' SkyCalc is developed by astronomers in ESO based on the Cerro Paranal Advanced Sky Model (Noll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Moehler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The atmospheric transmittance is affected by altitude, humidity, dust, precipitable water vapour (PWV), among which the altitude is the most important factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' SkyCalc only provides the atmospheric transmittance at three astronomical sites: Paranal (2400 m), La Silla (2600 m) and Extremely Large Telescope (ELT) site (3060 m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 1 shows the three transmittance curves of the sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We can see that three curves have same features that they are scaled according to different altitudes of three sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' This is reasonable because the geographic features of the three sites are very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Paranal Observatory is on the Cerro Paranal mountain, which is in the Atacama Desert of northern Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The La Silla Observatory is located on the outskirts of the Chilean Atacama Desert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The 40-metre-class ELT is on the Cerro Armazones mountain in the central part of the Atacama Desert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' WFST is on the Saishiteng mountain in the Gobi desert area on the Tibetan Plateau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We consider that the geographic features of the area are more similar to those of sites in the high-altitude Atacama desert than those of oceanic mountain areas, such as Mauna Kea in Hawaii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' It is a reasonable choice to obtain the atmospheric transmittance of the WFST site by using the spectra from SkyCalc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' So we get the atmospheric transmittance curve of the WFST site at an altitude of 4200 m by scaling the atmospheric transmittance curves of paranal, lasilla and ELT sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In our simulations, we assume that airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 and precipitable water vapour (PWV) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 1 also shows the result of scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3000 4000 5000 6000 7000 8000 9000 10000 11000 wavelength(Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 Transmission 10550 10560 10570 10580 10590 10600 10610 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='974 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='976 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='978 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='980 3060 m 2640 m 2400 m 4200 m Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1: The atmospheric transmittance curves of Paranal Observatory (2400 m), La Silla Observatory (2600 m) and the Extremely Large Telescope site (3060 m), the scaled transmittance curve of the WFST site (4200 m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We assume the WFST site has the same geographic features (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' high altitude Mountain and dry air) as the three ESO sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1 https://refractiveindex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='info/?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='shelf=glass&book=BK7&page=SCHOTT 2 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='eso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='org/observing/etc/bin/gen/form?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='INS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='MODE=swspectr+INS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='NAME=SKYCALC 4 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' As shown in Figure 2(a), combined system throughput, individual transmittance curves of the atmo- sphere and the corrector, the reflectivity of the primary mirror and the quantum efficiency of the CCD are plotted respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We also plot the original estimate of the system throughput for WFST by Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We can see that the updated system throughput is higher than the early expectation in most wave- lengths (Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The major reason is that the transmittances of ADC and optical lenses are higher than the early estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In order to obtain high efficiency in short wavelengths, WFST selects e2v standard Si back-illuminated CCD detectors with the astro multi-2 coating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The QE of the CCDs is also increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 2(b) shows the transmittance of the filters and the total throughput of WFST in six bands, which is calculated by using Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3000 4000 5000 6000 7000 8000 9000 10000 wavelength (Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 Efficiency a) Atmosphere Primary Mirror Lenses CCD Atmosphere + Primary Mirror + Lenses + CCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2018 Atmosphere + Primary Mirror + Lenses + CCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' This work 3000 4000 5000 6000 7000 8000 9000 10000 wavelength (Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 b) u g r i z w Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2: (a) The transmittance curves of the atmosphere (blue dot-dashed line), the optics including lenses and the ADC (green line), the reflectivity of the primary mirror (yellow line) and the quantum efficiency of the CCDs (cyan dot-dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The combined efficiency of the atmosphere, the optics and the CCDs is in purple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The red line shows the total efficiency of Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (b) The transmittance of each filter and the total efficiency in each WFST filter transmittance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 Noise of WFST Noise in astronomical CCD images mainly consists of the contributions from the artificial light on the ground, astrophysical sources, sky background, CCD dark current, and CCD readout noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The site of WFST is on Saishiteng mountain on the Tibetan Plateau, where the nearest residential area is Lenghu town which is ∼ 50 km from the observatory site and has a population of 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' There is no industrial activity and the ground light pollution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Haixi Mongolian and Tibetan Autonomous Prefecture of Qinghai Province has announced the 17800 square kilometres area of Lenghu as a dark night protecting region in the local law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' It protects the good observational conditions of the Lenghu astronomical site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2021) studied long-term astronomical conditions of the Lenghu site and pointed out that the sky background of a New Moon night can reach 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag arcsec−2 in the V band and the average night-sky brightness is around 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 mag arcsec−2 when the Moon is below the horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We adopt AB magnitude system in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The sky background spectrum of the Lenghu site is also calculated by the software SkyCalc (Noll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Moehler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The monthly averaged solar radio flux is equal to 130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 sfu, that is the solar 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='7 cm radio flux in the Sun median active level (Sparavigna 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Petrova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Because the solar activities will affect the sky background brightness, it is necessary to take the Limiting Magnitudes of WFST 5 solar activities into account when we estimate the sky background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We adopt the median values obtained from long-term solar monitoring programs as the baseline solar brightness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The spectral flux of one sky region is related to the Moon-Target separation and the Moon phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We designate the Moon phase with the Moon phase angle (θ) 0◦ (New Moon), 45◦ (Waxing), 90◦ (Half Moon Waxing), 135◦ (Waxing), 180◦ (Full Moon) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We assume the separation of the Moon and a target is always 45◦ in our calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' So the spectral flux of one region is only dependent on the altitude and the Moon phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We get the sky background spectra towards the Zenith under different Moon phase conditions at the Lenghu Observatory site by scaling the spectra of three ESO sites provided by SkyCalc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 3(a) shows the sky background spectrum at the altitude of 4200 m (θ = 180◦, here we just plot the spectra at a full Moon night because it is easier to see their difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' ), and the spectra of the three ESO sites at Full Moon night.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 3(b) shows the sky spectra at Lenghu site under six different Moon phase conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' As shown in the detail part of Figure 3(b), the sky background spectrum at a New Moon night (θ = 0◦) and the sky spectrum at a Dark night have almost the same flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3000 4000 5000 6000 7000 8000 9000 10000 11000 wavelength(Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 flux (photons s 1 Å 1 arcsec 2 m 2) a) = 180 5175 5200 5225 5250 5275 5300 5325 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='450 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='475 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='525 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='550 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='575 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='600 4200 m 3060 m 2640 m 2400 m 3000 4000 5000 6000 7000 8000 9000 10000 11000 wavelength(Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 flux (photons s 1 Å 1 arcsec 2 m 2) b) 4500 4600 4700 4800 4900 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='014 Dark night = 0 = 45 = 90 = 135 = 180 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3: (a) The sky background spectrum (purple) at Zenith at the altitude of 4200 m in the Full Moon condition, and the spectra of three ESO sites when the Moon phase is θ = 180◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (b) The Zenith sky spectra of the 4200 m site in different Moon phase conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The sky background spectrum of Moon phase θ = 180◦ and the spectrum of a dark night (when the Moon is under the horizon) have almost the same flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We can get the magnitude mV by integrating the sky background spectrum multiplied by the V band filter transmission curve: mV = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 × � log10 � ∞ 0 fλTband,λdλ � ∞ 0 Tband,λdλ � − 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='1 (2) where fλ is sky background spectral flux, Tband is the Johnson V band transmission curve (Bessell, 1990), ZP = −21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='1 is the zero point (Bessell & Murphy 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The modeled sky emission radiance flux from SkyCalc is in units of photon/s/m2/micron/arcsec2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Johnson V band sky background magnitude of a New Moon night with the SkyCalc model spectrum at an altitude of 4200 m is 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='74 mag arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We scale the 4200 m sky background spectrum so that the resulting spectrum has a V-band magnitude of 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 or 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 mag arcsec−2, corresponding to the best and the average sky brightness conditions at the Lenghu site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' As shown in Figure 3(b), there are differences among the sky spectra under different Moon 6 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' phase conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We scale these sky spectra at different Moon phases use the the same scaling factor in the new moon case, where we scale the spectrum from V θ=0◦ = 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='74 to 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 mag arcsec−2, so that differences among spectra at different Moon phases are not changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The estimated V band Zenith sky background magnitudes at the Lenghu site with different Moon phases are: V θ=0◦, V θ=45◦, V θ=90◦, V θ=135◦, V θ=180◦=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10, 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='29, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='28, 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='90 mag arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Lenghu sky background spectrum is calculated for airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' It can be scaled to another airmass by multiplying a factor a (Krisciunas & Schaefer 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' a = 10−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='172 (X−1)X 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 (3) when airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2, X is X = 1 � (1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='96 × sin (arccos ( 1 airmass))2) ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='18958 (4) Based on the sky background spectrum of the Lenghu site, we estimate the magnitudes of the sky background in each band mAB band: mAB band = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 × log10 �Skyband ZPband � (5) where ZPband = � ∞ 0 fluxABTband,λdλ (6) where fluxAB = 3631Jy for all frequencies, and Tband,λ is the transmittance curve of a particular band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Skyband = � ∞ 0 fλTband,λdλ (7) where fλ is sky background spectral flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Table 1 shows the sky background magnitudes mAB in WFST six bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Table 1: The sky background brightness mAB of WFST six bands in units of mag arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Moon Phases u g r i z w 0◦ 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='27 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='82 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='05 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='78 45◦ 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='02 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='49 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='66 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='93 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='03 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='64 90◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='37 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='90 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 135◦ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='86 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='21 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='08 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='12 180◦ 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='73 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='78 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='97 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='92 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80 Note: The sky spectra is calculated by SkyCalc when airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0, PWV = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We calculated the sky background brightness mAB when airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 Limiting Magnitudes of WFST Assuming the signal to noise ratio of WFST in all bands for a point source is S/N, we can write the formula of the S/N as : S N = S · A · τ � S · A · τ + 2 · npix · [(Sky · A · αpix + D) · τ + R2] (8) where S is the source signal with a constant spectral flux, τ is the standard exposure time (30 s), A is the effective area of the primary mirror (∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='12 × 104 cm2), αpix = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='111 arcsec2 is the area of one Limiting Magnitudes of WFST 7 pixel, D is the dark current of the CCD (D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='005 e−/pixel/s, @−100◦C), R2 is the readout noise of the CCD (R = 8 e− rms), npix is the total pixel number in the point spread function (PSF), the usage of a factor 2 is because we assume the calculation is performed on sky subtracted images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' An optimal PSF aperture of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='18 times of the full width at half maximum (FWHM) is adopted for a non-Adaptive Optics case according to the Integration Time Calculator (ITC) of Gemini3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' And the FWHM of the seeing degrades with the airmass and the wavelength as (airmass)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='6 × λ−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 eff .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Here λeff takes the value of 356.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='17, 476.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='34, 620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='57, 753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='07, 870.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='45, 612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='15 nm in the six bands ugrizw given by the Equation 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' λeff = � ∞ 0 λTband dλ � ∞ 0 Tband dλ (9) With the seeing = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 arcsec measured by Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2021) at 500 nm (Tokovinin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', 2003), we estimated the seeing values in different bands and airmass conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The sky signal actually lands on the detector is: Sky = � ∞ 0 fλToptTbandQECCD dλ (10) where Topt is the throughput of the optics (including the primary mirror, ADC and the 5 corrector lenses), QECCD is the quantum efficiency of the CCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We can solve the Equation 8 to obtain the signal of an astronomical object required at the detection limit of S/N = 5 and find the corresponding limiting magnitude mlim: mlim = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 × log10 � S 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 · ZPlim � (11) A factor 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 is used because according to the description of ITC, the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='18 FWHM sized aperture will contain 61% energy of a point source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The ZPlim is the system zero point flux: ZPlim = � ∞ 0 fluxABTatmoToptTbandqeCCD dλ (12) Table 2 lists the calculated limiting magnitudes of ugrizw six bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We calculated the limiting mag- nitudes of WFST at different Moon phases when the sky background brightness is V=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 mag and 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The results of a single exposure of 30 s and of coadded 100 frames with a total integration time of 100 × 30 s are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' It shows that WFST can reach 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='42 (25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95) mag in the g band with a 30 s (100 × 30 s) exposure under the conditions with the sky background brightness V=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag, seeing =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 arcseconds, airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 and PWV=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' If the sky background is V=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 mag, the above values are 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='32 (25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='85) mag for 30 s (100 × 30 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 3 DISCUSSION AND CONCLUSIONS In the current work, by considering the observational conditions of WFST, including throughput, quantum efficiency, the noise, the area of the primary mirror and the sky background brightness, we compute the limiting magnitudes of WFST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We get the sky background magnitudes in AB magnitude system in the Lenghu site at the New Moon night when airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2: u, g, r, i, z, w=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='27, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='82, 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='05, 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='78 mag arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' For the Lenghu darkest night condition (V=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag arcsec−2) and a exposure time 3 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='gemini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='edu/observing/resources/itc/itc-help 8 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Table 2: 5σ limiting magnitudes of WFST when airmass=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2, seeing = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 arcsec, precipitable water vapour (PWV) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 mm and Moon-object separation is 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Exposure time Moon Phase V band sky u g r i z w 30 s 0◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='31 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='42 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='43 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 30 s 45◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='27 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='89 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='40 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='49 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='54 30 s 90◦ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='29 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='04 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='86 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='62 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='26 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='43 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='23 30 s 135◦ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='28 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='64 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='34 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='21 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='31 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='79 30 s 180◦ 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='90 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='97 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='62 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='58 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='49 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='13 100 × 30 s 0◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='86 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='48 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='96 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='03 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='13 100 × 30 s 45◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='82 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='84 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='42 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='93 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='02 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='06 30 × 100 s 90◦ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='29 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='58 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='38 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='14 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='78 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='96 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='74 100 × 30 s 135◦ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='28 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='17 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='85 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='72 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='51 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='83 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 100 × 30 s 180◦ 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='90 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='48 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='12 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='09 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='51 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='64 30 s 0◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='26 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='32 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='83 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='37 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='47 30 s 45◦ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='21 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='19 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='77 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='28 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='37 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='40 30 s 90◦ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='74 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='48 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='12 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='29 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='09 30 s 135◦ 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='98 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='52 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='19 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='07 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='85 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='18 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='64 30 s 180◦ 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='60 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='83 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='47 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='44 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='35 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='86 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 100 × 30 s 0◦ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='81 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='85 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='36 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='83 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='90 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 100 × 30 s 45◦ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='76 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='72 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='30 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='80 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='89 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='92 100 × 30 s 90◦ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='99 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='48 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='25 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='01 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='65 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='83 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='60 100 × 30 s 135◦ 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='98 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='05 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='71 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='58 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='37 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='70 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='15 100 × 30 s 180◦ 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='60 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='34 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='98 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='86 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='38 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='49 Note: The V-band sky brightness is the Zenith sky background magnitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' of 30 s, the 5σ limiting magnitudes of WFST are: ulim, glim, rlim, ilim, zlim, wlim = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='31, 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='42, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='95, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='43, 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50, 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='61 mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The current estimates of limiting magnitudes are deeper than those in Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' This is because the current total throughput of WFST is higher than previous value, especially the throughput increases by ∼ 50% from ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='4 to ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='6 in gri bands (see Figure 2(a)), and the current Dark night sky background is lower than the previous estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Figure 4 compares the sky spectrum of New Moon night of the Lenghu site and the atmospheric transmittance curve between this work and Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We used SkyCalc to estimate the sky background spectrum and atmospheric transmittance, while Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018) used the software MODTRAN4 for estimating the atmospheric transmittance at the 5130 m Ali area and used a Hawaii sky background spectrum as a sky background spectral template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The Hawaii sky brightness in ugz bands is brighter than the current model when we scaled both of them into the same conditions of mV = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag arcsec−2 and airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 (see Figure 4 (a)), Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018) assumed the V band sky brightness is mV = 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50 mag arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' There is little difference between the current atmospheric transmittance model and the spectrum in Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018) (see Figure 4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Our scaled atmospheric transmittance is close to the model of MODTRAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We also obtain the limiting magnitudes of WFST under various conditions (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In Figure 5, the panel (a) shows the WFST limiting magnitudes of different signal-to-noise ratio when the exposure time equals to 30 s and 100 × 30 s respectively, the panel (b) shows the limiting magnitudes of different seeing 4 http://modtran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='spectral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='com/ Limiting Magnitudes of WFST 9 3000 4000 5000 6000 7000 8000 9000 10000 11000 wavelength (Å) 10 3 10 2 10 1 10 0 10 1 flux (photons s 1 Å 1 arcsec 2 m 2) a) Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018) This work 3000 4000 5000 6000 7000 8000 9000 10000 11000 wavelength (Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 Atmospheric Transmission b) Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018) This work Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 4: (a) The red line shows the sky background spectrum of Lenghu site at New Moon night (Moon phase θ = 0◦), mV = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag, airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The black dashed line shows the Hawaii sky background spectrum scaled into mV = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 mag and airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 in Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (b) The red line shows the atmospheric transmittance curve of Lenghu site estimated by SkyCalc in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The black dashed line shows the atmospheric transmittance curve of Shiquanhe astronomical site at an altitude of 5130 m at the Ali Area on the Tibetan Plateau estimated by the software MODTRAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' conditions when signal-to-noise ratio = 5 and the exposure time = 30 s, 100 × 30 s respectively, and the panel (c) shows the 5σ limiting magnitudes of different exposure times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' These results are calculated with the sky spectrum scaled into airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 condition at a New Moon night (Moon phase θ = 0◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 S/N 19 20 21 22 23 24 25 26 27 mag a) exposure time = 30 s exposure time = 100 × 30 s 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='00 seeing (arcsec) 20 21 22 23 24 25 26 mag b) exposure time = 30 s exposure time = 100 × 30 s 50 100 150 200 exposure time (s) 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='0 mag c) u g r i z w Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 5: (a) The limiting magnitudes of different S/N values when the exposure time is 30 s (dot-dashed line) and 100 × 30 s (solid line);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (b) The 5σ limiting magnitudes of different seeing conditions when the exposure time is 30 s (dot-dashed line) and 100 × 30 s (solid line);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (c) The 5σ limiting magnitudes of different exposure times when the seeing is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='75 arcsec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The conditions for a New Moon night (θ = 0◦) and airmass = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Note: The limiting magnitude curves of the g band (blue) and the w band (red) are so close that we can not distinguish the two curves easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The WFST survey data will cover the entire northern sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Its stacked scientific image data can be used to study asteroids, solar system, galaxies and cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Its light curves can be used to discover variable objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' The estimated WFST limiting redshift of Type Ia supernovae (SNe Ia) can reach z∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='64 (luminosity distance ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='3 × 103 Mpc) and z∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='67 (∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2 × 104 Mpc) when the exposure time is 30 s and 100 × 30 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' SNe Ia can be used to constrain the dark energy in the universe (Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', 1998) and directly measure the Hubble constant (Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' By simulating observations of the SNe Ia with the WFST at the Lenghu site, Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2022) estimate that above 104 pre-maximum SNe Ia will be discovered in one-year during the 10 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' wide or deep observations, which suggests that WFST will be a powerful facility in revealing the physics of SNe Ia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2022) computed the prospects of finding Tidal Disruption Events (TDEs) with the WFST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Their mock observations on 440 deg2 field (CosmoDC2 catalogue) show that ∼ 30 TDEs can be found per year if observed at ugrizw bands with 30 s exposures every 10 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' According to Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2022), the event rate for galaxy-lensed orphan afterglows of γ-ray bursts (GRBs) is to be less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='7 yr−1 for the whole sky survey of the WFST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2021) estimated the multi-messenger detection rate of Binary Neutron Star Mergers is about 300-3500 yr−1 with a GECAM-like detector for γ-ray emissions and an LSST/WFST detector for optical afterglows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2021) and Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' (2022) showed that the optimal detection rates of the KN-dominated and AG-dominated GRB afterglows events are ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='2/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='5/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='8/20 yr−1 and ∼500/300/600/3000 yr−1 for ZTF/Mephisto/WFST/LSST, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' There are also some studies looking forward to detecting Active galactic nucleus (AGN) and researching AGN physics using WFST survey data (Xu-Fan Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' in preparation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' There are large sky survey telescopes that have been built around the world, and a number of large sky survey telescopes are being built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' These projects have produced or will generate a large amount survey data and have an important impact in all fields of astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Among them, the WFST will be completed in 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' In the future, WFST (Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Shi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2018), together with Mephisto (Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' in preparation), Pan-STARRS (Jedicke & Pan-STARRS 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Chambers & Pan-STARRS Team 2016), SkyMapper (Schmidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Rakich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2006), ZTF (Bellm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019) and other telescopes will be able to carry out relay observations of the entire sky with large percentage time coverage, which will greatly enhance the development of the time-domain astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Acknowledgements This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' XDB 41000000, XDB 41010105), the National Science Foundation of China (NSFC, Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 12233008, 12173037, 11973038), the China Manned Space Project (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' CMS- CSST-2021-A07) and the Cyrus Chun Ying Tang Foundations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' We thank Fredrik T Rantakyrand Rodolfo Angeloni from Gemini Observatory for their patient elaboration on the Hawaii sky spectrum model and sky brightness measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' References Bellm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2014, in The Third Hot-wiring the Transient Universe Workshop, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Wozniak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Graham, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Mahabal, & R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Seaman, 27 Bellm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Kulkarni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Barlow, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019, PASP, 131, 068003 Bessell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Murphy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2012, PASP, 124, 140 Bessell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1990, PASP, 102, 1181 Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Pan-STARRS Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016, in American Astronomical Society Meeting Abstracts, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 227, American Astronomical Society Meeting Abstracts #227, 324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='07 Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 11101, Material Technologies and Applications to Optics, Structures, Components, and Sub-Systems IV, 111010D Deng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Yang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, Nature, 596, 353 Limiting Magnitudes of WFST 11 Fukugita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Ichikawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Gunn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1996, AJ, 111, 1748 Gao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Geng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Hu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, MNRAS Graham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Kulkarni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Bellm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019, PASP, 131, 078001 Hlozek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Albert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Balogh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019, in Canadian Long Range Plan for Astronomy and Astrophysics White Papers, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020, 51 Hu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Hu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, Universe, 9, 7 Jedicke, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Pan-STARRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2007, in AAS/Division for Planetary Sciences Meeting Abstracts, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 39, AAS/Division for Planetary Sciences Meeting Abstracts #39, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='02 Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Noll, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Kausch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Szyszka, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Kimeswenger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2013, A&A, 560, A91 Kent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1994, Ap&SS, 217, 27 Krisciunas, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Schaefer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1991, PASP, 103, 1033 Lei, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, Research in Astronomy and Astrophysics, 22, 025004 Lei, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Jiang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, Astronomical Research & Technology, 18, 115121 Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Jiang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Kong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, MNRAS, 513, 2422 Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2019, in Galactic Archaeology in the Gaia Era, 14 Lou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Liang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 11445, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114454A Lou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Liang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 10154, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 101542A Moehler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Modigliani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Freudling, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2014, A&A, 568, A9 Noll, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Kausch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Barden, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2012, A&A, 543, A92 Petrova, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Podladchikova, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Veronig, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, ApJS, 254, 9 Rakich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Blundell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Pentland, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 6267, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Stepp, 62670E Riess, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Filippenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Challis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 1998, AJ, 116, 1009 Riess, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Yuan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Macri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, ApJ, 934, L7 Schmidt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Keller, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Francis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Bessell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2005, in American Astronomical Society Meeting Abstracts, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 206, American Astronomical Society Meeting Abstracts #206, 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='09 Shi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zhao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2018, Acta Astronomica Sinica, 59, 22 Sparavigna, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2008, arXiv e-prints, arXiv:0804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='1941 Tokovinin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Baumont, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Vasquez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2003, MNRAS, 340, 52 Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Lou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Qian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Zuo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016, Optical Engineering, 55, 035105 Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Song, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Ai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, ApJ, 916, 54 Yuan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Deng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, Research in Astronomy and Astrophysics, 21, 074 Yuan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) 12 Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 11445, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114457M Zhao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2016, IEEE Geoscience and Remote Sensing Letters, 13, 1139 Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2021, arXiv e-prints, arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='10469 Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', Gao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=', & Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} +page_content=' 2022, ApJ, 938, 147' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE1T4oBgHgl3EQfSgPo/content/2301.03068v1.pdf'} diff --git a/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/2301.03295v1.pdf.txt b/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/2301.03295v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf930027a8fd20c9b2d5cf827846fa532ed28dca --- /dev/null +++ b/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/2301.03295v1.pdf.txt @@ -0,0 +1,1259 @@ +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL +REGRESSION +TORSTEN REUTER AND RAINER SCHWABE +Abstract. Improvements in technology lead to increasing availability of large +data sets which makes the need for data reduction and informative subsamples +ever more important. +In this paper we construct D-optimal subsampling +designs for polynomial regression in one covariate for invariant distributions +of the covariate. +We study quadratic regression more closely for specific +distributions. In particular we make statements on the shape of the resulting +optimal subsampling designs and the effect of the subsample size on the design. +To illustrate the advantage of the optimal subsampling designs we examine the +efficiency of uniform random subsampling. +1. Introduction +Data Reduction is a major challenge as technological advances have lead to a +massive increase in data collection to a point where traditional statistical methods +fail or computing power can not keep up. In this case we speak of big data. We +typically differentiate between the case where the number of covariates is much +larger than the number of observations and the case where the massive amount of +observations is the problem. The first case is well studied, most notably by Tibshirani +(1996) introducing LASSO, which utilizes ℓ1 penalization to find sparse parameter +vectors, thus fusing subset selection and ridge regression. The second case, often +referred to as massive data, can be tackled in two ways. Firstly in a probabilistic +fashion, creating random subsamples in a nonuniform manner. Prominent studies +include Drineas et al. (2006), Mahoney (2011) and Ma et al. (2014). They present +subsampling methods for linear regression models called algorithmic leveraging +that sample according to probabilities based on the normalized statistical leverage +scores of the covariate matrix. More recently Derezi´nski and Warmuth (2018) study +volume sampling, where subdata is chosen proportional to the squared volume of +the parallelepiped spanned by its observations. Conversely to these probabilistic +methods one can select subdata by applying deterministic rules. Shi and Tang +(2021) present such a method, that maximizes the minimal distance between two +observations in the subdata. Wang et al. (2021) propose orthogonal subsampling +inspired by orthogonal arrays. Most prominently, Wang et al. (2019) introduce +the information-based optimal subdata selection (IBOSS) to tackle big data linear +regression in a deterministic fashion based on D-optimality. +In this paper we study D-optimal subsampling designs for polynomial regression +in one covariate, where the goal is to select a percentage α of the full data that +maximizes the determinant of the information matrix. For the conventional study of +2020 Mathematics Subject Classification. Primary: 62K05. Secondary: 62R07. +Key words and phrases. Subdata, D-optimality, Massive Data, Polyonmial Regression. +Corresponding author: Torsten Reuter. E-mail address: torsten.reuter@ovgu.de. +1 +arXiv:2301.03295v1 [math.ST] 9 Jan 2023 + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +2 +approximate designs in this setting we refer to Gaffke and Heiligers (1996). Heiligers +and Schneider (1992) consider specifically cubic regression on a ball. We consider +D-optimal designs with measure α that are bounded from above by the distribution +of the known covariate. Such directly bounded designs were first studied by Wynn +(1977) and Fedorov (1989). Pronzato (2004) considers this setting using a form +of the subsampling design standardized to one and bounded by α−1 times the +distribution of the covariates. More recently, Pronzato and Wang (2021) studies +the same in the context of sequential subsampling. For the characterization of the +optimal subsampling designs we make use of an equivalence theorem by Sahm and +Schwabe (2001). This equivalence theorem enables us to construct such designs for +various settings of the distributional assumptions on the covariates. Here we will +only look at distributions of the covariate that are invariant to a sign change, i.e. +symmetric about the vertical axis. We discuss the shape of D-optimal subsampling +designs for polynomial regression of degree q first. We conclude that the D-optimal +design is equal to the bounding distribution in its support and the support of the +optimal design will be the union of at most q + 1 intervals that are symmetrically +placed around zero. We then study quadratic regression under several distributional +assumptions more closely. In particular we take a look at the percentage of mass of +the optimal design on the outer intervals compared to the inner one, which changes +drastically given the distribution of the covariate. In addition we examine the +efficiency of uniform random subsampling to illustrate the advantage of the optimal +designs. All numerical results are obtained by the Newton method implemented in +the R package nleqslv by Hasselman (2018). +The rest of this paper is organized as follows. +In Section 2 we specify the +polynomial model. In Section 3 we introduce the concept of continuous subsampling +designs and give characterizations for optimization. In Sections 4 and 5 we present +optimal designs in the case of linear and quadratic regression, respectively, for +various classes of distributions of the covariates. Section 6 contains some efficiency +considerations showing the strength of improvement of the performance of the +optimal design compared to random subsampling. The paper concludes with a +discussion in Section 7. Proofs are deferred to an Appendix. +2. Model Specification +We consider the situation of pairs (xi, yi) of data, where yi is the value of the +response variable Yi and xi is the value of a single covariate Xi for unit i = 1, . . . , n, +for very large numbers of units n. We assume that the dependence of the response +on the covariate is given by a polynomial regression model +Yi = β0 + β1Xi + · · · + βqXq +i + εi +with independent, homoscedastic random errors εi having zero mean (E(εi) = 0, +Var(εi) = σ2 +ε > 0). The largest exponent q denotes the degree of the polynomial +regression, and p = q + 1 is the number of regression parameters β0, . . . , βq to be +estimated, where, for each k = 1, . . . , q, the parameter βk is the coefficient for the kth +monomial xk, and β0 denotes the intercept. For example, for q = 1, we have ordinary +linear regression, Yi = β0 + β1Xi + εi, with p = 2 parameters β0 (intercept) and β1 +(slope) and, for q = 2, we have quadratic regression, Yi = β0 + β1Xi + β2X2 +i + εi, +with p = 3 and an additional curvature parameter β2. Further, we assume that + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +3 +the covariates Xi are identically distributed and that all covariates Xi and random +errors εi′ are independent. +For notational convenience, we write the polynomial regression as a general linear +model +Yi = f(Xi)⊤β + εi , +where f(x) = (1, x, . . . , xq)⊤ is the p-dimensional vector of regression functions and +β = (β0, β1, . . . , βq)⊤ is the p-dimensional vector of regression parameters. +3. Subsampling Design +We are faced with the problem that the responses Yi are expensive or difficult +to observe while the values xi of all covariates Xi are available. To overcome this +problem, we consider the situation that the responses Yi will be observed only for a +certain percentage α of the units (0 < α < 1) and that these units will be selected +on the basis of the knowledge of the values xi of the covariate for all units. As +an alternative motivation, we can consider a situation where all pairs (xi, yi) are +available but parameter estimation is computationally feasible only on a percentage +α of the data. In either case we want to find the subsample of pairs (xi, yi) that +yields the most precise estimation of the parameter vector β. +To obtain analytical results, the covariates Xi are supposed to have a continuous +distribution with density fX(x), and we assume that the distribution of the covariates +is known. The aim is to find a subsample of this distribution that covers a percentage +α of the distribution and that contains the most information. For this, we will +consider continuous designs ξ as measures of mass α on R with density fξ(x) +bounded by the density fX(x) of the covariates Xi such that +� +fξ(x) dx = α and +fξ(x) ≤ fX(x) for all x ∈ R. A subsample can then be generated according to such +a continuous design by accepting units i with probability fξ(xi)/fX(xi). +For a continuous design ξ, the information matrix M(ξ) is defined as M(ξ) = +� +f(x)f(x)⊤fξ(x) dx. In the present polynomial setup, M(ξ) = (mj+j′(ξ))j′=0,...,q +j=0,...,q , +where mk = +� +xkfξ(x) dx is the kth moment associated with the design ξ. Thus, it +has to be required that the distribution of Xi has a finite moment E(X2q +i ) of order +2q in order to guarantee that all entries in the information matrix M(ξ) exist for all +continuous designs ξ for which the density fξ(x) is bounded by fX(x). +The information matrix M(ξ) measures the performance of the design ξ in the +sense that the asymptotic covariance of the least squares estimator ˆβ based on a +subsample according to the design ξ is proportional to the inverse M(ξ)−1 of the +information matrix M(ξ) or, more precisely, nα( ˆβ−β) is asymptotically normal with +mean zero and covariance matrix σ2 +εM(ξ)−1. Note that for continuous designs ξ the +information matrix M(ξ) is of full rank and, hence, the inverse M(ξ)−1 exists. Based +on the relation to the asymptotic covariance matrix, it is desirable to maximize +the information matrix M(ξ). However, as well-known in design optimization, +maximization of the information matrix cannot be achieved uniformly with respect +to the Loewner ordering of positive-definiteness. Thus, commonly, a design criterion +which is a real valued functional of the information matrix M(ξ) will be maximized, +instead. We will focus here on the most popular design criterion in applications, the +D-criterion, in its common form log(det(M(ξ))) to be maximized. Maximization +of the D-criterion can be interpreted in terms of the asymptotic covariance matrix +to be the same as minimizing the volume of the confidence ellipsoid for the whole + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +4 +parameter vector β based on the least squares estimator or, equivalently, minimizing +the volume of the acceptance region for a Wald test on the whole model. The +subsampling design ξ∗ that maximizes the D-criterion log(det(M(ξ))) will be called +D-optimal, and its density is denoted by fξ∗(x). +To obtain D-optimal designs, we will make use of standard techniques coming +from constrained convex optimization and symmetrization. For convex optimization +we employ the directional derivative +FD(ξ, η) = lim +ϵ→0+ +1 +ϵ (log(det(M((1 − ϵ)ξ + ϵη))) − log(det(M(ξ)))) +of the D-criterion at a design ξ with non-singular information matrix M(ξ) in +the direction of a design η, where we allow here η to be a general design of +mass α that has not necessarily a density bounded by fX(x). Evaluating of the +directional derivative yields FD(ξ, η) = p − trace(M(ξ)−1M(η)) (compare Silvey, +1980, Example 3.8) which reduces to FD(ξ, ξx) = p − αf(x)⊤M(ξ)−1f(x) for a +one-point design η = ξx which assigns all mass α to a single setting x in the +design region. Equivalently, for one-point designs η = ξx, we may consider the +sensitivity function ψ(x, ξ) = αf(x)⊤M(ξ)−1f(x) which covers the essential part +of the directional derivative (ψ(x, ξ) = p − FD(ξ, ξx)). For the characterization +of the D-optimal continuous design, the constrained equivalence theorem under +Kuhn-Tucker conditions (see Sahm and Schwabe, 2001, Corollary 1 (c)) can be +reformulated in terms of the sensitivity function. +Theorem 3.1. The design ξ∗ is D-optimal if and only if there exist a threshold s∗ +and settings a1 > · · · > a2r for some r (1 ≤ r ≤ q) such that +(i) the D-optimal design ξ∗ is given by +fξ∗(x) = +� +fX(x) +if x ∈ X ∗ +0 +otherwise +(ii) ψ(x, ξ∗) ≥ s∗ for x ∈ X ∗, and +(iii) ψ(x, ξ∗) < s∗ for x ̸∈ X ∗, +where X ∗ = �r +k=0 Ik and I0 = [a1, ∞), Ir = (−∞, a2r], and Ik = [a2k+1, a2k], for +k = 1, . . . , r − 1, are mutually disjoint intervals. +The density fξ∗(x) = fX(x)1X ∗(x) = �r +k=0 fX(x)1Ik(x) of the D-optimal design +ξ∗ is concentrated on, at most, q + 1 intervals Ik. Here, 1A(x) denotes an indicator +function on the set A, i. e. 1A(x) = 1 for x ∈ A, and 1A(x) = 0 otherwise. The +density fξ∗(x) has a 0−1-property such that it is either equal to the density fX(x) of +the covariates (on X ∗) or equal to 0 (on the complement of X ∗). Then the generation +of a subsample according to the optimal continuous design ξ∗ can be implemented +easily by accepting all units i for which the value xi of the covariate is in X ∗ and +rejecting all other units with xi ̸∈ X ∗. The threshold s∗ can be interpreted as the +(1 − α)-quantile of the distribution of the sensitivity function ψ(Xi, ξ∗) as a function +of the random variable Xi (see Pronzato and Wang, 2021). +A further general concept to be used is equivariance. This can be employed +to transform the D-optimal design simultaneously with a transformation of the +distribution of the covariates. More precisely, the location scale transformation +Zi = σXi + µ of the covariates and their distribution is conformable with the +regression function f(x) in polynomial regression, and the D-criterion is equivariant +with respect to such transformations. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +5 +Theorem 3.2. Let fξ∗(x) be the density for a D-optimal design ξ∗ for covariates +Xi with density fX(x). Then fζ∗(z) = 1 +σfξ∗( z−µ +σ ) is the density for a D-optimal +design ζ∗ for covariates Zi = σXi + µ with density fZ(z) = 1 +σfX( z−µ +σ ). +In particular, also the optimal design ζ∗ is concentrated on, at most, p = q + 1 +intervals, and its density fζ∗(z) is either equal to the density fZ(z) of the covariates +Zi (on Z∗ = σX ∗ + µ) or it is equal to 0 (elsewhere) such that the optimal +subsampling can be implemented quite easily. +A further reduction of the optimization problem can be achieved by utilizing +symmetry properties. Therefore, we consider the transformation of sign change, +g(x) = −x, and assume that the distribution of the covariates is symmetric, +fX(−x) = fX(x) for all x. For a continuous design ξ, the design ξg transformed by +sign change has density fξg(x) = fξ(−x) and, thus, satisfies the boundedness condi- +tion fξg(x) ≤ fX(x), when the distribution of Xi is symmetric, and has the same +value for the D-criterion as ξ, log(det(M(ξg))) = log(det(M(ξ))). By the concavity +of the D-criterion, standard invariance arguments can be used as in Pukelsheim +(1993, Chapter 13) and Heiligers and Schneider (1992). In particular, any con- +tinuous design ξ is dominated by its symmetrization ¯ξ = (ξ + ξg)/2 with density +f¯ξ(x) = (fξ(x) + fξ(−x))/2 ≤ fX(x) such that log(det(M(¯ξ))) ≥ log(det(M(ξ))) +(Pukelsheim, 1993, Chapter 13.4). Hence, we can restrict the search for a D-optimal +design to symmetric designs ¯ξ with density f¯ξ(−x) = f¯ξ(x) which are invariant with +respect to sign change (¯ξg = ¯ξ). For these symmetric designs ¯ξ, the moments mk(¯ξ) +are zero for odd k and positive when k is even. Hence, the information matrix M(¯ξ) +is an even checkerboard matrix (see Jones and Willms, 2018) with positive entries +mj+j′(¯ξ) for even index sums and entries equal to zero when the index sum is odd. +The inverse M(¯ξ)−1 of the information matrix M(¯ξ) shares the structure of an even +checkerboard matrix. Thus, the sensitivity function ψ(x, ¯ξ) is a polynomial with +only terms of even order and is, hence, a symmetric function of x. This leads to a +simplification of the representation of the optimal design in Theorem 3.1 because +the support X ∗ of the optimal design ξ∗ will be symmetric. +Corollary 3.3. Let the distribution of Xi be symmetric. Then, for the D-optimal +design ξ∗ with density fξ∗(x) = �r +k=0 fX(x)1Ik(x) the boundaries a1, . . . , a2r of +the intervals Ik = [a2k+1, a2k] are symmetric, i. e. a2r+1−k = −ak and, similarly, +Ir+2−k = −Ik for the intervals. +This characterization of the optimal design ξ∗ will be illustrated in the next two +sections for ordinary linear regression (q = 1) and for quadratic regression (q = 2). +4. Optimal Subsampling for Linear Regression +In the case of ordinary linear regression Yi = β0 + β1Xi + εi we have +M(ξ∗) = +� +α +m1(ξ∗) +m1(ξ∗) +m2(ξ∗) +� +, +for the information matrix of the optimal design ξ∗. +The sensitivity function +is a polynomial of degree 2. To obtain the D-optimal continuous design ξ∗ by +Theorem 3.1, the boundary points a1 and a2 have to be determined to solve the +two nonlinear equations +P(Xi ≤ a2) + P(Xi ≥ a1) = α +(1) + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +6 +and +ψ(a1, ξ∗) = ψ(a2, ξ∗) . +(2) +The D-optimal continuous design ξ∗ has density fξ(x) = fX(x) for x ≤ a2 and for +x ≥ a1 while fξ(x) = 0 for a2 < x < a1. The corresponding subsampling design +then accepts those units i for which xi ≤ a2 or xi ≥ a1, and rejects all units i for +which a2 < xi < a1. +When the distribution of Xi is symmetric, Corollary 3.3 provides symmetry +a2 = −a1 of the boundary points. Hence, by the symmetry of the distribution, +P(Xi ≤ a2) = P(Xi ≥ a1) = α/2, and a1 has to be chosen as the (1 − α/2)-quantile +of the distribution of Xi to obtain the D-optimal continuous design. +Example 4.1 (normal distribution). If the covariates Xi come from a standard +normal distribution, then the optimal boundaries are the (α/2)- and the (1 − α/2)- +quantile ±z1−α/2, and unit i is accepted when |xi| ≥ z1−α/2. +For Xi having a general normal distribution with mean µ and variance σ2, the +optimal boundaries remain to be the (α/2)- and (1−α/2)-quantile a2 = µ−σz1−α/2 +and a1 = µ + σz1−α/2, respectively, by Theorem 3.2. +This approach applies accordingly to all distributions which are obtained by a +shift transformation of a symmetric distribution: Units will be accepted if their +values of the covariate lie in the lower or upper (α/2)-tail of the distribution. This +procedure can be interpreted as a theoretical counterpart in one dimension of the +IBOSS method proposed by Wang et al. (2019). +However, for asymmetric distributions, the optimal proportions for sampling from +the upper and lower tail will differ. +Example 4.2 (exponential distribution). If the covariates Xi come from a standard +exponential distribution with density fX(x) = e−x, x ≥ 0, we conclude from +Theorem 3.1 that fξ∗(x) = fX(x)1(−∞,a]∪[b,∞)(x). We can calculate the entries of +M(ξ∗) as functions of a1 = a and a2 = b as +m1(ξ∗) = 1 + (a + 1)e−a − (b + 1)e−b +m2(ξ∗) = 2 + (a2 + 2a + 2)e−a − (b2 + 2b + 2)e−b . +To obtain the optimal solutions for a and b, the two nonlinear equations (1) and (2) +come here to be +1 − e−b + e−a = α +and +f(a)⊤M(ξ∗)−1f(a) = f(b)⊤M(ξ∗)−1f(b) . +The results for selected values of α can be seen in Table 1. Additionally to the optimal +values for a and b, also the proportions P(Xi ≤ b) and P(Xi ≥ a) are presented in +Table 1 together with the percentage of mass allocated to the left interval [0, b]. In +Figure 1, the density fξ∗ of the optimal design ξ∗ and the corresponding sensitivity +function ψ(x, ξ∗) are exhibited for α = 0.5 and α = 0.3. Vertical lines indicate the +positions of the boundary points a and b, and the dotted horizontal line displays the +threshold s∗. +As could have been expected, less mass is assigned to the right tail +of the right-skewed distribution because observations from the right tail are more +influential and, thus, more observations seem to be required on the lighter left tail +for compensation. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +7 +Table 1. Numeric values for a and b for selected values of α in +the case of standard exponential Xi +α +b +P(Xi ≤ b) +a +P(Xi ≥ a) +% of mass on [0, b] +0.5 +0.39572 +0.32681 +1.75335 +0.17319 +65.36 +0.3 +0.21398 +0.19264 +2.23153 +0.10736 +64.21 +0.1 +0.06343 +0.06146 +3.25596 +0.03854 +61.46 +0.01 +0.00579 +0.00577 +5.46588 +0.00423 +57.71 +0.00 +0.25 +0.50 +0.75 +1.00 +0 +1 +2 +3 +4 +5 +x +Density +1 +2 +3 +4 +5 +0 +1 +2 +3 +4 +5 +x +Sensitivity function +(a) α = 0.5 +0.00 +0.25 +0.50 +0.75 +1.00 +0 +1 +2 +3 +4 +5 +x +Density +1 +2 +3 +4 +0 +1 +2 +3 +4 +5 +x +Sensitivity function +(b) α = 0.3. +Figure 1. Density of the optimal design (solid line) and the stan- +dard exponential distribution (dashed line, upper panels), and +sensitivity functions (lower panels) for α = 0.5 (left) and α = 0.3 +(right) +For Xi having an exponential distribution with general intensity λ > 0 (scale 1/λ), +the optimal boundary points remain to be the same quantiles as in the standard +exponential case, a1 = a/λ and a2 = b/λ, by Theorem 3.2. +5. Optimal Subsampling for Quadratic Regression +In the case of quadratic regression Yi = β0 + β1Xi + β2X2 +i + εi we have +M(¯ξ) = +� +� +α +0 +m2(¯ξ) +0 +m2(¯ξ) +0 +m2(¯ξ) +0 +m4(¯ξ) +� +� , +for the information matrix of a symmetric design ¯ξ. The corresponding sensitivity +function ψ(x, ¯ξ) is a polynomial of degree 4 and is symmetric in x. +According to Corollary 3.3, the density fξ∗(x) of the D-optimal continuous design +ξ∗ has, at most, three intervals that are symmetrically placed around zero, where +the density is equal to the bounding density fX(x), and fξ∗(x) is equal to zero +elsewhere. Thus the density fξ∗(x) of the D-optimal design has the following shape. +fξ∗(x) = fX(x)1(−∞,−a]∪[−b,b]∪[a,∞)(x) , +where a > b ≥ 0 and where we formally allow b = 0 which means that ψ(0, ξ∗) ≤ +0 and that the density fξ∗(x) is concentrated on only two intervals, fξ∗(x) = +fX(x)1{x∈(−∞,−a]∪[a,∞)}. Although the information matrix will be non-singular + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +8 +even in the case of two intervals (b = 0), the optimal design will typically include a +non-degenerate interior interval [−b, b], b > 0, as illustrated below in Theorem 5.2. +To obtain the D-optimal continuous design ξ∗ by Corollary 3.3, the boundary +points a = a1 and b = a2 (resp. b = 0) have to be determined to solve the two +nonlinear equations +P(|Xi| ≤ b) + P(|Xi| ≥ a) = α +(3) +and +ψ(a, ξ∗) = ψ(b, ξ∗) . +(4) +For finding the optimal solutions, we use the Newton method implemented in the R +package nleqslv by Hasselman (2018) to calculate numeric values for a and b based +on equations (3) and (4) for various symmetric distributions. +Example 5.1 (normal distribution). For the case that the covariates Xi come from +a standard normal distribution, results are given in Table 2 for some values of α. +Additionally to the optimal values for a and b, also the proportions P(Xi ≥ a) = +Table 2. Numeric values for a and b for selected values of α in +the case of standard normal Xi +α +a +1 − Φ(a) +b +2Φ(b) − 1 +% of mass on [−b, b] +0.5 +1.02800 +0.15198 +0.24824 +0.19605 +39.21 +0.3 +1.34789 +0.08885 +0.15389 +0.12231 +40.77 +0.1 +1.88422 +0.02977 +0.05073 +0.04046 +40.46 +0.01 +2.73996 +0.00307 +0.00483 +0.00386 +38.55 +P(Xi ≤ −a) = 1 − Φ(a) and P(−b ≤ Xi ≤ b) = 2Φ(b) − 1 are presented in Table 2 +together with the percentage of mass (2Φ(b) − 1)/α allocated to the interior interval +[−b, b]. In Figure 2, the density fξ∗ of the optimal design ξ∗ and the corresponding +sensitivity function ψ(x, ξ∗) are exhibited for α = 0.5 and α = 0.1. Vertical lines +0.0 +0.1 +0.2 +0.3 +0.4 +−2 +0 +2 +x +Density +1.7 +1.8 +1.9 +2.0 +−2 +0 +2 +x +Sensitivity function +(a) α = 0.5 +0.0 +0.1 +0.2 +0.3 +0.4 +−2 +0 +2 +x +Density +1.75 +2.00 +2.25 +2.50 +2.75 +−2 +0 +2 +x +Sensitivity function +(b) α = 0.1 +Figure 2. Density of the optimal design (solid line) and the stan- +dard normal distribution (dashed line, upper panels), and sensitivity +functions (lower panels) for α = 0.5 (left) and α = 0.1 (right) +indicate the positions of the boundary points −a, −b, b, and a, respectively. In the + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +9 +subplots of the sensitivity function, the dotted horizontal line displays the threshold +s∗. For other values of α, the plots are looking similar. +The numerical results in Table 2 suggest that the interior interval [−b, b] does +not vanish for any α (0 < α < 1). This will be established in the following theorem. +Theorem 5.2. Let the distribution of Xi be standard normal. +For all α ∈ +(0, 1), there exists b > 0 such that the D-optimal design ξ∗ has density fξ∗(x) = +fX(x)1{x∈(−∞,−a]∪[−b,b]∪[a,∞)}. +For Xi having a general normal distribution with mean µ and variance σ2, the +optimal boundary points remain to be the same quantiles as in the standard normal +case, a1, a4 = µ ± σa and a2, a3 = µ ± σb, by Theorem 3.2. +Example 5.3 (uniform distribution). If the covariates Xi are uniformly distributed +on [−1, 1] with density fX(x) = 1 +21[−1,1](x), we can obtain analytical results for the +dependence of the subsampling design on the proportion α to be selected. +The distribution of Xi is symmetric. By Corollary 3.3, the density of the D- +optimal continuous design ξ∗ has the shape +fξ∗(x) = 1 +21[−1,−a]∪[−b,b]∪[a,1](x) +where a and b are the solution of the following two equations +1 − a + b = α +and +f(a)⊤M(ξ∗)−1f(a) = f(b)⊤M(ξ∗)−1f(b) , +where the entries in the even checkerboard matrix M(ξ∗) are m0(ξ∗) = α, m2(ξ∗) = +1 +3(1 − a3 + b3), and m4(ξ∗) = 1 +5(1 − a5 + b5). Solving these equations results in +a(α) = 1 +2 +� +1 − α + +� +45 − 15α + 15α2 − 45α3 + 20α4 +45(1 − α) +− 4α +√ +5 +√ +45 − 90α + 90α2 − 75α3 + 57α4 − 27α5 + 5α6 +45(1 − α) +�1/2 � +(5) +and +b(α) = a − (1 − α) +(6) +for the dependence of a and b on α. The values of a and b are plotted in Figure 3. +There it can be seen that a and b both tend to 1/ +√ +5 as α tends to 1. Similar to the +normal distribution, the resulting values and illustrations are given in Table 3 and +Figure 4. +Also here, vertical lines indicate the positions of the boundary points −a, +−b, b, and a, and the dotted horizontal line displays the threshold s∗. Moreover, +the percentage of mass at the different intervals is displayed in Figure 5. +The results in Table 3 and Figure 5 suggest that the percentage of mass on all +three intervals [−1, −a], [−b, b], and [a, 1] tend to 1/3 as α tends to 0. We establish +this in the following theorem. +Theorem 5.4. Let Xi be uniformly distributed on [−1, 1] and ξ∗ +α be the optimal +subsampling design for α, 0 < α < 1, defined in equations (5) and (6). Then +limα→0 ξ∗ +α([−b, b])/α = 1/3. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +10 +0.00 +0.25 +0.50 +0.75 +1.00 +0.00 +0.25 +0.50 +0.75 +1.00 +α +a,b +Figure 3. Boundary points a and b in dependence on α +Table 3. Numeric values for a and b for selected values of α in +the case of uniform Xi on [−1, 1] +α +a +1 − P(Xi ≥ a) +b = P(−b ≤ Xi ≤ b) +% of mass on [−b, b] +0.5 +0.70983 +0.14508 +0.20983 +41.97 +0.3 +0.81737 +0.09132 +0.11737 +39.12 +0.1 +0.93546 +0.03227 +0.03546 +35.46 +0.01 +0.99336 +0.00332 +0.00336 +33.55 +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +−1.0 +−0.5 +0.0 +0.5 +1.0 +x +Density +2.00 +2.25 +2.50 +2.75 +3.00 +−1.0 +−0.5 +0.0 +0.5 +1.0 +x +Sensitivity function +(a) α = 0.5 +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +−1.0 +−0.5 +0.0 +0.5 +1.0 +x +Density +2.0 +2.5 +3.0 +3.5 +4.0 +−1.0 +−0.5 +0.0 +0.5 +1.0 +x +Sensitivity function +(b) α = 0.1 +Figure 4. Density of the optimal design (solid line) and the uni- +form distribution on [−1, 1] (dashed line, upper panels), and sen- +sitivity functions (lower panels) for α = 0.5 (left) and α = 0.1 +(right) +It is worth-while mentioning that the percentages of mass displayed in Figure 5 +are not monotonic over the whole range of α ∈ (0, 1), as, for example the mass at +the interior interval [−b, b] is increasing from 0.419666 at b = 0.50 to 0.448549 at +b = 0.92 and then slightly decreasing again to 0.447553 at b = 0.99. +In the two preceding examples it could be noticed that the mass of observations +is of comparable size for the three supporting intervals in the case of a normal and +of a uniform distribution with light tails. This will be different in the case of a +heavy-tailed distribution for the covariates Xi. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +11 +0.28 +0.30 +0.32 +0.25 +0.50 +0.75 +α +(1−a)/2α +0.33 +0.36 +0.39 +0.42 +0.45 +0.25 +0.50 +0.75 +α +b/α +Figure 5. Percentage of mass on [a, 1] (left) and [−b, b] (right) as +a function of α +6. Efficiency considerations +To exhibit the gain in using a D-optimal design compared to random subsampling, +we consider the performance of the uniform random subsampling design ξα of size +α, which has density fξα(x) = αfX(x), compared to the D-optimal subsampling +design ξ∗ +α with mass α. More precisely, the D-efficiency of any design ξ with mass +α is defined as +effD,α(ξ) = +� det(M(ξ)) +det(M(ξ∗α)) +�1/p +, +where p is the dimension of the parameter vector β. +For this definition the +homogeneous version (det(M(ξ)))1/p of the D-criterion is used which satisfies +(det(λM(ξ)))1/p = λ(det(M(ξ)))1/p (see Pukelsheim, 1993, Chapter 6.2). +For uniform random subsampling, the information matrix is given by M(ξα) = +αM(ξ1), where M(ξ1) is the information matrix for the full sample with raw moments +mk(ξ1) = E[Xk +i ] as entries in the (j, j′)th position, j +j′ = k. Thus, the D-efficiency +effD,α(ξα) can be nicely interpreted: When uniform random subsampling is used, the +inverse of the efficiency effD,α(ξα)−1 times α gives the sample size (mass) required +to obtain the same precision in terms of the D-criterion as when the D-optimal +design ξ∗ +α of mass α is used. For example, if the efficiency effD,α(ξα) is equal to 0.5, +then twice as many observations would be needed under uniform random sampling +than for a D-optimal subsampling design of size α. Of course, the full sample has +higher information than any proper subsample such that, obviously, effD,α(ξα) ≥ α +holds for uniform random subsampling. +For the examples of Sections 4 and 5, the efficiency of uniform random subsampling +is given in Table 4 for selected values of α and exhibited in Figure 6 for the full +range of α between 0 and 1 (solid lines). Here the determinant of the information +matrix is determined as in the examples of Sections 4 and 5 for the optimal designs +ξα∗ either numerically or by explicit formulas where available. +Both Table 4 and Figure 6 indicate that the efficiency of uniform random subsam- +pling is decreasing in all cases when the proportion α of subsampling gets smaller. +In the case of uniformly distributed covariates, the decrease is more or less linear +with a minimum value of approximately 0.58 for quadratic regression when α is +small. In the other cases, where the distribution of the covariates is unbounded, the +efficiency apparently decreases faster, when the proportion α is smaller than 10%, +and tends to 0 for α → 0. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +12 +Table 4. Efficiency for selected values of α +α +0.5 +0.3 +0.1 +0.01 +linear regression +normal +0.73376 +0.61886 +0.47712 +0.34403 +exponential +0.73552 +0.61907 +0.46559 +0.30690 +quadratic regression +normal +0.73047 +0.59839 +0.41991 +0.24837 +uniform +0.78803 +0.70475 +0.62411 +0.58871 +0.4 +0.6 +0.8 +1.0 +0.00 +0.25 +0.50 +0.75 +1.00 +α +Efficiency +(a) Linear regression, normal covariates +0.2 +0.4 +0.6 +0.8 +1.0 +0.00 +0.25 +0.50 +0.75 +1.00 +α +Efficiency +(b) Linear regression, exponential covari- +ates +0.2 +0.4 +0.6 +0.8 +1.0 +0.00 +0.25 +0.50 +0.75 +1.00 +α +Efficiency +(c) Quadratic regression, normal covariates +0.6 +0.7 +0.8 +0.9 +1.0 +0.00 +0.25 +0.50 +0.75 +1.00 +α +Efficiency +(d) Quadratic regression, uniform covari- +ates +Figure 6. Efficiency of uniform random subsampling (solid line) +and of an IBOSS-type design (dashed line) +The latter property can be easily seen for linear regression and symmetric +distribution: There, the efficiency effD,α(ξα) of uniform random sampling is bounded +from above by c/q1−α/2, where c = E(X2 +i )1/2 is a constant and q1−α/2 is the (1−α/2)- +quantile of the distribution of the covariates. When the distribution is unbounded +like the normal distribution, then these quantiles tend to infinity for α → 0 and, +hence, the efficiency tends to 0. Similar results hold for quadratic regression and +asymmetric distributions. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +13 +In any case, as can be seen from Table 4, the efficiency of uniform random +subsampling is quite low for reasonable proportions α ≤ 0.1 and, hence, the gain in +using the D-optimal subsampling design is substantial. +By equivariance arguments as indicated above in the examples of Sections 4 and +5, the present efficiency considerations carry over directly to covariates having a +general normal, exponential, or uniform distribution, respectively. +In the IBOSS approach by Wang et al. (2019), half of the proportion α is taken +from both tails of the data. The corresponding continuous subsampling design ξ′ +α +would be to choose the boundary points a1 and a2 to be the (1 − α/2)- and (α/2)- +quantile of the distribution of the covariates, respectively. For linear regression, +it can been seen from Corollary 3.3 that the design ξ′ +α is D-optimal when the +distribution of the covariates is symmetric. As the IBOSS procedure does not +use prior knowledge of the distribution, it would be tempting to investigate the +efficiency of the corresponding continuous subsampling design ξ′ +α under asymmetric +distributions. For the exponential distribution, this efficiency effD,α(ξ′ +α) is added to +the upper right panel in Figure 6 by a dashed line. There the design ξ′ +α shows a +remarkably high efficiency over the whole range of α with a minimum value 0.976 +at α = 0.332. +As an extension of IBOSS for quadratic regression, we may propose a procedure +which takes proportions α/3 from both tails of the data as well as from the center +of the data. This procedure can be performed without any prior knowledge of the +distribution of the covariates. The choice of the proportions α/3 is motivated by +the standard case D-optimal design on an interval where one third of the weight is +allocated to each of the endpoints and to the midpoint of the region. For a symmetric +distribution, the corresponding continuous subsampling design ξ′′ +α can be defined by +the boundary points a and b to be the (1 − α/3)- and (1/2 + α/6)-quantile of the +distribution of the covariates, respectively. In the case of the uniform distribution, +the design ξ′′ +α is the limiting D-optimal design for α → 0 by Theorem 5.4. For the +whole range of α and for the normal distribution, the efficiency effD,α(ξ′′ +α) is shown +in the lower panels of Figure 6 by dashed lines. In both cases, the design ξ′′ +α is +highly efficient over the whole range of α with minimum values 0.994 at α = 0.079 +for the normal distribution and 0.989 at α = 0.565 for the uniform distribution, +respectively. +7. Concluding Remarks +In this paper we have considered a theoretical approach to evaluate subsampling +designs under distributional assumptions on the covariates in the case of polynomial +regression on a single explanatory variable. Main emphasis was on D-optimal +designs. But many of the results may be extended to other optimality criteria like A- +and E-optimality from the Kiefer’s Φq-class of optimality criteria, IMSE-optimality +for predicting the mean response, or optimality criteria based on subsets or linear +functionals of parameters. +The D-optimal designs show a high performance compared to uniform random +subsampling. In particular, for small proportions, the efficiency of uniform random +subsampling tends to zero. This property is in accordance with the observation that +estimation based on subsampling according to IBOSS is “consistent” in the sense +that the mean squared error goes to zero with increasing population size even when +the size of the subsample is fixed. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +14 +We propose a generalization of the IBOSS method to quadratic regression which +does not require prior knowledge of the distribution of the covariates and which +performs remarkably well compared to the optimal design. However, an extension +to higher order polynomials, does not seem to be obvious. +Appendix A. Proofs +Before proving Theorem 3.1, we establish two preparatory lemmas on properties +of the sensitivity function ψ(x, ξ) for a continuous design ξ with density fξ(x) and +reformulate an equivalence theorem on constraint design optimality by Sahm and +Schwabe (2001) for the present setting. The first lemma deals with the shape of the +sensitivity function. +Lemma A.1. The sensitivity function ψ(x, ξ) is a polynomial of degree 2q with +positive leading term. +Proof of Lemma A.1. For a continuous design ξ with density fξ(x), the information +matrix M(ξ) and, hence, its inverse M(ξ)−1 is positive definite. Thus the last +diagonal element m(pp) of M(ξ)−1 is positive and, as f(x) = (1, x, . . . , xq)⊤, the +sensitivity function ψ(x, ξ) = f(x)⊤M(ξ)−1f(x) is a polynomial of degree 2q with +coefficient m(pp) > 0 of the leading term. +□ +The second lemma reveals a distributional property of the sensitivity function +considered as a function in the covariates Xi. +Lemma A.2. The random variable ψ(Xi, ξ) has a continuous cumulative distribu- +tion function. +Proof of Lemma A.2. As the sensitivity function ψ(x, ξ) is a non-constant poly- +nomial by Lemma A.1, the equation ψ(x, ξ) = s has only finitely many roots +x1, . . . , xℓ, say, by the fundamental theorem of algebra. Hence, P(ψ(Xi, ξ) = s) = +�ℓ +k=1 P(Xi = xk) = 0 by the continuity of the distribution of Xi which proves the +continuity of the cumulative distribution function of ψ(Xi, ξ). +□ +With the continuity of the distribution of ψ(Xi, ξ∗) the following equivalence +theorem can be obtained from Corollary 1(c) in Sahm and Schwabe (2001) for +the present setting by transition from the directional derivative to the sensitivity +function. +Theorem A.3 (Equivalence Theorem). The design ξ∗ is D-optimal if and only if +there exist a threshold s∗ and a subset X ∗ of the design region such that +(i) the D-optimal design ξ∗ is given by +fξ∗(x) = fX(x)1X ∗(x) +(ii) ψ(x, ξ∗) ≥ s∗ for x ∈ X ∗, and +(iii) ψ(x, ξ∗) < s∗ for x ̸∈ X ∗. +As P(ψ(Xi, ξ∗) ≥ s∗) = P(Xi ∈ X ∗) = +� +fξ∗(x) dx = α, the threshold s∗ is the +(1 − α)-quantile of the distribution of ψ(Xi, ξ∗). +Proof of Theorem 3.1. By Lemma A.1 the sensitivity function ψ(x, ξ) is a polyno- +mial in x of degree 2q with positive leading term. Using the same argument as in +the proof of Lemma A.2 we obtain that there are at most 2q roots of the equation +ψ(x, ξ∗) = s∗ and, hence, there are at most 2q sign changes in ψ(x, ξ∗) − s∗. As + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +15 +ψ(x, ξ∗) is a polynomial of even degree, also the number of (proper) sign changes has +to be even, and they occur at a1 > · · · > a2r, say, r ≤ q. Moreover, for 0 < α < 1, +X ∗ is a proper subset of the design region and, thus, there must be at least one sign +change, r ≥ 1. Finally, as the leading coefficient of ψ(x, ξ∗) is positive, ψ(x, ξ∗) gets +larger than s∗ for x → ±∞ and, hence, the outmost intervals [a1, ∞) and (−∞, a2r] +are included in the support X ∗ of ξ∗. By the interlacing property of intervals with +positive and negative sign for ψ(x, ξ∗) − s∗, the result follows. +□ +Proof of Theorem 3.2. First note that for any µ and σ > 0, the location scale +transformation z = σx + µ is conformable with the regression function f(x), i. e. +there exists a non-singular matrix Q such that f(σx + µ) = Qf(x) for all x. Then, +for any design ξ bounded by fX(x), the design ζ has density fζ(z) = 1 +σfξ( z−µ +σ ) +bounded by fZ(z) = 1 +σfX( z−µ +σ ). Then, by the transformation theorem for measure +integrals, it holds that +M(ζ) = +� +f(z)f(z)⊤ζ(dz) += +� +f(σx + µ)f(σx + µ)⊤ξ(dx) += +� +Qf(x)f(x)⊤Q⊤ξ(dx) += QM(ξ)Q⊤. +Therefore det(M(ζ)) = det(Q)2 det(M(ξ)). Thus ξ∗ maximizes the D-criterion over +the set of designs bounded by fX(x) if and only if ζ∗ maximizes the D-criterion +over the set of designs bounded by fZ(z). +□ +Proof of Corollary 3.3. The checkerboard structure of the information matrix M(ξ∗) +carries over to its inverse M(ξ∗)−1. Hence, the sensitivity function ψ(x, ξ∗) is an +even polynomial, which has only non.zero coefficients for even powers of x, and is +thus symmetric with respect to 0, i. e. ψ(−x, ξ∗) = ψ(x, ξ∗). Accordingly, also the +roots of ψ(x, ξ∗) = s∗ are symmetric with respect to 0. +□ +Proof of Theorem 5.2. Suppose there exists an α ∈ (0, 1) such that a = ∞. Then +b = z(1+α)/2, obviously and it must hold that ψ(z(1−α)/2, ξ∗) ≥ limx→∞ ψ(x, ξ∗). +Since M(ξ∗) is positive definite, the leading term of the polynomial ψ(x, ξ∗) in x is +positive and subsequently ψ(z(1−α)/2, ξ∗) < limx→∞ ψ(x, ξ∗). This is a contradiction +and therefore a < ∞ for all α ∈ (0, 1). +Suppose there exists an α ∈ (0, 1) such that b = 0. Then a = z1−α/2, obviously. +Further, it must hold that ψ(z1−α/2, ξ∗) ≥ ψ(0, ξ∗). We will show that this inequality +is in fact false. Because ξ∗ is invariant to the sign change we have +M(ξ∗) = +� +� +α +0 +m2(ξ∗) +0 +m2(ξ∗) +0 +m2(ξ∗) +0 +m4(ξ∗) +� +� +and thus +M(ξ∗)−1 = +� +� +� +m4(ξ∗) +αm4(ξ∗)−m2(ξ∗)2 +0 +−m2(ξ∗) +αm4(ξ∗)−m2(ξ∗)2 +0 +1 +m2(ξ∗) +0 +−m2(ξ∗) +αm4(ξ∗)−m2(ξ∗)2 +0 +α +αm4(ξ∗)−m2(ξ∗)2 +� +� +� , + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +16 +where +m2(ξ∗) = +� +R +x2fξ∗(x) dx = α + +� +2/πz1−α/2 exp +� +−z2 +1−α/2 +2 +� +, +m4(ξ∗) = +� +R +x4fξ∗(x) dx = +� +2/πz3 +1−α/2 exp +� +−z2 +1−α/2 +2 +� ++ 3m2(ξ∗). +We will write a instead of z1−α/2 from here on out for readability. For the directional +derivatives we have +ψ(0, ξ∗) = α(1 0 0)M(ξ∗)−1(1 0 0)⊤ += +αm4(ξ∗) +αm4(ξ∗) − m2(ξ∗)2 +and +ψ(a, ξ∗) = α(1 a a2)M(ξ∗)−1(1 a a2)⊤ += +αm4(ξ∗) +αm4(ξ∗) − m2(ξ∗)2 − c, +where +c = αa2 +� +2m2(ξ∗) +αm4(ξ∗) − m2(ξ∗)2 − +a2α +αm4(ξ∗) − m2(ξ∗)2 − +1 +m2(ξ∗) +� +. +c is continuous in α ∈ (0, 1) and does not have any roots in (0, 1). We can easily +check, that c > 0 for e.g. α = 0.1 and thus c > 0 for all α ∈ (0, 1). This yields +ψ(z1−α/2, ξ∗) < ψ(0, ξ∗) for all α ∈ (0, 1), which is a contradiction. +□ +Proof of Theorem 5.4. Firstly, we check if limα→0 b(α)/α = 1/3, as b(α)/α = +� b +−b ξ∗(dx)/ +� 1 +−1 ξ∗(dx) describes the percentage of mass on [−b, b]. +Note that +limα→0 b(α)/α is by definition the derivative of b(α) at the point α0 = 0. Thus we +consider the derivative of b. +db(α) +dα += 1 +2 + 1 +2 +� +u′(α)v(α) − u(α)v′(α) +v(α)2 +1 +2 +� +u(α)/v(α) +� +, +where +u(α) = 45 − 15α + 15α2 − 45α3 + 20α4 +− 4 +√ +5 +� +45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8, +c(α) = 4 +√ +5(90α − 270α2 + 360α3 − 375α4 + 342α5 − 189α6 + 40α7) +2 +√ +45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8 +u′(α) = −15 + 30α − 135α2 + 80α3 − c(α), +v(α) = 45 − 45α, +v′(α) = −45. +We have u(α0) = v(α0) = 45 and v′(α0) = −45. Note that c(α) > 0 for α ∈ (0, 0.85), +as the polynomial in the numerator has roots in α = 0, α ≈ 0.85316 with no roots +and positive values in between. Similarly, the polynomial in the denominator is +positive for all α ∈ (0, 1). To find u′(α0) we study the limit of c(α)2. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +17 +c(α)2 = 16 · 5(90α − 270α2 + 360α3 − 375α4 + 342α5 − 189α6 + 40α7)2 +4(45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8) += 80 · 902α2 + O(α3) +4 · 45α2 + O(α3) += 80 · 902 + O(α) +4 · 45 + O(α) . +Therefore +lim +α↘0 c(α)2 = 80 · 902 +4 · 45 += 3600. +This yields limα↘0 c(α) = 60, as c(α) > 0 for positive values of α close to 0. We +have u′(α0) = −75 and consequently limα→0 +b(α) +α += 1/3. +□ + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +18 +Acknowledgments +The work of the first author is supported by the Deutsche Forschungsgemeinschaft +(DFG, German Research Foundation) within GRK 2297 MathCoRe. +References +Micha�l Derezi´nski and Manfred K. Warmuth. Reverse iterative volume sampling +for linear regression. The Journal of Machine Learning Research, 19(1):853–891, +2018. +Petros Drineas, Michael W. Mahoney, and Shan Muthukrishnan. Sampling algo- +rithms for ℓ2 regression and applications. In Proceedings of the seventeenth annual +ACM-SIAM symposium on Discrete algorithm, pages 1127–1136, 2006. +Valerii V. Fedorov. Optimal design with bounded density: Optimization algorithms +of the exchange type. Journal of Statistical Planning and Inference, 22(1):1–13, +1989. +Norbert Gaffke and Berthold Heiligers. Approximate designs for polynomial regres- +sion: Invariance, admissibility, and optimality. In S. Ghosh and C.R. Rao, editors, +Handbook of Statistics 13, pages 1149–1199. Elsevier, 1996. +Berend Hasselman. nleqslv: Solve Systems of Nonlinear Equations, 2018. URL +https://CRAN.R-project.org/package=nleqslv. R package version 3.3.2. +Berthold Heiligers and Klaus Schneider. Invariant admissible and optimal designs +in cubic regression on the v-ball. Journal of statistical planning and inference, 31 +(1):113–125, 1992. +T. H. Jones and N. B. Willms. +Inverse eigenvalue problems for checkerboard +toeplitz matrices. +Journal of Physics: +Conference Series, 1047(1):012016, +2018. doi: 10.1088/1742-6596/1047/1/012016. URL https://doi.org/10.1088% +2F1742-6596%2F1047%2F1%2F012016. +Ping Ma, Michael W. Mahoney, and Bin Yu. A statistical perspective on algorithmic +leveraging. In International Conference on Machine Learning, pages 91–99. PMLR, +2014. +Michael W. Mahoney. Randomized algorithms for matrices and data. Foundations +and Trends® in Machine Learning, 3(2):123–224, 2011. ISSN 1935-8237. doi: +10.1561/2200000035. URL http://dx.doi.org/10.1561/2200000035. +Luc Pronzato. +A minimax equivalence theorem for optimum bounded design +measures. Statistics & probability letters, 68(4):325–331, 2004. +Luc Pronzato and HaiYing Wang. Sequential online subsampling for thinning +experimental designs. Journal of Statistical Planning and Inference, 212:169–193, +2021. +Friedrich Pukelsheim. Optimal Design of Experiments. Wiley, New York, 1993. +Michael Sahm and Rainer Schwabe. +A note on optimal bounded designs. +In +A. Atkinson, B. Bogacka, and A. Zhigljavsky, editors, Optimum Design 2000, +pages 131–140. Kluwer, Dordrecht, The Netherlands, 2001. +Chenlu Shi and Boxin Tang. Model-robust subdata selection for big data. Journal +of Statistical Theory and Practice, 15(4):1–17, 2021. +S.D. Silvey. Optimal design: an introduction to the theory for parameter estimation, +volume 1. Chapman and Hall, London, 1980. +Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the +Royal Statistical Society: Series B, 58(1):267–288, 1996. + +OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION +19 +HaiYing Wang, Min Yang, and John Stufken. Information-based optimal subdata +selection for big data linear regression. +Journal of the American Statistical +Association, 114(525):393–405, 2019. +Lin Wang, Jake Elmstedt, Weng Kee Wong, and Hongquan Xu. +Orthogonal +subsampling for big data linear regression. The Annals of Applied Statistics, 15 +(3):1273–1290, 2021. +Henry P. Wynn. Optimum designs for finite populations sampling. In S.S. Gupta, +D.S. Moore, editors, Statistical Decision Theory and Related Topics II, pages +471–478. Academic Press, New York, 1977. +Otto von Guericke University Magdeburg. Universit¨atsplatz 2, 39106 Magdeburg, +Germany +Email address: torsten.reuter@ovgu.de +Otto von Guericke University Magdeburg. Universit¨atsplatz 2, 39106 Magdeburg, +Germany +Email address: rainer.schwabe@ovgu.de + diff --git a/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/load_file.txt b/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..ac6594ab54dd4e929959f1758a7ca8629aeb9499 --- /dev/null +++ b/4tE1T4oBgHgl3EQfmQRh/content/tmp_files/load_file.txt @@ -0,0 +1,750 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf,len=749 +page_content='OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION TORSTEN REUTER AND RAINER SCHWABE Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In this paper we construct D-optimal subsampling designs for polynomial regression in one covariate for invariant distributions of the covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We study quadratic regression more closely for specific distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In particular we make statements on the shape of the resulting optimal subsampling designs and the effect of the subsample size on the design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To illustrate the advantage of the optimal subsampling designs we examine the efficiency of uniform random subsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Introduction Data Reduction is a major challenge as technological advances have lead to a massive increase in data collection to a point where traditional statistical methods fail or computing power can not keep up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In this case we speak of big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We typically differentiate between the case where the number of covariates is much larger than the number of observations and the case where the massive amount of observations is the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The first case is well studied, most notably by Tibshirani (1996) introducing LASSO, which utilizes ℓ1 penalization to find sparse parameter vectors, thus fusing subset selection and ridge regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The second case, often referred to as massive data, can be tackled in two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Firstly in a probabilistic fashion, creating random subsamples in a nonuniform manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Prominent studies include Drineas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2006), Mahoney (2011) and Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' They present subsampling methods for linear regression models called algorithmic leveraging that sample according to probabilities based on the normalized statistical leverage scores of the covariate matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' More recently Derezi´nski and Warmuth (2018) study volume sampling, where subdata is chosen proportional to the squared volume of the parallelepiped spanned by its observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Conversely to these probabilistic methods one can select subdata by applying deterministic rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Shi and Tang (2021) present such a method, that maximizes the minimal distance between two observations in the subdata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2021) propose orthogonal subsampling inspired by orthogonal arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Most prominently, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2019) introduce the information-based optimal subdata selection (IBOSS) to tackle big data linear regression in a deterministic fashion based on D-optimality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In this paper we study D-optimal subsampling designs for polynomial regression in one covariate, where the goal is to select a percentage α of the full data that maximizes the determinant of the information matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the conventional study of 2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Primary: 62K05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Secondary: 62R07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Subdata, D-optimality, Massive Data, Polyonmial Regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Corresponding author: Torsten Reuter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' E-mail address: torsten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='reuter@ovgu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='de.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='03295v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='ST] 9 Jan 2023 OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 2 approximate designs in this setting we refer to Gaffke and Heiligers (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Heiligers and Schneider (1992) consider specifically cubic regression on a ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We consider D-optimal designs with measure α that are bounded from above by the distribution of the known covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Such directly bounded designs were first studied by Wynn (1977) and Fedorov (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Pronzato (2004) considers this setting using a form of the subsampling design standardized to one and bounded by α−1 times the distribution of the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' More recently, Pronzato and Wang (2021) studies the same in the context of sequential subsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the characterization of the optimal subsampling designs we make use of an equivalence theorem by Sahm and Schwabe (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This equivalence theorem enables us to construct such designs for various settings of the distributional assumptions on the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Here we will only look at distributions of the covariate that are invariant to a sign change, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' symmetric about the vertical axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We discuss the shape of D-optimal subsampling designs for polynomial regression of degree q first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We conclude that the D-optimal design is equal to the bounding distribution in its support and the support of the optimal design will be the union of at most q + 1 intervals that are symmetrically placed around zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We then study quadratic regression under several distributional assumptions more closely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In particular we take a look at the percentage of mass of the optimal design on the outer intervals compared to the inner one, which changes drastically given the distribution of the covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In addition we examine the efficiency of uniform random subsampling to illustrate the advantage of the optimal designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' All numerical results are obtained by the Newton method implemented in the R package nleqslv by Hasselman (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Section 2 we specify the polynomial model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Section 3 we introduce the concept of continuous subsampling designs and give characterizations for optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Sections 4 and 5 we present optimal designs in the case of linear and quadratic regression, respectively, for various classes of distributions of the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Section 6 contains some efficiency considerations showing the strength of improvement of the performance of the optimal design compared to random subsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The paper concludes with a discussion in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Proofs are deferred to an Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Model Specification We consider the situation of pairs (xi, yi) of data, where yi is the value of the response variable Yi and xi is the value of a single covariate Xi for unit i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , n, for very large numbers of units n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We assume that the dependence of the response on the covariate is given by a polynomial regression model Yi = β0 + β1Xi + · · · + βqXq i + εi with independent, homoscedastic random errors εi having zero mean (E(εi) = 0, Var(εi) = σ2 ε > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The largest exponent q denotes the degree of the polynomial regression, and p = q + 1 is the number of regression parameters β0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , βq to be estimated, where, for each k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , q, the parameter βk is the coefficient for the kth monomial xk, and β0 denotes the intercept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For example, for q = 1, we have ordinary linear regression, Yi = β0 + β1Xi + εi, with p = 2 parameters β0 (intercept) and β1 (slope) and, for q = 2, we have quadratic regression, Yi = β0 + β1Xi + β2X2 i + εi, with p = 3 and an additional curvature parameter β2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Further, we assume that OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 3 the covariates Xi are identically distributed and that all covariates Xi and random errors εi′ are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For notational convenience, we write the polynomial regression as a general linear model Yi = f(Xi)⊤β + εi , where f(x) = (1, x, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , xq)⊤ is the p-dimensional vector of regression functions and β = (β0, β1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , βq)⊤ is the p-dimensional vector of regression parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Subsampling Design We are faced with the problem that the responses Yi are expensive or difficult to observe while the values xi of all covariates Xi are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To overcome this problem, we consider the situation that the responses Yi will be observed only for a certain percentage α of the units (0 < α < 1) and that these units will be selected on the basis of the knowledge of the values xi of the covariate for all units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As an alternative motivation, we can consider a situation where all pairs (xi, yi) are available but parameter estimation is computationally feasible only on a percentage α of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In either case we want to find the subsample of pairs (xi, yi) that yields the most precise estimation of the parameter vector β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To obtain analytical results, the covariates Xi are supposed to have a continuous distribution with density fX(x), and we assume that the distribution of the covariates is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The aim is to find a subsample of this distribution that covers a percentage α of the distribution and that contains the most information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For this, we will consider continuous designs ξ as measures of mass α on R with density fξ(x) bounded by the density fX(x) of the covariates Xi such that � fξ(x) dx = α and fξ(x) ≤ fX(x) for all x ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A subsample can then be generated according to such a continuous design by accepting units i with probability fξ(xi)/fX(xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For a continuous design ξ, the information matrix M(ξ) is defined as M(ξ) = � f(x)f(x)⊤fξ(x) dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the present polynomial setup, M(ξ) = (mj+j′(ξ))j′=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=',q j=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=',q , where mk = � xkfξ(x) dx is the kth moment associated with the design ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus, it has to be required that the distribution of Xi has a finite moment E(X2q i ) of order 2q in order to guarantee that all entries in the information matrix M(ξ) exist for all continuous designs ξ for which the density fξ(x) is bounded by fX(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The information matrix M(ξ) measures the performance of the design ξ in the sense that the asymptotic covariance of the least squares estimator ˆβ based on a subsample according to the design ξ is proportional to the inverse M(ξ)−1 of the information matrix M(ξ) or, more precisely, nα( ˆβ−β) is asymptotically normal with mean zero and covariance matrix σ2 εM(ξ)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Note that for continuous designs ξ the information matrix M(ξ) is of full rank and, hence, the inverse M(ξ)−1 exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Based on the relation to the asymptotic covariance matrix, it is desirable to maximize the information matrix M(ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' However, as well-known in design optimization, maximization of the information matrix cannot be achieved uniformly with respect to the Loewner ordering of positive-definiteness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus, commonly, a design criterion which is a real valued functional of the information matrix M(ξ) will be maximized, instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We will focus here on the most popular design criterion in applications, the D-criterion, in its common form log(det(M(ξ))) to be maximized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Maximization of the D-criterion can be interpreted in terms of the asymptotic covariance matrix to be the same as minimizing the volume of the confidence ellipsoid for the whole OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 4 parameter vector β based on the least squares estimator or, equivalently, minimizing the volume of the acceptance region for a Wald test on the whole model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The subsampling design ξ∗ that maximizes the D-criterion log(det(M(ξ))) will be called D-optimal, and its density is denoted by fξ∗(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To obtain D-optimal designs, we will make use of standard techniques coming from constrained convex optimization and symmetrization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For convex optimization we employ the directional derivative FD(ξ, η) = lim ϵ→0+ 1 ϵ (log(det(M((1 − ϵ)ξ + ϵη))) − log(det(M(ξ)))) of the D-criterion at a design ξ with non-singular information matrix M(ξ) in the direction of a design η, where we allow here η to be a general design of mass α that has not necessarily a density bounded by fX(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Evaluating of the directional derivative yields FD(ξ, η) = p − trace(M(ξ)−1M(η)) (compare Silvey, 1980, Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8) which reduces to FD(ξ, ξx) = p − αf(x)⊤M(ξ)−1f(x) for a one-point design η = ξx which assigns all mass α to a single setting x in the design region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Equivalently, for one-point designs η = ξx, we may consider the sensitivity function ψ(x, ξ) = αf(x)⊤M(ξ)−1f(x) which covers the essential part of the directional derivative (ψ(x, ξ) = p − FD(ξ, ξx)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the characterization of the D-optimal continuous design, the constrained equivalence theorem under Kuhn-Tucker conditions (see Sahm and Schwabe, 2001, Corollary 1 (c)) can be reformulated in terms of the sensitivity function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The design ξ∗ is D-optimal if and only if there exist a threshold s∗ and settings a1 > · · · > a2r for some r (1 ≤ r ≤ q) such that (i) the D-optimal design ξ∗ is given by fξ∗(x) = � fX(x) if x ∈ X ∗ 0 otherwise (ii) ψ(x, ξ∗) ≥ s∗ for x ∈ X ∗, and (iii) ψ(x, ξ∗) < s∗ for x ̸∈ X ∗, where X ∗ = �r k=0 Ik and I0 = [a1, ∞), Ir = (−∞, a2r], and Ik = [a2k+1, a2k], for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , r − 1, are mutually disjoint intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The density fξ∗(x) = fX(x)1X ∗(x) = �r k=0 fX(x)1Ik(x) of the D-optimal design ξ∗ is concentrated on, at most, q + 1 intervals Ik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Here, 1A(x) denotes an indicator function on the set A, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 1A(x) = 1 for x ∈ A, and 1A(x) = 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The density fξ∗(x) has a 0−1-property such that it is either equal to the density fX(x) of the covariates (on X ∗) or equal to 0 (on the complement of X ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then the generation of a subsample according to the optimal continuous design ξ∗ can be implemented easily by accepting all units i for which the value xi of the covariate is in X ∗ and rejecting all other units with xi ̸∈ X ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The threshold s∗ can be interpreted as the (1 − α)-quantile of the distribution of the sensitivity function ψ(Xi, ξ∗) as a function of the random variable Xi (see Pronzato and Wang, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A further general concept to be used is equivariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This can be employed to transform the D-optimal design simultaneously with a transformation of the distribution of the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' More precisely, the location scale transformation Zi = σXi + µ of the covariates and their distribution is conformable with the regression function f(x) in polynomial regression, and the D-criterion is equivariant with respect to such transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 5 Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Let fξ∗(x) be the density for a D-optimal design ξ∗ for covariates Xi with density fX(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then fζ∗(z) = 1 σfξ∗( z−µ σ ) is the density for a D-optimal design ζ∗ for covariates Zi = σXi + µ with density fZ(z) = 1 σfX( z−µ σ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In particular, also the optimal design ζ∗ is concentrated on, at most, p = q + 1 intervals, and its density fζ∗(z) is either equal to the density fZ(z) of the covariates Zi (on Z∗ = σX ∗ + µ) or it is equal to 0 (elsewhere) such that the optimal subsampling can be implemented quite easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A further reduction of the optimization problem can be achieved by utilizing symmetry properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Therefore, we consider the transformation of sign change, g(x) = −x, and assume that the distribution of the covariates is symmetric, fX(−x) = fX(x) for all x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For a continuous design ξ, the design ξg transformed by sign change has density fξg(x) = fξ(−x) and, thus, satisfies the boundedness condi- tion fξg(x) ≤ fX(x), when the distribution of Xi is symmetric, and has the same value for the D-criterion as ξ, log(det(M(ξg))) = log(det(M(ξ))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' By the concavity of the D-criterion, standard invariance arguments can be used as in Pukelsheim (1993, Chapter 13) and Heiligers and Schneider (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In particular, any con- tinuous design ξ is dominated by its symmetrization ¯ξ = (ξ + ξg)/2 with density f¯ξ(x) = (fξ(x) + fξ(−x))/2 ≤ fX(x) such that log(det(M(¯ξ))) ≥ log(det(M(ξ))) (Pukelsheim, 1993, Chapter 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Hence, we can restrict the search for a D-optimal design to symmetric designs ¯ξ with density f¯ξ(−x) = f¯ξ(x) which are invariant with respect to sign change (¯ξg = ¯ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For these symmetric designs ¯ξ, the moments mk(¯ξ) are zero for odd k and positive when k is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Hence, the information matrix M(¯ξ) is an even checkerboard matrix (see Jones and Willms, 2018) with positive entries mj+j′(¯ξ) for even index sums and entries equal to zero when the index sum is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The inverse M(¯ξ)−1 of the information matrix M(¯ξ) shares the structure of an even checkerboard matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus, the sensitivity function ψ(x, ¯ξ) is a polynomial with only terms of even order and is, hence, a symmetric function of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This leads to a simplification of the representation of the optimal design in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 because the support X ∗ of the optimal design ξ∗ will be symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Let the distribution of Xi be symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then, for the D-optimal design ξ∗ with density fξ∗(x) = �r k=0 fX(x)1Ik(x) the boundaries a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , a2r of the intervals Ik = [a2k+1, a2k] are symmetric, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' a2r+1−k = −ak and, similarly, Ir+2−k = −Ik for the intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This characterization of the optimal design ξ∗ will be illustrated in the next two sections for ordinary linear regression (q = 1) and for quadratic regression (q = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimal Subsampling for Linear Regression In the case of ordinary linear regression Yi = β0 + β1Xi + εi we have M(ξ∗) = � α m1(ξ∗) m1(ξ∗) m2(ξ∗) � , for the information matrix of the optimal design ξ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The sensitivity function is a polynomial of degree 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To obtain the D-optimal continuous design ξ∗ by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1, the boundary points a1 and a2 have to be determined to solve the two nonlinear equations P(Xi ≤ a2) + P(Xi ≥ a1) = α (1) OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 6 and ψ(a1, ξ∗) = ψ(a2, ξ∗) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2) The D-optimal continuous design ξ∗ has density fξ(x) = fX(x) for x ≤ a2 and for x ≥ a1 while fξ(x) = 0 for a2 < x < a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The corresponding subsampling design then accepts those units i for which xi ≤ a2 or xi ≥ a1, and rejects all units i for which a2 < xi < a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' When the distribution of Xi is symmetric, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 provides symmetry a2 = −a1 of the boundary points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Hence, by the symmetry of the distribution, P(Xi ≤ a2) = P(Xi ≥ a1) = α/2, and a1 has to be chosen as the (1 − α/2)-quantile of the distribution of Xi to obtain the D-optimal continuous design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 (normal distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' If the covariates Xi come from a standard normal distribution, then the optimal boundaries are the (α/2)- and the (1 − α/2)- quantile ±z1−α/2, and unit i is accepted when |xi| ≥ z1−α/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For Xi having a general normal distribution with mean µ and variance σ2, the optimal boundaries remain to be the (α/2)- and (1−α/2)-quantile a2 = µ−σz1−α/2 and a1 = µ + σz1−α/2, respectively, by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This approach applies accordingly to all distributions which are obtained by a shift transformation of a symmetric distribution: Units will be accepted if their values of the covariate lie in the lower or upper (α/2)-tail of the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This procedure can be interpreted as a theoretical counterpart in one dimension of the IBOSS method proposed by Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' However, for asymmetric distributions, the optimal proportions for sampling from the upper and lower tail will differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 (exponential distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' If the covariates Xi come from a standard exponential distribution with density fX(x) = e−x, x ≥ 0, we conclude from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 that fξ∗(x) = fX(x)1(−∞,a]∪[b,∞)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We can calculate the entries of M(ξ∗) as functions of a1 = a and a2 = b as m1(ξ∗) = 1 + (a + 1)e−a − (b + 1)e−b m2(ξ∗) = 2 + (a2 + 2a + 2)e−a − (b2 + 2b + 2)e−b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To obtain the optimal solutions for a and b, the two nonlinear equations (1) and (2) come here to be 1 − e−b + e−a = α and f(a)⊤M(ξ∗)−1f(a) = f(b)⊤M(ξ∗)−1f(b) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The results for selected values of α can be seen in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Additionally to the optimal values for a and b, also the proportions P(Xi ≤ b) and P(Xi ≥ a) are presented in Table 1 together with the percentage of mass allocated to the left interval [0, b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Figure 1, the density fξ∗ of the optimal design ξ∗ and the corresponding sensitivity function ψ(x, ξ∗) are exhibited for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Vertical lines indicate the positions of the boundary points a and b, and the dotted horizontal line displays the threshold s∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As could have been expected, less mass is assigned to the right tail of the right-skewed distribution because observations from the right tail are more influential and, thus, more observations seem to be required on the lighter left tail for compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 7 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Numeric values for a and b for selected values of α in the case of standard exponential Xi α b P(Xi ≤ b) a P(Xi ≥ a) % of mass on [0, b] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='39572 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='32681 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75335 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='17319 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='21398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='19264 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='23153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='10736 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='06343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='06146 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25596 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='03854 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00579 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00577 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='46588 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00423 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='71 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0 1 2 3 4 5 x Density 1 2 3 4 5 0 1 2 3 4 5 x Sensitivity function (a) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0 1 2 3 4 5 x Density 1 2 3 4 0 1 2 3 4 5 x Sensitivity function (b) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Density of the optimal design (solid line) and the stan- dard exponential distribution (dashed line, upper panels), and sensitivity functions (lower panels) for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 (left) and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 (right) For Xi having an exponential distribution with general intensity λ > 0 (scale 1/λ), the optimal boundary points remain to be the same quantiles as in the standard exponential case, a1 = a/λ and a2 = b/λ, by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimal Subsampling for Quadratic Regression In the case of quadratic regression Yi = β0 + β1Xi + β2X2 i + εi we have M(¯ξ) = � � α 0 m2(¯ξ) 0 m2(¯ξ) 0 m2(¯ξ) 0 m4(¯ξ) � � , for the information matrix of a symmetric design ¯ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The corresponding sensitivity function ψ(x, ¯ξ) is a polynomial of degree 4 and is symmetric in x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' According to Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3, the density fξ∗(x) of the D-optimal continuous design ξ∗ has, at most, three intervals that are symmetrically placed around zero, where the density is equal to the bounding density fX(x), and fξ∗(x) is equal to zero elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus the density fξ∗(x) of the D-optimal design has the following shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' fξ∗(x) = fX(x)1(−∞,−a]∪[−b,b]∪[a,∞)(x) , where a > b ≥ 0 and where we formally allow b = 0 which means that ψ(0, ξ∗) ≤ 0 and that the density fξ∗(x) is concentrated on only two intervals, fξ∗(x) = fX(x)1{x∈(−∞,−a]∪[a,∞)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Although the information matrix will be non-singular OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 8 even in the case of two intervals (b = 0), the optimal design will typically include a non-degenerate interior interval [−b, b], b > 0, as illustrated below in Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To obtain the D-optimal continuous design ξ∗ by Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3, the boundary points a = a1 and b = a2 (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' b = 0) have to be determined to solve the two nonlinear equations P(|Xi| ≤ b) + P(|Xi| ≥ a) = α (3) and ψ(a, ξ∗) = ψ(b, ξ∗) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (4) For finding the optimal solutions, we use the Newton method implemented in the R package nleqslv by Hasselman (2018) to calculate numeric values for a and b based on equations (3) and (4) for various symmetric distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 (normal distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the case that the covariates Xi come from a standard normal distribution, results are given in Table 2 for some values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Additionally to the optimal values for a and b, also the proportions P(Xi ≥ a) = Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Numeric values for a and b for selected values of α in the case of standard normal Xi α a 1 − Φ(a) b 2Φ(b) − 1 % of mass on [−b, b] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='02800 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='15198 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='24824 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='19605 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='34789 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='08885 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='15389 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='12231 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='88422 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='02977 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='05073 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='04046 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='73996 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00307 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00483 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00386 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='55 P(Xi ≤ −a) = 1 − Φ(a) and P(−b ≤ Xi ≤ b) = 2Φ(b) − 1 are presented in Table 2 together with the percentage of mass (2Φ(b) − 1)/α allocated to the interior interval [−b, b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Figure 2, the density fξ∗ of the optimal design ξ∗ and the corresponding sensitivity function ψ(x, ξ∗) are exhibited for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Vertical lines 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 −2 0 2 x Density 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −2 0 2 x Sensitivity function (a) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 −2 0 2 x Density 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 −2 0 2 x Sensitivity function (b) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Density of the optimal design (solid line) and the stan- dard normal distribution (dashed line, upper panels), and sensitivity functions (lower panels) for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 (left) and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 (right) indicate the positions of the boundary points −a, −b, b, and a, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 9 subplots of the sensitivity function, the dotted horizontal line displays the threshold s∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For other values of α, the plots are looking similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The numerical results in Table 2 suggest that the interior interval [−b, b] does not vanish for any α (0 < α < 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This will be established in the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Let the distribution of Xi be standard normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For all α ∈ (0, 1), there exists b > 0 such that the D-optimal design ξ∗ has density fξ∗(x) = fX(x)1{x∈(−∞,−a]∪[−b,b]∪[a,∞)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For Xi having a general normal distribution with mean µ and variance σ2, the optimal boundary points remain to be the same quantiles as in the standard normal case, a1, a4 = µ ± σa and a2, a3 = µ ± σb, by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 (uniform distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' If the covariates Xi are uniformly distributed on [−1, 1] with density fX(x) = 1 21[−1,1](x), we can obtain analytical results for the dependence of the subsampling design on the proportion α to be selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The distribution of Xi is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' By Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3, the density of the D- optimal continuous design ξ∗ has the shape fξ∗(x) = 1 21[−1,−a]∪[−b,b]∪[a,1](x) where a and b are the solution of the following two equations 1 − a + b = α and f(a)⊤M(ξ∗)−1f(a) = f(b)⊤M(ξ∗)−1f(b) , where the entries in the even checkerboard matrix M(ξ∗) are m0(ξ∗) = α, m2(ξ∗) = 1 3(1 − a3 + b3), and m4(ξ∗) = 1 5(1 − a5 + b5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Solving these equations results in a(α) = 1 2 � 1 − α + � 45 − 15α + 15α2 − 45α3 + 20α4 45(1 − α) − 4α √ 5 √ 45 − 90α + 90α2 − 75α3 + 57α4 − 27α5 + 5α6 45(1 − α) �1/2 � (5) and b(α) = a − (1 − α) (6) for the dependence of a and b on α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The values of a and b are plotted in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' There it can be seen that a and b both tend to 1/ √ 5 as α tends to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Similar to the normal distribution, the resulting values and illustrations are given in Table 3 and Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Also here, vertical lines indicate the positions of the boundary points −a, −b, b, and a, and the dotted horizontal line displays the threshold s∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Moreover, the percentage of mass at the different intervals is displayed in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The results in Table 3 and Figure 5 suggest that the percentage of mass on all three intervals [−1, −a], [−b, b], and [a, 1] tend to 1/3 as α tends to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We establish this in the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Let Xi be uniformly distributed on [−1, 1] and ξ∗ α be the optimal subsampling design for α, 0 < α < 1, defined in equations (5) and (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then limα→0 ξ∗ α([−b, b])/α = 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 α a,b Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Boundary points a and b in dependence on α Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Numeric values for a and b for selected values of α in the case of uniform Xi on [−1, 1] α a 1 − P(Xi ≥ a) b = P(−b ≤ Xi ≤ b) % of mass on [−b, b] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='70983 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='14508 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='20983 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='97 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='81737 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='09132 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='11737 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='93546 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='03227 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='03546 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='99336 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00332 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00336 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 x Density 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 x Sensitivity function (a) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 x Density 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 x Sensitivity function (b) α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Density of the optimal design (solid line) and the uni- form distribution on [−1, 1] (dashed line, upper panels), and sen- sitivity functions (lower panels) for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 (left) and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 (right) It is worth-while mentioning that the percentages of mass displayed in Figure 5 are not monotonic over the whole range of α ∈ (0, 1), as, for example the mass at the interior interval [−b, b] is increasing from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='419666 at b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='448549 at b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='92 and then slightly decreasing again to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='447553 at b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the two preceding examples it could be noticed that the mass of observations is of comparable size for the three supporting intervals in the case of a normal and of a uniform distribution with light tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This will be different in the case of a heavy-tailed distribution for the covariates Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 α (1−a)/2α 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 α b/α Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Percentage of mass on [a, 1] (left) and [−b, b] (right) as a function of α 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Efficiency considerations To exhibit the gain in using a D-optimal design compared to random subsampling, we consider the performance of the uniform random subsampling design ξα of size α, which has density fξα(x) = αfX(x), compared to the D-optimal subsampling design ξ∗ α with mass α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' More precisely, the D-efficiency of any design ξ with mass α is defined as effD,α(ξ) = � det(M(ξ)) det(M(ξ∗α)) �1/p , where p is the dimension of the parameter vector β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For this definition the homogeneous version (det(M(ξ)))1/p of the D-criterion is used which satisfies (det(λM(ξ)))1/p = λ(det(M(ξ)))1/p (see Pukelsheim, 1993, Chapter 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For uniform random subsampling, the information matrix is given by M(ξα) = αM(ξ1), where M(ξ1) is the information matrix for the full sample with raw moments mk(ξ1) = E[Xk i ] as entries in the (j, j′)th position, j +j′ = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus, the D-efficiency effD,α(ξα) can be nicely interpreted: When uniform random subsampling is used, the inverse of the efficiency effD,α(ξα)−1 times α gives the sample size (mass) required to obtain the same precision in terms of the D-criterion as when the D-optimal design ξ∗ α of mass α is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For example, if the efficiency effD,α(ξα) is equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5, then twice as many observations would be needed under uniform random sampling than for a D-optimal subsampling design of size α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Of course, the full sample has higher information than any proper subsample such that, obviously, effD,α(ξα) ≥ α holds for uniform random subsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the examples of Sections 4 and 5, the efficiency of uniform random subsampling is given in Table 4 for selected values of α and exhibited in Figure 6 for the full range of α between 0 and 1 (solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Here the determinant of the information matrix is determined as in the examples of Sections 4 and 5 for the optimal designs ξα∗ either numerically or by explicit formulas where available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Both Table 4 and Figure 6 indicate that the efficiency of uniform random subsam- pling is decreasing in all cases when the proportion α of subsampling gets smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the case of uniformly distributed covariates, the decrease is more or less linear with a minimum value of approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='58 for quadratic regression when α is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the other cases, where the distribution of the covariates is unbounded, the efficiency apparently decreases faster, when the proportion α is smaller than 10%, and tends to 0 for α → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 12 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Efficiency for selected values of α α 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='01 linear regression normal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='73376 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='61886 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='47712 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='34403 exponential 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='73552 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='61907 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='46559 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='30690 quadratic regression normal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='73047 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='59839 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='41991 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='24837 uniform 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='78803 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='70475 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='62411 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='58871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 α Efficiency (a) Linear regression, normal covariates 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 α Efficiency (b) Linear regression, exponential covari- ates 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 α Efficiency (c) Quadratic regression, normal covariates 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='00 α Efficiency (d) Quadratic regression, uniform covari- ates Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Efficiency of uniform random subsampling (solid line) and of an IBOSS-type design (dashed line) The latter property can be easily seen for linear regression and symmetric distribution: There, the efficiency effD,α(ξα) of uniform random sampling is bounded from above by c/q1−α/2, where c = E(X2 i )1/2 is a constant and q1−α/2 is the (1−α/2)- quantile of the distribution of the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' When the distribution is unbounded like the normal distribution, then these quantiles tend to infinity for α → 0 and, hence, the efficiency tends to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Similar results hold for quadratic regression and asymmetric distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 13 In any case, as can be seen from Table 4, the efficiency of uniform random subsampling is quite low for reasonable proportions α ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 and, hence, the gain in using the D-optimal subsampling design is substantial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' By equivariance arguments as indicated above in the examples of Sections 4 and 5, the present efficiency considerations carry over directly to covariates having a general normal, exponential, or uniform distribution, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the IBOSS approach by Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' (2019), half of the proportion α is taken from both tails of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The corresponding continuous subsampling design ξ′ α would be to choose the boundary points a1 and a2 to be the (1 − α/2)- and (α/2)- quantile of the distribution of the covariates, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For linear regression, it can been seen from Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 that the design ξ′ α is D-optimal when the distribution of the covariates is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As the IBOSS procedure does not use prior knowledge of the distribution, it would be tempting to investigate the efficiency of the corresponding continuous subsampling design ξ′ α under asymmetric distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the exponential distribution, this efficiency effD,α(ξ′ α) is added to the upper right panel in Figure 6 by a dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' There the design ξ′ α shows a remarkably high efficiency over the whole range of α with a minimum value 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='976 at α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='332.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As an extension of IBOSS for quadratic regression, we may propose a procedure which takes proportions α/3 from both tails of the data as well as from the center of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This procedure can be performed without any prior knowledge of the distribution of the covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The choice of the proportions α/3 is motivated by the standard case D-optimal design on an interval where one third of the weight is allocated to each of the endpoints and to the midpoint of the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For a symmetric distribution, the corresponding continuous subsampling design ξ′′ α can be defined by the boundary points a and b to be the (1 − α/3)- and (1/2 + α/6)-quantile of the distribution of the covariates, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In the case of the uniform distribution, the design ξ′′ α is the limiting D-optimal design for α → 0 by Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the whole range of α and for the normal distribution, the efficiency effD,α(ξ′′ α) is shown in the lower panels of Figure 6 by dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In both cases, the design ξ′′ α is highly efficient over the whole range of α with minimum values 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='994 at α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='079 for the normal distribution and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='989 at α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='565 for the uniform distribution, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Concluding Remarks In this paper we have considered a theoretical approach to evaluate subsampling designs under distributional assumptions on the covariates in the case of polynomial regression on a single explanatory variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Main emphasis was on D-optimal designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' But many of the results may be extended to other optimality criteria like A- and E-optimality from the Kiefer’s Φq-class of optimality criteria, IMSE-optimality for predicting the mean response, or optimality criteria based on subsets or linear functionals of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The D-optimal designs show a high performance compared to uniform random subsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In particular, for small proportions, the efficiency of uniform random subsampling tends to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This property is in accordance with the observation that estimation based on subsampling according to IBOSS is “consistent” in the sense that the mean squared error goes to zero with increasing population size even when the size of the subsample is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 14 We propose a generalization of the IBOSS method to quadratic regression which does not require prior knowledge of the distribution of the covariates and which performs remarkably well compared to the optimal design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' However, an extension to higher order polynomials, does not seem to be obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Proofs Before proving Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1, we establish two preparatory lemmas on properties of the sensitivity function ψ(x, ξ) for a continuous design ξ with density fξ(x) and reformulate an equivalence theorem on constraint design optimality by Sahm and Schwabe (2001) for the present setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The first lemma deals with the shape of the sensitivity function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The sensitivity function ψ(x, ξ) is a polynomial of degree 2q with positive leading term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Proof of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For a continuous design ξ with density fξ(x), the information matrix M(ξ) and, hence, its inverse M(ξ)−1 is positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus the last diagonal element m(pp) of M(ξ)−1 is positive and, as f(x) = (1, x, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , xq)⊤, the sensitivity function ψ(x, ξ) = f(x)⊤M(ξ)−1f(x) is a polynomial of degree 2q with coefficient m(pp) > 0 of the leading term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ The second lemma reveals a distributional property of the sensitivity function considered as a function in the covariates Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The random variable ψ(Xi, ξ) has a continuous cumulative distribu- tion function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Proof of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As the sensitivity function ψ(x, ξ) is a non-constant poly- nomial by Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1, the equation ψ(x, ξ) = s has only finitely many roots x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' , xℓ, say, by the fundamental theorem of algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Hence, P(ψ(Xi, ξ) = s) = �ℓ k=1 P(Xi = xk) = 0 by the continuity of the distribution of Xi which proves the continuity of the cumulative distribution function of ψ(Xi, ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ With the continuity of the distribution of ψ(Xi, ξ∗) the following equivalence theorem can be obtained from Corollary 1(c) in Sahm and Schwabe (2001) for the present setting by transition from the directional derivative to the sensitivity function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3 (Equivalence Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The design ξ∗ is D-optimal if and only if there exist a threshold s∗ and a subset X ∗ of the design region such that (i) the D-optimal design ξ∗ is given by fξ∗(x) = fX(x)1X ∗(x) (ii) ψ(x, ξ∗) ≥ s∗ for x ∈ X ∗, and (iii) ψ(x, ξ∗) < s∗ for x ̸∈ X ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As P(ψ(Xi, ξ∗) ≥ s∗) = P(Xi ∈ X ∗) = � fξ∗(x) dx = α, the threshold s∗ is the (1 − α)-quantile of the distribution of ψ(Xi, ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' By Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 the sensitivity function ψ(x, ξ) is a polyno- mial in x of degree 2q with positive leading term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Using the same argument as in the proof of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2 we obtain that there are at most 2q roots of the equation ψ(x, ξ∗) = s∗ and, hence, there are at most 2q sign changes in ψ(x, ξ∗) − s∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' As OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 15 ψ(x, ξ∗) is a polynomial of even degree, also the number of (proper) sign changes has to be even, and they occur at a1 > · · · > a2r, say, r ≤ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Moreover, for 0 < α < 1, X ∗ is a proper subset of the design region and, thus, there must be at least one sign change, r ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Finally, as the leading coefficient of ψ(x, ξ∗) is positive, ψ(x, ξ∗) gets larger than s∗ for x → ±∞ and, hence, the outmost intervals [a1, ∞) and (−∞, a2r] are included in the support X ∗ of ξ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' By the interlacing property of intervals with positive and negative sign for ψ(x, ξ∗) − s∗, the result follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' First note that for any µ and σ > 0, the location scale transformation z = σx + µ is conformable with the regression function f(x), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' there exists a non-singular matrix Q such that f(σx + µ) = Qf(x) for all x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then, for any design ξ bounded by fX(x), the design ζ has density fζ(z) = 1 σfξ( z−µ σ ) bounded by fZ(z) = 1 σfX( z−µ σ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then, by the transformation theorem for measure integrals, it holds that M(ζ) = � f(z)f(z)⊤ζ(dz) = � f(σx + µ)f(σx + µ)⊤ξ(dx) = � Qf(x)f(x)⊤Q⊤ξ(dx) = QM(ξ)Q⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Therefore det(M(ζ)) = det(Q)2 det(M(ξ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus ξ∗ maximizes the D-criterion over the set of designs bounded by fX(x) if and only if ζ∗ maximizes the D-criterion over the set of designs bounded by fZ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ Proof of Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The checkerboard structure of the information matrix M(ξ∗) carries over to its inverse M(ξ∗)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Hence, the sensitivity function ψ(x, ξ∗) is an even polynomial, which has only non.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='zero coefficients for even powers of x, and is thus symmetric with respect to 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' ψ(−x, ξ∗) = ψ(x, ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Accordingly, also the roots of ψ(x, ξ∗) = s∗ are symmetric with respect to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ Proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Suppose there exists an α ∈ (0, 1) such that a = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then b = z(1+α)/2, obviously and it must hold that ψ(z(1−α)/2, ξ∗) ≥ limx→∞ ψ(x, ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Since M(ξ∗) is positive definite, the leading term of the polynomial ψ(x, ξ∗) in x is positive and subsequently ψ(z(1−α)/2, ξ∗) < limx→∞ ψ(x, ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This is a contradiction and therefore a < ∞ for all α ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Suppose there exists an α ∈ (0, 1) such that b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Then a = z1−α/2, obviously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Further, it must hold that ψ(z1−α/2, ξ∗) ≥ ψ(0, ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We will show that this inequality is in fact false.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Because ξ∗ is invariant to the sign change we have M(ξ∗) = � � α 0 m2(ξ∗) 0 m2(ξ∗) 0 m2(ξ∗) 0 m4(ξ∗) � � and thus M(ξ∗)−1 = � � � m4(ξ∗) αm4(ξ∗)−m2(ξ∗)2 0 −m2(ξ∗) αm4(ξ∗)−m2(ξ∗)2 0 1 m2(ξ∗) 0 −m2(ξ∗) αm4(ξ∗)−m2(ξ∗)2 0 α αm4(ξ∗)−m2(ξ∗)2 � � � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 16 where m2(ξ∗) = � R x2fξ∗(x) dx = α + � 2/πz1−α/2 exp � −z2 1−α/2 2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' m4(ξ∗) = � R x4fξ∗(x) dx = � 2/πz3 1−α/2 exp � −z2 1−α/2 2 � + 3m2(ξ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We will write a instead of z1−α/2 from here on out for readability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' For the directional derivatives we have ψ(0, ξ∗) = α(1 0 0)M(ξ∗)−1(1 0 0)⊤ = αm4(ξ∗) αm4(ξ∗) − m2(ξ∗)2 and ψ(a, ξ∗) = α(1 a a2)M(ξ∗)−1(1 a a2)⊤ = αm4(ξ∗) αm4(ξ∗) − m2(ξ∗)2 − c, where c = αa2 � 2m2(ξ∗) αm4(ξ∗) − m2(ξ∗)2 − a2α αm4(ξ∗) − m2(ξ∗)2 − 1 m2(ξ∗) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' c is continuous in α ∈ (0, 1) and does not have any roots in (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We can easily check, that c > 0 for e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1 and thus c > 0 for all α ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This yields ψ(z1−α/2, ξ∗) < ψ(0, ξ∗) for all α ∈ (0, 1), which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ Proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Firstly, we check if limα→0 b(α)/α = 1/3, as b(α)/α = � b −b ξ∗(dx)/ � 1 −1 ξ∗(dx) describes the percentage of mass on [−b, b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Note that limα→0 b(α)/α is by definition the derivative of b(α) at the point α0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Thus we consider the derivative of b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' db(α) dα = 1 2 + 1 2 � u′(α)v(α) − u(α)v′(α) v(α)2 1 2 � u(α)/v(α) � , where u(α) = 45 − 15α + 15α2 − 45α3 + 20α4 − 4 √ 5 � 45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8, c(α) = 4 √ 5(90α − 270α2 + 360α3 − 375α4 + 342α5 − 189α6 + 40α7) 2 √ 45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8 u′(α) = −15 + 30α − 135α2 + 80α3 − c(α), v(α) = 45 − 45α, v′(α) = −45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We have u(α0) = v(α0) = 45 and v′(α0) = −45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Note that c(α) > 0 for α ∈ (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='85), as the polynomial in the numerator has roots in α = 0, α ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='85316 with no roots and positive values in between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Similarly, the polynomial in the denominator is positive for all α ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' To find u′(α0) we study the limit of c(α)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 17 c(α)2 = 16 · 5(90α − 270α2 + 360α3 − 375α4 + 342α5 − 189α6 + 40α7)2 4(45α2 − 90α3 + 90α4 − 75α5 + 57α6 − 27α7 + 5α8) = 80 · 902α2 + O(α3) 4 · 45α2 + O(α3) = 80 · 902 + O(α) 4 · 45 + O(α) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Therefore lim α↘0 c(α)2 = 80 · 902 4 · 45 = 3600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' This yields limα↘0 c(α) = 60, as c(α) > 0 for positive values of α close to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' We have u′(α0) = −75 and consequently limα→0 b(α) α = 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' □ OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 18 Acknowledgments The work of the first author is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within GRK 2297 MathCoRe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' References Micha�l Derezi´nski and Manfred K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Warmuth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Reverse iterative volume sampling for linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The Journal of Machine Learning Research, 19(1):853–891, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Petros Drineas, Michael W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Mahoney, and Shan Muthukrishnan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Sampling algo- rithms for ℓ2 regression and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pages 1127–1136, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Valerii V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Fedorov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimal design with bounded density: Optimization algorithms of the exchange type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of Statistical Planning and Inference, 22(1):1–13, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Norbert Gaffke and Berthold Heiligers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Approximate designs for polynomial regres- sion: Invariance, admissibility, and optimality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Ghosh and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Rao, editors, Handbook of Statistics 13, pages 1149–1199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Elsevier, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Berend Hasselman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' nleqslv: Solve Systems of Nonlinear Equations, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' URL https://CRAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='R-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='org/package=nleqslv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' R package version 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Berthold Heiligers and Klaus Schneider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Invariant admissible and optimal designs in cubic regression on the v-ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of statistical planning and inference, 31 (1):113–125, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Jones and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Willms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Inverse eigenvalue problems for checkerboard toeplitz matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of Physics: Conference Series, 1047(1):012016, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1088/1742-6596/1047/1/012016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1088% 2F1742-6596%2F1047%2F1%2F012016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Ping Ma, Michael W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Mahoney, and Bin Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A statistical perspective on algorithmic leveraging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 91–99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' PMLR, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Michael W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Mahoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Randomized algorithms for matrices and data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Foundations and Trends® in Machine Learning, 3(2):123–224, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' ISSN 1935-8237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1561/2200000035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' URL http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='1561/2200000035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Luc Pronzato.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A minimax equivalence theorem for optimum bounded design measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Statistics & probability letters, 68(4):325–331, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Luc Pronzato and HaiYing Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Sequential online subsampling for thinning experimental designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of Statistical Planning and Inference, 212:169–193, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Friedrich Pukelsheim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimal Design of Experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Wiley, New York, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Michael Sahm and Rainer Schwabe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' A note on optimal bounded designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Atkinson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Bogacka, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Zhigljavsky, editors, Optimum Design 2000, pages 131–140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Kluwer, Dordrecht, The Netherlands, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Chenlu Shi and Boxin Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Model-robust subdata selection for big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of Statistical Theory and Practice, 15(4):1–17, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Silvey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimal design: an introduction to the theory for parameter estimation, volume 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Chapman and Hall, London, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Robert Tibshirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Regression shrinkage and selection via the lasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B, 58(1):267–288, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' OPTIMAL SUBSAMPLING DESIGN FOR POLYNOMIAL REGRESSION 19 HaiYing Wang, Min Yang, and John Stufken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Information-based optimal subdata selection for big data linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Journal of the American Statistical Association, 114(525):393–405, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Lin Wang, Jake Elmstedt, Weng Kee Wong, and Hongquan Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Orthogonal subsampling for big data linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' The Annals of Applied Statistics, 15 (3):1273–1290, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Henry P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Wynn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Optimum designs for finite populations sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' In S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Gupta, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Moore, editors, Statistical Decision Theory and Related Topics II, pages 471–478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Academic Press, New York, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Otto von Guericke University Magdeburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Universit¨atsplatz 2, 39106 Magdeburg, Germany Email address: torsten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='reuter@ovgu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='de Otto von Guericke University Magdeburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content=' Universit¨atsplatz 2, 39106 Magdeburg, Germany Email address: rainer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='schwabe@ovgu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} +page_content='de' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE1T4oBgHgl3EQfmQRh/content/2301.03295v1.pdf'} diff --git a/59E2T4oBgHgl3EQfOwac/content/2301.03752v1.pdf b/59E2T4oBgHgl3EQfOwac/content/2301.03752v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e4786b08508b0110b26d2c1e1d43ec10f25bd2b5 --- /dev/null +++ b/59E2T4oBgHgl3EQfOwac/content/2301.03752v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:807a366ad91cd18e36af773a193e899de5eac49369982a4075305aec5a1c6e08 +size 11799878 diff --git a/5NE2T4oBgHgl3EQfOgaA/vector_store/index.faiss b/5NE2T4oBgHgl3EQfOgaA/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..6cf492833f70726bc353f98e3199252fd90f3ae5 --- /dev/null +++ b/5NE2T4oBgHgl3EQfOgaA/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd31cb7c528c2558d26ae4d0efe3bd4866951959fad15a2ce4bf5143cdf771d9 +size 7012397 diff --git a/5NE2T4oBgHgl3EQfOgaA/vector_store/index.pkl b/5NE2T4oBgHgl3EQfOgaA/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..5a022de73a8f3ae825ce26648f26e1b500678b5a --- /dev/null +++ b/5NE2T4oBgHgl3EQfOgaA/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fb0a2930745e7f34ca75781c6285c1ab7cd0bd8e58e85bd265fbc93b62cb1993 +size 253668 diff --git a/5NFKT4oBgHgl3EQfSS3g/vector_store/index.faiss b/5NFKT4oBgHgl3EQfSS3g/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..106880eb1d03a3b416a271d74f667dd94fe77bfa --- /dev/null +++ b/5NFKT4oBgHgl3EQfSS3g/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:61dd7250041fa7c1febe1bfe3408f4df70a19282c3f935b7c1b7314487903b2b +size 4456493 diff --git a/5tE0T4oBgHgl3EQfvwEb/vector_store/index.faiss b/5tE0T4oBgHgl3EQfvwEb/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..997450bd4c2a504703b0db6d2ba6e05bc720692b --- /dev/null +++ b/5tE0T4oBgHgl3EQfvwEb/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c57577209828f8ae96a1b891435d06ffc41754bcd72fb8df2ef46587ee045505 +size 2949165 diff --git a/6tAyT4oBgHgl3EQfQfaP/vector_store/index.faiss b/6tAyT4oBgHgl3EQfQfaP/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..688db18879fbadcb320b850c167d9dccec22744b --- /dev/null +++ b/6tAyT4oBgHgl3EQfQfaP/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e408747852e84f25d27b3491bdcc067116abad028fb630ec1e24210a802a2cc9 +size 852013 diff --git a/6tE0T4oBgHgl3EQfwAE6/vector_store/index.faiss b/6tE0T4oBgHgl3EQfwAE6/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..b4e9af34048fa018299ee7792ce4aca43bfdead8 --- /dev/null +++ b/6tE0T4oBgHgl3EQfwAE6/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:848fea1722ab343e0d4e873bf5b11e0e8f97efcfdfbb06c3eee21feec9f90039 +size 5832749 diff --git a/6tFKT4oBgHgl3EQf_i4o/vector_store/index.pkl b/6tFKT4oBgHgl3EQf_i4o/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..161a536aab5974fc6c7d36efae05e42fd24d46f1 --- /dev/null +++ b/6tFKT4oBgHgl3EQf_i4o/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8e6da9b13e7da2b95089bae5c3d2ba10561289db5748091e932be95e741e5086 +size 209220 diff --git a/79FJT4oBgHgl3EQfnCyN/content/tmp_files/2301.11590v1.pdf.txt b/79FJT4oBgHgl3EQfnCyN/content/tmp_files/2301.11590v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..22d99144d5e97d36a8e401708b7cc131cf6f0b3e --- /dev/null +++ b/79FJT4oBgHgl3EQfnCyN/content/tmp_files/2301.11590v1.pdf.txt @@ -0,0 +1,2253 @@ + +1 +BUCKLING-INDUCED TRANSMISSION SWITCHING IN +PHONONIC WAVEGUIDES IN THE PRESENCE OF DISORDER +Ali Kanj1, Alexander F. Vakakis1, Sameh Tawfick1,2 +1Department of Mechanical Science and Engineering, University of Illinois at Urbana- +Champaign, Illinois 61801, United States +2The Beckman Institute of Advanced Science and Technology, University of Illinois at +Urbana-Champaign, Illinois 61801, United States +On-chip phononic circuits tailor the transmission of elastic waves, which can couple to +electronic and photonic systems, enabling new signal manipulation capabilities. Phononic +circuits rely on waveguides that transmit elastic waves within desired frequency +passbands, typically designed based on the Bloch modes of the waveguide constitutive +cell, assuming linearity and periodicity. MEMS waveguides composed of coupled +drumhead (membrane) resonators offer tunable MHz operation frequencies for +applications in nonlinear optomechanics, topological insulators, phononic cavities, and +acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the +switching of signal transmission in drumhead-resonator waveguides due to thermoelastic +buckling. The ROM shows that buckling amplifies existing structural disorders, breaking +the periodicity required for waveguide transmission through the first passband. This +periodicity breaking manifests in the localization of the first-passband modes, like +classical Anderson localization caused by disorders. The proposed ROM is essential to +study the investigated phenomena since Bloch mode analysis fails for weakly-disordered +(< 5%) finite waveguides due to the disorder amplification caused by the thermoelastic +buckling. The illustrated transmission control should be useful for logical acoustic +operations, like switching, and can be extended to 2D circuits in the future. +I. Introduction +Phononic circuits are gaining increased interest because they tailor the propagation of +elastic and acoustic waves, which is advantageous for signal manipulation. For example, +phononic circuits are useful for cellular phone duplexers by serving as acoustic isolators and +mirrors [1] [2] [3]. In medical ultrasound applications and acoustic nondestructive tests, +phononic circuits promise to miniaturize the imaging aperture [4] [5] [6], decouple the electro- +acoustic transduction [7] [8], and slow the signal for smaller delay lines [9] [10] [11]. +Moreover, nanostructural phononics operating in the hypersonic (GHz to THz) frequencies +enable thermal management [12] [13] [14], photonic-phononic interactions [15] [16], and +quantum information control [17] [18]. Phononic structures offer readily-achievable +nonlinearities allowing for strong optomechanical nonlinearities [19] [20], targeted-energy +transfer [21] [22], and passive structural nonreciprocity [23] [24] [25]. +Phononic circuits require accurately designed and fabricated waveguides to spatially +constrain the acoustic transmission within a specific frequency range referred to as the +passband (or the transmission band). In the passband, the temporal frequencies are linked to + + +2 +the spatial frequencies (i.e., the wavenumbers) through the dispersion relation of the medium, +providing additional control over the acoustic transmission [1] [26]. This temporal and spatial +selectiveness stems from the dynamic characteristics of the unit cells whose periodic repetition +forms the waveguide. Therefore, the unit cell design is directly linked to the waveguide +characteristics via the Bloch modes of the unit cell. The Bloch modes are the vibrational modes +that the unit cell exhibits under Floquet boundary conditions with a wavenumber spanning the +irreducible Brillouin zone (IBZ) [26]. This approach calculates the possible wavenumber- +frequency relationship known as the band structure of the phononic crystal (i.e., the unit cell). +This band structure matches the transmission in an infinite periodic waveguide of the same +repeated unit cell [26]. +Bloch modes predict the transmission of sufficiently long and weakly-disordered +waveguides [5] [6] [12] [16] [27] [28], although fabricated waveguides are neither infinite nor +perfectly periodic. In these cases, the finite-structure modal frequencies lie within (or close to) +the Bloch modes passbands [26]. For example, such a waveguide of 𝑁 cells possesses at most +𝑁 finite-structure modes for every passband; increasing 𝑁 makes the 𝑁 modes more densely +packed within the passband leading to the continuous Bloch-modes band structure as 𝑁 → +∞. +The dense packing of modes originates from the structural periodicity whose absence (i.e., +aperiodicity) generates frequency-distinct modes that cannot approximate the passbands. In +addition, the periodicity causes (spatially-) extended mode shapes that permit the transmission +of a signal between the ends of the structure [26]. These features – the approximate passband +and the extended mode shapes – are acoustically attractive and enable a finite periodic structure +to operate as a waveguide. The Bloch mode approach is computationally efficient in linear +periodic systems because it enables the tailoring of a single unit cell to estimate the behavior +of the entire waveguide. On the other hand, it significantly deviates from experimental results +when the number of unit cells is limited, when there is aperiodicity (structural asymmetry) in +the devices (whether intentional or uncontrolled), and when nonlinearities are profound. +Considering repetitive arrays of drumhead resonators composed of coupled flexible micro- +membranes, we have recently shown that thermoelastic buckling of the membranes can switch +the acoustic transmission [29]. Waveguides made from coupled drumhead resonators were first +proposed by Hatanaka et al. in 2013 [30], who showed that they sustain megahertz-to-gigahertz +mechanical vibrations with high quality factors (high Qs) and optical finesse, features which +are valuable in mechanical, electrical, and optical applications [31, 32, 33]. For instance, +optomechanical interactions favor large surface-area structures (like the drumhead resonators) + + +3 +over beams/cantilevers [32, 33, 34]. Another advantage of the drumhead resonators is their +manufacturability via conventional micro/nanofabrication [32, 33], while allowing for in-situ +structural tunability and actuation via piezoelectric [30, 34], electrostatic [35], and thermal +control [29]. Therefore, drumhead resonators were applied in tunable optical cavities [36] and +low-loss nonlinear optomechanical coupling [37]. Moreover, coupling drumhead resonators in +the form of arrays, like the devices studied in this article, served in realizing phononic +transistors [30], tunable 1D phononic waveguides [35], cavity-switchable waveguides [38], and +on-chip 2D topological insulators [39]. +In this work, we study the mechanism of transmission switching in the drumhead-resonator +waveguides reported in [29], a phenomenon that has previously been attributed to buckling- +induced aperiodicity. Specifically, we develop a reduced-order model (ROM) that mimics the +experiments observed in [29] (section II). The ROM accounts for out-of-plane translation, +rotation, and coupling to accurately predict the first and second passbands of the waveguides +as functions of the buckling state. The ROM uses the concept of the von Mises truss [40] to +capture the effect of buckling on drumhead-resonator waveguides, as illustrated in the electro- +thermoelastic tunability of individual drumhead resonators in [41]. In turn, the von Mises +trusses permit modeling and predictive analysis of the drumhead-resonator waveguides via +lumped springs and rigid bodies, presenting simpler models that are amenable to analytical +studies compared to finite element models (e.g., continuous beams on elastic foundations). +With the von Mises ROM, we calculate the Bloch modes (section III), and compare them +to the transmission of (60-cell) finite waveguides in cases of perfect periodicity and (< 5%) +weak disorder (section IV). We investigate the acoustics of the finite waveguides by subjecting +their first cell to nonzero initial velocities and monitoring the resulting free responses in the +time and frequency domains as functions of the spatial propagation of wave packets in the +waveguide. We find that when the weakly-disordered finite waveguides are close to their +critical buckling state, the transmission through the first passband vanishes. Stronger disorder +results in a larger range of temperatures where the first passband does not transmit elastic +waves. This contrasts with the corresponding perfectly-periodic finite waveguide (i.e., with no +disorder), where the first passband transmits elastic waves at all considered temperatures, even +at the onsite of critical buckling. As for the second passband, the acoustic transmission persists +for all considered disorders and temperatures. +To thoroughly explain the effect of buckling on the transmission, we inspect the +dependencies of the mode shapes of the considered waveguides on temperature (section V). +The results show that the transmission-switching is associated with converting the mode shapes + + +4 +from extended over the entire waveguide to localized at some cells. This localization of mode +shapes with disorders conforms to Anderson's localization originally discovered in +electromagnetic waves [42] [43] [44] and then applied in elastic settings [27] [28] [45]. Finally, +we present an evaluation of this buckling-switchable transmission on a finite element model +(FEM) of the experimental waveguide studied in [29] with 5% disorder far from, or close to +critical buckling (supplemental Video.S2). The FEM simulations agree with the predictions of +the ROM, thus conclusively proving that weak disorder leads to loss of transmission in the +repetitive array of drumhead resonators due to buckling. +II. Description of the waveguide and the reduced-order model (ROM) +In this work, we study the phononic waveguides shown in Fig. 1a. This waveguide consists +of repetitive cells capable of transmitting flexural acoustic waves [29] [38] [46] [47]. This +waveguide was studied in [29], where the cells are drumhead-like membranes composed of +Silicone Nitride (SiNx) suspended by an etched Silicone Oxide (SiO2) layer on top of a Silicone +(Si) substrate. The involved materials and fabrication methods induce residual stresses in the +waveguide, whose cells buckle as depicted in Fig. 1b by atomic force microscopy (AFM) +conducted in [29]. +In Fig. 1c, we show the effect of buckling on the elastic transmission of the waveguide of +Fig. 1a [29]. The temperature in Fig. 1c controls the state of buckling in the waveguide, where +lower temperature increases compressions between cells to provoke stronger buckling. At each +temperature, the colormap in Fig. 1c corresponds to the frequency response measured at the +middle cell of the waveguide due to the electrostatic actuation of the gold (Au) pad covering +the first cell (cf. Fig. 1a). At high temperatures in Fig. 1c (i.e., above ~230 K), the waveguide +exhibits three frequency regimes of effective transmission corresponding to the first three +passbands (labeled as I, II, and III). A decrease in temperature from 280 K down to ~230 K +decreases the mean frequency of all the passbands, indicating a softening behavior. During this + + + + +5 + +Fig. 1. Thermally buckled elastic waveguide: (a) Schematic drawing of a MEMS phononic +waveguide made of coupled drumhead-resonators [29]; (b) 3D topography map of 3 cells of +the waveguide [29] measured using atomic force microscopy (AFM) – the colormap shows the +out-of-plane deflections resulting from buckling in the structure; (c) measured transmission in +the waveguide [29] as a function of temperature and frequency of excitation applied to the first +cell in the waveguide – the colormap depicts the amplitude of oscillations at the middle of the +waveguide, which shows that the temperature change eliminates the transmission in passband +I and detunes the frequency of passbands I, II, and III; schematic drawings of the proposed +reduced-order model (ROM) of the waveguide undergoing thermal buckling showing (d) +undeformed and (e) deformed states. + +softening, passband I diminishes its bandwidth until collapsing at ~230 K, whereas passbands +II and III maintain an almost constant bandwidth. Reducing the temperature to below ~230 K +completely eliminates passband I and increases the mean frequencies of passbands II and III +while possessing almost constant bandwidths. The observed temperature-dependent changes +in the frequency passbands and the switch in frequency detuning imply that the waveguide at +~230 K is in a critical buckling state associated with the softest structural configuration (since +buckling indicates minimum linearized stiffness). Accordingly, the waveguide is pre-buckled +for temperatures > ~230 K and post-buckled for temperatures < ~230 K, based on [29]. In both +buckling regimes, the frequency detuning of passbands II and III are direct consequences of +the buckling state of the waveguide. However, the frequency detuning of passband I and its + +SiNx +Au +Transmission (a.u.) +a +c +0 +40 +I=I +Frequency (MHz) +SiO2 +30 +b +II +20 +13 +10 +80 +180 +280 +0 +Temperature (K) +d +mi-1, Ji-1 +mi, Ji +mi+1, Ji+1 +e +Qi +Qi-1 +Qi+1 +k-² T2 / k-1 T=1 +kTC +Q +9 +9 +Q +0 +Q +TEi +ui +ui+1 +ki-1 +QB +QB +77 +kB +qs +qs +L +L +L +L +6 +transmission loss in the post-buckled regime necessitates both buckling and disorder in the +waveguide [29]. +To further investigate this relationship between disorder, buckling, and elastic transmission +in the considered waveguide, we propose the reduced-order model (ROM) depicted in Figs. +1d-e. This ROM captures the thermally-mediated elastic buckling based on the ROM of a +single cell introduced in [41], exhibiting very good predictive capacity. Here, we extend the +ROM of [41] to account for the coupling between the cells in the waveguide and model the +acoustics of the entire phononic waveguide. Accordingly, we allocate to each cell a +translational degree-of-freedom (DoF) (as in [41]) and a rotational DoF to capture passbands I +and II, respectively. +As shown in Fig. 1d, each cell of index 𝑖 in the waveguide consists of a rigid mass 𝑚! with +a moment of inertia 𝐽!. Cell 𝑖 undergoes the motion illustrated in Fig. 1e with translational +coordinate 𝑢! and rotation angle 𝜃!. The translation deforms the grounding springs of +stiffnesses 𝑘! +" and 𝑘! +# representing the restoring forces for bending and stretching, respectively. +As in [41], these translational bending and stretching springs are confined at distances 𝑑" and +𝑑# (see Fig. 1e) while possessing free (undeformed) lengths 𝐿" and 𝐿#, respectively; clearly, a +free length larger than the confinement distance (i.e., 𝐿" > 𝑑" and 𝐿# > 𝑑#) introduces +compressive strains (precompression) in the cell. We assume that the remaining springs in the +ROM are undeformed at their undeformed positions. For example, the springs with stiffnesses +𝑇! +", 𝑘!$% +& , 𝑘! +&, 𝑇!$% +& , and 𝑇! +& attached to the cell of index 𝑖 don’t apply any forces or torques in +Fig. 1d. The grounding torsional spring of stiffness 𝑇! +" lumps the bending effects that oppose +the rotation 𝜃! due to the grounded boundary of the drumhead. The coupling springs with +stiffnesses 𝑘! +& and 𝑇! +& account for the force and torque, respectively, applied by cell 𝑖 to cell +(𝑖 + 1) due to the deformations illustrated in Fig. 1e. Lastly, we represent the lattice length +separating two successive cells by the length 𝐿 (see Figs. 1d-e). +III. Bloch modes of a single cell +In a previous article [41], we described the static equilibrium and the equations of motion +of a single drumhead resonator and identified its system parameters, which we refer to as the +reference cell parameters. These parameters are the translating mass 𝑚'() and springs 𝑘'() +" + +and 𝑘'() +# + (we use the subscript “𝑅𝑒𝑓” to label the reference cell), which are reproduced in +Table I. We start by studying the Bloch modes of an infinite waveguide based on a repetition + + +7 +of this reference unit cell, as shown in Fig. 1d-e. The grounding translating springs exert the +force 𝐹! +"*+, at the cell 𝑖 ∈ { 1, 2, … } and the temperature 𝑇 expressed for any translational +displacement 𝑢! as: +𝐹! +"*+,(𝑢!; 𝑇) = 𝑘! +"𝑑" ?𝑢! +𝑑" − 𝛿"(𝑇)B + 𝑘! +-𝑢! +⎣ +⎢ +⎢ +⎡ +1 − 1 + 𝛿#(𝑇) +F1 + G𝑢! +𝑑#H +. +⎦ +⎥ +⎥ +⎤ +. +(1) +In (1), 𝛿"(𝑇) and 𝛿#(𝑇) are the temperature-dependent bending and stretching strains, +respectively, stemming from the thermal expansion and the fabrication-residual stresses in the +cells. We characterize these strains by the following temperature dependencies (as discussed +in [41]), +𝛿"(𝑇) ≝ 𝑑" − 𝐿" +𝐿" += 𝛽/ + 𝛽%𝑇 + 𝛽.𝑇. +(2a) +𝛿#(𝑇) ≝ 𝑑# − 𝐿# +𝐿# += 𝛾/ + 𝛾%𝑇, +(2b) +with the values of 𝛽/, 𝛽%, 𝛽., 𝛾/, and 𝛾% listed in Table I. We assume that these temperature +dependencies govern the strains of all the cells in the waveguide. Moreover, we +nondimensionalize the forces in this work by 𝑘'() +" +𝑑" leading to the following nondimensional +buckling force, +𝐹P! +"*+,(𝑢P!; 𝑇) = 𝑢P! − 𝛿"(𝑇) + 𝜅! +-𝑢P! +⎣ +⎢ +⎢ +⎢ +⎢ +⎡ +1 − 1 + 𝛿#(𝑇) +R1 + G𝑢P! +𝑑̅#H +. +⎦ +⎥ +⎥ +⎥ +⎥ +⎤ +, +(3) +where 𝜅! +- ≝ 𝑘! +-/𝑘! +", 𝑑̅# ≝ 𝑑#/𝑑", and 𝑢P! ≝ 𝑢!/𝑑" with the overbar denoting a +nondimensionalized entity. +Focusing on the reference cell which undergoes only translation while connected to 𝑘'() +" + +and 𝑘'() +# +, we find its equilibrium displacement 𝑢P'() +012(𝑇) by solving the following equation: + +𝛿" +𝛿# +𝑑̅# +𝜅'() +- + +% +.3 FΛ'() +" + [MHz] +𝜒 +𝛽/ +𝛽% [K-1] +𝛽. [K-2] +𝛾/ +𝛾% [K-1] +7.65 -3.47E-2 3.81E-5 +1.9 +-4.07E-3 +1 +1 +9.40 +1/12 + +Table I. Parameters of the reference cell [41]. + + +8 + +Fig. 2. Thermal buckling of the infinite perfectly periodic waveguide (i.e., Bloch modes): (a) +Static equilibrium of a single cell as a function of temperature based on (4); (b) frequency +dispersion curves as a function of the nondimensional wavenumber of the Bloch modes at a +temperature of 390 K, 370 K, and 350 K; (c) Bloch-modes frequency extrema as a function of +temperature illustrating the transmission detuning in an infinite perfectly-periodic waveguide +– we depict the Bloch-modes frequency extrema with 𝑘4/𝐿 close to 0 rad by the filled circles, +whereas the extrema with 𝑘4/𝐿 close to 𝜋 rad by open circles; also the blue and green colors +in (b, c) represent the Bloch-mode passbands I and II, respectively. + +𝐹P'() +"*+,X𝑢P'() +012; 𝑇Y = 0 with the maximum satisfying +567!"# +$%&' +5*8!"# X𝑢P'(); 𝑇Y[ +*8!"#9*8!"# +()* > 0 +(4) +The maximum condition in (4) ensures 𝑢P'() +012 to be the most stable equilibrium solution, which +should be favored experimentally. In Fig. 2a, we plot the values of 𝑢P'() +012 as a function of +temperature based on (4), (3), (2), and the reference parameters in Table I. We observe that the +single cell translates upwards due to cooling, which increases the internal compressions leading +to buckling of the cell [41]. +To study the effect of buckling on wave transmission, we evaluate the Bloch modes of the +cell at each temperature shown in Fig. 2a. The Bloch modes correspond to the infinite +waveguide of Fig. 1e-d made of cells whose parameters are identical to the considered single +cell. In this perfectly periodic infinite waveguide, all the cells attain at 𝑇 the equilibrium state +of 𝑢P! +012 = 𝑢P'() +012(𝑇) and 𝜃! +012 = 0 rad for all 𝑖 ∈ {1,2,3, … , +∞}. At every instant 𝑡, we track +the oscillations of the 𝑖th cell about its equilibrium state via the perturbation coordinates: +𝑣̅!(𝑡) ≝ 𝑢P!(𝑡) − 𝑢P! +012, +(5a) +ℎP!(𝑡) ≝ 𝐿P𝜃!(𝑡) − 𝐿P𝜃! +012, where 𝐿P ≝ 𝐿/𝑑". +(5b) +The above coordinates allow writing Newton’s second law on any cell of index 𝑖 > 1 in +Fig. 1d-e as, + +a +350 K +b +c +350 K +Static +390 K +370 K +350 K +0.4 +(MHz) +12 +(MHz) +12 +390 K +B +370 K +0.2 +370K +10 +10 +,EQM +0 +390 K +8 +8 +-0.2 +6 +9 +400 +375 +350 +0 +π O +O +T +400 +375 +350 +Temperature (K) +k. / L (rad) +Temperature (K) +9 +𝜇! a1 +0 +0 +𝜒b c +5+:7, +5;+ +5+<8, +5;+ +d + 𝜇!$% e +−Λ!$% +& +− +=,-. +/ +. +=,-. +/ +. +=,-. +/ +> − Γ!$% +& g h𝑣̅!$% +ℎP!$% +i + +j𝜇!$% e +Λ!$% +& +$=,-. +/ +. +$=,-. +/ +. +=,-. +/ +> + Γ!$% +& g + 𝜇! e +Λ! +& + Λ! +"*+, +=, +/ +. +=, +/ +. +=, +/ +> + Γ! +& + Γ! +"gk h𝑣̅! +ℎP! +i + +𝜇! e +−Λ! +& +=, +/ +. +− +=, +/ +. +=, +/ +> − Γ! +&g h𝑣̅!?% +ℎP!?% +i = l0 +0m, +(6) +where 𝜇! ≝ 𝑚!/𝑚'(), 𝜒 ≝ 𝐽!/𝑚!𝐿., Λ! +"*+,(𝑇) ≝ Λ! +" 567, +$%&' +5*8, [ +*8,9*8, +()*(-) +, Λ! +" ≝ 𝑘! +"/𝑚!, Λ! +& ≝ +𝑘! +&/𝑚!, Γ! +& ≝ 𝑇! +&/(𝑚!𝐿.), and Γ! +" ≝ 𝑇! +"/(𝑚B𝐿.). Equation (6) only considers the linearized +dynamics of the undamped 𝑖th cell. Note that the nondimensionalization in (6) results in +(squared) frequency-like parameters (i.e., Λ! +"*+,, Λ! +&, Γ! +", and Γ! +&). This parameter conversion +offers an advantage when comparing the model to experiments because frequencies are easier +to identify than stiffnesses and directly affect the performance of the waveguides. For instance, +we deduce the value of Λ'() +" + listed in Table I from the experiments of a single cell in [41]. For +the remaining frequency-like parameters, we assume the following relationships for all 𝑖 ∈ +{𝑅𝑒𝑓, 1, 2,3, … }: +Λ! +&(𝑇) = 0.2 ?Λ! +C(𝑇) − +min +DE/→>// H Λ! +C(𝑇)B +(7a) +Γ! +" = 1 +12 Λ! +" +(7b) +Γ! +&(𝑇) = 1 +12 a3Λ! +&(𝑇) − 3 +4 Γ! +"b. +(7c) +To calculate the Bloch modes of a single cell, we apply the Floquet boundary conditions of +h𝑣̅! +ℎP! +i = 𝒑!𝑒IJ'0 +1 !?K;L with a normalized wavenumber 𝑘4/𝐿, a modal frequency of 𝜔, a modal +vector 𝒑!, and the imaginary number 𝑗. = −1. Additionally, we assume that all cells are +identical to the single cell with parameters listed in Table I, transforming (6) into the following +boundary value problem: +j−𝜔. a1 +0 +0 +𝜒b + e +2 G1 − cos +,0 +M H Λ'() +& ++ Λ'() +"*+, +−Λ'() +& +sin +,0 +M +… +(8) + + +10 +… +Λ'() +& +sin +,0 +M +% +. G1 + cos +,0 +M H Λ'() +& ++ 2 G1 − cos +,0 +M H Γ'() +& ++ Γ'() +" gk 𝒑! = l0 +0m. +For all 𝑘4/𝐿 ∈ [0, 𝜋] rad, the irreducible Brillouin zone (IBZ) is defined by the respective +pair of eigenfrequencies 𝜔 that zero the determinant of the matrix operating on 𝒑! in (8). These +eigenfrequencies are the Bloch modes’ frequencies forming the dispersion curves in Fig. 2b at +390 K, 370 K, and 350 K for the single cell. The lower (blue) and upper (green) curves in Fig. +2b correspond to passbands I and II of the transmission in the perfectly periodic infinite +waveguide, respectively. We depict the transmission of this waveguide in Fig. 2c, where we +collect the extrema (maxima and minima) of passbands I and II (like in Fig. 2b) for the +temperature 𝑇 ∈ [350, 400] K. +Fig. 2c shows that cooling from 400 to ~370 K reduces the mean frequencies of both +passbands while narrowing the bandwidth of passband I. Cooling below ~370 to 350 K +increases again the mean frequencies of both passbands while widening the bandwidth of +passband I. The first cooling phase from 400 to ~370 K in Fig. 2c resembles the cooling phase +in Fig 1c between 280 and ~230 K. However, the second cooling phase between ~370 to 350 +K in Fig. 2c diverges fundamentally from the experimental transmission in Fig. 1c between +~230 and ~80 K, where the transmission in passband I does not reemerge. Therefore, the ROM +buckling cannot eliminate the transmission of passband I in a perfectly periodic infinite +waveguide. This loss of transmission with buckling necessitates the consideration of disorder +(i.e., the break of perfect periodicity) in the waveguide as previously established in [29]. +Note that we adopt the relationships in (7) to emulate the experimental transmission in Fig +1c between 280 and ~230 K. For this reason, we select Λ! +&(𝑇) in (7a) to decrease until the +transmission vanishes at the point of minimum frequency, +min +DE/→>// H Λ! +C(𝑇), leading to the +shrinkage of passband I between 400 and ~370 K in Fig. 2c. In (7b), we assume that the rotation +of the cell centerline (of length 𝐿) deflects an elastic foundation of stiffness density 𝑘! +"/𝐿. In +(7c), we impose a temperature-constant bandwidth for passband II like the measurements in +Fig. 1c. The temperature-detuning of the mean frequencies of the passbands in Fig. 2c is +considered for the identified parameters (i.e, Λ'() +" +, 𝛽/, 𝛽%, 𝛽., 𝛾/, and 𝛾%) of the ROM in [41], +which slightly deviate from those in the devices used in Fig. 1c (extracted in [29]). + + +11 +IV. Temporal transmission in finite waveguides +We focus now on the waveguide disorder resulting from the thickness variation between +the cells. We assume a thickness variation of the form, +ℎ! − ℎ'() +ℎ'() += 𝜎< +4 +⎩ +⎪ +⎨ +⎪ +⎧ +j2 +€𝑁 + 1 +2 +− 𝑖€ +𝑁 + 1 +2 +− 1 +− 1k +•‚‚‚‚‚ƒ‚‚‚‚‚„ +N, ++ 𝑟!([−1, 1]) +⎭ +⎪ +⎬ +⎪ +⎫ +, +(9) +for 𝑖 ∈ {1,2, … , 𝑁}, where we denote by ℎ! the thickness of the 𝑖th cell, ℎ'() the thickness of +the reference cell discussed in the previous section, 𝜎< the level of thickness disorder, and +𝑟!([−1, 1]) a random rational number ∈ [−1, 1] generated at each 𝑖. We introduce the random +number 𝑟! to account for the random errors of the fabrication process. The 𝑠! term in (9) +represents the systematic errors resulting from wet etching that forms the waveguide cells as +explained in [29] [38] [46] [47]. +The holes at the center of the cells in Fig. 1a-b are etching holes through which the etchant +attacks the underlying layer and suspends the cells. Thus, there is a higher (linear) density of +etching holes at the middle of the waveguide (of index +O?% +. ) compared to the ends (of indices +1 and 𝑁). This higher etching-holes density increases the etching rate leading to over-etching +at the middle of the waveguide compared to its ends [29]. We model this over-etching by 𝑠! in +(9) as a linear distribution of the cell position from the middle of the waveguide. Figs. 3a-b +show two examples of thickness variation with 𝜎< = 0% (i.e., perfectly periodic waveguide) +and 𝜎< = 5%, respectively. +The thickness variation implies a corresponding variation in the dynamical properties of +the cells. Based on the theory of the mechanics circular plates [48] [49] and the assumption in +[41], the thickness affects the parameters of the 𝑖th cell in Fig. 1d-e as follows: +𝜅! +# +𝜅'() +# + = ‹ ℎ! +ℎ'() +Œ +$. +, +(10a) +Λ! +" +Λ'() +" += ‹ ℎ! +ℎ'() +Œ +. +. +(10b) +The scaling relationships (10) with the expressions in (7) quantify the effect of the cell’s +thickness on the ROM parameters. +With the ROM of Fig. 1d-e, we apply Newton’s 1st law to calculate the static equilibrium +(𝑢P! +012, 𝐿P 𝜃! +012) of each cell 𝑖 ∈ {1, 2, … , 𝑁} in the 𝑁 cells waveguide using, + + +12 +⎩ +⎪ +⎪ +⎪ +⎪ +⎪ +⎨ +⎪ +⎪ +⎪ +⎪ +⎪ +⎧𝐹P% +"*+,X𝑢P% +012; 𝑇Y +0 + +⋮ + +𝐹P! +"*+,X𝑢P! +012; 𝑇Y +0 + +⋮ + +𝐹PO +"*+,X𝑢PO +012; 𝑇Y +0 +⎭ +⎪ +⎪ +⎪ +⎪ +⎪ +⎬ +⎪ +⎪ +⎪ +⎪ +⎪ +⎫ +•‚‚‚‚‚ƒ‚‚‚‚‚„ +𝑸8$%&' ++ 𝐾•#;Q; +⎩ +⎪ +⎪ +⎪ +⎪ +⎪ +⎨ +⎪ +⎪ +⎪ +⎪ +⎪ +⎧ 𝑢P% +012 +𝐿P𝜃% +012 + +⋮ + +𝑢P! +012 +𝐿P𝜃! +012 + +⋮ + +𝑢PO +012 +𝐿P𝜃O +012⎭ +⎪ +⎪ +⎪ +⎪ +⎪ +⎬ +⎪ +⎪ +⎪ +⎪ +⎪ +⎫ +•‚‚ƒ‚‚„ +𝒒8 ()* += 𝟎, +(11) +where 𝐹P! +"*+,X𝑢P! +012; 𝑇Y is the thermo-elastic buckling force expressed in (3). In (11), we +assume small angles of deformation allowing the approximation sin 𝜃! +012 ≈ 𝜃! +012 while +neglecting the longitudinal displacement of the cells’ ends. Under this approximation, we +express the nondimensional static stiffness 𝐾•#;Q; as, +𝐾•#;Q; = +⎣ +⎢ +⎢ +⎢ +⎢ +⎢ +⎢ +⎢ +⎡ +𝒦•% + + + +0.×.(O$.) + + + + + + +⋱ + + + + + + + + +0.×.(!$.) + +𝒦•! + +0.×.(O$!$%) + + + + + + + + +⋱ + + + + + + +0.×.(O$.) + + + +𝒦•O +⎦ +⎥ +⎥ +⎥ +⎥ +⎥ +⎥ +⎥ +⎤ +, +(12a) +with 0T×U denoting a zero-filled matrix of 𝑀 rows by 𝑃 columns, +𝒦•% = e +𝜇%Λ% +& + +V.=./ +. + +−𝜇%Λ% +& + +V.=./ +. +V.=./ +. + +𝜇% G +=./ +> + Γ% +& + Γ% +"H + +− +V.=./ +. + +𝜇% G +=./ +> − Γ% +&H +g, +(12b) +𝒦•! = – +−𝜇!$%Λ!$% +& +− +V,-.=,-. +/ +. +𝜇!$%Λ!$% +& ++ 𝜇!Λ! +& +V,-.=,-. +/ +. +𝜇!$% — +=,-. +/ +> − Γ!$% +& ˜ +$V,-.=,-. +/ +?V,=, +/ +. + … +… +$V,-.=,-. +/ +?V,=, +/ +. +−𝜇!Λ! +& +V,=, +/ +. +𝜇!$% — +=,-. +/ +> + Γ!$% +& ˜ + 𝜇! — +=, +/ +> + Γ! +& + Γ! +"˜ +− +V,=, +/ +. +𝜇! — +=, +/ +> − Γ! +&˜ +™, +(12c) +for 2 ≤ 𝑖 ≤ 𝑁 − 1, and, + + + + +13 + +Fig. 3. Effect of weak thickness disorder on the static equilibrium of finite waveguides: (a, b) +Thickness profile relative to the reference thickness ℎ'(), and (c, d) static deflections at 400, +390, 380, 370, 360, and 350 K of (a), and (b, d) the weakly (𝜎< = 5%) disordered 60-cell +waveguide ROM of (b); refer to (9) for the definition of the disorder parameter 𝜎<; in addition, +in (c, d), the thick segments represent the rigid masses of the cells in the ROM of Fig. 1d-e +translating and rotating according to the computed equilibria from (11). + +𝒦•O = e +−𝜇O$%ΛO$% +& +− +V2-.=2-. +/ +. +V2-.=2-. +/ +. +𝜇O$% G +=2-. +/ +> +− ΓO$% +& +H + … +… +𝜇O$%ΛO$% +& +− +V2-.=2-. +/ +. +− +V2-.=2-. +/ +. +𝜇O$% G +=2-. +/ +> ++ ΓO$% +& +H + 𝜇OΓO +"g, +(12d) +where Λ! +&, Γ! +", and Γ! +& are defined in (7). +We solve (11) via “fsolve” (gradient descent method) in MATLAB®. In the numerical +solver, the starting guesses for 𝑢P! +012 in (11) correspond to the equilibria of individual cells in +(1), see Fig. 2a. We assign the differences X𝑢P!?% +012 − 𝑢P! +012Y as starting guesses for 𝐿P𝜃! +012 for +𝑖 ∈ {1, 2, … , 𝑁 − 1}, and 𝐿P𝜃O$% +012 as the guess for 𝐿P𝜃O +012. Fig. 3c-d display the computed +equilibria of (11) at different temperatures in the perfectly periodic and weakly disordered +waveguides of Fig. 3a-b, respectively. In Fig. 3c-d, each segment (thick dashed line) represents +a cell in the ROM of Fig. 1d-e translated and rotated according to the equilibrium of (11). +In Fig. 3c, the cells at equilibrium undergo the same translational deflections without +rotation, which results from the perfect periodicity of the waveguide of Fig. 3a. For instance, +the weakly-disordered waveguide of Fig. 3b attains equilibrium with different cell translations + +Perfect periodicity: oh = 0% +Weak disorder: n = 5% +a +b +(%) +102.5 +102.5 +100 +100 +97.5 +97.5 +1 +20 +40 +60 +1 +20 +40 +60 +Cell number +Cell number +c +d +0.4 +0.4 +350 K +B +a +0.2 +0.2 +360 K +EQM +370 K +0 +0 +380 K +390 K +-0.2 +-0.2 +400K +1 +20 +40 +09 +1 +20 +40 +60 +Cell number +Cell number +14 +and rotations, as shown in Fig. 3d. For both waveguides of Figs. 3c-d, the cooling increases the +cells' baseline translational deflections going from negative to positive values between 400 K +and 350 K(like the individual cell in Fig. 2a). Moreover, each 10 K of cooling induces larger +deflections at lower temperatures in Figs. 3c-d, which mirrors the buckling susceptibility +observed in Fig. 2a. +At this point, we linearize the dynamics around the calculated equilibria to study the +transmission in the finite waveguides for varying temperatures. Using the perturbation +coordinates in (5), the linearized equations yield, +𝑀• 5+𝒒8 +5;+ + (𝐾•"*+, + 𝐾•#;Q;) +•‚‚‚‚ƒ‚‚‚‚„ +W8 + 𝒒• = 𝟎, +(13) +where 𝒒• = œ𝑣̅%, ℎP%, … , 𝑣̅!, ℎP!, … , 𝑣̅O, ℎPO• +-, 𝐾•#;Q; is defined in (12), 𝐾•"*+, corresponds to the +2𝑁 × 2𝑁 matrix whose diagonal contains the linear stiffnesses of the buckling forces, +𝐾•"*+, = diagX𝜇%Λ% +"*+,, 0, … , 𝜇!Λ! +"*+,, 0 , … , 𝜇OΛO +"*+,, 0Y, +(14) +and 𝑀• denotes the nondimensional mass matrix expressed as: + + +𝑀• = +⎣ +⎢ +⎢ +⎢ +⎢ +⎢ +⎢ +⎢ +⎡ +ℳ•% + + + +0.×.(O$%) + + + + + + +⋱ + + + + + + + + +0.×.(!$%) + +ℳ•! + +0.×.(O$!) + + + + + + + + +⋱ + + + + + + +0.×.(O$%) + + + +ℳ•O +⎦ +⎥ +⎥ +⎥ +⎥ +⎥ +⎥ +⎥ +⎤ +, +(15) + where ℳ•! = 𝜇! a1 +0 +0 +𝜒b for 𝑖 ∈ {1, 2, 3, … , 𝑁}. In this work, we solve for the acoustics of the +waveguides by direct integration of (13) using MATLAB® “ode45” function. +To this end, we consider the solution of (13) subject to a nonzero initial translational +velocity at cell 1 and all other initial conditions set to zero: +𝒒𝟎 ≝ 𝒒•(𝑡 = 0) = 𝟎 and 𝒒̇ 𝟎 ≝ +5𝒒8 +5; (𝑡 = 0) = c +10$D𝜇% +0 +𝟎.(O$%)×% +d. +(16) +The initial conditions (16) induce a motion that propagates in the waveguides as depicted in +Fig. 4-5 and the supplemental Video.S1. This motion enables the study of wave transmission +in the considered finite waveguides. In Figs. 4-5 and supplemental Video.S1, we consider the +responses of the waveguides of Figs. 3a-b at 390 K, to address the effect of weak disorder at a + + + + +15 + +Fig. 4. Elastic wave transmission through the perfectly periodic finite waveguide of Fig. 3a at +390 K: Temporal responses in terms of (a) the translations 𝑣̅Y and (b) the rotational ℎPY +perturbation coordinates of (from left to right) cell 𝑛 ∈ {1, 20, 40, 60} due to the initial +conditions in (16) (the rightmost plots in (a, b) show zoomed-in views of the responses of cell +60 in the period [16, 20] μs); (c) spatiotemporal evolution of the normalized mechanical energy +𝐸! +T(+ ~230 K and post-buckled for temperatures < ~230 K, based on [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In both buckling regimes, the frequency detuning of passbands II and III are direct consequences of the buckling state of the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' However, the frequency detuning of passband I and its SiNx Au Transmission (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') a c 0 40 I=I Frequency (MHz) SiO2 30 b II 20 13 10 80 180 280 0 Temperature (K) d mi-1, Ji-1 mi, Ji mi+1, Ji+1 e Qi Qi-1 Qi+1 k-² T2 / k-1 T=1 kTC Q 9 9 Q 0 Q TEi ui ui+1 ki-1 QB QB 77 kB qs qs L L L L 6 transmission loss in the post-buckled regime necessitates both buckling and disorder in the waveguide [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' To further investigate this relationship between disorder, buckling, and elastic transmission in the considered waveguide, we propose the reduced-order model (ROM) depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' This ROM captures the thermally-mediated elastic buckling based on the ROM of a single cell introduced in [41], exhibiting very good predictive capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Here, we extend the ROM of [41] to account for the coupling between the cells in the waveguide and model the acoustics of the entire phononic waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Accordingly, we allocate to each cell a translational degree-of-freedom (DoF) (as in [41]) and a rotational DoF to capture passbands I and II, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d, each cell of index 𝑖 in the waveguide consists of a rigid mass 𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' with a moment of inertia 𝐽!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='. Cell 𝑖 undergoes the motion illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1e with translational coordinate 𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' and rotation angle 𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='. The translation deforms the grounding springs of stiffnesses 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " and 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' # representing the restoring forces for bending and stretching, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' As in [41], these translational bending and stretching springs are confined at distances 𝑑" and 𝑑# (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1e) while possessing free (undeformed) lengths 𝐿" and 𝐿#, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' clearly, a free length larger than the confinement distance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', 𝐿" > 𝑑" and 𝐿# > 𝑑#) introduces compressive strains (precompression) in the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We assume that the remaining springs in the ROM are undeformed at their undeformed positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For example, the springs with stiffnesses 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ", 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & , 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &, 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & , and 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & attached to the cell of index 𝑖 don’t apply any forces or torques in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The grounding torsional spring of stiffness 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " lumps the bending effects that oppose the rotation 𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' due to the grounded boundary of the drumhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The coupling springs with stiffnesses 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & and 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & account for the force and torque, respectively, applied by cell 𝑖 to cell (𝑖 + 1) due to the deformations illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Lastly, we represent the lattice length separating two successive cells by the length 𝐿 (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Bloch modes of a single cell In a previous article [41], we described the static equilibrium and the equations of motion of a single drumhead resonator and identified its system parameters, which we refer to as the reference cell parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' These parameters are the translating mass 𝑚\'() and springs 𝑘\'() " and 𝑘\'() # (we use the subscript “𝑅𝑒𝑓” to label the reference cell), which are reproduced in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We start by studying the Bloch modes of an infinite waveguide based on a repetition 7 of this reference unit cell, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The grounding translating springs exert the force 𝐹!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+, at the cell 𝑖 ∈ { 1, 2, … } and the temperature 𝑇 expressed for any translational displacement 𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' as: 𝐹!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,(𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇) = 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "𝑑" ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑑" − 𝛿"(𝑇)B + 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ⎣ ⎢ ⎢ ⎡ 1 − 1 + 𝛿#(𝑇) F1 + G𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑑#H .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ⎦ ⎥ ⎥ ⎤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (1) In (1), 𝛿"(𝑇) and 𝛿#(𝑇) are the temperature-dependent bending and stretching strains, respectively, stemming from the thermal expansion and the fabrication-residual stresses in the cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We characterize these strains by the following temperature dependencies (as discussed in [41]), 𝛿"(𝑇) ≝ 𝑑" − 𝐿" 𝐿" = 𝛽/ + 𝛽%𝑇 + 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (2a) 𝛿#(𝑇) ≝ 𝑑# − 𝐿# 𝐿# = 𝛾/ + 𝛾%𝑇, (2b) with the values of 𝛽/, 𝛽%, 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', 𝛾/, and 𝛾% listed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We assume that these temperature dependencies govern the strains of all the cells in the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Moreover, we nondimensionalize the forces in this work by 𝑘\'() " 𝑑" leading to the following nondimensional buckling force, 𝐹P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,(𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇) = 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' − 𝛿"(𝑇) + 𝜅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1 − 1 + 𝛿#(𝑇) R1 + G𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑑̅#H .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ , (3) where 𝜅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ≝ 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' /𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ", 𝑑̅# ≝ 𝑑#/𝑑", and 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ≝ 𝑢!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/𝑑" with the overbar denoting a nondimensionalized entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Focusing on the reference cell which undergoes only translation while connected to 𝑘\'() " and 𝑘\'() # , we find its equilibrium displacement 𝑢P\'() 012(𝑇) by solving the following equation: 𝛿" 𝛿# 𝑑̅# 𝜅\'() % .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='3 FΛ\'() " [MHz] 𝜒 𝛽/ 𝛽% [K-1] 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' [K-2] 𝛾/ 𝛾% [K-1] 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='65 -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='47E-2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='81E-5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='07E-3 1 1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='40 1/12 Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Parameters of the reference cell [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 8 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Thermal buckling of the infinite perfectly periodic waveguide (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', Bloch modes): (a) Static equilibrium of a single cell as a function of temperature based on (4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (b) frequency dispersion curves as a function of the nondimensional wavenumber of the Bloch modes at a temperature of 390 K, 370 K, and 350 K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (c) Bloch-modes frequency extrema as a function of temperature illustrating the transmission detuning in an infinite perfectly-periodic waveguide – we depict the Bloch-modes frequency extrema with 𝑘4/𝐿 close to 0 rad by the filled circles, whereas the extrema with 𝑘4/𝐿 close to 𝜋 rad by open circles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' also the blue and green colors in (b, c) represent the Bloch-mode passbands I and II, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝐹P\'() "*+,X𝑢P\'() 012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇Y = 0 with the maximum satisfying 567!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "# $%&\' 5*8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "# X𝑢P\'();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇Y[ 8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='"#9*8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "# ()* > 0 (4) The maximum condition in (4) ensures 𝑢P\'() 012 to be the most stable equilibrium solution, which should be favored experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" 2a, we plot the values of 𝑢P'() 012 as a function of temperature based on (4), (3), (2), and the reference parameters in Table I." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We observe that the single cell translates upwards due to cooling, which increases the internal compressions leading to buckling of the cell [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' To study the effect of buckling on wave transmission, we evaluate the Bloch modes of the cell at each temperature shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The Bloch modes correspond to the infinite waveguide of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1e-d made of cells whose parameters are identical to the considered single cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In this perfectly periodic infinite waveguide, all the cells attain at 𝑇 the equilibrium state of 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" 012 = 𝑢P'() 012(𝑇) and 𝜃!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 = 0 rad for all 𝑖 ∈ {1,2,3, … , +∞}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' At every instant 𝑡, we track the oscillations of the 𝑖th cell about its equilibrium state via the perturbation coordinates: 𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (𝑡) ≝ 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (𝑡) − 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012, (5a) ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (𝑡) ≝ 𝐿P𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (𝑡) − 𝐿P𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012, where 𝐿P ≝ 𝐿/𝑑".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (5b) The above coordinates allow writing Newton’s second law on any cell of index 𝑖 > 1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e as, a 350 K b c 350 K Static 390 K 370 K 350 K 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='4 (MHz) 12 (MHz) 12 390 K B 370 K 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 370K 10 10 ,EQM 0 390 K 8 8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 6 9 400 375 350 0 π O O T 400 375 350 Temperature (K) k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / L (rad) Temperature (K) 9 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' a1 0 0 𝜒b c 5+:7, 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='+ 5+<8, 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='+ d + 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% e −Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & − =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > − Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & g h𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% i + j𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% e Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & $=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' $=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & g + 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' e Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & + Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+, =, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =, / > + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "gk h𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' i + 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' e −Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & =, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' − =, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' =, / > − Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &g h𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='% ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='% i = l0 0m, (6) where 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ≝ 𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content="/𝑚'(), 𝜒 ≝ 𝐽!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,(𝑇) ≝ Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " 567, $%&\' 5*8, [ 8,9*8, ()*(-) , Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " ≝ 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "/𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & ≝ 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &/𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & ≝ 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &/(𝑚!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ), and Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " ≝ 𝑇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "/(𝑚B𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Equation (6) only considers the linearized dynamics of the undamped 𝑖th cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Note that the nondimensionalization in (6) results in (squared) frequency-like parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,, Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &, Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ", and Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' This parameter conversion offers an advantage when comparing the model to experiments because frequencies are easier to identify than stiffnesses and directly affect the performance of the waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For instance, we deduce the value of Λ\'() " listed in Table I from the experiments of a single cell in [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For the remaining frequency-like parameters, we assume the following relationships for all 𝑖 ∈ {𝑅𝑒𝑓, 1, 2,3, … }: Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &(𝑇) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' C(𝑇) − min DE/→>// H Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' C(𝑇)B (7a) Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " = 1 12 Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " (7b) Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &(𝑇) = 1 12 a3Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &(𝑇) − 3 4 Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (7c) To calculate the Bloch modes of a single cell, we apply the Floquet boundary conditions of h𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' i = 𝒑!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content="𝑒IJ'0 1 !" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='L with a normalized wavenumber 𝑘4/𝐿, a modal frequency of 𝜔, a modal vector 𝒑!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', and the imaginary number 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Additionally, we assume that all cells are identical to the single cell with parameters listed in Table I, transforming (6) into the following boundary value problem: j−𝜔.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' a1 0 0 𝜒b + e 2 G1 − cos ,0 M H Λ\'() & + Λ\'() "*+, −Λ\'() & sin ,0 M … (8) 10 … Λ\'() & sin ,0 M % .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' G1 + cos ,0 M H Λ\'() & + 2 G1 − cos ,0 M H Γ\'() & + Γ\'() " gk 𝒑!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' = l0 0m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For all 𝑘4/𝐿 ∈ [0, 𝜋] rad, the irreducible Brillouin zone (IBZ) is defined by the respective pair of eigenfrequencies 𝜔 that zero the determinant of the matrix operating on 𝒑!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' in (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' These eigenfrequencies are the Bloch modes’ frequencies forming the dispersion curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2b at 390 K, 370 K, and 350 K for the single cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The lower (blue) and upper (green) curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2b correspond to passbands I and II of the transmission in the perfectly periodic infinite waveguide, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We depict the transmission of this waveguide in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c, where we collect the extrema (maxima and minima) of passbands I and II (like in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2b) for the temperature 𝑇 ∈ [350, 400] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c shows that cooling from 400 to ~370 K reduces the mean frequencies of both passbands while narrowing the bandwidth of passband I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Cooling below ~370 to 350 K increases again the mean frequencies of both passbands while widening the bandwidth of passband I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The first cooling phase from 400 to ~370 K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c resembles the cooling phase in Fig 1c between 280 and ~230 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' However, the second cooling phase between ~370 to 350 K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c diverges fundamentally from the experimental transmission in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1c between ~230 and ~80 K, where the transmission in passband I does not reemerge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Therefore, the ROM buckling cannot eliminate the transmission of passband I in a perfectly periodic infinite waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' This loss of transmission with buckling necessitates the consideration of disorder (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', the break of perfect periodicity) in the waveguide as previously established in [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Note that we adopt the relationships in (7) to emulate the experimental transmission in Fig 1c between 280 and ~230 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For this reason, we select Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &(𝑇) in (7a) to decrease until the transmission vanishes at the point of minimum frequency, min DE/→>// H Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' C(𝑇), leading to the shrinkage of passband I between 400 and ~370 K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In (7b), we assume that the rotation of the cell centerline (of length 𝐿) deflects an elastic foundation of stiffness density 𝑘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "/𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In (7c), we impose a temperature-constant bandwidth for passband II like the measurements in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The temperature-detuning of the mean frequencies of the passbands in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2c is considered for the identified parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e, Λ\'() " , 𝛽/, 𝛽%, 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', 𝛾/, and 𝛾%) of the ROM in [41], which slightly deviate from those in the devices used in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1c (extracted in [29]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 11 IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Temporal transmission in finite waveguides We focus now on the waveguide disorder resulting from the thickness variation between the cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We assume a thickness variation of the form, ℎ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" − ℎ'() ℎ'() = 𝜎< 4 ⎩ ⎪ ⎨ ⎪ ⎧ j2 €𝑁 + 1 2 − 𝑖€ 𝑁 + 1 2 − 1 − 1k ‚‚‚‚‚ƒ‚‚‚‚‚„ N, + 𝑟!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ([−1, 1]) ⎭ ⎪ ⎬ ⎪ ⎫ , (9) for 𝑖 ∈ {1,2, … , 𝑁}, where we denote by ℎ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" the thickness of the 𝑖th cell, ℎ'() the thickness of the reference cell discussed in the previous section, 𝜎< the level of thickness disorder, and 𝑟!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ([−1, 1]) a random rational number ∈ [−1, 1] generated at each 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We introduce the random number 𝑟!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' to account for the random errors of the fabrication process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The 𝑠!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' term in (9) represents the systematic errors resulting from wet etching that forms the waveguide cells as explained in [29] [38] [46] [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The holes at the center of the cells in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1a-b are etching holes through which the etchant attacks the underlying layer and suspends the cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Thus, there is a higher (linear) density of etching holes at the middle of the waveguide (of index O?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='% .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ) compared to the ends (of indices 1 and 𝑁).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' This higher etching-holes density increases the etching rate leading to over-etching at the middle of the waveguide compared to its ends [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We model this over-etching by 𝑠!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' in (9) as a linear distribution of the cell position from the middle of the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3a-b show two examples of thickness variation with 𝜎< = 0% (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', perfectly periodic waveguide) and 𝜎< = 5%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' The thickness variation implies a corresponding variation in the dynamical properties of the cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Based on the theory of the mechanics circular plates [48] [49] and the assumption in [41], the thickness affects the parameters of the 𝑖th cell in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e as follows: 𝜅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" # 𝜅'() # = ‹ ℎ!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" ℎ'() Œ $." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' , (10a) Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' " Λ\'() " = ‹ ℎ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" ℎ'() Œ ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (10b) The scaling relationships (10) with the expressions in (7) quantify the effect of the cell’s thickness on the ROM parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' With the ROM of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e, we apply Newton’s 1st law to calculate the static equilibrium (𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012, 𝐿P 𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012) of each cell 𝑖 ∈ {1, 2, … , 𝑁} in the 𝑁 cells waveguide using, 12 ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧𝐹P% "*+,X𝑢P% 012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇Y 0 ⋮ 𝐹P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,X𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇Y 0 ⋮ 𝐹PO "*+,X𝑢PO 012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" 𝑇Y 0 ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎫ ‚‚‚‚‚ƒ‚‚‚‚‚„ 𝑸8$%&' + 𝐾•#;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ 𝑢P% 012 𝐿P𝜃% 012 ⋮ 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 𝐿P𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 ⋮ 𝑢PO 012 𝐿P𝜃O 012⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎫ ‚‚ƒ‚‚„ 𝒒8 ()* = 𝟎, (11) where 𝐹P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,X𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝑇Y is the thermo-elastic buckling force expressed in (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In (11), we assume small angles of deformation allowing the approximation sin 𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 ≈ 𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 while neglecting the longitudinal displacement of the cells’ ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Under this approximation, we express the nondimensional static stiffness 𝐾•#;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' as, 𝐾•#;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ 𝒦•% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='(O$.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') ⋱ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') 𝒦•!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (O$!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$%) ⋱ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='(O$.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') 𝒦•O ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ , (12a) with 0T×U denoting a zero-filled matrix of 𝑀 rows by 𝑃 columns, 𝒦•% = e 𝜇%Λ% & V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' −𝜇%Λ% & V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇% G =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ > + Γ% & + Γ% "H − V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇% G =.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='/ > − Γ% &H g, (12b) 𝒦•!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' = – −𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$%Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & − V,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$%Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & + 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & V,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% — =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > − Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & ˜ $V,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='V,=, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' … … $V,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='V,=, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' −𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & V,=, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% — =,-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$% & ˜ + 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' — =, / > + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & + Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "˜ − V,=, / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' — =, / > − Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &˜ ™, (12c) for 2 ≤ 𝑖 ≤ 𝑁 − 1, and, 13 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" Effect of weak thickness disorder on the static equilibrium of finite waveguides: (a, b) Thickness profile relative to the reference thickness ℎ'(), and (c, d) static deflections at 400, 390, 380, 370, 360, and 350 K of (a), and (b, d) the weakly (𝜎< = 5%) disordered 60-cell waveguide ROM of (b);" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' refer to (9) for the definition of the disorder parameter 𝜎<;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' in addition, in (c, d), the thick segments represent the rigid masses of the cells in the ROM of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e translating and rotating according to the computed equilibria from (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝒦•O = e −𝜇O$%ΛO$% & − V2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' V2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇O$% G =2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > − ΓO$% & H … … 𝜇O$%ΛO$% & − V2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' − V2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='=2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 𝜇O$% G =2-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' / > + ΓO$% & H + 𝜇OΓO "g, (12d) where Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' &, Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ", and Γ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' & are defined in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We solve (11) via “fsolve” (gradient descent method) in MATLAB®.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In the numerical solver, the starting guesses for 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 in (11) correspond to the equilibria of individual cells in (1), see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' We assign the differences X𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='% 012 − 𝑢P!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012Y as starting guesses for 𝐿P𝜃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 012 for 𝑖 ∈ {1, 2, … , 𝑁 − 1}, and 𝐿P𝜃O$% 012 as the guess for 𝐿P𝜃O 012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3c-d display the computed equilibria of (11) at different temperatures in the perfectly periodic and weakly disordered waveguides of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3a-b, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3c-d, each segment (thick dashed line) represents a cell in the ROM of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 1d-e translated and rotated according to the equilibrium of (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3c, the cells at equilibrium undergo the same translational deflections without rotation, which results from the perfect periodicity of the waveguide of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For instance, the weakly-disordered waveguide of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3b attains equilibrium with different cell translations Perfect periodicity: oh = 0% Weak disorder: n = 5% a b (%) 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='5 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='5 100 100 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='5 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='5 1 20 40 60 1 20 40 60 Cell number Cell number c d 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='4 350 K B a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 360 K EQM 370 K 0 0 380 K 390 K 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='2 400K 1 20 40 09 1 20 40 60 Cell number Cell number 14 and rotations, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' For both waveguides of Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=" 3c-d, the cooling increases the cells' baseline translational deflections going from negative to positive values between 400 K and 350 K(like the individual cell in Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Moreover, each 10 K of cooling induces larger deflections at lower temperatures in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3c-d, which mirrors the buckling susceptibility observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' At this point, we linearize the dynamics around the calculated equilibria to study the transmission in the finite waveguides for varying temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Using the perturbation coordinates in (5), the linearized equations yield, 𝑀• 5+𝒒8 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='+ + (𝐾•"*+, + 𝐾•#;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') ‚‚‚‚ƒ‚‚‚‚„ W8 𝒒• = 𝟎, (13) where 𝒒• = œ𝑣̅%, ℎP%, … , 𝑣̅!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', ℎP!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=', … , 𝑣̅O, ℎPO• , 𝐾•#;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' is defined in (12), 𝐾•"*+, corresponds to the 2𝑁 × 2𝑁 matrix whose diagonal contains the linear stiffnesses of the buckling forces, 𝐾•"*+, = diagX𝜇%Λ% "*+,, 0, … , 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' "*+,, 0 , … , 𝜇OΛO "*+,, 0Y, (14) and 𝑀• denotes the nondimensional mass matrix expressed as: 𝑀• = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ ℳ•% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (O$%) ⋱ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='$%) ℳ•!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='(O$!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=') ⋱ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (O$%) ℳ•O ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ , (15) where ℳ•!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' = 𝜇!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' a1 0 0 𝜒b for 𝑖 ∈ {1, 2, 3, … , 𝑁}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In this work, we solve for the acoustics of the waveguides by direct integration of (13) using MATLAB® “ode45” function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' To this end, we consider the solution of (13) subject to a nonzero initial translational velocity at cell 1 and all other initial conditions set to zero: 𝒒𝟎 ≝ 𝒒•(𝑡 = 0) = 𝟎 and 𝒒̇ 𝟎 ≝ 5𝒒8 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (𝑡 = 0) = c 10$D𝜇% 0 𝟎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (O$%)×% d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (16) The initial conditions (16) induce a motion that propagates in the waveguides as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 4-5 and the supplemental Video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' This motion enables the study of wave transmission in the considered finite waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' In Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 4-5 and supplemental Video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content='S1, we consider the responses of the waveguides of Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3a-b at 390 K, to address the effect of weak disorder at a 15 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' Elastic wave transmission through the perfectly periodic finite waveguide of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' 3a at 390 K: Temporal responses in terms of (a) the translations 𝑣̅Y and (b) the rotational ℎPY perturbation coordinates of (from left to right) cell 𝑛 ∈ {1, 20, 40, 60} due to the initial conditions in (16) (the rightmost plots in (a, b) show zoomed-in views of the responses of cell 60 in the period [16, 20] μs);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' (c) spatiotemporal evolution of the normalized mechanical energy 𝐸!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79FJT4oBgHgl3EQfnCyN/content/2301.11590v1.pdf'} +page_content=' T(+ 0. In practice, one uses small timesteps +τ ≪ 1 for accuracy/stability, leading to the last case: there will always exist a solution Xn close +to Xn+1, and a second preimage, far away from the region of our interest, and arguably physically +irrelevant (this second Xn → −∞ as τ → 0). On the other hand, as τ grows, the two roots move +closer to each other, J0(F) moves close to the regime of our simulations, and noninvertibility can +have visible implications on the predicted dynamics. Thus, choosing a small timestep in explicit +integrators guarantees desirable accuracy, and simultaneously practically mitigates noninvertibility +pathologies in the dynamics. +3 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Invertibility in transformations between neural networks +Training two neural networks for the +same regression or classification task practically never gives identical network parameters. Numer- +ous criteria exist for comparing the performance of different models (e.g. accuracy in classification, +or mean-squared loss in regression). Here we explore whether two different models can be cal- +ibrated to each other (leading to a de facto implicit function problem). Extending our analysis +provides invertibility guarantees for the transformation from the output of network 1 to the output +of network 2 (and vice versa). +3. Invertibility certification of neural networks and of transformations between them +Here we pose the verification of local invertibility of continuous functions as an optimization prob- +lem. We then show that for ReLU networks, this leads to a mixed-integer linear/quadratic program. +For an integer q ≥ 1, we denote the Lq-ball centered at xc by Bq(xc, r) = {x ∈ Rn | ∥x−xc∥q ≤ r} +(the notation also holds when q → +∞). +Problem 1 (Local Invertibility of NNs) +Given a neural network f : Rm �→ Rm and a point +xc ∈ Rm in the input space, we want to find the largest radius r > 0 such that f is invertible on +Bq(xc, r), i.e., f(x1) ̸= f(x2) for all x1, x2 ∈ Bq(xc, r), x1 ̸= x2. +Another relevant problem is to verify whether, for a particular point, a nearby point exists with +the same forward image. This is of particular interest in assessing invertibility of discrete-time +dynamical systems around a given trajectory. We formally state the problem as follows: +Problem 2 (Pseudo Local Invertibility of NNs) +Given a neural network f : Rm �→ Rm and a +point xc ∈ Rm in the input space, we want to find the largest radius R > 0 such that f(x) ̸= f(xc) +for all x ∈ Bq(xc, R), x ̸= xc. +If r and R are the optimal radii in problems 1 and 2 respectively, we must have r ≤ R. For +Problem 1, the ball Bq(xc, r) just “touches” the J0 set; for Problem 2, the ball Bq(xc, R) extends +to the “other” closest preimage of f(xc). Figure 1 illustrates both concepts in the one-dimensional +case. For the scalar function y = f(x) and around a particular input xc, we show the nearest bounds +of local invertibility and pseudo invertibility. The points Q1 = (xQ1, yQ1) and Q2 = (xQ2, yQ2) +are the two closest turning points (elements of the J0 set) to the point C = (xc, yc); f is uniquely +invertible (bi-Lipschitz) on the open interval (xQ1, xQ2), so that the optimal solution to Problem 1 +is: r = min{|xQ1 − xc|, |xQ2 − xc|} = |xQ1 − xc|. Noting that M1 = (xM1, yM1) and M2 = +(xM2, yM2) are the two closest points that have the same y-coordinate as the point C = (xc, yc), the +optimal solution to Problem 2 is R = min{|xM1 − xc|, |xM2 − xc|} = |xM1 − xc|. +4 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Figure 1: Illustration of problems 1 (distance to invertibility boundary, red) and 2 (distance to pseudo invert- +ibility boundary, blue). +We now state our first result, posing the local invertibility of a function (such as a neural net- +work) as a constrained optimization problem. +Theorem 1 (Local Invertibility of Continuous Functions) +Let f : Rm → Rm be a continuous +function and B ⊂ Rm be a compact set. Consider the following optimization problem, +p⋆ ←max +∥x1 − x2∥ +subject to x1, x2 ∈ B, +f(x1) = f(x2). +(4) +Then f is invertible on B if and only if p⋆ = 0. +Theorem 2 (Pseudo Local Invertibility) +Let f : Rm → Rm be a continuous function and B ⊂ +Rm be a compact set. Suppose xc ∈ B. Consider the following optimization problem, +P ⋆ ← max +∥x − xc∥ +subject to x ∈ B, +f(x) = f(xc). +(5) +Then we have f(x) ̸= f(xc) for all x ∈ B \ {xc} if and only if P ⋆ = 0. +Note that by adding the equality constraints x = x1, xc = x2 to the optimization problem (4), +we obtain the optimization problem (5). Hence, we will only focus on (4) in what follows. +Invertibility certification of ReLU networks via mixed-integer programming +We now show +that for a given ball B∞(xc, r) in the input space, and piecewise linear networks with ReLU activa- +tions, the optimization problem in (4) can be cast as an MILP. +A single ReLU constraint y = max(0, x) with pre-activation bounds x ≤ x ≤ ¯x can be +equivalently described by the following mixed-integer linear constraints (Tjeng et al. (2017)): +y = max(0, x), x ≤ x ≤ ¯x ⇐⇒ {y ≥ 0, y ≥ x, y ≤ x − x(1 − t), y ≤ ¯xt, t ∈ {1, 0}}, +(6) +where the binary variable t ∈ {1, 0} is an indicator of the activation function being active (y = x) or +inactive (y = 0). Now consider an ℓ-layer feed-forward fully-connected ReLU network with input +x given by the following recursions, +x(k+1) = max(W (k)x(k) + b(k), 0) for k = 0, · · · , ℓ − 1; f(x(0)) = W (ℓ)x(ℓ) + b(ℓ), +(7) +5 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +where x(k) ∈ Rnk gives the input to the (k + 1)-th layer (specifically, we have x = x(0) and +n0 = m), W (k) ∈ Rnk+1×nk, b(k) ∈ Rnk+1 are the weight matrices and bias vectors of the affine +layers. We denote n = �ℓ +k=1 nk the total number of neurons. Suppose l(k) and u(k) are known +elementwise lower and upper bounds on the input to the (k + 1)-th activation layer, i.e., l(k) ≤ +W (k)x(k) + b(k) ≤ u(k). Then the neural network equations are equivalent to a set of mixed-integer +constraints as follows: +x(k+1) = max(W (k)x(k) + b(k), 0) ⇔ +� +� +� +� +� +x(k+1) ≥ W (k)x(k) + b(k) +x(k+1) ≤ W (k)x(k) + b(k) − l(k) ⊙ (1nk+1 − t(k)) +x(k+1) ≥ 0, +x(k+1) ≤ u(k) ⊙ t(k), +(8) +where t(k) ∈ {1, 0}nk+1 is a vector of binary variables for the (k + 1)-th activation layer and 1nk+1 +denotes vector of all 1’s in Rnk+1. We note that the element-wise pre-activation bounds {l(k), u(k)} +can be precomputed by, for example, interval bound propagation or linear programming, assuming +known bounds on the input of the neural network (Weng et al. (2018); Zhang et al. (2018); Hein and +Andriushchenko (2017); Wang et al. (2018); Wong and Kolter (2018)). Since the state-of-the-art +solvers for mixed-integer programming are based on branch & bound algorithms (Land and Doig +(1960); Beasley (1996)), tight pre-activation bounds will allow the algorithm to prune branches +more efficiently and reduce the total running time. +Local invertibility certificates via mixed-integer programming +Having represented the neural net- +work equations by mixed-integer constraints, it remains to encode the objective function ∥x1 − x2∥ +of (4) as well as the set B. We assume that B is an L∞ ball around a given point xc, i.e., B = +B∞(xc, r). Furthermore, for the sake of space, we only consider L∞ norms for the objective func- +tion. Specifically, consider the equality w = ∥x1 − x2∥∞. This equality can be encoded as mixed- +integer linear constraints by introducing 2n0 mutually exclusive indicator variables, which leads to +the following MILP: +p⋆ ← max w subject to ∥x1 − xc∥∞ ≤ r, ∥x2 − xc∥∞ ≤ r +(I) : +� +� +� +� +� +(x1 − x2) ≤ w1n0 ≤ (x1 − x2) + 4r(1n0 − f) +−(x1 − x2) ≤ w1n0 ≤ −(x1 − x2) + 4r(1n0 − f′) +f + f′ ≤ 1n0, 1⊤ +n0(f + f′) = 1, f, f′ ∈ {0, 1}n0 +(II) : W (ℓ)x(ℓ) +1 += W (ℓ)x(ℓ) +2 +(9) +for k = 0, · · · , ℓ − 1 : +(III) : +� +� +� +� +� +x(k+1) +1 +≥ W (k)x(k) +1 ++ b(k), x(k+1) +2 +≥ W (k)x(k) +2 ++ b(k) +x(k+1) +1 +≤ W (k)x(k) +1 ++ b(k) − l(k) ⊙ (1 − t(k)), x(k+1) +2 +≤ W (k)x(k) +2 ++ b(k) − l(k) ⊙ (1 − t(k)) +x(k+1) +1 +≥ 0, x(k+1) +2 +≥ 0, x(k+1) +1 +≤ u(k) ⊙ t(k), x(k+1) +2 +≤ u(k) ⊙ t(k); t(k), s(k) ∈ {0, 1}nk+1, +where the set of constraints in (I) model the objective function ∥x1−x2∥∞, and the set of constraints +(III) encode the network x(k+1) +1 += max(W (k)x(k) +1 +b(k), 0) and x(k+1) +2 += max(W (k)x(k) +2 +b(k), 0). +The constraint (II) enforces that f(x1) = f(x2). This optimization problem (4) has 2(n0 + n) +integer variables. +6 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Remark 3 If we instead use the ℓ2 norm both for the objective function and the ball B2(xc, r), +we will arrive at a mixed-integer quadratic program (MIQP). However, (9) remains an MILP if we +change them to ℓ1 norms. +Largest region of invertibility +For a fixed radius r ≥ 0, the optimization problem (9) either verifies +whether f is invertible on B∞(xc, r) or it finds counterexamples x1 ̸= x2 such that f(x1) = f(x2). +Thus, we can find the maximal r by performing a bisection search on r (Problem 1). +To close this section, we consider the problem of invertibility certification in transformations +between two functions (and in particular two neural networks). +Problem 3 (Transformation Invertibility) Given two functions f1, f2 : Rm → Rm and a partic- +ular point xc ∈ Rm in the input space, we would like to find the largest ball Bq(xc, r) over which +the output of f2 is a function of the output of f1 (and vice versa). +Theorem 4 +Let f1 : Rm → Rn, f2 : Rm → Rn be two continuous functions and B ⊂ Rm be a +compact set. Consider the following optimization problem, +p⋆ +12 ← max +∥f2(x1) − f2(x2)∥ +subject to x1, x2 ∈ B, +f1(x1) = f1(x2). +(10) +Then the output of f2 is a function of the output of f1 on B if and only if p⋆ +12 = 0. +Similar to Problem 1, we can pose Problem 3 as a mixed-integer program. Furthermore, we can +also define p⋆ +21, whose zero value determines whether output of f1 is a function of output of f2 over +B. It is straightforward to see that p⋆ +12 = p⋆ +21 = 0 if and only if output of f2 is an invertible function +of output of f1. +4. Numerical Experiments +We now present experiments with ReLU multi-layer perceptrons (MLPs) in both (a) regression +problems, and also in (b) transformations between two ReLU networks. +1D Example +We use a 1-10-10-1 randomly generated fully-connected neural network f(x) with +ReLU activations. We find the largest interval around the points x = −1.8; −1; −0.3 on which f is +invertible (Problem 1); we also find the largest interval around the point x = −1 for which no other +interior points map to f(−1) (Problem 2). The results are plotted in Figure 2, where intervals in +red and blue respectively represent the optimal solutions for the two problems. The largest certified +radii are 0.157, 0.322 and 0.214 for Problem 1 and 0.553 for Problem 2. +7 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Figure 2: +Solutions to Problem 1 (left, red) and Problem 2 (right, blue) for the MLP corresponding to a +randomly-generated ReLU network (see text). +2D Example: a disrete-time integrator. +The Brusselator (Tyson (1973)) is a system of two ODEs +for the two variables (x, y), depending on the parameters (a, b); it describes oscillatory dynamics in +a theoretical chemical reaction scheme. We use its forward-Euler discretization with step τ, +xn+1 = xn + τ(a + x2 +nyn − (b + 1)xn), yn+1 = yn + τ(bxn − x2 +nyn). +(11) +Rearranging and eliminating yn+1 in (11) we obtain: +τ(1 − τ)x3 +n + τ(τa − xn+1 − yn+1)x2 +n + (τb + τ − 1)xn + (xn+1 − τa) = 0. +(12) +Equation (12) is a cubic for xn given (xn+1, yn+1) when τ ̸= 1. By varying the parameters a, b and +τ, we see the past states (xn, yn)T of point (xn+1, yn+1)T (also called “inverses” or “preimages”) +may be multi-valued, so that this discrete-time system is, in general, noninvertible. We fix a = 1 +and consider how inverses will be changing (a) with b for fixed τ = 0.15; and (b) with τ, for fixed +b = 2. +We are interested in training a neural network that learns this time-τ mapping; for a fixed set +of parameter values, this is a network from 3D to 2D: (xn+1, yn+1)T ≈ N(xn, yn; p)T , where +p ∈ R is the parameter. The network dynamics will be parameter-dependent if we set p ≡ b, or +timestep-dependent if p ≡ τ. The first layer of such an MLP reads +W (0) +� +� +xn +yn +p +� +� + b(0) = (W (0)(e1 + e2)) +�xn +yn +� ++ (pW (0)e3 + b(0)), +(13) +where e1,2,3 ∈ R3 are indicator vectors. Here we trained two separate MLPs, ione with b and one +with τ dependence. For fixed p (either b or τ) each of these two networks N can be thought of as a +MLP mapping from R2 to R2, by slightly modifying the weights and biases in the first linear layer. +Parameter-dependent Inverses +It is useful to start with a brief discussion of the dynamics and +noninvertibilities in the ground-truth system (see Figure 3). Consider a state located on the invariant +circle (IC, shown in orange), for we therefore know there exists at least one preimage also on this +IC. In Figure 3 we indeed see that every point on the IC has three preimages: one still on the IC, and +two extra inverses (in green and purple) after one iteration, all three loops map to the orange one, +8 + +-4 +-2 +1.5 +1 +-0.5 +0 +c0 +-4 +-2 +1.5 +1 +-0.5 +0 +cCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +and then remain forward invariant. The phase space, upon iteration, folds along the two branches +of the J0 curve (sets of red points). For lower values of b, these three closed loops do not intersect +each other. As b increases the (orange) attractor will become tangent to, and subsequently intersect +J0, leading to an interaction with the other (green) preimage branch. At this point the dynamics +predicted by the network become unphysical (beyond just inaccurate). +Figure 3: Attractors (and their multiple inverses) for several parameter values of the discrete Brusselator +neural network for τ = 0.15. Notice the relative positions of the J0 curves (red), the “main” preimage locus +(yellow), and the “extra” preimages (green, purple). When the attractor starts interacting with the J0 curve +and, therefore, with these extra preimages, the dynamic behavior degenerates quantitatively and qualitatively +(see also Rico-Martinez et al. (1993)). +After convergence of training, we employ our algorithm to obtain noninvertibility certificates +for the resulting MLP, and plot results for b = 2.1 in Figure 4. In Figure 4, we arbitrarily select one +representative point, marked by triangle (△), on the attractor (the orange invariant circle); we know +there exists one inverse also located on the attractor, see the nearby cross (+); we call this the primal +inverse. Our algorithm will produce two regions for this point, one for each of our problems (squares +of constant L∞ distance in 2D). As a sanity check, we also compute the J0 sets (the red point), as +well as a few additional inverses, beyond the primal ones with the help of a numerical root solver +and automatic differentiation (Baydin et al. (2017)). Clearly, the smaller square neighborhood just +hits the J0 curve, while the larger one extends to the closest non-primal inverse of the attractor. +Timestep-dependent Inverses +In the right two subfigures of Figure 4, we explore the effect of +varying the time horizon τ. We compare a single Euler step of the ground truth ODE to the MLP +approximating the same time τ map, and find that, for both of them, smaller time horizons lead to +larger regions of invertibility. +9 + +(a,b)= (1, 2) +(a,b)= (1, 2.5) +(a,b)= (1, 3.2) +『, F-1() +f-1(r) +f-1(r)" +0 +X +X +xCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +5 +0 +5 +10 +x +5.0 +2.5 +0.0 +2.5 +5.0 +7.5 +10.0 +y +J0 +Attractor +Image +Inverses +5.0 +2.5 +0.0 +2.5 +5.0 +x +4 +2 +0 +2 +4 +6 +y +the Brusselator Integrator +J0( = 0.05) +J0( = 0.30) +5.0 +2.5 +0.0 +2.5 +5.0 +x +the Brusselator Network +Figure 4: Left: illustration of our solution to Problems 1 and 2 for the Brusselator network with (a, b) = +(1, 2.1). For a particular reference point on the attractor, we show the neighborhoods found by our algorithms. +They clearly locate the closest point on the J0 curve / the closest “extra preimage” of the point of interest. Last +two: plots of J0 curves at different τ with (a, b) = (1, 2), for both the Euler integrator and our Brusselator +ReLU network. Small timesteps lead to progressively more remote J0 curves. Notice also the piecewise linear +nature of the J0 curve for the ReLU network; its accurate computation constitutes an interesting challenge by +itself. +Network Transformation Example: Learning the Van der Pol Equation +Here, to test our al- +gorithm on the problem of transformations between networks 3, we trained two networks on the +same regression task. Our data comes from the 2D Van der Pol equation dx1/dt = x2, dx2/dt = +µ(1 − x2 +1)x2 − x1, where the input and output are the initial and final states of 1000 short solution +trajectories of duration 0.2 for µ = 1, when a stable limit cycle exists. The initial states are uni- +formly sampled in the region [−3, 3]×[−3, 3]. The neural network A used to learn the time-τ = 0.2 +map is a 2-32-32-2 MLP, while the neural network B is a retrained sparse version of A, where half +of the weight entries are pruned (set to zero) based on Zhu and Gupta (2018). To visualize the per- +formances of the two networks, two trajectories, generated by respectively iterating each network +function for a fixed number of times starting from a common given initial state have been plotted in +the left subplot of Figure 5. The ODE solution trajectory starting at the same initial state with same +overall time duration is also shown. We see that both network functions A and B exhibit long term +oscillations; the shapes of both attractors appear to only have small visual differences from the true +ODE solution (the red curve). +These two network functions were then used to illustrate the algorithm for Problem 3. Here we +chose a center point xc = (0, 0)T , computed and plotted the mappable regions (the regions over +which there is a one-to-one mapping between the output of one network and the output of the other, +i.e. where one network can be calibrated to the other). This was done for two subcases (see the right +subfigure of Figure 5): (a) where the output of network B is a function of the output of network A +(the square with white bounds centered at the red point, radius 3.0820), and vice versa, where the +output of network A is a function of the output of the network B (the square with black bounds +centered at the red point, radius 3.6484). This also gives us the “common” region (the interior +of the white square) where both networks can be calibrated to each other. For validation we also +computed the Jacobian values of network A and network B on every grid point of the input domain, +and shown that the white square touches the J0 curve of network A, while the black square touches +the J0 curve of network B. Inside the black square the Jacobian of network B remains positive, so +that network B is invertible (i.e. there exists a mapping from fB(x) to x, or equivalently, f−1 +B (x)); +10 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +therefore we can find the mapping from fB(x) to fA(x) by composing the mapping from fB(x) to +x with the mapping from x to fA(x) (the function fA(x) itself). The size of the white square can be +similarly rationalized, validating our computation. +2 +0 +2 +x1 +3 +2 +1 +0 +1 +2 +3 +x2 +ode solution +NN A (original) +NN B (pruned) +5 +0 +5 +x1 +4 +2 +0 +2 +4 +x2 +rAB = 3.0820 (white), rBA = 3.6484 (black) +det(JA) < 0, det(JB) < 0 +det(JA) < 0, det(JB) > 0 +det(JA) > 0, det(JB) < 0 +det(JA) > 0, det(JB) > 0 +Figure 5: Left: Trajectories of the ODE solution for the Van der Pol system (red), and their discrete-time +neural network approximations (blue and green). All three trajectories begin at the same initial state. While +the ODE solution curve is smooth due to its continuous-time nature, the others are just straight line segments +connecting consecutive states (discrete-time dynamics). However, it is clear that all three systems have visu- +ally nearby long-time dynamic attractors, corroborating the good performance of the network and its pruned +version. Right: visualization of MILP computation results, along with signs of Jacobian values of networks +on the grid points of the input domain. Here, the center of the region is shown in red, while the white and +black boundaries quantify the mappable region between outputs of network A and network B. +Sparsity +40 % +50 % +60 % +Network B +B1 +B2 +B3 +B4 +B5 +B6 +B7 +B8 +B9 +rAB +3.0820 +3.0820 +3.0820 +3.0820 +3.0820 +3.0820 +3.0820 +3.0820 +3.0820 +rBA +3.4609 +3.1055 +3.8555 +3.6484 +2.6523 +3.8203 +3.6328 +3.9727 +4.5547 +Table 1: The radii of the mappable regions between the original network A and its pruned versions B. rAB +relates to the region within which fB(x) is a function of fA(x). +As a sanity check, we consructed eight more pruned networks; two of them have 50% sparsity +(networks B5 and B6), three have 40% sparsity (networks B1, B2 and B3) and the others have 60% +sparsity (networks B7, B8 and B9). Above we discussed network B4 For each pruned network, we +computed the radii of the regions of interest (aka rAB and rBA). The results are listed in Table 1. +All pruned networks {Bi} share the same radii rAB, consistent with the invertibility of A itself. +Since rA = 3.0820, A is invertible in the ball we computed, and the existence of the mapping +fA(x) �→ fB(x) follows by composition of fA(x) �→ x and x �→ fB(x). Based on these few +computational experiments one might very tentatively surmise a trend: the higher the pruning (e.g. +60%) the larger the invertibility guarantee for the pruned network. In our work the input and output +11 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +dimensions are the same (e.g. m = n in Problem 3). However, this condition is not necessary, and +our algorithm can be conceptually extended to classification problems, where in general m ≫ n. +5. Conclusions +In this paper, we revisited noninvertibility issues that arise in discrete-time dynamical systems inte- +grators) as well as in neural networks that perform approximations of the same (time-series related) +task. We argued that such noninvertibility may have dramatic pathological consequences, going +beyond just inaccuracies, in the dynamics predicted by the networks. We also extended the analysis +to transformations between different neural networks. We formulated three problems that provide a +quantifiable assessment of “local” invertibility for any given, arbitrarily selected input. Specifically, +for functions like MLPs with ReLU activations, these problems were formulated as mixed-integer +programs. We then performed experiments on regression tasks. An extension of our algorithm to +ResNets. can be found in the Appendix. +Future directions include developing structure-exploiting methods to globally solve these MIPs +more efficiently, and for larger networks. On the other hand, given that convolution and aver- +age pooling are linear operations, while max pooling is piecewise linear, it is natural to adapt our +algorithms to convolutional neural networks like AlexNet (Krizhevsky et al. (2017)) or VGG (Si- +monyan and Zisserman (2015)). The successful application of our algorithm to ResNet architectures +(He et al. (2016)) holds promise for applicability also to recursive architectures (Lu et al. (2018); +E (2017)), such as fractal networks (Larsson et al. (2017)), poly-inception networks (Zhang et al. +(2016)), and RevNet (Gomez et al. (2017)). We are working on making the algorithm practical for +continuous differentiable activations like tanh or Swish (Ramachandran et al. (2017)), and for other +piecewise activations like gaussian error linear units (GELUs, Hendrycks and Gimpel (2016)). We +are particularly interested in the case when the input and output domains are of different dimension +(e.g., classifiers). +References +R. Adomaitis and I. Kevrekidis. Noninvertibility and the structure of basins of attraction in a model +adaptive control system. Journal of Nonlinear Science, 1:95–105, 1991. +Lynton Ardizzone, Jakob Kruse, Sebastian Wirkert, Daniel Rahner, Eric W Pellegrini, Ralf S +Klessen, Lena Maier-Hein, Carsten Rother, and Ullrich K¨othe. Analyzing inverse problems with +invertible neural networks. arXiv preprint arXiv:1808.04730, 2018. +Lynton Ardizzone, Jakob Kruse, Sebastian J. Wirkert, D. Rahner, Eric W. Pellegrini, R. Klessen, +L. Maier-Hein, C. Rother, and U. K¨othe. Analyzing inverse problems with invertible neural +networks. ArXiv, abs/1808.04730, 2019. +Atılım G¨unes Baydin, Barak A. Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind. +Automatic differentiation in machine learning: A survey. J. Mach. Learn. Res., 18(1):5595–5637, +January 2017. ISSN 1532-4435. +J. E. Beasley, editor. Advances in Linear and Integer Programming. Oxford University Press, Inc., +USA, 1996. ISBN 0198538561. +12 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Jens Behrmann, S¨oren Dittmer, Pascal Fernsel, and P. Maass. Analysis of invariance and robustness +via invertibility of relu-networks. ArXiv, abs/1806.09730, 2018. +Jens Behrmann, Will Grathwohl, Ricky T. Q. Chen, David Duvenaud, and Joern-Henrik Jacob- +sen. +Invertible residual networks. +In Kamalika Chaudhuri and Ruslan Salakhutdinov, edi- +tors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of +Proceedings of Machine Learning Research, pages 573–582. PMLR, 09–15 Jun 2019. URL +http://proceedings.mlr.press/v97/behrmann19a.html. +Jens Behrmann, Paul Vicol, Kuan-Chieh Wang, Roger Grosse, and Joern-Henrik Jacobsen. Under- +standing and mitigating exploding inverses in invertible neural networks. In Arindam Banerjee +and Kenji Fukumizu, editors, Proceedings of The 24th International Conference on Artificial +Intelligence and Statistics, volume 130 of Proceedings of Machine Learning Research, pages +1792–1800. PMLR, 13–15 Apr 2021. URL http://proceedings.mlr.press/v130/ +behrmann21a.html. +Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham. Reversible +architectures for arbitrarily deep residual neural networks. +In Sheila A. McIlraith and Kil- +ian Q. Weinberger, editors, Proceedings of the Thirty-Second AAAI Conference on Artificial In- +telligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and +the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New +Orleans, Louisiana, USA, February 2-7, 2018, pages 2811–2818. AAAI Press, 2018. +URL +https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16517. +Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural ordinary dif- +ferential equations. In Proceedings of the 32nd International Conference on Neural Information +Processing Systems, NIPS’18, page 6572–6583, Red Hook, NY, USA, 2018. Curran Associates +Inc. +Ricky TQ Chen, Jens Behrmann, David Duvenaud, and J¨orn-Henrik Jacobsen. Residual flows for +invertible generative modeling. In Neural Information Processing Systems, 2019. URL https: +//arxiv.org/abs/1906.02735. +Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: non-linear independent components es- +timation. In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning +Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Workshop Track Proceedings, +2015. URL http://arxiv.org/abs/1410.8516. +Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density estimation using real NVP. In 5th +International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, +2017, Conference Track Proceedings. OpenReview.net, 2017. URL https://openreview. +net/forum?id=HkpbnH9lx. +Jeff Donahue and Karen Simonyan. Large scale adversarial representation learning. Advances in +neural information processing systems, 32, 2019. +Weinan E. A proposal on machine learning via dynamical systems. Communications in Mathemat- +ics and Statistics, 5(1):1–11, 3 2017. doi: 10.1007/s40304-017-0103-z. Dedicated to Professor +Chi-Wang Shu on the occasion of his 60th birthday. +13 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Christos E. Frouzakis, Laura Gardini, Ioannis G. Kevrekidis, Gilles Millerioux, and Christian Mira. +On some properties of invariant sets of two-dimensional noninvertible maps. International Jour- +nal of Bifurcation and Chaos, 07(06):1167–1194, 1997. +doi: 10.1142/S0218127497000972. +URL https://doi.org/10.1142/S0218127497000972. +N. Gicquel, J.S. Anderson, and I.G. Kevrekidis. Noninvertibility and resonance in discrete-time +neural networks for time-series processing. +Physics Letters A, 238(1):8–18, 1998. +ISSN +0375-9601. +doi: +https://doi.org/10.1016/S0375-9601(97)00753-6. +URL https://www. +sciencedirect.com/science/article/pii/S0375960197007536. +Aidan N Gomez, Mengye Ren, Raquel Urtasun, and Roger B Grosse. The reversible residual net- +work: Backpropagation without storing activations. Advances in neural information processing +systems, 30, 2017. +Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- +nition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages +770–778, 2016. doi: 10.1109/CVPR.2016.90. +Matthias Hein and Maksym Andriushchenko. Formal guarantees on the robustness of a classifier +against adversarial manipulation. In Advances in Neural Information Processing Systems, pages +2266–2276, 2017. +Dan Hendrycks and Kevin Gimpel. Bridging nonlinearities and stochastic regularizers with gaussian +error linear units. CoRR, abs/1606.08415, 2016. URL http://arxiv.org/abs/1606. +08415. +J¨orn-Henrik Jacobsen, Jens Behrmann, Richard Zemel, and Matthias Bethge. Excessive invariance +causes adversarial vulnerability. arXiv preprint arXiv:1811.00401, 2018. +H. Jaeger. Controlling recurrent neural networks by conceptors. ArXiv, abs/1403.3369, 2014. +Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. Imagenet classification with deep con- +volutional neural networks. Commun. ACM, 60(6):84–90, May 2017. ISSN 0001-0782. doi: +10.1145/3065386. URL https://doi.org/10.1145/3065386. +A. H. Land and A. G. Doig. +An automatic method of solving discrete programming prob- +lems. Econometrica, 28(3):497–520, 1960. ISSN 00129682, 14680262. URL http://www. +jstor.org/stable/1910129. +Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Fractalnet: Ultra-deep neural net- +works without residuals. In ICLR, 2017. +Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong. Beyond finite layer neural networks: +Bridging deep architectures and numerical differential equations. In Jennifer Dy and Andreas +Krause, editors, Proceedings of the 35th International Conference on Machine Learning, vol- +ume 80 of Proceedings of Machine Learning Research, pages 3282–3291, Stockholm, Stock- +holm Sweden, 10–15 Jul 2018. PMLR. URL http://proceedings.mlr.press/v80/ +lu18d.html. +14 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Matthew MacKay, Paul Vicol, Jimmy Ba, and Roger Grosse. Reversible recurrent neural networks. +In Proceedings of the 32nd International Conference on Neural Information Processing Systems, +NIPS’18, page 9043–9054, Red Hook, NY, USA, 2018. Curran Associates Inc. +Stefan T. Radev, Ulf K. Mertens, Andreas Voss, Lynton Ardizzone, and Ullrich K¨othe. Bayesflow: +Learning complex stochastic models with invertible neural networks. IEEE Transactions on Neu- +ral Networks and Learning Systems, pages 1–15, 2020. doi: 10.1109/TNNLS.2020.3042395. +Prajit Ramachandran, Barret Zoph, and Quoc V. Le. Swish: a self-gated activation function. CoRR, +2017. URL http://arxiv.org/abs/1710.05941v1. +R. Rico-Martinez, I.G. Kevrekidis, and R.A. Adomaitis. Noninvertibility in neural networks. In +IEEE International Conference on Neural Networks, pages 382–386 vol.1, 1993. doi: 10.1109/ +ICNN.1993.298587. +Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale im- +age recognition. In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on +Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track +Proceedings, 2015. URL http://arxiv.org/abs/1409.1556. +Yang Song, Chenlin Meng, and Stefano Ermon. Mintnet: Building invertible neural networks with +masked convolutions. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch´e-Buc, E. Fox, and +R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran As- +sociates, Inc., 2019. URL https://proceedings.neurips.cc/paper/2019/file/ +70a32110fff0f26d301e58ebbca9cb9f-Paper.pdf. +Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, +and Rob Fergus. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199, 2013. +Floris Takens. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, +Warwick 1980: Proceedings of a Symposium Held at the University of Warwick 1979/80, pages +366–381, Berlin, Heidelberg, 1981. Springer Berlin Heidelberg. ISBN 978-3-540-38945-3. doi: +10.1007/BFb0091924. URL https://doi.org/10.1007/BFb0091924. +Takeshi Teshima, Isao Ishikawa, Koichi Tojo, Kenta Oono, Masahiro Ikeda, and Masashi Sugiyama. +Coupling-based invertible neural networks are universal diffeomorphism approximators, 2020. +Vincent Tjeng, Kai Xiao, and Russ Tedrake. Evaluating robustness of neural networks with mixed +integer programming. arXiv preprint arXiv:1711.07356, 2017. +Florian Tram`er, Jens Behrmann, Nicholas Carlini, Nicolas Papernot, and J¨orn-Henrik Jacobsen. +Fundamental tradeoffs between invariance and sensitivity to adversarial perturbations. In Inter- +national Conference on Machine Learning, pages 9561–9571. PMLR, 2020. +John J. Tyson. Some further studies of nonlinear oscillations in chemical systems. The Journal +of Chemical Physics, 58(9):3919–3930, 1973. doi: 10.1063/1.1679748. URL https://doi. +org/10.1063/1.1679748. +15 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana. Efficient formal safety +analysis of neural networks. In Advances in Neural Information Processing Systems, pages 6367– +6377, 2018. +Tsui-Wei Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Duane Boning, Inderjit S +Dhillon, and Luca Daniel. Towards fast computation of certified robustness for relu networks. +arXiv preprint arXiv:1804.09699, 2018. +Eric Wong and Zico Kolter. Provable defenses against adversarial examples via the convex outer +adversarial polytope. In International Conference on Machine Learning, pages 5286–5295, 2018. +Huan Zhang, Tsui-Wei Weng, Pin-Yu Chen, Cho-Jui Hsieh, and Luca Daniel. +Efficient neural +network robustness certification with general activation functions. In Advances in Neural Infor- +mation Processing Systems, pages 4939–4948, 2018. +Xingcheng Zhang, Zhizhong Li, Chen Change Loy, and Dahua Lin. Polynet: A pursuit of structural +diversity in very deep networks. arXiv preprint arXiv:1611.05725, 2016. +Michael Zhu and Suyog Gupta. To prune, or not to prune: Exploring the efficacy of pruning for +model compression. In 6th International Conference on Learning Representations, ICLR 2018, +Vancouver, BC, Canada, April 30 - May 3, 2018, Workshop Track Proceedings. OpenReview.net, +2018. URL https://openreview.net/forum?id=Sy1iIDkPM. +16 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Appendix A. Further Discussions +A.1. Invertibilty in View of Lipschitz Constants +One can consider the neural network inversion problem in terms of Lipschitz continuity and the +Lipschitz constant. Indeed, quantifying invertibility of a neural network (more generally, a function) +is intimately connected with its Lipschitz constant. +Definition 5 (Lipschitz continuity and Lipschitz constant) A function F : B ⊆ Rm �→ Rm is +Lipschitz continuous on B if there exists a non-negative constant L ≥ 0 such that +||F(x1) − F(x2)|| +||x1 − x2|| +≤ L, +∀x1, x2 ∈ B, x1 ̸= x2. +(14) +The smallest such L is called the Lipschitz constant of F, L = Lip(F). +A generalization for Definition 5 is the bi-Lipschitz map defined as follows. +Definition 6 (bi-Lipschitz continuity and bi-Lipschitz constant) Suppose F : B ⊆ Rm �→ Rm +is globally Lipschitz continuous with Lipschitz constant L. Now we define another nonnegative +constant L′ ≥ 0 such that +L′ ≤ ||F(x1) − F(x2)|| +||x1 − x2|| +, +∀x1, x2 ∈ Rm, x1 ̸= x2. +(15) +If the largest such L′ is strictly positive, then (15) shows F is invertible on B due to F(x1) ̸= F(x2) +given x1 ̸= x2. Moreover, one could easily derive (1/L′) = Lip(F −1), where F −1 is the inverse +function of F. We also say F is bi-Lipschitz continuous in this case, with bi-Lipschitz constant +L∗ = max {L, 1/L′}. +A.2. Structure of Preimages for the Learned Map of the Brusselator Flow +As discussed in the main paper, we trained a network to approximate the time-τ Euler map (16) for +the Brusselator. The attractor (locus of long-term image points) is a small amplitude, stable invariant +circle (IC), the discrete time analog of the ODE stable limit cycle. We mark four representative +points on it (Q, R, S, and T) and divide it into parts A, B1, B2, and C between these points, so +as to facilitate the description of the dynamics and its multiple (due to noninvertibility) preimages. +The locus of red points (the locus on which the determinant of the Jacobian of the network changes +sign, or, in the language of noninvertible systems, the J0 curve) separates state space here into five +distinct regions I, . . . , V, each with different preimage behavior, as illustrated in Figure A.1. For +smooth maps, like the Brusselator forward Euler discretization or a tanh activation neural network, +J0 is the locus of points for which the determinant of the map Jacobian is zero (and therefore, the +map is singular). In those cases, the curve is easy to compute through continuation algorithms. +For ReLU activations, however, this locus is nontrivial to compute through algebraic solvers, and +piecewise smooth computational techniques or brute force exploration must be used to locate it; see +the inset in Figure, where the color intensity indicates the magnitude, red for positive and blue for +negative, of the map Jacobian determinant. After we locate the J0 points however, we see that they +17 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +define the I through V (and implicitly, through forward iteration of the J0 curve, regions A through +C on the IC): +𝐵1 +𝑄 +𝑅 +𝑆 +𝑇 +𝑄′′ = 𝑄′′′ +𝑅′′ = 𝑅′′′ +𝑆′′ = 𝑆′′′ +𝑇′′ = 𝑇′′′ +I +II +III +IV +V +𝐶 +𝐵2 +𝐴 +𝑅′ +Figure A.1: Top: Structure of Preimages and (top inset; positive is red, and negative is blue) magnitude +of the map Jacobian determinant for the Brusselator network with b = 2.1. Bottom: Labeling of key +representative points and important regions; see text. This is a qualitative rendering of the relevant regions in +the top figure, deformed to enhance visualization. +• Each point in part A (shown in yellow), has three inverses, located in regions I, II and III +respectively. The “physically meaningful inverse”, the one in III, is contained in the IC itself. +18 + +Attractor +Inverses +Jo +Determinant of +Jacobian +B1 +B2 +C +IVCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +• Points in part C (shown in cyan) similarly have inverses located in regions III, IV and V. +• Finally, we label two segments of the IC, located between the A and C segments, as B1 +and B2 (shown in dark green, with solid line and dashed lines, respectively). Points in these +portions of the IC only have a single inverse each (that we could find within the picture): the +one located on the attractor itself in region III. +It is informative to study the location and behavior of preimages as a phase point is moved along +the invariant circle. At the transitions from either Bi part into A (or C), two preimages (initially +one preimage with multiplicity two) are born touching the J0 curve, at the junction between I and +II (or IV and V). Notice also the “extra preimages” of the points R and Q (R′′, R′′′, Q′′, Q′′′) +off the invariant circle, on J0. The physically meaningful preimages (R′, Q′) lie on the invariant +circle itself; one of them, R′, close to R, in shown in the figure. As we move further into the A +(or C) parts of the attractor, the “extra” two preimages separate, traverse the two blue wings of the +preimage isolas, and then collide again on the J0 curve as the phase point transitions from A (or C) +into the other Bi part. +A.3. Noninvertibility in Partially Observed Dynamic Histories +Recall that the forward Euler discretization of the Brusselator is a two-dimensional map +� xn+1 = xn + τ(a + x2 +nyn − (b + 1)xn), +yn+1 = yn + τ(bxn − x2 +nyn). +(16) +In (16), we have two equations, but five unknowns (xn, yn, xn+1, yn+1, τ), so the system is in +principle solvable only if three of them are given. This leads to +�5 +3 +� += 10 possible cases, enu- +merated below, which can be thought of as generalizations of the inversion studied in depth in the +representative paper Adomaitis and Kevrekidis (1991); Frouzakis et al. (1997). +1. (xn, yn, τ) ⇒ (xn+1, yn+1). (This is the usual forward dynamics case.) The evolution is +unique (by direct substitution into (16)). +2. (xn+1, yn+1, τ) ⇒ (xn, yn). (This is the case studied in depth in the paper.) The backward- +in-time dynamic behavior is now multi-valued. Substituting equation (18) into the equation +for yn+1 in system (16) we obtain +τ(1 − τ)x3 +n + τ(τa − xn+1 − yn+1)x2 +n + (τb + τ − 1)xn + (xn+1 − τa) = 0. +(17) +(17) is a cubic equation w.r.t. xn if τ ̸= 0 and τ ̸= 1, which may lead to three distinct +real roots, two distinct real roots (with one of them multiplicity 2), or one real root (with +multiplicity 3, or with two extra complex roots). We can then substitute the solution of xn +into (18) to obtain yn. +3. (xn, xn+1, τ) ⇒ (yn, yn+1). Here we know the x history, and want to infer the y history: +create an observer of y from x. This is very much in the spirit of the Takens embedding theo- +rem Takens (1981), where one uses delayed measurements of one state variable as surrogates +of other, unmeasured state variables. For our particular Brusselator example, the y dynamics +inferred are unique. For the system (16), we rearrange the equation of xn+1 to obtain: +yn = xn+1 − xn + τ(b + 1)xn − τa +τx2n +, +(18) +19 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +which shows the solution for yn is unique. Substituting (18) into (16) gives yn+1. +4. (yn, yn+1, τ) ⇒ (xn, xn+1). Now we use history observations for y in order to infer the x +history. The inference of the x dynamic behavior is now multi-valued. From the system (16), +we can rearrange the equation of yn+1 to obtain +τynx2 +n − τbxn + (yn+1 − yn) = 0. +(19) +(19) is a quadratic equation w.r.t. xn if τ ̸= 0 and yn ̸= 0, which may lead to two distinct +real roots, one real root with multiplicity 2, or two (nonphysical) complex roots. We can then +substitute (19) into (18) to obtain yn. +5. (xn, yn+1, τ) ⇒ (yn, xn+1). We now work with mixed, asynchronous history observations. +For this particular choice of observations the inferred dynamic behavior is unique. For the +system (16), we can rearrange the equation of yn+1 and obtain +yn = yn+1 − τbxn +1 − τx2n +, +(20) +which shows that the solution for yn is unique. Then we can substitute (20) into (16) to obtain +xn+1. +6. (yn, xn+1, τ) ⇒ (xn, yn+1). Interestingly, for this alternative set of asynchronous history +observations, the inferred dynamic is multi-valued. From the system (16), we can rearrange +the equation of xn+1 and obtain +τynx2 +n + (1 − τ − τb)xn + (τa − xn+1) = 0. +(21) +(21) is a quadratic equation w.r.t. xn if τ ̸= 0 and yn ̸= 0, which may lead to two distinct +real roots, one real root with multiplicity 2, or two complex roots. We can then substitute (21) +into (16) to obtain yn+1. +7. (xn, yn, xn+1) ⇒ (τ, yn+1). This is an interesting twist: several asynchronous observations, +but no time label. Is this set of observations possible ? Does there exist a time interval τ +consistent with these observations ? And how many possible τ values and possible “history +completions” exist ? For this example, the inferred possible history is unique. For the system +(16), we can rearrange the equation of xn+1 and obtain +τ = +xn+1 − xn +a + x2nyn − (b + 1)xn +, +(22) +which shows that the solution for τ is unique. We can then substitute (22) into (16) to obtain +yn+1. The remaining cases are alternative formulations of the same “reconstructing history +from partial observations” setting. +8. (xn, yn, yn+1) ⇒ (τ, xn+1). The inferred history is again unique. For the system (16), we +can rearrange the equation of yn+1 and obtain +τ = yn+1 − yn +bxn − x2nyn +, +(23) +which shows that the solution for τ is unique. We can then substitute (23) into (16) to obtain +xn+1. +20 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +9. (yn, xn+1, yn+1) ⇒ (τ, xn). The inferred history is now multi-valued. Substituting equation +(22) in the equation for yn+1 in system (16) we obtain: +ynx3 +n+((yn−yn+1)yn−b−xn+1yn)x2 +n+(bxn+1+(b+1)(yn+1−yn))xn+a(yn−yn+1) = 0. +(24) +(24) is a cubic equation w.r.t. xn if yn ̸= 0, which may lead to three distinct real roots, two +distinct real roots (with one of them multiplicity 2), or one real root (with multiplicity 3, or +with two extra complex roots). Then we could substitute the solution of xn into (22) to obtain +τ. +10. (xn, xn+1, yn+1) ⇒ (τ, yn). The inferred history is again multi-valued. Substituting equation +(18) in the equation for yn+1 in system (16) we obtain: +x2 +n(a − xn)τ 2 + (x3 +n − (xn+1 + yn+1)x2 +n + (b + 1)xn − a)τ + (xn+1 − xn) = 0. +(25) +(25) is a quadratic equation w.r.t. τ if xn ̸= 0 and xn ̸= a, which may lead to two distinct +real roots, one real root with multiplicity 2, or two complex roots. We can then substitute (25) +into (18) to obtain yn. +As a demonstration, we select the last of these cases, in which τ is an unknown, and show +that multiple consistent “history completions”, i.e. multiple roots can be found; see Table A.1. +Roots with negative or complex τ are possible, while negative timestep could be considered as a +backward-time integration, complex results have to be filtered out as nonphysical. The methodology +and algorithms in our paper are clearly applicable in providing certifications for regions of existence +of unique consistent solutions; we are currently exploring this computationally. +Given +Unknowns +xn +xn+1 +yn+1 +τ1 +τ2 +yn,1 +yn,2 +4.88766 +1.62663 +2.27734 +0.27018 +0.12996 +0.06670 +-0.47845 +2.36082 +3.27177 +2.13372 +-1.51470 +0.07929 +0.98342 +3.15257 +2.19914 +1.97336 +3.22943 +-1.51394 +-0.02572 +1.18823 +2.97282 +4.60127 +2.27780 +2.21088 +(0.09960 ± 0.14337i) +(0.24609 ± 0.51630i) +Table A.1: (xn, xn+1, yn+1) ⇒ (τ, yn), where a = 1, b = 2. +A.4. Extensions to Residual Architectures +We demonstrate that our algorithms are also applicable to residual networks with ReLU activations. +The MILP method does not extend in a simple way to networks with tanh or sigmoid activation, but +we show here that simple algebraic formulas, like the residual connection, are addressable in this +framework. This follows from the fact that the identity function is equivalent to a ReLU multi-layer +perceptron (MLP) with an arbitrary number of hidden layers, +x = g(x) − g(−x) = g(g(x)) − g(g(−x)) = g(g(g(x))) − g(g(g(−x))) = · · · , +(26) +where g(x) = max(0, x) is the ReLU function. Because ReLU is idempotent g(g(x)) = g(x), we +are able to add more and more nested versions in the right side of (26). Thus one could transform a +ReLU ResNet with fully-connected layers to a single ReLU MLP by applying the equivalence (26). +21 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Proposition 7 A ReLU ResNet with ℓ fully-connected layers in its residual architecture is equiva- +lent to an MLP with the same number of layers. +Proof Suppose f : Rm �→ Rm is a ResNet. We can rewrite y = f(x) as +y =W (ℓ)g(W (ℓ−1)g(· · · g(W (0)x + b(0)) + · · · ) + b(ℓ−1)) + b(ℓ) + x +=W (ℓ)g(W (ℓ−1)g(· · · g(W (0)x + b(0)) + · · · ) + b(ℓ−1)) + b(ℓ) ++ Img(Img(· · · g(Imx) + · · · )) + (−Im)g(Img(· · · g(−Imx) + · · · )) +=(W (ℓ), Im, −Im)g( +� +� +W (ℓ−1) +Im +−Im +� +� g(· · · g( +� +� +W (0) +Im +−Im +� +� x + +� +� +b(0) +0m +0m +� +�) + · · · ) ++ +� +� +b(ℓ−1) +0m +0m +� +�) + b(l). +(27) +Here, Im ∈ Rm×m is an identity matrix, and 0m ∈ Rm is a zero vector. If we denote +W ′(0) = +� +� +W (0) +Im +−Im +� +� , W ′(ℓ) = (W (ℓ), Im, −Im), +W ′(j) = +� +� +W (j) +Im +−Im +� +� for j = 1, 2, · · · , ℓ − 1, +b′(k) = +� +� +b(k) +0m +0m +� +� for k = 0, 1, · · · , ℓ − 1, and b′(ℓ) = b(ℓ), +(28) +then the function +y = W ′(ℓ)g(W ′(ℓ−1)g(· · · g(W ′(0)x + b′(0)) + · · · ) + b′(ℓ−1)) + b′(ℓ) +(29) +is a ReLU MLP with ℓ layers. +Structurally Invertible Networks. It is interesting to consider how our algorithm would per- +form when the network under study is invertible by architectural construction (e.g. an invertible +ResNet (“i-ResNet”, Behrmann et al. (2019)). Then there is only the trivial solution to the MILP in +(9) for any r > 0 (two identical points). What we can do in such cases is to request a certificate of +guarantee that we are sufficiently far from noninvertibility boundaries – e.g. by a threshold larger +than, say, 106. This is suggestive of global invertibility of the i-ResNet, and serves as a sanity check +of the algorithm. +Computational Effort. In general, several key factors impact the computational time of the +MILP: the input dimension n0, the number of layers ℓ, the total number of neurons �ℓ +i=1 ni, and +the radius parameter r. Because a multi-layer network can be approximated to desired accuracy by +a single-layer network with enough neurons, we will perform our experiment with a single-layer +perceptron (ℓ = 1) and observe the dependence of the running time on n0, n1 and r by optimizing +22 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +starting from multiple randomly-generated i-ResNets. To reduce the influence of difficult i-ResNet +parameters that might cause the optimizer to stall, diverge, converge very slowly, or (of most con- +cern) halt by our 30-minute timeout, we track the median of the running times for replicate experi- +ments. See Figure A.2 for these results. +5.0 +7.5 +10.0 +12.5 +15.0 +17.5 +20.0 +Radius +10 +1 +100 +101 +102 +103 +Time(s) +n0 = 4, n1 = 10 +n0 = 6, n1 = 10 +n0 = 8, n1 = 10 +5.0 +7.5 +10.0 +12.5 +15.0 +17.5 +20.0 +Radius +n0 = 6, n1 = 10 +n0 = 6, n1 = 20 +n0 = 6, n1 = 50 +Figure A.2: Running time of the algorithm on a single-layer invertible ResNet as the network size varies. +We observe that the n0 hyperparameter has a greater impact on the running time than the n1 hyper- +parameter. +Appendix B. Proof of Theorems and Corollaries +B.1. Proposition Regarding Solutions to Problem 1 and Problem 2 +Proposition +For a given function f : Rm �→ Rm and a point xc ∈ Rm, if r and R are optimal +solutions to problems 1 and 2 respectively, then we must have r ≤ R. +Consider a point x ∈ Bq(xc, r)\{xc}. Since f is invertible on Bq(xc, r), we must have f(x′) ̸= +f(x) for all x′ ∈ Bq(xc, r) \ {x}. In particular, by choosing x = xc, we have f(x′) ̸= f(xc) for all +x′ ∈ Bq(xc, r) \ {x}. Thus, we must have r ≤ R. +B.2. Proof of Theorem 1 +Theorem Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set. Consider +the following optimization problem, +p⋆ ←max +∥x − y∥ +subject to x, y ∈ B, +f(x) = f(y). +(30) +Then f is invertible on B if and only if p⋆ = 0. +23 + +CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING +Suppose f is invertible on B. Then for all x, y ∈ B for which f(x) = f(y), we must have +x = y. Therefore, the objective function for Problem 1 is zero on the feasible set. Hence, p⋆ = 0. +Conversely, suppose p⋆ = 0. Then x = y for all x, y ∈ B such that f(x) = f(y), hence invertibility. +B.3. Proof of Theorem 2 +Theorem +Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set. Suppose +xc ∈ B. Consider the following optimization problem, +P ⋆ ← max +∥x − xc∥ +subject to x ∈ B, +f(x) = f(xc). +(31) +Then we have f(x) ̸= f(xc) for all x ∈ B \ {xc} if and only if P ⋆ = 0. +Suppose f(x) ̸= f(xc) for all x ∈ B \{xc}. Then, the only feasible point in the optimization of +Problem 2 is x = xc. Hence, P ⋆ = 0. Conversely, start by assuming P ⋆ = 0. Suppose there exists +a x′ ∈ B \ {xc} such that f(x′) = f(xc). Then, we must have 0 < ∥x′ − xc∥ ≤ P ⋆ = 0, which is +a contradiction. Therefore, we must have f(x) ̸= f(xc) for all x ∈ B \ {xc}. +B.4. Proof of Theorem 4 +Theorem +Let f1 : Rm → Rn, f2 : Rm → Rn be two continuous functions and B ⊂ Rm be a +compact set. Consider the following optimization problem, +p⋆ +12 ← max +∥f2(x(1)) − f2(x(2))∥ +subject to x(1), x(2) ∈ B, +f1(x(1)) = f1(x(2)). +(32) +Then (a) f2 is a function of f1 on B if and only if (b) p⋆ +12 = 0. +We first set up a definition (with a slight abuse of notation) of preimage set to simplify our proof. +Definition 8 For a given function f : X �→ Y, X ⊆ Rm, Y ⊆ Rn, the preimage of y ∈ Y is +f−1(y) = {x ∈ X | f(x) = y}. +We then prove the following theorem. +Theorem 9 For two functions fi : X �→ Yi, X ⊆ Rm, Yi ⊆ Rn, i = 1, 2, we have (a) output of f2 +is a function of output of f1 if and only if (c) output of f2 is constant over the preimage set f−1 +1 (y1) +for all y1 ∈ Y1. +Proof We will show the equivalence of (a) and (c). +(c) ⇒ (a): If f−1 +1 (y1) is a singleton {x1}, then f2(x1) = y2 ∈ Y2 is the only value correspond- +ing to y1. Otherwise, we could arbitrarily choose two different values xA, xB ∈ f−1 +1 (y1), and we +must have f2(xA) = f2(xB) = y2 ∈ Y2. Therefore, we can find a unique y2 ∈ Y2 that corresponds +to the given y1, which infers the existence of a mapping from Y1 to Y2. +(a) ⇒ (c): We prove this by contradiction. Suppose f2 is a function of output of f1, and +∃y1 ∈ Y1 and ∃xA, xB ∈ f−1 +1 (y1) such that f2(xA) ̸= f2(xB) (i.e. f2 is constant over f−1 +1 (y1)). +Therefore, we can find a y1 ∈ Y1 simultaneously corresponding to two different values f2(xA) and +f2(xB) in Y2, showing the contradiction with (a). +It is not hard to show (b) “p∗ +12 = 0” in (32) is equivalent with the statement that f2(x) is constant +for ∀x ∈ f−1 +1 (f1(x)), which is just rephrasing of (c) by denoting y1 = f1(x), and therefore, we +show the equivalence of (a) and (b). +24 + diff --git a/7NFKT4oBgHgl3EQfUS2Q/content/tmp_files/load_file.txt b/7NFKT4oBgHgl3EQfUS2Q/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6ed4f177c237e27c8124f6521752d12455f2494c --- /dev/null +++ b/7NFKT4oBgHgl3EQfUS2Q/content/tmp_files/load_file.txt @@ -0,0 +1,965 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf,len=964 +page_content='ArXiv 1–24 Certified Invertibility in Neural Networks via Mixed-Integer Programming Tianqi Cui TCUI3@JHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='EDU Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA Thomas Bertalan TOM@TOMBERTALAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='COM Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA George Pappas PAPPASG@SEAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='UPENN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='EDU Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA Manfred Morari MORARI@SEAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='UPENN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='EDU Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA Yannis Kevrekidis YANNISK@JHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='EDU Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA Mahyar Fazlyab MAHYARFAZLYAB@JHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='EDU Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA Abstract Neural networks are notoriously vulnerable to adversarial attacks – small imperceptible perturba- tions that can change the network’s output drastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In the reverse direction, there may exist large, meaningful perturbations that leave the network’s decision unchanged (excessive invariance, nonivertibility).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We study the latter phenomenon in two contexts: (a) discrete-time dynamical sys- tem identification, as well as (b) calibration of the output of one neural network to the output of another (neural network matching).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We characterize noninvertibility through the lens of mathemat- ical optimization, in which the global solution quantifies the “safety” of the network predictions: their distance from the noninvertibility boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For ReLU networks and Lp norms (p = 1, 2, ∞), we formulate these optimization problems as mixed-integer programs (MIPs) that apply to neural network approximators of dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We also discuss the applicability of our results to invertibility certification in transformations between neural networks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' at different levels of pruning).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Introduction Despite achieving high performance in a variety of classification and regression tasks, neural net- works are not always guaranteed to satisfy certain desired properties after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A prominent example is adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Neural networks can be overly sensitive to carefully designed input perturbations (Szegedy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2013)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This intriguing property holds in the reverse direction too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In classification problems, neural networks can also be excessively insensitive to large pertur- bations, causing two semantically different inputs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', images) to be classified in the same category (Jacobsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Indeed, a fundamental trade-off has been shown between adversarial ro- bustness and excessive invariance (Tram`er et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2020)), which is mathematically related to the noninvertibility of the map defined by the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' © T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Cui, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Bertalan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Pappas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Morari, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kevrekidis & M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Fazlyab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='11783v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='LG] 27 Jan 2023 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING To mitigate noninvertibility, and hence excessive invariance, one can consider invertible-by- design architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Invertible neural networks (INNs) have been used to design generative models (Donahue and Simonyan (2019)), implement memory-saving gradient computation (Gomez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)), and solve inverse problems (Ardizzone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' However, commonly-used INN ar- chitectures suffer from exploding inverses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' in this paper, we therefore consider the problem of cer- tifying the (possible) nonivertibility of conventional neural networks after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Specifically, we study two relevant invertibility problems: (i) local invertibility of neural networks: given a dynami- cal system whose time-τ map is parameterized by a neural network, we verify whether it is locally invertible around a certain input (or trajectory) and compute the largest region of local invertibil- ity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' and (ii) local invertibility of transformations between neural networks: we certify whether two (assumed “equivalent”) neural networks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', related through pruning) can be transformed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' cal- ibrated) to each other locally via an invertible transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We develop mathematical tools based on mixed-integer linear/quadratic programming for the characterization of noninvertibility that are applicable to both (a) neural network approximators of dynamics, as well as to (b) transformations between neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Related work Noninvertibility in neural networks was studied in the 1990s (Gicquel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (1998);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Rico-Martinez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (1993));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' more recently, several papers focus on the global invertibility property in neural networks (see Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Teshima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' MacKay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Jaeger (2014)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Analyzing invertibility of neural networks (Behrmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018)) and constructing invertible architectures arises in many contexts, such as generative modeling (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)), inverse problems (Ardizzone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)) or probabilistic inference (Radev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2020)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Neural networks invertible by design have been developed for these applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Some of the these networks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' RevNet (Gomez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)), NICE (Dinh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2015)), real NVP (Dinh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017))) partition the input domains and use affine or coupling transformations as the forward pass, keeping the Jacobians (block-)triangular with nonzero diagonal elements, resulting in nonzero determinants;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' others, like i-ResNet (Behrmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)) have no analytical forms for the inverse dynamics, yet their finite bi-Lipschitz constants can be derived: both methods can guar- antee global invertibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A comprehensive analysis is found in (Behrmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' However, a theoretical understanding of the expressiveness of these architectures, as well as of their universal approximation properties, is still incomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Compared to standard networks like multi-layer perceptrons (MLPs) or convolutional neural networks (CNNs), the novel invertible neural networks (INNs) become computationally demanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Neural ODE (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018)) use an alternative method to compute gradients for backward propagation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' i-ResNet (Behrmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)) has restrictions on the norm of every weight matrix to be enforced during the training pro- cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In most cases, the input domain of interest is a small subset of the whole space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For example, the grey-scale image domain in computer vision problems is [0, 1]H×W (where H and W are height and width of images), and it is unnecessary to consider the whole space RH×W .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We thus focus on local invertibility: how do we know if our network is invertible on a given finite domain, and if not, how do we quantify noninvertibility?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Beyond classification problems, noninvertibility can also lead to catastrophic consequences in regression, and more specifically in dynamical systems prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The flow of smooth differential equations is invertible when it exists;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' yet traditional numerical integrators used to approximate them can be noninvertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Neural network approximations of the corresponding time-τ map also suffer 2 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING from this potential pathology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In this paper, we initially study noninvertibility in the context of dynamical systems predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Local invertibility of dynamical systems and neural networks Continuous-time dynamical systems, in particular autonomous ordinary differential equations (ODEs) have the form dX(t)/dt = f(X(t)), X(t = t0) = X0, where X(t) ∈ Rm are the state variables of interest;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f : Rm �→ Rm relates the states to their time derivatives and X0 ∈ Rm is the initial con- dition at t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' If f is uniformly Lipschitz continuous in X and continuous in t, the Cauchy-Lipschitz theorem guarantees the existence and uniqueness of the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In practice, we observe the states X(t) at discrete points in time, starting at t0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For a fixed timestep τ ∈ R+, and ∀n ∈ N, tn = nτ denotes the n-th time stamp, and Xn = X(t = tn) the corresponding state values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Now we will have: Xn+1 := F(Xn) = Xn + � tn+1 tn f(X(t))dt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Xn = F −1(Xn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (1) This equation also works as the starting point of many numerical ODE solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the time-τ map in (1), the inverse function theorem provides a sufficient condition for its invertibility: If F is a continuously differentiable function from an open set B of Rm into Rm, and the Jacobian determinant of F at p is non-zero, then F is invertible near p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Thus, if we define the noninvertibility locus as the set J0(F) = {p ∈ B : det(JF (p)) = 0}, then the condition J0(F) = ∅ guarantees global invertibility of F (notice that this condition is not necessary: the scalar function F(X) = X3 provides a counterexample).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' If F is continuous over B but not everywhere differentiable, then the definition of J0 set should be altered to: J0(F) = {p ∈ B : ∀N0(p), ∃ p1, p2 ∈ N0(p), p1 ̸= p2, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' det(JF (p1)) det(JF (p2)) ≤ 0} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', (2) the set of points where the determinant discontinuously changes sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Numerical integrators are (often) noninvertible Numerically approximating the finite integral in (1) can introduce noninvertibility in the transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here is a simple one-dimensional illustra- tive ODE example: dX/dt = f(X) = X2 + bX + c, X(t = 0) = X0, where b, c ∈ R are two fixed parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The analytical solution (1) is invertible;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' however a forward-Euler discretization with step τ gives Xn+1 = F(Xn) = Xn + τ(X2 n + bXn + c) ⇒ τX2 n + (τb + 1)Xn + (τc − Xn+1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (3) Given a fixed Xn+1, Equation (3) is quadratic w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' this determines the local invertibility of F based on ∆ = (τb + 1)2 − 4τ(τc − Xn+1): no real root if ∆ < 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' one real root with multiplicity 2 if ∆ = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' and two distinct real roots if ∆ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In practice, one uses small timesteps τ ≪ 1 for accuracy/stability, leading to the last case: there will always exist a solution Xn close to Xn+1, and a second preimage, far away from the region of our interest, and arguably physically irrelevant (this second Xn → −∞ as τ → 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' On the other hand, as τ grows, the two roots move closer to each other, J0(F) moves close to the regime of our simulations, and noninvertibility can have visible implications on the predicted dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Thus, choosing a small timestep in explicit integrators guarantees desirable accuracy, and simultaneously practically mitigates noninvertibility pathologies in the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 3 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Invertibility in transformations between neural networks Training two neural networks for the same regression or classification task practically never gives identical network parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Numer- ous criteria exist for comparing the performance of different models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' accuracy in classification, or mean-squared loss in regression).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here we explore whether two different models can be cal- ibrated to each other (leading to a de facto implicit function problem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Extending our analysis provides invertibility guarantees for the transformation from the output of network 1 to the output of network 2 (and vice versa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Invertibility certification of neural networks and of transformations between them Here we pose the verification of local invertibility of continuous functions as an optimization prob- lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We then show that for ReLU networks, this leads to a mixed-integer linear/quadratic program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For an integer q ≥ 1, we denote the Lq-ball centered at xc by Bq(xc, r) = {x ∈ Rn | ∥x−xc∥q ≤ r} (the notation also holds when q → +∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Problem 1 (Local Invertibility of NNs) Given a neural network f : Rm �→ Rm and a point xc ∈ Rm in the input space, we want to find the largest radius r > 0 such that f is invertible on Bq(xc, r), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', f(x1) ̸= f(x2) for all x1, x2 ∈ Bq(xc, r), x1 ̸= x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Another relevant problem is to verify whether, for a particular point, a nearby point exists with the same forward image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This is of particular interest in assessing invertibility of discrete-time dynamical systems around a given trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We formally state the problem as follows: Problem 2 (Pseudo Local Invertibility of NNs) Given a neural network f : Rm �→ Rm and a point xc ∈ Rm in the input space, we want to find the largest radius R > 0 such that f(x) ̸= f(xc) for all x ∈ Bq(xc, R), x ̸= xc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' If r and R are the optimal radii in problems 1 and 2 respectively, we must have r ≤ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For Problem 1, the ball Bq(xc, r) just “touches” the J0 set;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' for Problem 2, the ball Bq(xc, R) extends to the “other” closest preimage of f(xc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Figure 1 illustrates both concepts in the one-dimensional case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the scalar function y = f(x) and around a particular input xc, we show the nearest bounds of local invertibility and pseudo invertibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The points Q1 = (xQ1, yQ1) and Q2 = (xQ2, yQ2) are the two closest turning points (elements of the J0 set) to the point C = (xc, yc);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f is uniquely invertible (bi-Lipschitz) on the open interval (xQ1, xQ2), so that the optimal solution to Problem 1 is: r = min{|xQ1 − xc|, |xQ2 − xc|} = |xQ1 − xc|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Noting that M1 = (xM1, yM1) and M2 = (xM2, yM2) are the two closest points that have the same y-coordinate as the point C = (xc, yc), the optimal solution to Problem 2 is R = min{|xM1 − xc|, |xM2 − xc|} = |xM1 − xc|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 4 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Figure 1: Illustration of problems 1 (distance to invertibility boundary, red) and 2 (distance to pseudo invert- ibility boundary, blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We now state our first result, posing the local invertibility of a function (such as a neural net- work) as a constrained optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Theorem 1 (Local Invertibility of Continuous Functions) Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, p⋆ ←max ∥x1 − x2∥ subject to x1, x2 ∈ B, f(x1) = f(x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (4) Then f is invertible on B if and only if p⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Theorem 2 (Pseudo Local Invertibility) Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose xc ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, P ⋆ ← max ∥x − xc∥ subject to x ∈ B, f(x) = f(xc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (5) Then we have f(x) ̸= f(xc) for all x ∈ B \\ {xc} if and only if P ⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Note that by adding the equality constraints x = x1, xc = x2 to the optimization problem (4), we obtain the optimization problem (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Hence, we will only focus on (4) in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Invertibility certification of ReLU networks via mixed-integer programming We now show that for a given ball B∞(xc, r) in the input space, and piecewise linear networks with ReLU activa- tions, the optimization problem in (4) can be cast as an MILP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A single ReLU constraint y = max(0, x) with pre-activation bounds x ≤ x ≤ ¯x can be equivalently described by the following mixed-integer linear constraints (Tjeng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)): y = max(0, x), x ≤ x ≤ ¯x ⇐⇒ {y ≥ 0, y ≥ x, y ≤ x − x(1 − t), y ≤ ¯xt, t ∈ {1, 0}}, (6) where the binary variable t ∈ {1, 0} is an indicator of the activation function being active (y = x) or inactive (y = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Now consider an ℓ-layer feed-forward fully-connected ReLU network with input x given by the following recursions, x(k+1) = max(W (k)x(k) + b(k), 0) for k = 0, · · · , ℓ − 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f(x(0)) = W (ℓ)x(ℓ) + b(ℓ), (7) 5 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING where x(k) ∈ Rnk gives the input to the (k + 1)-th layer (specifically, we have x = x(0) and n0 = m), W (k) ∈ Rnk+1×nk, b(k) ∈ Rnk+1 are the weight matrices and bias vectors of the affine layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We denote n = �ℓ k=1 nk the total number of neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose l(k) and u(k) are known elementwise lower and upper bounds on the input to the (k + 1)-th activation layer, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', l(k) ≤ W (k)x(k) + b(k) ≤ u(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then the neural network equations are equivalent to a set of mixed-integer constraints as follows: x(k+1) = max(W (k)x(k) + b(k), 0) ⇔ � � � � � x(k+1) ≥ W (k)x(k) + b(k) x(k+1) ≤ W (k)x(k) + b(k) − l(k) ⊙ (1nk+1 − t(k)) x(k+1) ≥ 0, x(k+1) ≤ u(k) ⊙ t(k), (8) where t(k) ∈ {1, 0}nk+1 is a vector of binary variables for the (k + 1)-th activation layer and 1nk+1 denotes vector of all 1’s in Rnk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We note that the element-wise pre-activation bounds {l(k), u(k)} can be precomputed by, for example, interval bound propagation or linear programming, assuming known bounds on the input of the neural network (Weng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Hein and Andriushchenko (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Wong and Kolter (2018)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Since the state-of-the-art solvers for mixed-integer programming are based on branch & bound algorithms (Land and Doig (1960);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Beasley (1996)), tight pre-activation bounds will allow the algorithm to prune branches more efficiently and reduce the total running time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Local invertibility certificates via mixed-integer programming Having represented the neural net- work equations by mixed-integer constraints, it remains to encode the objective function ∥x1 − x2∥ of (4) as well as the set B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We assume that B is an L∞ ball around a given point xc, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', B = B∞(xc, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Furthermore, for the sake of space, we only consider L∞ norms for the objective func- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Specifically, consider the equality w = ∥x1 − x2∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This equality can be encoded as mixed- integer linear constraints by introducing 2n0 mutually exclusive indicator variables,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' which leads to the following MILP: p⋆ ← max w subject to ∥x1 − xc∥∞ ≤ r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ∥x2 − xc∥∞ ≤ r (I) : � � � � � (x1 − x2) ≤ w1n0 ≤ (x1 − x2) + 4r(1n0 − f) −(x1 − x2) ≤ w1n0 ≤ −(x1 − x2) + 4r(1n0 − f′) f + f′ ≤ 1n0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 1⊤ n0(f + f′) = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f′ ∈ {0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 1}n0 (II) : W (ℓ)x(ℓ) 1 = W (ℓ)x(ℓ) 2 (9) for k = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' · · · ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ℓ − 1 : (III) : � � � � � x(k+1) 1 ≥ W (k)x(k) 1 + b(k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' x(k+1) 2 ≥ W (k)x(k) 2 + b(k) x(k+1) 1 ≤ W (k)x(k) 1 + b(k) − l(k) ⊙ (1 − t(k)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' x(k+1) 2 ≤ W (k)x(k) 2 + b(k) − l(k) ⊙ (1 − t(k)) x(k+1) 1 ≥ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' x(k+1) 2 ≥ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' x(k+1) 1 ≤ u(k) ⊙ t(k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' x(k+1) 2 ≤ u(k) ⊙ t(k);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' t(k), s(k) ∈ {0, 1}nk+1, where the set of constraints in (I) model the objective function ∥x1−x2∥∞, and the set of constraints (III) encode the network x(k+1) 1 = max(W (k)x(k) 1 +b(k), 0) and x(k+1) 2 = max(W (k)x(k) 2 +b(k), 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The constraint (II) enforces that f(x1) = f(x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This optimization problem (4) has 2(n0 + n) integer variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 6 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Remark 3 If we instead use the ℓ2 norm both for the objective function and the ball B2(xc, r), we will arrive at a mixed-integer quadratic program (MIQP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' However, (9) remains an MILP if we change them to ℓ1 norms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Largest region of invertibility For a fixed radius r ≥ 0, the optimization problem (9) either verifies whether f is invertible on B∞(xc, r) or it finds counterexamples x1 ̸= x2 such that f(x1) = f(x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Thus, we can find the maximal r by performing a bisection search on r (Problem 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' To close this section, we consider the problem of invertibility certification in transformations between two functions (and in particular two neural networks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Problem 3 (Transformation Invertibility) Given two functions f1, f2 : Rm → Rm and a partic- ular point xc ∈ Rm in the input space, we would like to find the largest ball Bq(xc, r) over which the output of f2 is a function of the output of f1 (and vice versa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Theorem 4 Let f1 : Rm → Rn, f2 : Rm → Rn be two continuous functions and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, p⋆ 12 ← max ∥f2(x1) − f2(x2)∥ subject to x1, x2 ∈ B, f1(x1) = f1(x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (10) Then the output of f2 is a function of the output of f1 on B if and only if p⋆ 12 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Similar to Problem 1, we can pose Problem 3 as a mixed-integer program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Furthermore, we can also define p⋆ 21, whose zero value determines whether output of f1 is a function of output of f2 over B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' It is straightforward to see that p⋆ 12 = p⋆ 21 = 0 if and only if output of f2 is an invertible function of output of f1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Numerical Experiments We now present experiments with ReLU multi-layer perceptrons (MLPs) in both (a) regression problems, and also in (b) transformations between two ReLU networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 1D Example We use a 1-10-10-1 randomly generated fully-connected neural network f(x) with ReLU activations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We find the largest interval around the points x = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' −1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='3 on which f is invertible (Problem 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' we also find the largest interval around the point x = −1 for which no other interior points map to f(−1) (Problem 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The results are plotted in Figure 2, where intervals in red and blue respectively represent the optimal solutions for the two problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The largest certified radii are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='157, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='322 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='214 for Problem 1 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='553 for Problem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 7 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Figure 2: Solutions to Problem 1 (left, red) and Problem 2 (right, blue) for the MLP corresponding to a randomly-generated ReLU network (see text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 2D Example: a disrete-time integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The Brusselator (Tyson (1973)) is a system of two ODEs for the two variables (x, y), depending on the parameters (a, b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' it describes oscillatory dynamics in a theoretical chemical reaction scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We use its forward-Euler discretization with step τ, xn+1 = xn + τ(a + x2 nyn − (b + 1)xn), yn+1 = yn + τ(bxn − x2 nyn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (11) Rearranging and eliminating yn+1 in (11) we obtain: τ(1 − τ)x3 n + τ(τa − xn+1 − yn+1)x2 n + (τb + τ − 1)xn + (xn+1 − τa) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (12) Equation (12) is a cubic for xn given (xn+1, yn+1) when τ ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' By varying the parameters a, b and τ, we see the past states (xn, yn)T of point (xn+1, yn+1)T (also called “inverses” or “preimages”) may be multi-valued, so that this discrete-time system is, in general, noninvertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We fix a = 1 and consider how inverses will be changing (a) with b for fixed τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' and (b) with τ, for fixed b = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We are interested in training a neural network that learns this time-τ mapping;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' for a fixed set of parameter values, this is a network from 3D to 2D: (xn+1, yn+1)T ≈ N(xn, yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' p)T , where p ∈ R is the parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The network dynamics will be parameter-dependent if we set p ≡ b, or timestep-dependent if p ≡ τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The first layer of such an MLP reads W (0) � � xn yn p � � + b(0) = (W (0)(e1 + e2)) �xn yn � + (pW (0)e3 + b(0)), (13) where e1,2,3 ∈ R3 are indicator vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here we trained two separate MLPs, ione with b and one with τ dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For fixed p (either b or τ) each of these two networks N can be thought of as a MLP mapping from R2 to R2, by slightly modifying the weights and biases in the first linear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Parameter-dependent Inverses It is useful to start with a brief discussion of the dynamics and noninvertibilities in the ground-truth system (see Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider a state located on the invariant circle (IC, shown in orange), for we therefore know there exists at least one preimage also on this IC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Figure 3 we indeed see that every point on the IC has three preimages: one still on the IC, and two extra inverses (in green and purple) after one iteration, all three loops map to the orange one, 8 4 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 0 c0 4 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 0 cCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING and then remain forward invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The phase space, upon iteration, folds along the two branches of the J0 curve (sets of red points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For lower values of b, these three closed loops do not intersect each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' As b increases the (orange) attractor will become tangent to, and subsequently intersect J0, leading to an interaction with the other (green) preimage branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' At this point the dynamics predicted by the network become unphysical (beyond just inaccurate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Figure 3: Attractors (and their multiple inverses) for several parameter values of the discrete Brusselator neural network for τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Notice the relative positions of the J0 curves (red), the “main” preimage locus (yellow), and the “extra” preimages (green, purple).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' When the attractor starts interacting with the J0 curve and, therefore, with these extra preimages, the dynamic behavior degenerates quantitatively and qualitatively (see also Rico-Martinez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (1993)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' After convergence of training, we employ our algorithm to obtain noninvertibility certificates for the resulting MLP, and plot results for b = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1 in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Figure 4, we arbitrarily select one representative point, marked by triangle (△), on the attractor (the orange invariant circle);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' we know there exists one inverse also located on the attractor, see the nearby cross (+);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' we call this the primal inverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Our algorithm will produce two regions for this point, one for each of our problems (squares of constant L∞ distance in 2D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' As a sanity check, we also compute the J0 sets (the red point), as well as a few additional inverses, beyond the primal ones with the help of a numerical root solver and automatic differentiation (Baydin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Clearly, the smaller square neighborhood just hits the J0 curve, while the larger one extends to the closest non-primal inverse of the attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Timestep-dependent Inverses In the right two subfigures of Figure 4, we explore the effect of varying the time horizon τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We compare a single Euler step of the ground truth ODE to the MLP approximating the same time τ map, and find that, for both of them, smaller time horizons lead to larger regions of invertibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 9 (a,b)= (1, 2) (a,b)= (1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5) (a,b)= (1, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2) 『, F-1() f-1(r) f-1(r)" 0 X X xCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING 5 0 5 10 x 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 y J0 Attractor Image Inverses 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 x 4 2 0 2 4 6 y the Brusselator Integrator J0( = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='05) J0( = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='30) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 x the Brusselator Network Figure 4: Left: illustration of our solution to Problems 1 and 2 for the Brusselator network with (a, b) = (1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For a particular reference point on the attractor, we show the neighborhoods found by our algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' They clearly locate the closest point on the J0 curve / the closest “extra preimage” of the point of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Last two: plots of J0 curves at different τ with (a, b) = (1, 2), for both the Euler integrator and our Brusselator ReLU network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Small timesteps lead to progressively more remote J0 curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Notice also the piecewise linear nature of the J0 curve for the ReLU network;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' its accurate computation constitutes an interesting challenge by itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Network Transformation Example: Learning the Van der Pol Equation Here, to test our al- gorithm on the problem of transformations between networks 3, we trained two networks on the same regression task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Our data comes from the 2D Van der Pol equation dx1/dt = x2, dx2/dt = µ(1 − x2 1)x2 − x1, where the input and output are the initial and final states of 1000 short solution trajectories of duration 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2 for µ = 1, when a stable limit cycle exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The initial states are uni- formly sampled in the region [−3, 3]×[−3, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The neural network A used to learn the time-τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2 map is a 2-32-32-2 MLP, while the neural network B is a retrained sparse version of A, where half of the weight entries are pruned (set to zero) based on Zhu and Gupta (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' To visualize the per- formances of the two networks, two trajectories, generated by respectively iterating each network function for a fixed number of times starting from a common given initial state have been plotted in the left subplot of Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The ODE solution trajectory starting at the same initial state with same overall time duration is also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We see that both network functions A and B exhibit long term oscillations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' the shapes of both attractors appear to only have small visual differences from the true ODE solution (the red curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' These two network functions were then used to illustrate the algorithm for Problem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here we chose a center point xc = (0, 0)T , computed and plotted the mappable regions (the regions over which there is a one-to-one mapping between the output of one network and the output of the other, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' where one network can be calibrated to the other).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This was done for two subcases (see the right subfigure of Figure 5): (a) where the output of network B is a function of the output of network A (the square with white bounds centered at the red point, radius 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820), and vice versa, where the output of network A is a function of the output of the network B (the square with black bounds centered at the red point, radius 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6484).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This also gives us the “common” region (the interior of the white square) where both networks can be calibrated to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For validation we also computed the Jacobian values of network A and network B on every grid point of the input domain, and shown that the white square touches the J0 curve of network A, while the black square touches the J0 curve of network B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Inside the black square the Jacobian of network B remains positive, so that network B is invertible (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' there exists a mapping from fB(x) to x, or equivalently, f−1 B (x));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 10 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING therefore we can find the mapping from fB(x) to fA(x) by composing the mapping from fB(x) to x with the mapping from x to fA(x) (the function fA(x) itself).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The size of the white square can be similarly rationalized, validating our computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 2 0 2 x1 3 2 1 0 1 2 3 x2 ode solution NN A (original) NN B (pruned) 5 0 5 x1 4 2 0 2 4 x2 rAB = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 (white), rBA = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6484 (black) det(JA) < 0, det(JB) < 0 det(JA) < 0, det(JB) > 0 det(JA) > 0, det(JB) < 0 det(JA) > 0, det(JB) > 0 Figure 5: Left: Trajectories of the ODE solution for the Van der Pol system (red), and their discrete-time neural network approximations (blue and green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' All three trajectories begin at the same initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' While the ODE solution curve is smooth due to its continuous-time nature, the others are just straight line segments connecting consecutive states (discrete-time dynamics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' However, it is clear that all three systems have visu- ally nearby long-time dynamic attractors, corroborating the good performance of the network and its pruned version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Right: visualization of MILP computation results, along with signs of Jacobian values of networks on the grid points of the input domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here, the center of the region is shown in red, while the white and black boundaries quantify the mappable region between outputs of network A and network B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Sparsity 40 % 50 % 60 % Network B B1 B2 B3 B4 B5 B6 B7 B8 B9 rAB 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820 rBA 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='4609 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1055 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='8555 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6484 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6523 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='8203 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6328 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='9727 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5547 Table 1: The radii of the mappable regions between the original network A and its pruned versions B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' rAB relates to the region within which fB(x) is a function of fA(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' As a sanity check, we consructed eight more pruned networks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' two of them have 50% sparsity (networks B5 and B6), three have 40% sparsity (networks B1, B2 and B3) and the others have 60% sparsity (networks B7, B8 and B9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Above we discussed network B4 For each pruned network, we computed the radii of the regions of interest (aka rAB and rBA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The results are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' All pruned networks {Bi} share the same radii rAB, consistent with the invertibility of A itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Since rA = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0820, A is invertible in the ball we computed, and the existence of the mapping fA(x) �→ fB(x) follows by composition of fA(x) �→ x and x �→ fB(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Based on these few computational experiments one might very tentatively surmise a trend: the higher the pruning (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 60%) the larger the invertibility guarantee for the pruned network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In our work the input and output 11 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING dimensions are the same (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' m = n in Problem 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' However, this condition is not necessary, and our algorithm can be conceptually extended to classification problems, where in general m ≫ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Conclusions In this paper, we revisited noninvertibility issues that arise in discrete-time dynamical systems inte- grators) as well as in neural networks that perform approximations of the same (time-series related) task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We argued that such noninvertibility may have dramatic pathological consequences, going beyond just inaccuracies, in the dynamics predicted by the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We also extended the analysis to transformations between different neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We formulated three problems that provide a quantifiable assessment of “local” invertibility for any given, arbitrarily selected input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Specifically, for functions like MLPs with ReLU activations, these problems were formulated as mixed-integer programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We then performed experiments on regression tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' An extension of our algorithm to ResNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' can be found in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Future directions include developing structure-exploiting methods to globally solve these MIPs more efficiently, and for larger networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' On the other hand, given that convolution and aver- age pooling are linear operations, while max pooling is piecewise linear, it is natural to adapt our algorithms to convolutional neural networks like AlexNet (Krizhevsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)) or VGG (Si- monyan and Zisserman (2015)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The successful application of our algorithm to ResNet architectures (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2016)) holds promise for applicability also to recursive architectures (Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' E (2017)), such as fractal networks (Larsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)), poly-inception networks (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2016)), and RevNet (Gomez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We are working on making the algorithm practical for continuous differentiable activations like tanh or Swish (Ramachandran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2017)), and for other piecewise activations like gaussian error linear units (GELUs, Hendrycks and Gimpel (2016)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We are particularly interested in the case when the input and output domains are of different dimension (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', classifiers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' References R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Adomaitis and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kevrekidis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Noninvertibility and the structure of basins of attraction in a model adaptive control system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Journal of Nonlinear Science, 1:95–105, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Lynton Ardizzone, Jakob Kruse, Sebastian Wirkert, Daniel Rahner, Eric W Pellegrini, Ralf S Klessen, Lena Maier-Hein, Carsten Rother, and Ullrich K¨othe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Analyzing inverse problems with invertible neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='04730, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Lynton Ardizzone, Jakob Kruse, Sebastian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Wirkert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Rahner, Eric W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Pellegrini, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Klessen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Maier-Hein, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Rother, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' K¨othe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Analyzing inverse problems with invertible neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ArXiv, abs/1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='04730, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Atılım G¨unes Baydin, Barak A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Automatic differentiation in machine learning: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', 18(1):5595–5637, January 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISSN 1532-4435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Beasley, editor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Advances in Linear and Integer Programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Oxford University Press, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', USA, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISBN 0198538561.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 12 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Jens Behrmann, S¨oren Dittmer, Pascal Fernsel, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Maass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Analysis of invariance and robustness via invertibility of relu-networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ArXiv, abs/1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='09730, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Jens Behrmann, Will Grathwohl, Ricky T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Chen, David Duvenaud, and Joern-Henrik Jacob- sen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Invertible residual networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Kamalika Chaudhuri and Ruslan Salakhutdinov, edi- tors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 573–582.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' PMLR, 09–15 Jun 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='press/v97/behrmann19a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Jens Behrmann, Paul Vicol, Kuan-Chieh Wang, Roger Grosse, and Joern-Henrik Jacobsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Under- standing and mitigating exploding inverses in invertible neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Arindam Banerjee and Kenji Fukumizu, editors, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, volume 130 of Proceedings of Machine Learning Research, pages 1792–1800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' PMLR, 13–15 Apr 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='press/v130/ behrmann21a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Reversible architectures for arbitrarily deep residual neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Sheila A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' McIlraith and Kil- ian Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Weinberger, editors, Proceedings of the Thirty-Second AAAI Conference on Artificial In- telligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2-7, 2018, pages 2811–2818.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' AAAI Press, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='aaai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/ocs/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='php/AAAI/AAAI18/paper/view/16517.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Ricky T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Neural ordinary dif- ferential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS’18, page 6572–6583, Red Hook, NY, USA, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Curran Associates Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Ricky TQ Chen, Jens Behrmann, David Duvenaud, and J¨orn-Henrik Jacobsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Residual flows for invertible generative modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Neural Information Processing Systems, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https: //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/abs/1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='02735.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Laurent Dinh, David Krueger, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' NICE: non-linear independent components es- timation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Workshop Track Proceedings, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/abs/1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='8516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Density estimation using real NVP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' OpenReview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='net, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' net/forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='id=HkpbnH9lx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Jeff Donahue and Karen Simonyan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Large scale adversarial representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Advances in neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Weinan E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A proposal on machine learning via dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Communications in Mathemat- ics and Statistics, 5(1):1–11, 3 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1007/s40304-017-0103-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Dedicated to Professor Chi-Wang Shu on the occasion of his 60th birthday.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 13 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Christos E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Frouzakis, Laura Gardini, Ioannis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kevrekidis, Gilles Millerioux, and Christian Mira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' On some properties of invariant sets of two-dimensional noninvertible maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' International Jour- nal of Bifurcation and Chaos, 07(06):1167–1194, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1142/S0218127497000972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1142/S0218127497000972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Gicquel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Anderson, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kevrekidis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Noninvertibility and resonance in discrete-time neural networks for time-series processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Physics Letters A, 238(1):8–18, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISSN 0375-9601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1016/S0375-9601(97)00753-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='com/science/article/pii/S0375960197007536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Aidan N Gomez, Mengye Ren, Raquel Urtasun, and Roger B Grosse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The reversible residual net- work: Backpropagation without storing activations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Advances in neural information processing systems, 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Deep residual learning for image recog- nition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Matthias Hein and Maksym Andriushchenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Formal guarantees on the robustness of a classifier against adversarial manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 2266–2276, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Dan Hendrycks and Kevin Gimpel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Bridging nonlinearities and stochastic regularizers with gaussian error linear units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' CoRR, abs/1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='08415, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/abs/1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 08415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' J¨orn-Henrik Jacobsen, Jens Behrmann, Richard Zemel, and Matthias Bethge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Excessive invariance causes adversarial vulnerability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='00401, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Jaeger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Controlling recurrent neural networks by conceptors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ArXiv, abs/1403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='3369, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Alex Krizhevsky, Ilya Sutskever, and Geoffrey E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Imagenet classification with deep con- volutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ACM, 60(6):84–90, May 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISSN 0001-0782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1145/3065386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1145/3065386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Land and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Doig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' An automatic method of solving discrete programming prob- lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Econometrica, 28(3):497–520, 1960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISSN 00129682, 14680262.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' jstor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/stable/1910129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Gustav Larsson, Michael Maire, and Gregory Shakhnarovich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Fractalnet: Ultra-deep neural net- works without residuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, vol- ume 80 of Proceedings of Machine Learning Research, pages 3282–3291, Stockholm, Stock- holm Sweden, 10–15 Jul 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='press/v80/ lu18d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 14 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Matthew MacKay, Paul Vicol, Jimmy Ba, and Roger Grosse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Reversible recurrent neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS’18, page 9043–9054, Red Hook, NY, USA, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Curran Associates Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Stefan T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Radev, Ulf K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Mertens, Andreas Voss, Lynton Ardizzone, and Ullrich K¨othe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Bayesflow: Learning complex stochastic models with invertible neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' IEEE Transactions on Neu- ral Networks and Learning Systems, pages 1–15, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1109/TNNLS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='3042395.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Prajit Ramachandran, Barret Zoph, and Quoc V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Swish: a self-gated activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' CoRR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/abs/1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='05941v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Rico-Martinez, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Kevrekidis, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Adomaitis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Noninvertibility in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In IEEE International Conference on Neural Networks, pages 382–386 vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1109/ ICNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='298587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Karen Simonyan and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Very deep convolutional networks for large-scale im- age recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/abs/1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Yang Song, Chenlin Meng, and Stefano Ermon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Mintnet: Building invertible neural networks with masked convolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Larochelle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Beygelzimer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=" d'Alch´e-Buc, E." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Fox, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Garnett, editors, Advances in Neural Information Processing Systems, volume 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Curran As- sociates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='cc/paper/2019/file/ 70a32110fff0f26d301e58ebbca9cb9f-Paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Intriguing properties of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='6199, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Floris Takens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Detecting strange attractors in turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Dynamical Systems and Turbulence, Warwick 1980: Proceedings of a Symposium Held at the University of Warwick 1979/80, pages 366–381, Berlin, Heidelberg, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Springer Berlin Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' ISBN 978-3-540-38945-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1007/BFb0091924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1007/BFb0091924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Takeshi Teshima, Isao Ishikawa, Koichi Tojo, Kenta Oono, Masahiro Ikeda, and Masashi Sugiyama.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Coupling-based invertible neural networks are universal diffeomorphism approximators, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Vincent Tjeng, Kai Xiao, and Russ Tedrake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Evaluating robustness of neural networks with mixed integer programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='07356, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Florian Tram`er, Jens Behrmann, Nicholas Carlini, Nicolas Papernot, and J¨orn-Henrik Jacobsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Fundamental tradeoffs between invariance and sensitivity to adversarial perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Inter- national Conference on Machine Learning, pages 9561–9571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' John J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Tyson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Some further studies of nonlinear oscillations in chemical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The Journal of Chemical Physics, 58(9):3919–3930, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1679748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1679748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 15 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Efficient formal safety analysis of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 6367– 6377, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Tsui-Wei Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Duane Boning, Inderjit S Dhillon, and Luca Daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Towards fast computation of certified robustness for relu networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='09699, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Eric Wong and Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Provable defenses against adversarial examples via the convex outer adversarial polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 5286–5295, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Huan Zhang, Tsui-Wei Weng, Pin-Yu Chen, Cho-Jui Hsieh, and Luca Daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Efficient neural network robustness certification with general activation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In Advances in Neural Infor- mation Processing Systems, pages 4939–4948, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Xingcheng Zhang, Zhizhong Li, Chen Change Loy, and Dahua Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Polynet: A pursuit of structural diversity in very deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' arXiv preprint arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='05725, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Michael Zhu and Suyog Gupta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' To prune, or not to prune: Exploring the efficacy of pruning for model compression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Workshop Track Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' OpenReview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='net, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' URL https://openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='net/forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='id=Sy1iIDkPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 16 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Further Discussions A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Invertibilty in View of Lipschitz Constants One can consider the neural network inversion problem in terms of Lipschitz continuity and the Lipschitz constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Indeed, quantifying invertibility of a neural network (more generally, a function) is intimately connected with its Lipschitz constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Definition 5 (Lipschitz continuity and Lipschitz constant) A function F : B ⊆ Rm �→ Rm is Lipschitz continuous on B if there exists a non-negative constant L ≥ 0 such that ||F(x1) − F(x2)|| ||x1 − x2|| ≤ L, ∀x1, x2 ∈ B, x1 ̸= x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (14) The smallest such L is called the Lipschitz constant of F, L = Lip(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A generalization for Definition 5 is the bi-Lipschitz map defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Definition 6 (bi-Lipschitz continuity and bi-Lipschitz constant) Suppose F : B ⊆ Rm �→ Rm is globally Lipschitz continuous with Lipschitz constant L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Now we define another nonnegative constant L′ ≥ 0 such that L′ ≤ ||F(x1) − F(x2)|| ||x1 − x2|| , ∀x1, x2 ∈ Rm, x1 ̸= x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (15) If the largest such L′ is strictly positive, then (15) shows F is invertible on B due to F(x1) ̸= F(x2) given x1 ̸= x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Moreover, one could easily derive (1/L′) = Lip(F −1), where F −1 is the inverse function of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We also say F is bi-Lipschitz continuous in this case, with bi-Lipschitz constant L∗ = max {L, 1/L′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Structure of Preimages for the Learned Map of the Brusselator Flow As discussed in the main paper, we trained a network to approximate the time-τ Euler map (16) for the Brusselator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The attractor (locus of long-term image points) is a small amplitude, stable invariant circle (IC), the discrete time analog of the ODE stable limit cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We mark four representative points on it (Q, R, S, and T) and divide it into parts A, B1, B2, and C between these points, so as to facilitate the description of the dynamics and its multiple (due to noninvertibility) preimages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The locus of red points (the locus on which the determinant of the Jacobian of the network changes sign, or, in the language of noninvertible systems, the J0 curve) separates state space here into five distinct regions I, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' , V, each with different preimage behavior, as illustrated in Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For smooth maps, like the Brusselator forward Euler discretization or a tanh activation neural network, J0 is the locus of points for which the determinant of the map Jacobian is zero (and therefore, the map is singular).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In those cases, the curve is easy to compute through continuation algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For ReLU activations, however, this locus is nontrivial to compute through algebraic solvers, and piecewise smooth computational techniques or brute force exploration must be used to locate it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' see the inset in Figure, where the color intensity indicates the magnitude, red for positive and blue for negative, of the map Jacobian determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' After we locate the J0 points however, we see that they 17 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING define the I through V (and implicitly, through forward iteration of the J0 curve, regions A through C on the IC): 𝐵1 𝑄 𝑅 𝑆 𝑇 𝑄′′ = 𝑄′′′ 𝑅′′ = 𝑅′′′ 𝑆′′ = 𝑆′′′ 𝑇′′ = 𝑇′′′ I II III IV V 𝐶 𝐵2 𝐴 𝑅′ Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1: Top: Structure of Preimages and (top inset;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' positive is red, and negative is blue) magnitude of the map Jacobian determinant for the Brusselator network with b = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Bottom: Labeling of key representative points and important regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' see text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This is a qualitative rendering of the relevant regions in the top figure, deformed to enhance visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Each point in part A (shown in yellow), has three inverses, located in regions I, II and III respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The “physically meaningful inverse”, the one in III, is contained in the IC itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 18 Attractor Inverses Jo Determinant of Jacobian B1 B2 C IVCERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Points in part C (shown in cyan) similarly have inverses located in regions III, IV and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Finally, we label two segments of the IC, located between the A and C segments, as B1 and B2 (shown in dark green, with solid line and dashed lines, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Points in these portions of the IC only have a single inverse each (that we could find within the picture): the one located on the attractor itself in region III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' It is informative to study the location and behavior of preimages as a phase point is moved along the invariant circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' At the transitions from either Bi part into A (or C), two preimages (initially one preimage with multiplicity two) are born touching the J0 curve, at the junction between I and II (or IV and V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Notice also the “extra preimages” of the points R and Q (R′′, R′′′, Q′′, Q′′′) off the invariant circle, on J0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The physically meaningful preimages (R′, Q′) lie on the invariant circle itself;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' one of them, R′, close to R, in shown in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' As we move further into the A (or C) parts of the attractor, the “extra” two preimages separate, traverse the two blue wings of the preimage isolas, and then collide again on the J0 curve as the phase point transitions from A (or C) into the other Bi part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Noninvertibility in Partially Observed Dynamic Histories Recall that the forward Euler discretization of the Brusselator is a two-dimensional map � xn+1 = xn + τ(a + x2 nyn − (b + 1)xn), yn+1 = yn + τ(bxn − x2 nyn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (16) In (16), we have two equations, but five unknowns (xn, yn, xn+1, yn+1, τ), so the system is in principle solvable only if three of them are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This leads to �5 3 � = 10 possible cases, enu- merated below, which can be thought of as generalizations of the inversion studied in depth in the representative paper Adomaitis and Kevrekidis (1991);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Frouzakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, yn, τ) ⇒ (xn+1, yn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (This is the usual forward dynamics case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=') The evolution is unique (by direct substitution into (16)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn+1, yn+1, τ) ⇒ (xn, yn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (This is the case studied in depth in the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=') The backward- in-time dynamic behavior is now multi-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Substituting equation (18) into the equation for yn+1 in system (16) we obtain τ(1 − τ)x3 n + τ(τa − xn+1 − yn+1)x2 n + (τb + τ − 1)xn + (xn+1 − τa) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (17) (17) is a cubic equation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' xn if τ ̸= 0 and τ ̸= 1, which may lead to three distinct real roots, two distinct real roots (with one of them multiplicity 2), or one real root (with multiplicity 3, or with two extra complex roots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute the solution of xn into (18) to obtain yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, xn+1, τ) ⇒ (yn, yn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Here we know the x history, and want to infer the y history: create an observer of y from x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This is very much in the spirit of the Takens embedding theo- rem Takens (1981), where one uses delayed measurements of one state variable as surrogates of other, unmeasured state variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For our particular Brusselator example, the y dynamics inferred are unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the system (16), we rearrange the equation of xn+1 to obtain: yn = xn+1 − xn + τ(b + 1)xn − τa τx2n , (18) 19 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING which shows the solution for yn is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Substituting (18) into (16) gives yn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (yn, yn+1, τ) ⇒ (xn, xn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Now we use history observations for y in order to infer the x history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The inference of the x dynamic behavior is now multi-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' From the system (16), we can rearrange the equation of yn+1 to obtain τynx2 n − τbxn + (yn+1 − yn) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (19) (19) is a quadratic equation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' xn if τ ̸= 0 and yn ̸= 0, which may lead to two distinct real roots, one real root with multiplicity 2, or two (nonphysical) complex roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute (19) into (18) to obtain yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, yn+1, τ) ⇒ (yn, xn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We now work with mixed, asynchronous history observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For this particular choice of observations the inferred dynamic behavior is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the system (16), we can rearrange the equation of yn+1 and obtain yn = yn+1 − τbxn 1 − τx2n , (20) which shows that the solution for yn is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then we can substitute (20) into (16) to obtain xn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (yn, xn+1, τ) ⇒ (xn, yn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Interestingly, for this alternative set of asynchronous history observations, the inferred dynamic is multi-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' From the system (16), we can rearrange the equation of xn+1 and obtain τynx2 n + (1 − τ − τb)xn + (τa − xn+1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (21) (21) is a quadratic equation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' xn if τ ̸= 0 and yn ̸= 0, which may lead to two distinct real roots, one real root with multiplicity 2, or two complex roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute (21) into (16) to obtain yn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, yn, xn+1) ⇒ (τ, yn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This is an interesting twist: several asynchronous observations, but no time label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Is this set of observations possible ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Does there exist a time interval τ consistent with these observations ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' And how many possible τ values and possible “history completions” exist ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For this example, the inferred possible history is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the system (16), we can rearrange the equation of xn+1 and obtain τ = xn+1 − xn a + x2nyn − (b + 1)xn , (22) which shows that the solution for τ is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute (22) into (16) to obtain yn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The remaining cases are alternative formulations of the same “reconstructing history from partial observations” setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, yn, yn+1) ⇒ (τ, xn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The inferred history is again unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' For the system (16), we can rearrange the equation of yn+1 and obtain τ = yn+1 − yn bxn − x2nyn , (23) which shows that the solution for τ is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute (23) into (16) to obtain xn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 20 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (yn, xn+1, yn+1) ⇒ (τ, xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The inferred history is now multi-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Substituting equation (22) in the equation for yn+1 in system (16) we obtain: ynx3 n+((yn−yn+1)yn−b−xn+1yn)x2 n+(bxn+1+(b+1)(yn+1−yn))xn+a(yn−yn+1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (24) (24) is a cubic equation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' xn if yn ̸= 0, which may lead to three distinct real roots, two distinct real roots (with one of them multiplicity 2), or one real root (with multiplicity 3, or with two extra complex roots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then we could substitute the solution of xn into (22) to obtain τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (xn, xn+1, yn+1) ⇒ (τ, yn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The inferred history is again multi-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Substituting equation (18) in the equation for yn+1 in system (16) we obtain: x2 n(a − xn)τ 2 + (x3 n − (xn+1 + yn+1)x2 n + (b + 1)xn − a)τ + (xn+1 − xn) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (25) (25) is a quadratic equation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' τ if xn ̸= 0 and xn ̸= a, which may lead to two distinct real roots, one real root with multiplicity 2, or two complex roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can then substitute (25) into (18) to obtain yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' As a demonstration, we select the last of these cases, in which τ is an unknown, and show that multiple consistent “history completions”, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' multiple roots can be found;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' see Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Roots with negative or complex τ are possible, while negative timestep could be considered as a backward-time integration, complex results have to be filtered out as nonphysical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The methodology and algorithms in our paper are clearly applicable in providing certifications for regions of existence of unique consistent solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' we are currently exploring this computationally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Given Unknowns xn xn+1 yn+1 τ1 τ2 yn,1 yn,2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='88766 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='62663 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='27734 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='27018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='12996 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='06670 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='47845 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='36082 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='27177 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='13372 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='51470 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='07929 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='98342 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='15257 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='19914 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='97336 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='22943 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='51394 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='02572 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='18823 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='97282 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='60127 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='27780 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='21088 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='09960 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='14337i) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='24609 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='51630i) Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1: (xn, xn+1, yn+1) ⇒ (τ, yn), where a = 1, b = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Extensions to Residual Architectures We demonstrate that our algorithms are also applicable to residual networks with ReLU activations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' The MILP method does not extend in a simple way to networks with tanh or sigmoid activation, but we show here that simple algebraic formulas, like the residual connection, are addressable in this framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This follows from the fact that the identity function is equivalent to a ReLU multi-layer perceptron (MLP) with an arbitrary number of hidden layers, x = g(x) − g(−x) = g(g(x)) − g(g(−x)) = g(g(g(x))) − g(g(g(−x))) = · · · , (26) where g(x) = max(0, x) is the ReLU function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Because ReLU is idempotent g(g(x)) = g(x), we are able to add more and more nested versions in the right side of (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Thus one could transform a ReLU ResNet with fully-connected layers to a single ReLU MLP by applying the equivalence (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 21 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Proposition 7 A ReLU ResNet with ℓ fully-connected layers in its residual architecture is equiva- lent to an MLP with the same number of layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof Suppose f : Rm �→ Rm is a ResNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We can rewrite y = f(x) as y =W (ℓ)g(W (ℓ−1)g(· · · g(W (0)x + b(0)) + · · · ) + b(ℓ−1)) + b(ℓ) + x =W (ℓ)g(W (ℓ−1)g(· · · g(W (0)x + b(0)) + · · · ) + b(ℓ−1)) + b(ℓ) + Img(Img(· · · g(Imx) + · · · )) + (−Im)g(Img(· · · g(−Imx) + · · · )) =(W (ℓ), Im, −Im)g( � � W (ℓ−1) Im −Im � � g(· · · g( � � W (0) Im −Im � � x + � � b(0) 0m 0m � �) + · · · ) + � � b(ℓ−1) 0m 0m � �) + b(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (27) Here, Im ∈ Rm×m is an identity matrix, and 0m ∈ Rm is a zero vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' If we denote W ′(0) = � � W (0) Im −Im � � , W ′(ℓ) = (W (ℓ), Im, −Im), W ′(j) = � � W (j) Im −Im � � for j = 1, 2, · · · , ℓ − 1, b′(k) = � � b(k) 0m 0m � � for k = 0, 1, · · · , ℓ − 1, and b′(ℓ) = b(ℓ), (28) then the function y = W ′(ℓ)g(W ′(ℓ−1)g(· · · g(W ′(0)x + b′(0)) + · · · ) + b′(ℓ−1)) + b′(ℓ) (29) is a ReLU MLP with ℓ layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Structurally Invertible Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' It is interesting to consider how our algorithm would per- form when the network under study is invertible by architectural construction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' an invertible ResNet (“i-ResNet”, Behrmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then there is only the trivial solution to the MILP in (9) for any r > 0 (two identical points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' What we can do in such cases is to request a certificate of guarantee that we are sufficiently far from noninvertibility boundaries – e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' by a threshold larger than, say, 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' This is suggestive of global invertibility of the i-ResNet, and serves as a sanity check of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Computational Effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In general, several key factors impact the computational time of the MILP: the input dimension n0, the number of layers ℓ, the total number of neurons �ℓ i=1 ni, and the radius parameter r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Because a multi-layer network can be approximated to desired accuracy by a single-layer network with enough neurons, we will perform our experiment with a single-layer perceptron (ℓ = 1) and observe the dependence of the running time on n0, n1 and r by optimizing 22 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING starting from multiple randomly-generated i-ResNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' To reduce the influence of difficult i-ResNet parameters that might cause the optimizer to stall, diverge, converge very slowly, or (of most con- cern) halt by our 30-minute timeout, we track the median of the running times for replicate experi- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' See Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2 for these results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 Radius 10 1 100 101 102 103 Time(s) n0 = 4, n1 = 10 n0 = 6, n1 = 10 n0 = 8, n1 = 10 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='5 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='0 Radius n0 = 6, n1 = 10 n0 = 6, n1 = 20 n0 = 6, n1 = 50 Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2: Running time of the algorithm on a single-layer invertible ResNet as the network size varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We observe that the n0 hyperparameter has a greater impact on the running time than the n1 hyper- parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof of Theorems and Corollaries B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proposition Regarding Solutions to Problem 1 and Problem 2 Proposition For a given function f : Rm �→ Rm and a point xc ∈ Rm, if r and R are optimal solutions to problems 1 and 2 respectively, then we must have r ≤ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider a point x ∈ Bq(xc, r)\\{xc}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Since f is invertible on Bq(xc, r), we must have f(x′) ̸= f(x) for all x′ ∈ Bq(xc, r) \\ {x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' In particular, by choosing x = xc, we have f(x′) ̸= f(xc) for all x′ ∈ Bq(xc, r) \\ {x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Thus, we must have r ≤ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof of Theorem 1 Theorem Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, p⋆ ←max ∥x − y∥ subject to x, y ∈ B, f(x) = f(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (30) Then f is invertible on B if and only if p⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 23 CERTIFIED INVERTIBILITY IN NEURAL NETWORKS VIA MIXED-INTEGER PROGRAMMING Suppose f is invertible on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then for all x, y ∈ B for which f(x) = f(y), we must have x = y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Therefore, the objective function for Problem 1 is zero on the feasible set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Hence, p⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Conversely, suppose p⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then x = y for all x, y ∈ B such that f(x) = f(y), hence invertibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof of Theorem 2 Theorem Let f : Rm → Rm be a continuous function and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose xc ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, P ⋆ ← max ∥x − xc∥ subject to x ∈ B, f(x) = f(xc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (31) Then we have f(x) ̸= f(xc) for all x ∈ B \\ {xc} if and only if P ⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose f(x) ̸= f(xc) for all x ∈ B \\{xc}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then, the only feasible point in the optimization of Problem 2 is x = xc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Hence, P ⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Conversely, start by assuming P ⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose there exists a x′ ∈ B \\ {xc} such that f(x′) = f(xc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Then, we must have 0 < ∥x′ − xc∥ ≤ P ⋆ = 0, which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Therefore, we must have f(x) ̸= f(xc) for all x ∈ B \\ {xc}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof of Theorem 4 Theorem Let f1 : Rm → Rn, f2 : Rm → Rn be two continuous functions and B ⊂ Rm be a compact set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Consider the following optimization problem, p⋆ 12 ← max ∥f2(x(1)) − f2(x(2))∥ subject to x(1), x(2) ∈ B, f1(x(1)) = f1(x(2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (32) Then (a) f2 is a function of f1 on B if and only if (b) p⋆ 12 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We first set up a definition (with a slight abuse of notation) of preimage set to simplify our proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Definition 8 For a given function f : X �→ Y, X ⊆ Rm, Y ⊆ Rn, the preimage of y ∈ Y is f−1(y) = {x ∈ X | f(x) = y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' We then prove the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Theorem 9 For two functions fi : X �→ Yi, X ⊆ Rm, Yi ⊆ Rn, i = 1, 2, we have (a) output of f2 is a function of output of f1 if and only if (c) output of f2 is constant over the preimage set f−1 1 (y1) for all y1 ∈ Y1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Proof We will show the equivalence of (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (c) ⇒ (a): If f−1 1 (y1) is a singleton {x1}, then f2(x1) = y2 ∈ Y2 is the only value correspond- ing to y1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Otherwise, we could arbitrarily choose two different values xA, xB ∈ f−1 1 (y1), and we must have f2(xA) = f2(xB) = y2 ∈ Y2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Therefore, we can find a unique y2 ∈ Y2 that corresponds to the given y1, which infers the existence of a mapping from Y1 to Y2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' (a) ⇒ (c): We prove this by contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Suppose f2 is a function of output of f1, and ∃y1 ∈ Y1 and ∃xA, xB ∈ f−1 1 (y1) such that f2(xA) ̸= f2(xB) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' f2 is constant over f−1 1 (y1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' Therefore, we can find a y1 ∈ Y1 simultaneously corresponding to two different values f2(xA) and f2(xB) in Y2, showing the contradiction with (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' It is not hard to show (b) “p∗ 12 = 0” in (32) is equivalent with the statement that f2(x) is constant for ∀x ∈ f−1 1 (f1(x)), which is just rephrasing of (c) by denoting y1 = f1(x), and therefore, we show the equivalence of (a) and (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} +page_content=' 24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NFKT4oBgHgl3EQfUS2Q/content/2301.11783v1.pdf'} diff --git a/8dE2T4oBgHgl3EQflgcs/content/tmp_files/2301.03988v1.pdf.txt b/8dE2T4oBgHgl3EQflgcs/content/tmp_files/2301.03988v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..30a1f960ebd22bf5a83e4f5e7c3300b4b33c0a0c --- /dev/null +++ b/8dE2T4oBgHgl3EQflgcs/content/tmp_files/2301.03988v1.pdf.txt @@ -0,0 +1,1518 @@ +Preprint +SANTACODER: DON’T REACH FOR THE STARS! +Loubna Ben Allal* +Hugging Face +Raymond Li* +ServiceNow Research +Denis Kocetkov* +ServiceNow Research +Chenghao Mou +Independent +Christopher Akiki +Leipzig University and ScaDS.AI +Carlos Munoz Ferrandis +Hugging Face +Niklas Muennighoff +Hugging Face +Mayank Mishra +IBM Research +Alex Gu +MIT +Manan Dey +SAP +Logesh Kumar Umapathi +Saama Technologies +Carolyn Jane Anderson +Wellesley College +Yangtian Zi +Northeastern University +Joel Lamy Poirier +ServiceNow Research +Hailey Schoelkopf +EleutherAI +Sergey Troshin +University of Amsterdam +Dmitry Abulkhanov +Huawei Noah’s Ark Lab +Manuel Romero +Independent +Michael Lappert +Berner Fachhochschule +Francesco De Toni +UWA +Bernardo Garc´ıa del R´ıo +Flowrite +Qian Liu +Sea AI Lab +Shamik Bose +Independent +Urvashi Bhattacharyya +Discover Dollar Pvt Ltd +Terry Yue Zhuo +CSIRO’s Data61 and Monash University +Ian Yu +PIISA +Paulo Villegas +Telefonica I+D +Marco Zocca +Unfold ML +Sourab Mangrulkar +Hugging Face +David Lansky +Independent +Huu Nguyen +Ontocord, LLC +Danish Contractor +IBM Research +Luis Villa +Independent +Jia Li +Independent +Dzmitry Bahdanau +ServiceNow Research +Yacine Jernite +Hugging Face +Sean Hughes +ServiceNow +Daniel Fried +Carnegie Mellon University +Arjun Guha +Northeastern University and Roblox +Harm de Vries‡ +ServiceNow Research +Leandro von Werra‡∗ +Hugging Face +ABSTRACT +∗Corresponding authors (denoted by ‡) can be contacted at contact@bigcode-project.org +1 +arXiv:2301.03988v1 [cs.SE] 9 Jan 2023 + +Preprint +The BigCode project is an open-scientific collaboration working on the responsi- +ble development of large language models for code.1 This tech report describes +the progress of the collaboration until December 2022, outlining the current state +of the Personally Identifiable Information (PII) redaction pipeline, the experi- +ments conducted to de-risk the model architecture, and the experiments investi- +gating better preprocessing methods for the training data. We train 1.1B param- +eter models on the Java, JavaScript, and Python subsets of The Stack (Kocetkov +et al., 2022) and evaluate them on the MultiPL-E text-to-code benchmark (Cas- +sano et al., 2022). We find that more aggressive filtering of near-duplicates can +further boost performance and, surprisingly, that selecting files from repositories +with 5+ GitHub stars deteriorates performance significantly. Our best model out- +performs previous open-source multilingual code generation models (InCoder- +6.7B and CodeGen-Multi-2.7B) in both left-to-right generation and infilling on +the Java, JavaScript, and Python portions of MultiPL-E, despite being a sub- +stantially smaller model. All models are released under an OpenRAIL license +at https://hf.co/bigcode. +1 +INTRODUCTION +Over the last two years, we have witnessed tremendous progress in the development of code generat- +ing AI assistants (Chen et al., 2021; Chowdhery et al., 2022; Nijkamp et al., 2022; Fried et al., 2022; +Li et al., 2022; Athiwaratkun et al., 2022). Machine learning models are now capable of assisting +professional developers through the synthesis of novel code snippets, not only from surrounding +code fragments, but also from natural language instructions. The models powering these code com- +pletion systems are usually referred to as Large Language Models for Code—or code LLMs—and +are created by training large transformer neural networks (Vaswani et al., 2017) on big corpora of +source code. However, with the exception of a few small-scale efforts (Xu et al., 2022), there is +generally a lack of transparency on the development of code LLMs in the research community, in +part due to their commercial value and the legal uncertainty around distributing training data and +models. Some groups have released model weights (Fried et al., 2022; Nijkamp et al., 2022) or pro- +vided access to the model through a paid API service (Chen et al., 2021; Athiwaratkun et al., 2022), +but these works did not release the full training data or the preprocessing methods that were used. +BigCode2 is an open scientific collaboration working on the responsible development of large lan- +guage models for code, empowering the machine learning and open-source communities through +open governance. BigCode was inspired by the BigScience project, an open-scientific collaboration +which culminated in July 2022 with the release of a large multi-lingual language model (Scao et al., +2022). As in BigScience, various BigCode working groups focus on relevant subtopics such as +collecting datasets, implementing methods for training code LLMs, developing an evaluation suite, +and discussing ethical best practices for these powerful models. For example, the Legal, Ethics, and +Governance working group has explored questions on data licensing, attribution of generated code to +original code, the redaction of Personally Identifiable Information (PII), and the risks of outputting +malicious code. In earlier work, the BigCode community released The Stack v1.1 (Kocetkov et al., +2022), a 6.4 TB dataset of permissively licensed source code in 384 programming languages. That +work also introduced “Am I in The Stack”,3 a governance tool for developers to check whether their +source is part of the dataset, and an opt-out form for those who wish to have their code removed +from the dataset.4 +In this tech report, we summarize the learnings of the BigCode community in developing the Santa +models, a set of 1.1B-parameter models trained on the Java, JavaScript, and Python subsets of The +Stack and evaluated on MultiPL-E (Cassano et al., 2022). We describe the first steps of the commu- +nity towards developing larger code models and report experiments to de-risk the model architecture +and the data processing pipeline. Specifically, the contributions of this report can be summarized as +follows: +1See https://www.bigcode-project.org +2See https://www.bigcode-project.org +3https://huggingface.co/spaces/bigcode/in-the-stack +4https://www.bigcode-project.org/docs/about/the-stack/ +2 + +Preprint +• We describe the current state of the PII redaction pipeline. We detail how we create a PII +benchmark of 400 code files, describe the filters for detecting emails, ip addresses, and +secret keys, and analyze its performance on the annotation benchmark. All experiments in +this work are conducted on the PII-redacted version of The Stack. +• We run ablations for Multi Query Attention (MQA) (Shazeer, 2019; Chowdhery et al., +2022; Li et al., 2022) and Fill-in-the-Middle (FIM) (Fried et al., 2022; Bavarian et al., +2022). MQA can significantly speed-up inference for larger batch sizes, while FIM en- +ables code models to do infilling tasks. We find that both changes only slightly deteriorate +downstream performance compared to baseline models. +• We investigate the impact of 4 preprocessing methods on the training data: filtering files +from repositories with 5+ GitHub stars, filtering files with a high comments-to-code ratio, +more aggressive filtering of near-duplicates, and filtering files with a low character-to-token +ratio. We observe modest impact of the new filters except for the stars filter, which deterio- +rates performance on text2code benchmarks significantly. This is an interesting result given +that previous work has explicitly filtered for GitHub Stars as a proxy for data quality (Gao +et al., 2020; Xu et al., 2022). +• Using the findings from these experiments, we train a final 1.1B parameter model, dubbed +SantaCoder, on Python, JavaScript, and Java. This model obtains comparable or stronger +performance than previous open-source multilingual models, InCoder-6.7B and CodeGen- +Multi-2.7B, on code generation and infilling tasks on the MultiPL-E benchmark for these +three languages, despite being substantially smaller. +2 +RELATED WORK +Code LLMs +Recently, there has been an increasing amount of research on using large-scale trans- +former models to analyze or generate source code. Many studies have focused on using decoder-only +models with a causal language modeling objective (Chen et al., 2021; Austin et al., 2021; Nijkamp +et al., 2022; Christopoulou et al., 2022; Izadi et al., 2022; Xu et al., 2022; Athiwaratkun et al., 2022), +while other studies have investigated encoder (Feng et al., 2020a; Kanade et al., 2020) and encoder- +decoder architectures (Li et al., 2022; Ahmad et al., 2021; Wang et al., 2021; Roziere et al., 2021). +Bavarian et al. (2022); Fried et al. (2022) propose to use decoder-only models for code-infilling +tasks using a causal masking mechanism, and Bavarian et al. (2022) argues that training with such +a fill-in-the middle (FIM) objective does not harm the model’s ability to do left-to-right generation. +Shazeer (2019) proposes Multi Query Attention (MQA), an architectural change to the transformer +neural network in which key and value embeddings are shared across attention heads, resulting in +lower memory requirements and faster inference for large batch settings. Multi Query Attention was +implemented in AlphaCode (Li et al., 2022) and PaLM (Chowdhery et al., 2022). +Evaluating text-to-code +The correctness of generated code can be tested using unit tests, a method +for approximating semantic equivalence. Textual similarity metrics have also been used to evaluate +code (Feng et al., 2020b; Ren et al., 2020); however, they have been shown to correlate only weakly +with code correctness (Austin et al., 2021; Chen et al., 2021). +Many single-language benchmarks for evaluating code completion exist (Kulal et al., 2019; Iyer +et al., 2018; Zhong et al., 2017; Yu et al., 2018; Austin et al., 2021; Hendrycks et al., 2021; Chen +et al., 2021; Austin et al., 2021; Athiwaratkun et al., 2022; Lai et al., 2022). Two of the most popular +benchmarks for Python are HumanEval (Chen et al., 2021) and MBPP (Austin et al., 2021), which +consist of a natural language description of a function and a set of unit tests. +MultiPL-E (Cassano et al., 2022) extends two popular benchmarks for code completion, MBPP +and HumanEval, to 18 additional languages. The doctests, function signatures, and unit tests for +each benchmark suite are automatically compiled to new languages. Python-specific terminology +in the prompt is automatically replaced with the equivalent terminology used for each programming +language. MBXP (Athiwaratkun et al., 2022) is a concurrent benchmark that uses a similar approach, +but differs in the details of type inference, prompt construction, and evaluation. In particular, MBXP +uses the same set of assertions in the prompt that it uses to test the correctness of generated solutions. +In contrast, MultiPL-E keeps the tests hidden from the model and only uses them to test correctness. +3 + +Preprint +Evaluating other tasks +Code generation models have also been used to solve a variety of tasks +(Tufano et al., 2020; Feng et al., 2020b; Ahmed & Devanbu, 2022; Hellendoorn et al., 2018; Pradel +et al., 2020). CodeXGLUE (Lu et al., 2021) is a set of 14 datasets for evaluating code generation +models. The tasks include code-to-code tasks like clone detection, code repair, and code translation; +text-to-code tasks like code search and code generation; and code-to-text tasks like generating doc- +umentation. The programming languages included vary by task; the most common are Python and +Java. +3 +OPT-OUT PROCESS +Developers who do not wish their source code to be used for training code LLMs are given the op- +portunity to opt-out of The Stack (Kocetkov et al., 2022). We received 9 opt-out requests before the +cut-off date for removing data (31 October 2022). These individuals accounted for 299 repositories. +Of these, 161 were already excluded from The Stack v1.0 (because they did not have a permissive +license), and 138 were in The Stack v1.0. We honored the requests to opt-out and removed these +repositories from The Stack v1.1. After the cut-off date (31 October 2022), we have received more +requests for requests and we will remove these repositories prior to releasing The Stack v1.2. +4 +REDACTING PERSONALLY IDENTIFIABLE INFORMATION +We describe our first efforts to redact PII from The Stack. +4.1 +PII BENCHMARK +We construct a PII benchmark by annotating the following entities on a small subset of The Stack: +names, emails, usernames, passwords, IP addresses, API keys, and SSH keys. We pre-filtered 400 +samples from a total of 4000 code files that were likely to contain Personally Identifiable Information +(PII). We first select 4000 code files from 11 programming languages, with a total of 800 samples +for Python and C++, 400 samples for Java, JavaScript, TypeScript, and PHP, and 160 samples for +C, C#, Markdown, Go, and Ruby. To detect keys in these samples, we used the detect-secrets tool5 +with all default plugins activated. In addition, we used regular expressions to detect emails, IPv4 +and IPv6 addresses, see Appendix C.1. Twelve members of the BigCode community annotated the +files on the LightTag platform6, with one annotator assigned per file. After the annotation phase, one +member reviewed all the annotation tags. To further increase annotation quality, we ran our initial +PII detection tools on the annotated files and manually corrected any incorrect annotations identified +as false positives or false negatives. +4.2 +PII DETECTION AND REDACTION +For the first iteration of the PII redaction pipeline, we focus on emails, IP addresses, and keys, and +leave the detection of names, usernames, and passwords for future work. +Emails +We use a regular expression to detect emails, see Appendix C.1. We replace detected +emails with [random 5 character string]@example.com. +IP addresses +We use regular expressions for IPv4 and IPv6 IP addresses, see Appendix C.1. In +addition, we check if the detected IP addresses have a valid format using the ipaddress python +package. We also do not select IP addresses of the format a.b.c.d where a, b, c and d are single digit +numbers, except if the words “dns” or “server” appear in the neighboring context (100 characters +before or after). These detected addresses were mostly false positives, consisting of package and +release versions. Lastly, we do not anonymize private IP addresses7 and popular DNS servers, as we +don’t consider them sensitive information. See Appendix C.2 for the full list. +We replace detected IP addresses with one of 5 randomly generated IP addresses. +5https://github.com/Yelp/detect-secrets +6https://www.lighttag.io/ +7They are non-internet facing IP addresses used in internal networks +4 + +Preprint +Figure 1: Precision and recall of PII de- +tection tools. +Figure 2: Distribution of PII detected +in The Stack for Python, Java and +JavaScript. +Keys +We employed the detect-secrets tool to identify secret keys in the code files. To this +end, we kept all the regex and entropy based plugins, including the AWS key detector, the GitHub +Token detector, the Azure storage key detector, and the Base64 High Entropy String detector. You +can find the full list of plugins in Appendix C.4. We deactivated keyword detectors because they +were detecting commonly used words like ”password” rather than actual secret keys. To remove +false positives, we activated filters like UUIDs and string-like secret filtering, see the full list in +Appendix C.3. We also observed that entropy detectors sometimes detected human-readable text +like paths and URLs as secrets, even when adjusting the entropy threshold. To address this issue, we +added a gibberish8 detector filter on top of detect-secrets to verify that the detected string was +actually gibberish. Additionally, we noticed that hashes were sometimes falsely detected as secret +keys. To mitigate this problem, we added a hash filter that verifies the size of the detected string +and checks for the presence of keywords like “sha”, “md5”, “hash”, and “byte” in the neighboring +context. Finally, to avoid corrupting any files, we prevent the removal of keys from files where +words like “sha” or “hash” are mentioned in more than 2% of the number of lines. +4.3 +PERFORMANCE ANALYSIS +Evaluation on PII benchmark +We evaluated our PII detection pipeline on the benchmark we +annotated. The 400 files contained 214 emails, 99 IP addresses and 34 secret keys. Figure 1 shows +the precision and recall for each PII entity. Email and IP address detection perform well, with a +precision and recall above 90% for emails and above 80% for IP addresses. While key detection +also achieves almost 80% precision, its recall is much lower (slightly above 50%). We found that +the key detection pipeline was especially sensitive to the precision-recall trade-off, as including more +plugins or disabling some filters detected more keys but also increased the number of false positives. +PII detection on The Stack +We run the PII pipeline on the Python, Java and JavaScript subsets +of The Stack v1.1 (Kocetkov et al., 2022). Table 1 shows some statistics on the number of files +containing PII and the total number of secrets found. Some files containing PII are not modified if +they contain only private IP addresses or popular DNS servers, as explained in the previous section. +The number of files containing PII is significantly lower for JavaScript compared to Python and +Java, but this could be due to the fact that JavaScript files were filtered based on line length and +percentage of alphanumeric characters before running PII detection. We also observe that Python +and JavaScript have a higher number of secrets per file compared to Java. +To better understand these results, we computed the relevant percentiles in Table 2. We can see that +Java indeed has fewer secrets per file, and that almost 0.1% of the files contain a large number of +secrets (about 100). We found that some of these files contained multiple instances of PII, such as +emails stored in some form of database, or are files containing long encodings and key-like strings +8https://github.com/domanchi/gibberish-detector +5 + +1.0 +Precision +Recall +0.8 +0.6 +0.4 - +0.2 +EMAIL +IP_ADDRESS +KEY2M +Python +Java +JavaScript +1M +100k +EMAIL +KEY +IP_ADDRESSPreprint +Language +# files +# files with PII +# secrets +# modified files +Python +15,148,604 +1,224,632 +3,255,053 +1,040,809 +Java +25,124,914 +1,588,453 +2,757,169 +1,506,766 +JavaScript* +23,670,848 +835,198 +2,468,183 +744,842 +Table 1: Statistics from running PII detection on The Stack. JavaScript files initially went through +line-length filtering. Modified files are those altered during PII redaction. +Language +mean +median +95th percentile +99th percentile +99.9th percentile +Python +2.7 +1 +6 +23 +135 +Java +1.7 +1 +3 +11 +63 +JavaScript +3.3 +1 +7 +30 +197 +Table 2: Statistics of the number of detected PII per file in The Stack. +that are split into multiple keys. Finally, we also plot the distributions of detected secrets by entity +type in Figure 2. For this graph, we filtered out files with more than 100 secrets, but this did not +change the distribution of PII across languages. We observe that IP addresses are most often found +in Python, keys in JavaScript and emails in Java. +5 +EXPERIMENTS +5.1 +DATASET, MODEL, AND TRAINING DETAILS +Dataset +The base training dataset for the experiments in this paper contains 268 GB of Python, +Java and JavaScript files from The Stack v1.1 (Kocetkov et al., 2022) after removing data from opt- +out requests, near-deduplication, PII-redaction (see Section 4), and filtering based on line-length +and percentage of alphanumeric characters. This dataset was also decontaminated by removing +files that contained test-samples from the following benchmarks: HumanEval (Chen et al., 2021), +APPS (Hendrycks et al., 2021), MBPP (Austin et al., 2021) and MultiPL-E (Cassano et al., 2022). +Tokenizer +Seeing as the Santa models were the first models our community would train, our +design choices for the tokenizer were modulated by a conservative approach, partly based on in- +sights developed during the development of InCoder (Fried et al., 2022). We train a Hugging Face +Tokenizer (MOI et al., 2022) using the Byte-Pair Encoding (BPE) algorithm on raw bytes with a +vocabulary size of 49,152 tokens. This tokenizer was trained on 600,000 rows (Around 2.6 GB) of +data—200,000 for each language—which were pre-tokenized using a digit splitter and the default +GPT-2 pre-tokenizer regex before being converted to bytes. +Training details +Our base model is a 1.1B-parameter decoder-only transformer with FIM and +MQA trained in float16. It has 24 layers, 16 heads and a hidden-size of 2048. The model is +trained for 300K iterations with a global batch-size of 192 using Adam (Kingma & Ba, 2015) with +β1 = 0.9, β2 = 0.95, ϵ = 10−8 and a weight-decay of 0.1. A total of 118B tokens are seen in +training. The learning-rate is set to 2 × 10−4 and follows a cosine decay after warming up for 2% of +the training steps. Each training run takes 3.1 days to complete on 96 Tesla V100 GPUs for a total +of 1.05 × 1021 FLOPs. The final model described in Section 6.2 uses twice the amount of compute. +5.2 +ARCHITECTURE ABLATIONS +We perform ablation experiments to de-risk the model architecture and training objective. Specif- +ically, we investigate Fill-in-the-Middle (Bavarian et al., 2022) and Multi Query Attention +(MQA) (Shazeer, 2019). +FIM vs No-FIM +Recent works (Fried et al., 2022; Bavarian et al., 2022) have shown that autore- +gressive language-models can learn to infill code snippets by random transformation of the training +6 + +Preprint +Language +Base +Stars +Comments-to-code +Near-dedup +Tokenizer fertility +Python +75.6 GB +26.6 GB +65.6 GB +62.0 GB +72.5 GB +Java +110 GB +35.8 GB +92.7 GB +88.4 GB +105.5 GB +JavaScript +82.7 GB +20.8 GB +57.5 GB +65.1 GB +76.4 GB +Table 3: Data volume after additional filtering of the Python, Java, JavaScript subsets of The Stack. +data. Bavarian et al. (2022) argue that such data transformations do not harm the left-to-right gen- +erative capabilities of the model. Following Bavarian et al. (2022), we implement FIM as a random +transformation of the input sequence and split each training document into three parts uniformly +at random: prefix, middle and suffix. Each part is prepended with a corresponding sentinel token, +then documents are rearranged to put the middle part at the end of the sequence. The autoregressive +training objective is unchanged. We use context-level FIM, apply transformations at the character +level, use a FIM-rate of 0.5 and SPM+PSM joint training. We compare our base model to a model +that was trained with the standard left-to-right objective only (No-FIM). +Multi Query Attention vs Multi Head Attention +Shazeer (2019) proposes Multi Query Atten- +tion (MQA), an architectural change to transformer that shares key and value embeddings across +attention heads. Compared to Multi Head Attention (MHA), this lowers the memory bandwidth +requirements at generation time and results in faster inference. We compare our base model to a +similar model using MHA instead, with the same hyper-parameters otherwise. Note that the MHA +model has more parameters (1.3B) than the base model in this setting. +5.3 +DATA FILTERING ABLATIONS +We experiment with a number of preprocessing methods applied to the base dataset, described in +Section 5.1. Note that the filters are applied on top of the other filters such as near-deduplication, +line length filtering, etc. +GitHub stars +Do popular repositories contain good quality code? We use GitHub stars as a proxy +metric. We set the minimum threshold to 5 stars, as we believe that a lower number of stars would +not be an indicator of popularity. This filter removes more than 60% of the data (in terms of volume), +see Table 3. Note that more than 40% of the files do not have stars and that setting the threshold to +10 stars would remove an additional 5% of the data. +Comment-to-code ratio +Good code should be well documented. With this assumption, we filter +files with a high comments-to-code ratio. We use the ast and tokenize modules to extract +docstrings and comments from Python files, and Pygments to extract comments from Java and +JavaScript files. We then analyze the comment-to-code character ratio. We find that about 20% of +Python and Java files and 45% of JavaScript files have no comments. We use a minimum threshold +of 1%, removing an additional 3% of files in each language. We also find that files with a ratio above +80% have poor quality, so we filter them out, eliminating 2% of data in all languages. Overall, this +comment-to-code filter removes 20% of the data in terms of volume. +More near-deduplication +Previous work (Kocetkov et al., 2022) has demonstrated the effective- +ness of deduplication in boosting the performance of code LLMs. Based on this finding, we investi- +gate whether more aggressive near-deduplication can further improve performance. To this end, we +conduct experiments on a 100K subset of the base dataset. In the original deduplication pipeline, we +implemented a false positive check on top of the MinHash LSH9 output. This added processing +time, but was necessary due to a high false positive rate of around 15%. To remove more duplicates +while maintaining a low false positive rate and a low false negative rate, we switch to using 5-gram +for min-hashing, and 0.7 for the Jaccard Similarity threshold, without any additional false positive +checks after the initial near-deduplication. As a result, we see additionally 16%–20% fewer files +than the original already-deduplicated base dataset (see Table 3), and a decrease in both the esti- +9https://github.com/ekzhu/datasketch +7 + +Preprint +Language +Attention +FIM +HumanEval +MBPP +Java +Multi Query Attention + +0.35 +0.54 +Multi Head Attention + +0.36 +0.55 +Multi Query Attention + +0.37 +0.55 +JavaScript +Multi Query Attention + +0.33 +0.64 +Multi Head Attention + +0.37 +0.67 +Multi Query Attention + +0.37 +0.65 +Python +Multi Query Attention + +0.36 +0.67 +Multi Head Attention + +0.38 +0.70 +Multi Query Attention + +0.39 +0.68 +Table 4: Pass@100 results for the architecture ablations on HumanEval and MBPP. +Model +Java +JavaScript +Python +Baseline +0.64 +0.61 +0.42 +GitHub stars +0.54 +0.57 +0.37 +Comments-to-code +0.62 +0.59 +0.44 +More near deduplication +0.66 +0.57 +0.45 +Tokenizer fertility +0.67 +0.65 +0.45 +Final +0.62 +0.60 +0.44 +Table 5: Fill-in-the-middle results for the data filtering ablations on MultiPL-HumanEval. Each +number reports the fraction of lines where the model exactly reproduces a single line of code that is +held out from the body of a function in a held out problem. +mated false positive rate (from 15% to 5%) and the estimated false negative rate for documents with +high similarities (from 35% to 24%). +Tokenizer fertility +Can we use the tokenizer to remove low-quality files from the dataset? We +experiment with filtering files with a low character-to-token ratio10. For each language, we find that +files with a ratio below the 5th percentile are usually of poor quality, but increasing the threshold may +eliminate some good-quality files. We therefore set the cutoff value for this ratio to the following +values: 2.5 for Python, 2.9 for Java, and 2.6 for JavaScript. This filters out roughly 4% to 5% of +data. Note that these values depend highly on the tokenizer and the data. This filter may also be +biased against files with non-English comments. +5.4 +EVALUATION +Text2code evaluation +The text2code task involves generating the body of a function from a +prompt that includes a function description, the function signature (its name and arguments), and +optionally a handful of example inputs and outputs. Every problem is accompanied by a set of +hidden test cases, which are used to determine if the generated function is correct. We use the +MultiPL-E text2code benchmark Cassano et al. (2022), which is derived from HumanEval Chen +et al. (2021) and MBPP Austin et al. (2021) (the “sanitized” subset of MBPP.). Whereas the latter +two benchmarks target Python, MultiPL-E has a suite of compilers that translate HumanEval and +MBPP to 18 other programming languages. Since our models are only trained on Java, JavaScript, +and Python, we only evaluate them on these three languages. +We use the methodology of Chen et al. (2021) and we calculate pass@k rates for (k = 1, 10, 100) +for every problem. Intuitively, pass@1 estimates the likelihood a model will generate a correct +solution in a single attempt, whereas pass@10 and pass@100 estimate the likelihood that the model +will generate a correct solution given 10 and 100 attempts respectively. Following the literature, +10We slightly abuse the term tokenizer fertility in this work as it usually refers to the average number of +subwords per token, where a token is determined by the true tokenizer of the programming language. See e.g. +(Rust et al., 2021) +8 + +Preprint +Figure 3: HumanEval pass@100 performance throughout training for all models. Note that evalua- +tion shown here is based on OpenAI Python prompts and might differ (slightly) from the MultiPL-E +prompts used in the rest of this paper. +we sample 200 completions at temperatures 0.2 and 0.8 and use 0.2 to estimate pass@1 and 0.8 for +pass@10 and pass@100. +Fill-in-the-middle evaluation +To evaluate fill-in-the-middle, we use the single-line exact match +metric, which was introduced by Fried et al. (2022) and also employed by Bavarian et al. (2022). For +every benchmark problem, we mask out a single line of text from the function body (i.e., not from +the function description or signature), and prompt the model to fill in that line of code. We exclude +blank lines and comments, and count the number of times the model produces exactly the masked out +line. This benchmark requires working solutions for problems, which MultiPL-E does not have. (A +text2code benchmark like MultiPL-E only needs hidden tests.) Instead, of writing solutions by hand, +we use solutions generated by a code generation model, which is the approach of Athiwaratkun et al. +(2022). Specifically, we use working solutions produced by code-davinci-002 at temperature +0.8. Note that this approach does not produce solutions to every problem, since not all problems +are solvable. Moreover, for uniformity, we use this approach for Python as well, even though hand- +written Python solutions exist for our benchmarks. We only report fill-in-the-middle evaluations for +the data filtering ablations. +6 +RESULTS +6.1 +ABLATIONS +For the architecture ablations, we report the results on text2code benchmarks in Table 4. For the +data filtering ablations, we show the text2code results in Figure 4 and report the fill-in-the middle +evaluations in Table 5. We show the HumanEval performance throughout all training runs in Figure +3. You can find the full results tables of the text2code experiments are Appendix A. +Slight drop in performance for MQA +We see a small drop in performance for Multi Query +Attention (MQA) compared to Multi Head Attention (MHA). As shown in Table 4, the MHA model +improves pass@100 with 1-4% on HumanEval and with 1-3% on MBPP. We specifically observe +noticeable improvements for the JavaScript versions of the text2code benchmarks. However, it +should be noted that the MHA model has more parameters (1.3B) than the MQA model (1.1B), +and a head-to-head comparison might, therefore, not be entirely fair. We think that the inference +speed-ups of MQA might outweigh the small drop in performance. +9 + +0.45 +0.40 +0.35 +0.30 +350M-theStackv1near-dedup-pass@100 +Base-pass@100 +0.25 +Arch: No Fim -pass@100 +Arch: MHA -pass@100 +Dataset:comments-pass@1oo +0.20 +Dataset:stars-pass@1oo +Dataset: fertility -pass@100 +0.15 +Dataset: near-dedup-pass@1o0 +Final (near-dedup + comments)-pass@100 +. +50 +100 +150 +200 +Number of tokens seen in training (B)Preprint +Multi−HumanEval Pass@100 +Multi−MBPP Pass@100 +Multi−HumanEval Pass@10 +Multi−MBPP Pass@10 +Multi−HumanEval Pass@1 +Multi−MBPP Pass@1 +Java +JavaScript +Python +Java +JavaScript +Python +0.0 +0.2 +0.4 +0.6 +0.8 +0.0 +0.2 +0.4 +0.6 +0.8 +0.0 +0.2 +0.4 +0.6 +0.8 +Language +Estimate +Model +Baseline +Comments +Dedup Alt +Fertility +Stars +Final +Figure 4: Pass@k rates on Multi-HumanEval and Multi-MBPP by model and language +Left-to-right pass@100 +Fill-in-the-middle ex. match +Model +Size +Java +JavaScript +Python +Java +JavaScript +Python +InCoder +6.7B +0.36 +0.38 +0.47 +0.49 +0.51 +0.31 +CodeGen-multi +2.7B +0.42 +0.39 +0.39 + + + +CodeGen-mono +2.7B + + +0.57 + + + +Codex11 +2.5B + + +0.60 + + + +SantaCoder +1.1B +0.41 +0.47 +0.49 +0.62 +0.60 +0.44 +Table 6: Comparing the performance of the final version of SantaCoder with InCoder (Fried et al., +2022), CodeGen (Nijkamp et al., 2022), and Codex (Chen et al., 2021) on left-to-right (HumanEval +pass@100) and fill-in-the-middle benchmarks (HumanEval line filling, exact match). +FIM for cheap +We observe a minor drop in performance of the FIM model compared to the +No-FIM model. Specifically, we see that the pass@100 performance of the FIM model is 2-4% +lower on HumanEval and 1% lower on MBPP. While Bavarian et al. (2022) presented evidence +for the existence of a FIM-for-free property (i.e., arguing that autoregressive models can be trained +with FIM without harming left-to-right capabilities), we do find a small but consistent drop of FIM +models on left-to-right text2code benchmarks. +11This is the performance of a Codex model reported by Chen et al. (2021). It is not clear if this model is +available via the OpenAI API. +10 + +Preprint +Modest impact of near-deduplication, comments, and fertility filter +On text2code benchmarks, +we observe small gains for the near-deduplication and comment-to-code filters and a neutral effect +of the tokenizer filter. The near-deduplication filter improves HumanEval performance by 1-3% and +MBPP by 1-4% across the three programming languages. The comment-to-code filter improves +HumanEval performance by 0-2% but decreases MBPP performance in certain cases (Java). See +Appendix A for the full results table. On fill-in-the-middle benchmarks, we see that the tokenizer +fertility filter performs well, improving performance by 2-4% across the three languages. The near- +duplication and comments filters have a mixed effect, improving fill-in-the-middle performance for +Python but deteriorating performance for JavaScript. +GitHub stars deteriorate performance +Surprisingly, we find that the GitHub stars filter performs +poorly. On HumanEval and MBPP, the pass@100 performance consistently drops by 3-6% across +the three languages. On the fill-in-the-middle benchmark, the performance drops by 5-11% (Table +5). Note that the stars filter removes the most data (over 60%) and, therefore, raises the question +whether the performance difference is due to the smaller dataset. However, as can be seen in Figure +3, HumanEval pass@100 diverged early on in training, indicating that the drop in performance is +not only due to data size but also data quality. +6.2 +FINAL MODEL +Based on the insights from the architecture and dataset ablations, we train a final model, which we +call SantaCoder, with MQA and FIM and the two data filters that yielded the best results: more near- +deduplication and comments-to-code filter. We train this model for 600K iterations (236B tokens) +and keep all other hyper-parameters the same. +Improved text2code performance +Doubling the training iterations leads to much stronger +text2code performance on MultiPL-E, significantly boosting performance across all benchmarks +and programming languages (see Figure 4). Looking at the performance throughout training (Figure +3), it is likely that longer training can further increase performance. Surprisingly, we find that the +final training run did not improve the fill-in-the-middle evaluations (see Table 5), at least on these +single line infilling tasks. +Comparison to InCoder, CodeGen, and Codex +Table 6 compares our SantaCoder model to +comparably-sized code generation models from previous work on the MultiPL-E benchmark, using +the methodology described in Section 5.4. We find that our model generally outperforms previ- +ous open-source multi-language code generation models despite being smaller, outperforming the +InCoder 6.7B (Fried et al., 2022) model on both left-to-right generation and single line fill-in-the- +middle infilling across languages, and obtaining comparable or stronger performance to CodeGen- +multi 2.7B (Nijkamp et al., 2022). +7 +CONCLUSION +We described the progress of the BigCode project until December 2022. The community took its +first steps towards redacting PII and demonstrated that regular expressions are reasonably effective +at detecting emails and IP addresses. Future work should focus on increasing the precision and recall +of secret keys, as well as detecting other sensitive information such as names, usernames, and pass- +word. Using the PII-redacted version of The Stack, we conducted a series of architectural and data +filtering ablations. One of our main findings was that filtering for Github stars consistently decreased +performance across all benchmarks and programming languages. Using the findings of these abla- +tion studies, we trained a final 1.1B model—dubbed SantaCoder—for 236B tokens and showed it +is able to outperform previous multi-lingual code models (InCoder-6.7B and CodeGen-Multi-2.7B) +on both left-to-right generation and infilling tasks. We anticipate that larger architectures and more +training data will be able to produce stronger multilingual, infilling-capable models, and plan to +continue to scale the findings from our investigations here. +11 + +Preprint +8 +CONTRIBUTIONS +Model license +Carlos Munoz Ferrandis, Christopher Akiki, Danish Contractor, Harm de Vries, +Huu Nguyen, Leandro von Werra, Luis Villa, Sean Hughes, Yacine Jernite, David Lansky +PII redaction +Loubna Ben Allal, Jia Li, Paulo Villegas, Harm de Vries, Leandro Von Werra, +Christopher Akiki, Ian Yu, Michael Lappert, Urvashi Bhattacharyya, Shamik Bose, Bernardo Garc´ıa +del R´ıo, Francesco De Toni, Terry Yue Zhuo, Qian Liu, Manuel Romero +Dataset +Denis Kocetkov, Chenghao Mou, Loubna Ben Allal, Leandro von Werra, Dmitry Ab- +ulkhanov, Christopher Akiki, Raymond Li +Tokenizer +Christopher Akiki, Sergey Troshin, Dmitry Abulkhanov, Daniel Fried, Leandro von +Werra, Harm de Vries +Training and architecture +Raymond Li, Daniel Fried, Hailey Schoelkopf, Joel Lamy Poirier, +Qian Liu, Niklas Muennighoff, Loubna Ben Allal, Dzmitry Bahdanau, Harm de Vries, Leandro von +Werra +Opt out +Sean Hughes, Carlos Munoz Ferrandis, Christopher Akiki, Denis Kocetkov, Harm de +Vries, Huu Nguyen, Leandro von Werra, Luis Villa +Evaluation +Arjun Guha, Yangtian Zi, Carolyn Jane Anderson, Loubna Ben Allal, Raymond Li, +Niklas Muennighoff, Manan Dey, Logesh Kumar Umapathi, Leandro von Werra, Harm de Vries, +Marco Zocca +Inference +Mayank Mishra, Alex Gu, Joel Lamy Poirier, Leandro von Werra, Harm de Vries, +Sourab Mangrulka +Acknowledgement +We thank ServiceNow and HuggingFace for the provided compute resources. +REFERENCES +Wasi Ahmad, Saikat Chakraborty, Baishakhi Ray, and Kai-Wei Chang. Unified pre-training for +program understanding and generation. +In Proceedings of the 2021 Conference of the North +American Chapter of the Association for Computational Linguistics: Human Language Tech- +nologies, pp. 2655–2668, Online, June 2021. Association for Computational Linguistics. URL +https://www.aclweb.org/anthology/2021.naacl-main.211. +Toufique Ahmed and Premkumar Devanbu. +Multilingual training for software engineering. +In +Proceedings of the 44th International Conference on Software Engineering. ACM, 2022. doi: +10.1145/3510003.3510049. +Ben Athiwaratkun, Sanjay Krishna Gouda, Zijian Wang, Xiaopeng Li, Yuchen Tian, Ming Tan, +Wasi Uddin Ahmad, Shiqi Wang, Qing Sun, Mingyue Shang, Sujan Kumar Gonugondla, Hantian +Ding, Varun Kumar, Nathan Fulton, Arash Farahani, Siddhartha Jain, Robert Giaquinto, Haifeng +Qian, Murali Krishna Ramanathan, Ramesh Nallapati, Baishakhi Ray, Parminder Bhatia, Sudipta +Sengupta, Dan Roth, and Bing Xiang. Multi-lingual evaluation of code generation models, 2022. +URL https://arxiv.org/abs/2210.14868. +Jacob Austin, Augustus Odena, Maxwell Nye, Maarten Bosma, Henryk Michalewski, David Dohan, +Ellen Jiang, Carrie Cai, Michael Terry, Quoc Le, et al. Program synthesis with large language +models. arXiv preprint arXiv:2108.07732, 2021. +Mohammad Bavarian, Heewoo Jun, Nikolas Tezak, John Schulman, Christine McLeavey, Jerry +Tworek, and Mark Chen. Efficient training of language models to fill in the middle, 2022. URL +https://arxiv.org/abs/2207.14255. +12 + +Preprint +Loubna Ben Allal, Niklas Muennighoff, and Leandro Von Werra. +A framework for the +evaluation of code generation models. +https://github.com/bigcode-project/ +bigcode-evaluation-harness, December 2022. +Federico Cassano, John Gouwar, Daniel Nguyen, Sydney Nguyen, Luna Phipps-Costin, Donald +Pinckney, Ming-Ho Yee, Yangtian Zi, Carolyn Jane Anderson, Molly Q Feldman, Arjun Guha, +Michael Greenberg, and Abhinav Jangda. A scalable and extensible approach to benchmarking +nl2code for 18 programming languages, 2022. +URL https://arxiv.org/abs/2208. +08227. +Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared +Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, +Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, +Scott Gray, Nick Ryder, Mikhail Pavlov, Alethea Power, Lukasz Kaiser, Mohammad Bavarian, +Clemens Winter, Philippe Tillet, Felipe Petroski Such, Dave Cummings, Matthias Plappert, Fo- +tios Chantzis, Elizabeth Barnes, Ariel Herbert-Voss, William Hebgen Guss, Alex Nichol, Alex +Paino, Nikolas Tezak, Jie Tang, Igor Babuschkin, Suchir Balaji, Shantanu Jain, William Saunders, +Christopher Hesse, Andrew N. Carr, Jan Leike, Josh Achiam, Vedant Misra, Evan Morikawa, Alec +Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob Mc- +Grew, Dario Amodei, Sam McCandlish, Ilya Sutskever, and Wojciech Zaremba. Evaluating large +language models trained on code. arXiv preprint, 2021. +Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam +Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, Parker Schuh, +Kensen Shi, Sasha Tsvyashchenko, Joshua Maynez, Abhishek Rao, Parker Barnes, Yi Tay, Noam +Shazeer, Vinodkumar Prabhakaran, Emily Reif, Nan Du, Ben Hutchinson, Reiner Pope, James +Bradbury, Jacob Austin, Michael Isard, Guy Gur-Ari, Pengcheng Yin, Toju Duke, Anselm Lev- +skaya, Sanjay Ghemawat, Sunipa Dev, Henryk Michalewski, Xavier Garcia, Vedant Misra, Kevin +Robinson, Liam Fedus, Denny Zhou, Daphne Ippolito, David Luan, Hyeontaek Lim, Barret +Zoph, Alexander Spiridonov, Ryan Sepassi, David Dohan, Shivani Agrawal, Mark Omernick, +Andrew M. Dai, Thanumalayan Sankaranarayana Pillai, Marie Pellat, Aitor Lewkowycz, Er- +ica Moreira, Rewon Child, Oleksandr Polozov, Katherine Lee, Zongwei Zhou, Xuezhi Wang, +Brennan Saeta, Mark Diaz, Orhan Firat, Michele Catasta, Jason Wei, Kathy Meier-Hellstern, +Douglas Eck, Jeff Dean, Slav Petrov, and Noah Fiedel. +Palm: +Scaling language model- +ing with pathways. +CoRR, abs/2204.02311, 2022. +doi: 10.48550/arXiv.2204.02311. +URL +https://doi.org/10.48550/arXiv.2204.02311. +Fenia Christopoulou, Gerasimos Lampouras, Milan Gritta, Guchun Zhang, Yinpeng Guo, Zhongqi +Li, Qi Zhang, Meng Xiao, Bo Shen, Lin Li, Hao Yu, Li Yan, Pingyi Zhou, Xin Wang, Yuchi Ma, +Ignacio Iacobacci, Yasheng Wang, Guangtai Liang, Jiansheng Wei, Xin Jiang, Qianxiang Wang, +and Qun Liu. Pangu-coder: Program synthesis with function-level language modeling, 2022. +URL https://arxiv.org/abs/2207.11280. +Zhangyin Feng, Daya Guo, Duyu Tang, Nan Duan, Xiaocheng Feng, Ming Gong, Linjun Shou, +Bing Qin, Ting Liu, Daxin Jiang, and Ming Zhou. CodeBERT: A pre-trained model for pro- +gramming and natural languages. In Findings of the Association for Computational Linguistics: +EMNLP 2020, pp. 1536–1547, Online, November 2020a. Association for Computational Lin- +guistics. doi: 10.18653/v1/2020.findings-emnlp.139. URL https://aclanthology.org/ +2020.findings-emnlp.139. +Zhangyin Feng, Daya Guo, Duyu Tang, Nan Duan, Xiaocheng Feng, Ming Gong, Linjun Shou, Bing +Qin, Ting Liu, Daxin Jiang, and Ming Zhou. Codebert: A pre-trained model for programming and +natural languages. arXiv preprint arXiv:2002.08155, 2020b. doi: 10.48550/ARXIV.2002.08155. +URL https://arxiv.org/abs/2002.08155. +Daniel Fried, Armen Aghajanyan, Jessy Lin, Sida Wang, Eric Wallace, Freda Shi, Ruiqi Zhong, +Wen-tau Yih, Luke Zettlemoyer, and Mike Lewis. Incoder: A generative model for code infilling +and synthesis, 2022. URL https://arxiv.org/abs/2204.05999. +Leo Gao, Stella Biderman, Sid Black, Laurence Golding, Travis Hoppe, Charles Foster, Jason +Phang, Horace He, Anish Thite, Noa Nabeshima, Shawn Presser, and Connor Leahy. The Pile: +An 800GB dataset of diverse text for language modeling, 2020. +13 + +Preprint +Leo Gao, Jonathan Tow, Stella Biderman, Sid Black, Anthony DiPofi, Charles Foster, Laurence +Golding, Jeffrey Hsu, Kyle McDonell, Niklas Muennighoff, Jason Phang, Laria Reynolds, Eric +Tang, Anish Thite, Ben Wang, Kevin Wang, and Andy Zou. A framework for few-shot lan- +guage model evaluation, September 2021. URL https://doi.org/10.5281/zenodo. +5371628. +Vincent J. Hellendoorn, Christian Bird, Earl T. Barr, and Miltiadis Allamanis. Deep Learning Type +Inference. In Fse, 2018. +Dan Hendrycks, Steven Basart, Saurav Kadavath, Mantas Mazeika, Akul Arora, Ethan Guo, Collin +Burns, Samir Puranik, Horace He, Dawn Song, and Jacob Steinhardt. Measuring coding challenge +competence with APPS. arXiv preprint arXiv:2105.09938, 2021. doi: 10.48550/ARXIV.2105. +09938. URL https://arxiv.org/abs/2105.09938. +Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt. +CodeSearchNet challenge: +Evaluating the state of semantic code search. +arXiv preprint +arXiv:1909.09436, 2019. +Srinivasan Iyer, Ioannis Konstas, Alvin Cheung, and Luke Zettlemoyer. Mapping language to code +in programmatic context. arXiv preprint arXiv:1808.09588, 2018. +Maliheh Izadi, Roberta Gismondi, and Georgios Gousios. Codefill: Multi-token code completion by +jointly learning from structure and naming sequences. In Proceedings of the 44th International +Conference on Software Engineering, ICSE ’22, pp. 401–412, New York, NY, USA, 2022. Asso- +ciation for Computing Machinery. ISBN 9781450392211. doi: 10.1145/3510003.3510172. URL +https://doi.org/10.1145/3510003.3510172. +Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi. Learning and evaluating +contextual embedding of source code. In Proceedings of the 37th International Conference on +Machine Learning, ICML’20. JMLR.org, 2020. +Diederik P. Kingma and Jimmy Ba. +Adam: A method for stochastic optimization. +In Yoshua +Bengio and Yann LeCun (eds.), 3rd International Conference on Learning Representations, ICLR +2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015. URL http: +//arxiv.org/abs/1412.6980. +Denis Kocetkov, Raymond Li, Loubna Ben Allal, Jia Li, Chenghao Mou, Carlos Mu˜noz Ferrandis, +Yacine Jernite, Margaret Mitchell, Sean Hughes, Thomas Wolf, Dzmitry Bahdanau, Leandro von +Werra, and Harm de Vries. The Stack: 3 TB of permissively licensed source code. Preprint, +2022. +Sumith Kulal, Panupong Pasupat, Kartik Chandra, Mina Lee, Oded Padon, Alex Aiken, and Percy S +Liang. Spoc: Search-based pseudocode to code. In H. Wallach, H. Larochelle, A. Beygelzimer, +F. d'Alch´e-Buc, E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Sys- +tems, volume 32. Curran Associates, Inc., 2019. URL https://proceedings.neurips. +cc/paper/2019/file/7298332f04ac004a0ca44cc69ecf6f6b-Paper.pdf. +Yuhang Lai, Chengxi Li, Yiming Wang, Tianyi Zhang, Ruiqi Zhong, Luke Zettlemoyer, Scott Wen +tau Yih, Daniel Fried, Sida Wang, and Tao Yu. Ds-1000: A natural and reliable benchmark for +data science code generation. ArXiv, abs/2211.11501, 2022. +Yujia Li, David Choi, Junyoung Chung, Nate Kushman, Julian Schrittwieser, R´emi Leblond, Tom +Eccles, James Keeling, Felix Gimeno, Agustin Dal Lago, Thomas Hubert, Peter Choy, Cyprien +de Masson d’Autume, Igor Babuschkin, Xinyun Chen, Po-Sen Huang, Johannes Welbl, Sven +Gowal, Alexey Cherepanov, James Molloy, Daniel Mankowitz, Esme Sutherland Robson, Push- +meet Kohli, Nando de Freitas, Koray Kavukcuoglu, and Oriol Vinyals. Competition-level code +generation with alphacode. arXiv preprint arXiv:2203.07814, 2022. +Shuai Lu, Daya Guo, Shuo Ren, Junjie Huang, Alexey Svyatkovskiy, Ambrosio Blanco, Colin +Clement, Dawn Drain, Daxin Jiang, Duyu Tang, et al. Codexglue: A machine learning benchmark +dataset for code understanding and generation. arXiv preprint arXiv:2102.04664, 2021. +14 + +Preprint +Anthony MOI, Nicolas Patry, Pierric Cistac, Pete, Funtowicz Morgan, Sebastian P¨utz, Mishig, Bjarte +Johansen, Thomas Wolf, Sylvain Gugger, Clement, Julien Chaumond, Lysandre Debut, Franc¸ois +Garillot, Luc Georges, dctelus, JC Louis, MarcusGrass, Taufiquzzaman Peyash, 0xflotus, Alan +deLevie, Alexander Mamaev, Arthur, Cameron, Colin Clement, Dagmawi Moges, David Hewitt, +Denis Zolotukhin, and Geoffrey Thomas. huggingface/tokenizers: Rust 0.13.2, November 2022. +URL https://doi.org/10.5281/zenodo.7298413. +Erik Nijkamp, Bo Pang, Hiroaki Hayashi, Lifu Tu, Huan Wang, Yingbo Zhou, Silvio Savarese, and +Caiming Xiong. A conversational paradigm for program synthesis. arXiv preprint, 2022. +Michael Pradel, Georgios Gousios, Jason Liu, and Satish Chandra. TypeWriter: Neural Type Pre- +diction with Search-Based Validation. In Esecfse, 2020. +Shuo Ren, Daya Guo, Shuai Lu, Long Zhou, Shujie Liu, Duyu Tang, Neel Sundaresan, Ming Zhou, +Ambrosio Blanco, and Shuai Ma. Codebleu: a method for automatic evaluation of code synthesis, +2020. URL https://arxiv.org/abs/2009.10297. +Baptiste Roziere, Marie-Anne Lachaux, Marc Szafraniec, and Guillaume Lample. Dobf: A deob- +fuscation pre-training objective for programming languages. arXiv preprint arXiv:2102.07492, +2021. +Phillip Rust, Jonas Pfeiffer, Ivan Vuli´c, Sebastian Ruder, and Iryna Gurevych. How good is your to- +kenizer? on the monolingual performance of multilingual language models. In Proceedings of the +59th Annual Meeting of the Association for Computational Linguistics and the 11th International +Joint Conference on Natural Language Processing (Volume 1: Long Papers), pp. 3118–3135, On- +line, August 2021. Association for Computational Linguistics. doi: 10.18653/v1/2021.acl-long. +243. URL https://aclanthology.org/2021.acl-long.243. +Teven Le Scao, Angela Fan, Christopher Akiki, Ellie Pavlick, Suzana Ili´c, Daniel Hesslow, Roman +Castagn´e, Alexandra Sasha Luccioni, Franc¸ois Yvon, Matthias Gall´e, et al. Bloom: A 176b- +parameter open-access multilingual language model. arXiv preprint arXiv:2211.05100, 2022. +Noam Shazeer. Fast transformer decoding: One write-head is all you need. CoRR, abs/1911.02150, +2019. URL http://arxiv.org/abs/1911.02150. +Michele Tufano, Dawn Drain, Alexey Svyatkovskiy, Shao Kun Deng, and Neel Sundaresan. Unit +test case generation with transformers and focal context. arXiv preprint arXiv:2009.10297, 2020. +doi: 10.48550/ARXIV.2009.05617. URL https://arxiv.org/abs/2009.05617. +Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, +Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Infor- +mation Processing Systems, pp. 5998–6008, 2017. +Yue Wang, Weishi Wang, Shafiq Joty, and Steven C.H. Hoi. +CodeT5: Identifier-aware unified +pre-trained encoder-decoder models for code understanding and generation. In Proceedings of +the 2021 Conference on Empirical Methods in Natural Language Processing, pp. 8696–8708, +Online and Punta Cana, Dominican Republic, November 2021. Association for Computational +Linguistics. doi: 10.18653/v1/2021.emnlp-main.685. URL https://aclanthology.org/ +2021.emnlp-main.685. +Frank F. Xu, Uri Alon, Graham Neubig, and Vincent Josua Hellendoorn. A systematic evalua- +tion of large language models of code. In Proceedings of the 6th ACM SIGPLAN International +Symposium on Machine Programming, MAPS 2022, pp. 1–10, New York, NY, USA, 2022. Asso- +ciation for Computing Machinery. ISBN 9781450392730. doi: 10.1145/3520312.3534862. URL +https://doi.org/10.1145/3520312.3534862. +Tao Yu, Rui Zhang, Kai Yang, Michihiro Yasunaga, Dongxu Wang, Zifan Li, James Ma, Irene Li, +Qingning Yao, Shanelle Roman, Zilin Zhang, and Dragomir Radev. Spider: A large-scale human- +labeled dataset for complex and cross-domain semantic parsing and text-to-sql task, 2018. URL +https://arxiv.org/abs/1809.08887. +Victor Zhong, Caiming Xiong, and Richard Socher. Seq2sql: Generating structured queries from +natural language using reinforcement learning, 2017. +URL https://arxiv.org/abs/ +1709.00103. +15 + +Preprint +A +FULL TEXT2CODE RESULTS +We report the full results of all experiments. Table 7 and 8 show the full results for the data filtering +ablations on HumanEval and MBPP, respectively. Table 9 and 10 reports the full results for the +architecture ablations on HumanEval and MBPP, respectively. +Language +Model +Pass@1 +Pass@10 +Pass@100 +Java +Baseline +0.1 +0.19 +0.35 +GitHub stars +0.08 +0.16 +0.3 +Comments-to-code ratio +0.11 +0.2 +0.35 +More near deduplication +0.13 +0.22 +0.38 +Tokenizer fertility +0.11 +0.19 +0.35 +JavaScript +Baseline +0.12 +0.19 +0.33 +GitHub stars +0.08 +0.15 +0.3 +Comments-to-code ratio +0.12 +0.2 +0.35 +More near deduplication +0.14 +0.2 +0.37 +Tokenizer fertility +0.1 +0.19 +0.35 +Python +Baseline +0.12 +0.21 +0.36 +GitHub stars +0.1 +0.18 +0.31 +Comments-to-code ratio +0.14 +0.22 +0.38 +More near deduplication +0.13 +0.22 +0.37 +Tokenizer fertility +0.14 +0.21 +0.36 +Table 7: Full results for data filtering ablations on HumanEval +16 + +Preprint +Language +Model +Pass@1 +Pass@10 +Pass@100 +Java +Baseline +0.23 +0.37 +0.54 +GitHub stars +0.18 +0.33 +0.49 +Comments-to-code ratio +0.22 +0.37 +0.52 +More near deduplication +0.23 +0.38 +0.55 +Tokenizer fertility +0.22 +0.38 +0.53 +JavaScript +Baseline +0.25 +0.43 +0.64 +GitHub stars +0.19 +0.37 +0.59 +Comments-to-code ratio +0.25 +0.44 +0.65 +More near deduplication +0.26 +0.45 +0.66 +Tokenizer fertility +0.24 +0.43 +0.65 +Python +Baseline +0.27 +0.47 +0.67 +GitHub stars +0.24 +0.41 +0.63 +Comments-to-code ratio +0.3 +0.48 +0.69 +More near deduplication +0.31 +0.49 +0.71 +Tokenizer fertility +0.28 +0.47 +0.68 +Table 8: Full results for data filtering ablations on MBPP +Language +Attention +FIM +Pass@1 +Pass@10 +Pass@100 +Java +Multi Query Attention + +0.1 +0.19 +0.35 +Multi Head Attention + +0.12 +0.21 +0.36 +Multi Query Attention + +0.11 +0.21 +0.37 +JavaScript +Multi Query Attention + +0.12 +0.19 +0.33 +Multi Head Attention + +0.13 +0.21 +0.37 +Multi Query Attention + +0.14 +0.21 +0.37 +Python +Multi Query Attention + +0.12 +0.21 +0.36 +Multi Head Attention + +0.13 +0.24 +0.38 +Multi Query Attention + +0.14 +0.23 +0.39 +Table 9: Full results for architecture ablations on HumanEval +17 + +Preprint +Language +Attention +FIM +Pass@1 +Pass@10 +Pass@100 +Java +Multi Query Attention + +0.23 +0.37 +0.54 +Multi Head Attention + +0.23 +0.38 +0.55 +Multi Query Attention + +0.23 +0.37 +0.55 +JavaScript +Multi Query Attention + +0.25 +0.43 +0.64 +Multi Head Attention + +0.26 +0.46 +0.67 +Multi Query Attention + +0.23 +0.44 +0.65 +Python +Multi Query Attention + +0.27 +0.47 +0.67 +Multi Head Attention + +0.31 +0.49 +0.7 +Multi Query Attention + +0.28 +0.47 +0.68 +Table 10: Full results for architecture ablations on MBPP +Model Family +Variant +BLEU +InCoder +6.7B +16.04 +CodeGen-Mono +16B +20.56 +SantaCoder +Baseline +17.67 +SantaCoder +No-FIM +17.71 +SantaCoder +MHA +17.72 +SantaCoder +Bf16 +17.67 +SantaCoder +GitHub Stars +18.04 +SantaCoder +Comments-to-code +17.81 +SantaCoder +More near deduplication +17.65 +SantaCoder +Tokenizer fertility +17.64 +SantaCoder +Final +18.13 +Table 11: CodeXGLUE (Lu et al., 2021) Python Docstring generation smoothed 4-gram BLEU +scores using the same methodology as Fried et al. (2022) (L-R single). Models are evaluated zero- +shot, greedily and with a maximum generation length of 128. +B +DOCSTRING GENERATION +In addition to code completion benchmarks, we also report results on docstring generation. To this +end, we evaluate our models on CodeXGLUE code-to-text Lu et al. (2021), which is a benchmark +constructed from CodeSearchNet Husain et al. (2019). We use the bigcode-evaluation-harness li- +brary Ben Allal et al. (2022), which is derived from lm-evaluation-harness Gao et al. (2021). Models +are prompted with a Python function signature and asked to output a corresponding docstring. Re- +sults are shown in Table 11. +Findings +We find all BigCode Santa variants with 1.1B parameters to outperform the 6.7B In- +Coder model (Fried et al., 2022), which we attribute to differences in the training datasets. Among +BigCode models, variants trained on more Python perform better: The stars variant with 32% of +Python in its training corpus outperforms the tokenizer fertility variant with only 28.5% of Python +(see proportions in Table 3). The bfloat16 is the same as the no-fim variant, except for the lat- +ter being trained in float16. There’s no notable performance difference between the two, likely +because at our small scale of 1.1B parameters we did not face any training instabilites. +Qualitative examples +Below is an example prompt from CodeXGLUE. Model generations and +the correct solution are in Table 12. +def dailymotion_download(url, output_dir=’.’, merge=True, +info_only=False, **kwargs): +""" +18 + +Preprint +Model Family +Variant +Generation +InCoder +6.7B +Download a video from Dailymotion. +CodeGen-Mono +16B +Downloads Dailymotion videos by URL. +SantaCoder +Baseline +Download Dailymotion videos. +SantaCoder +FIM +Download a video from a dailymotion video. +SantaCoder +MHA +Download a video from a Dailymotion video. +SantaCoder +bf16 +Download video from dailymotion.com. +SantaCoder +GitHub stars +Download media from dailymotion.com +SantaCoder +Comments-to-code +Download a video from Dailymotion. +SantaCoder +More near deduplication +Download a dailymotion video. +SantaCoder +Tokenizer fertility +Download a video from Dailymotion. +Correct solution +Downloads Dailymotion videos by URL. +Table 12: CodeXGLUE (Lu et al., 2021) Python Docstring generation examples. +C +PII +C.1 +REGULAR EXPRESSIONS +Email addresses +We used the following regular expression to detect emails. +email_pattern = r’’’ +(?<= ˆ | [\b\s@,?!;:)(’".\p{Han}<] ) +( +[ˆ\b\s@?!;,:)(’"<]+ +@ +[ˆ\b\s@!?;,/]* +[ˆ\b\s@?!;,/:)(’">.] +\. +\p{L} \w{1,} +) +(?= $ | [\b\s@,?!;:)(’".\p{Han}>] ) +’’’ +We replace detected emails with [random 5 character string]@example.com. +IP addresses +We used the following regular expressions to detect IPv4 and IPv6 addresses. +ipv4_pattern = r"(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?) +(?:\.(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)){3}" +ipv6_pattern = r"(?:[0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F +]{1,4}|(?:[0-9a-fA-F]{1,4}:){1,7}:|(?:[0-9a-fA-F]{1,4}:) +{1,6}:[0-9a-fA-F]{1,4}|(?:[0-9a-fA-F]{1,4}:){1,5}(?::[0-9a-fA- +F]{1,4}){1,2}|(?:[0-9a-fA-F]{1,4}:){1,4}(?::[0-9a-fA-F]{1,4}) +{1,3}|(?:[0-9a-fA-F]{1,4}:){1,3}(?::[0-9a-fA-F]{1,4}) +{1,4}|(?:[0-9a-fA-F]{1,4}:){1,2}(?::[0-9a-fA-F]{1,4}) +{1,5}|[0-9a-fA-F]{1,4}:(?:(?::[0-9a-fA-F]{1,4}){1,6}) +|:(?:(?::[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(?::[0-9a-fA-F]{0,4}) +{0,4}%[0-9a-zA-Z]{1,}|::(?:ffff(?::0{1,4}){0,1}:) +{0,1}(?:(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])\.) +{3,3}(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])|(?:[0-9a-fA- +F]{1,4}:){1,4}:(?:(?:25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9]) +\.){3,3}(25[0-5]|(?:2[0-4]|1{0,1}[0-9]){0,1}[0-9])" +ip_pattern = ( +r"(?:ˆ|[\b\s@?,!;:\’\")(.\p{Han}])(" ++ r"|".join([ipv4_pattern, ipv6_pattern]) +19 + +Preprint ++ ")(?:$|[\s@,?!;:’\"(.\p{Han}])" +) +Data pre-filtering +This is the regular expression we used to pre-filter the annotation dataset for +data containing emails. +email_pattern = r’([ˆ\s@,?!;:\’\"=)(]+@[ˆ,\s!?;,\’\"=]{3,}[\.][ˆ\s +\b\’\"@,?!;:)(.]+)’ +For IP addresses, we used the same regular expression as the one used for PII detection. +C.2 +LIST OF PRIVATE IP ADDRESSES AND POPULAR DNS SERVERS +• 8.8.8.8 +• 8.8.4.4 +• 1.1.1.1 +• 1.0.0.1 +• 76.76.19.19 +• 76.223.122.150 +• 9.9.9.9 +• 149.112.112.112 +• 208.67.222.222 +• 208.67.220.220 +• 8.26.56.26 +• 8.20.247.20 +• 94.140.14.14 +• 94.140.15.15 +C.3 +DETECT-SECRETS FILTERS +• detect secrets.filters.heuristic.is potential uuid +• detect secrets.filters.heuristic.is likely id string +• detect secrets.filters.heuristic.is templated secret +• detect secrets.filters.heuristic.is sequential string +Implementation +available +at +https://github.com/bigcode-project/ +bigcode-dataset/blob/6b3f54751b6e38e1ed70f2307331d6943ba39eae/ +pii/utils/keys_detection.py#L11. +C.4 +DETECT-SECRETS PLUGINS +• ArtifactoryDetector +• AWSKeyDetector +• Base64HighEntropyString +• HexHighEntropyString +• AzureStorageKeyDetector +• CloudantDetector +• DiscordBotTokenDetector +• GitHubTokenDetector +20 + +Preprint +• IbmCloudIamDetector +• IbmCosHmacDetector +• JwtTokenDetector +• MailchimpDetector +• NpmDetector +• SendGridDetector +• SlackDetector +• SoftlayerDetector +• StripeDetector +• TwilioKeyDetector +Implementation +available +at +https://github.com/bigcode-project/ +bigcode-dataset/blob/6b3f54751b6e38e1ed70f2307331d6943ba39eae/ +pii/utils/keys_detection.py#L19. +21 + diff --git a/8dE2T4oBgHgl3EQflgcs/content/tmp_files/load_file.txt b/8dE2T4oBgHgl3EQflgcs/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..736ecf87e4cc981011c0ddcc7c64bb9847a9c376 --- /dev/null +++ b/8dE2T4oBgHgl3EQflgcs/content/tmp_files/load_file.txt @@ -0,0 +1,1393 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf,len=1392 +page_content='Preprint SANTACODER: DON’T REACH FOR THE STARS!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Loubna Ben Allal* Hugging Face Raymond Li* ServiceNow Research Denis Kocetkov* ServiceNow Research Chenghao Mou Independent Christopher Akiki Leipzig University and ScaDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='AI ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Carlos Munoz Ferrandis ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Hugging Face ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Niklas Muennighoff ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Hugging Face ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Mayank Mishra ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='IBM Research ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Alex Gu ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='MIT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Manan Dey ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='SAP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Logesh Kumar Umapathi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Saama Technologies ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Carolyn Jane Anderson ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Wellesley College ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Yangtian Zi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Northeastern University ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Joel Lamy Poirier ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='ServiceNow Research ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Hailey Schoelkopf ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='EleutherAI ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Sergey Troshin ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='University of Amsterdam ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Dmitry Abulkhanov ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Huawei Noah’s Ark Lab ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Manuel Romero ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Independent ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Michael Lappert ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Berner Fachhochschule ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Francesco De Toni ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='UWA ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Bernardo Garc´ıa del R´ıo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Flowrite ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Qian Liu ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Sea AI Lab ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Shamik Bose ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Independent ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Urvashi Bhattacharyya ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Discover Dollar Pvt Ltd ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Terry Yue Zhuo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='CSIRO’s Data61 and Monash University ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Ian Yu ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='PIISA ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Paulo Villegas ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Telefonica I+D ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Marco Zocca ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Unfold ML ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Sourab Mangrulkar ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Hugging Face ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='David Lansky ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Independent ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Huu Nguyen ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='Ontocord,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' LLC Danish Contractor IBM Research Luis Villa Independent Jia Li Independent Dzmitry Bahdanau ServiceNow Research Yacine Jernite Hugging Face Sean Hughes ServiceNow Daniel Fried Carnegie Mellon University Arjun Guha Northeastern University and Roblox Harm de Vries‡ ServiceNow Research Leandro von Werra‡∗ Hugging Face ABSTRACT ∗Corresponding authors (denoted by ‡) can be contacted at contact@bigcode-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='03988v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='SE] 9 Jan 2023 Preprint The BigCode project is an open-scientific collaboration working on the responsi- ble development of large language models for code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 This tech report describes the progress of the collaboration until December 2022, outlining the current state of the Personally Identifiable Information (PII) redaction pipeline, the experi- ments conducted to de-risk the model architecture, and the experiments investi- gating better preprocessing methods for the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We train 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B param- eter models on the Java, JavaScript, and Python subsets of The Stack (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) and evaluate them on the MultiPL-E text-to-code benchmark (Cas- sano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We find that more aggressive filtering of near-duplicates can further boost performance and, surprisingly, that selecting files from repositories with 5+ GitHub stars deteriorates performance significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Our best model out- performs previous open-source multilingual code generation models (InCoder- 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B and CodeGen-Multi-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B) in both left-to-right generation and infilling on the Java, JavaScript, and Python portions of MultiPL-E, despite being a sub- stantially smaller model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' All models are released under an OpenRAIL license at https://hf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='co/bigcode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 1 INTRODUCTION Over the last two years, we have witnessed tremendous progress in the development of code generat- ing AI assistants (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Chowdhery et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nijkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Machine learning models are now capable of assisting professional developers through the synthesis of novel code snippets, not only from surrounding code fragments, but also from natural language instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The models powering these code com- pletion systems are usually referred to as Large Language Models for Code—or code LLMs—and are created by training large transformer neural networks (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2017) on big corpora of source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' However, with the exception of a few small-scale efforts (Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), there is generally a lack of transparency on the development of code LLMs in the research community, in part due to their commercial value and the legal uncertainty around distributing training data and models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Some groups have released model weights (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nijkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) or pro- vided access to the model through a paid API service (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), but these works did not release the full training data or the preprocessing methods that were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' BigCode2 is an open scientific collaboration working on the responsible development of large lan- guage models for code, empowering the machine learning and open-source communities through open governance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' BigCode was inspired by the BigScience project, an open-scientific collaboration which culminated in July 2022 with the release of a large multi-lingual language model (Scao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' As in BigScience, various BigCode working groups focus on relevant subtopics such as collecting datasets, implementing methods for training code LLMs, developing an evaluation suite, and discussing ethical best practices for these powerful models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' For example, the Legal, Ethics, and Governance working group has explored questions on data licensing, attribution of generated code to original code, the redaction of Personally Identifiable Information (PII), and the risks of outputting malicious code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In earlier work, the BigCode community released The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), a 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 TB dataset of permissively licensed source code in 384 programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' That work also introduced “Am I in The Stack”,3 a governance tool for developers to check whether their source is part of the dataset, and an opt-out form for those who wish to have their code removed from the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 In this tech report, we summarize the learnings of the BigCode community in developing the Santa models, a set of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B-parameter models trained on the Java, JavaScript, and Python subsets of The Stack and evaluated on MultiPL-E (Cassano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We describe the first steps of the commu- nity towards developing larger code models and report experiments to de-risk the model architecture and the data processing pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Specifically, the contributions of this report can be summarized as follows: 1See https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='bigcode-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org 2See https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='bigcode-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org 3https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='co/spaces/bigcode/in-the-stack 4https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='bigcode-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/docs/about/the-stack/ 2 Preprint We describe the current state of the PII redaction pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We detail how we create a PII benchmark of 400 code files, describe the filters for detecting emails, ip addresses, and secret keys, and analyze its performance on the annotation benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' All experiments in this work are conducted on the PII-redacted version of The Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We run ablations for Multi Query Attention (MQA) (Shazeer, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Chowdhery et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) and Fill-in-the-Middle (FIM) (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' MQA can significantly speed-up inference for larger batch sizes, while FIM en- ables code models to do infilling tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We find that both changes only slightly deteriorate downstream performance compared to baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We investigate the impact of 4 preprocessing methods on the training data: filtering files from repositories with 5+ GitHub stars, filtering files with a high comments-to-code ratio, more aggressive filtering of near-duplicates, and filtering files with a low character-to-token ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We observe modest impact of the new filters except for the stars filter, which deterio- rates performance on text2code benchmarks significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This is an interesting result given that previous work has explicitly filtered for GitHub Stars as a proxy for data quality (Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Using the findings from these experiments, we train a final 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B parameter model, dubbed SantaCoder, on Python, JavaScript, and Java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This model obtains comparable or stronger performance than previous open-source multilingual models, InCoder-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B and CodeGen- Multi-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B, on code generation and infilling tasks on the MultiPL-E benchmark for these three languages, despite being substantially smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 2 RELATED WORK Code LLMs Recently, there has been an increasing amount of research on using large-scale trans- former models to analyze or generate source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Many studies have focused on using decoder-only models with a causal language modeling objective (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nijkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopoulou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Izadi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), while other studies have investigated encoder (Feng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Kanade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020) and encoder- decoder architectures (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ahmad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Roziere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) propose to use decoder-only models for code-infilling tasks using a causal masking mechanism, and Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) argues that training with such a fill-in-the middle (FIM) objective does not harm the model’s ability to do left-to-right generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shazeer (2019) proposes Multi Query Attention (MQA), an architectural change to the transformer neural network in which key and value embeddings are shared across attention heads, resulting in lower memory requirements and faster inference for large batch settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Multi Query Attention was implemented in AlphaCode (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) and PaLM (Chowdhery et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Evaluating text-to-code The correctness of generated code can be tested using unit tests, a method for approximating semantic equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Textual similarity metrics have also been used to evaluate code (Feng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' however, they have been shown to correlate only weakly with code correctness (Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Many single-language benchmarks for evaluating code completion exist (Kulal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Iyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Zhong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hendrycks et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Lai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Two of the most popular benchmarks for Python are HumanEval (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) and MBPP (Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021), which consist of a natural language description of a function and a set of unit tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' MultiPL-E (Cassano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) extends two popular benchmarks for code completion, MBPP and HumanEval, to 18 additional languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The doctests, function signatures, and unit tests for each benchmark suite are automatically compiled to new languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Python-specific terminology in the prompt is automatically replaced with the equivalent terminology used for each programming language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' MBXP (Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) is a concurrent benchmark that uses a similar approach, but differs in the details of type inference, prompt construction, and evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In particular, MBXP uses the same set of assertions in the prompt that it uses to test the correctness of generated solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In contrast, MultiPL-E keeps the tests hidden from the model and only uses them to test correctness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 3 Preprint Evaluating other tasks Code generation models have also been used to solve a variety of tasks (Tufano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Feng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ahmed & Devanbu, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hellendoorn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Pradel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CodeXGLUE (Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) is a set of 14 datasets for evaluating code generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The tasks include code-to-code tasks like clone detection, code repair, and code translation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' text-to-code tasks like code search and code generation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' and code-to-text tasks like generating doc- umentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The programming languages included vary by task;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' the most common are Python and Java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 3 OPT-OUT PROCESS Developers who do not wish their source code to be used for training code LLMs are given the op- portunity to opt-out of The Stack (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We received 9 opt-out requests before the cut-off date for removing data (31 October 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' These individuals accounted for 299 repositories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Of these, 161 were already excluded from The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 (because they did not have a permissive license), and 138 were in The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We honored the requests to opt-out and removed these repositories from The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' After the cut-off date (31 October 2022), we have received more requests for requests and we will remove these repositories prior to releasing The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 4 REDACTING PERSONALLY IDENTIFIABLE INFORMATION We describe our first efforts to redact PII from The Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 PII BENCHMARK We construct a PII benchmark by annotating the following entities on a small subset of The Stack: names, emails, usernames, passwords, IP addresses, API keys, and SSH keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We pre-filtered 400 samples from a total of 4000 code files that were likely to contain Personally Identifiable Information (PII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We first select 4000 code files from 11 programming languages, with a total of 800 samples for Python and C++, 400 samples for Java, JavaScript, TypeScript, and PHP, and 160 samples for C, C#, Markdown, Go, and Ruby.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To detect keys in these samples, we used the detect-secrets tool5 with all default plugins activated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In addition, we used regular expressions to detect emails, IPv4 and IPv6 addresses, see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Twelve members of the BigCode community annotated the files on the LightTag platform6, with one annotator assigned per file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' After the annotation phase, one member reviewed all the annotation tags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To further increase annotation quality, we ran our initial PII detection tools on the annotated files and manually corrected any incorrect annotations identified as false positives or false negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 PII DETECTION AND REDACTION For the first iteration of the PII redaction pipeline, we focus on emails, IP addresses, and keys, and leave the detection of names, usernames, and passwords for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Emails We use a regular expression to detect emails, see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We replace detected emails with [random 5 character string]@example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' IP addresses We use regular expressions for IPv4 and IPv6 IP addresses, see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In addition, we check if the detected IP addresses have a valid format using the ipaddress python package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We also do not select IP addresses of the format a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='d where a, b, c and d are single digit numbers, except if the words “dns” or “server” appear in the neighboring context (100 characters before or after).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' These detected addresses were mostly false positives, consisting of package and release versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Lastly, we do not anonymize private IP addresses7 and popular DNS servers, as we don’t consider them sensitive information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' See Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 for the full list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We replace detected IP addresses with one of 5 randomly generated IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/Yelp/detect-secrets 6https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='lighttag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='io/ 7They are non-internet facing IP addresses used in internal networks 4 Preprint Figure 1: Precision and recall of PII de- tection tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Figure 2: Distribution of PII detected in The Stack for Python, Java and JavaScript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Keys We employed the detect-secrets tool to identify secret keys in the code files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To this end, we kept all the regex and entropy based plugins, including the AWS key detector, the GitHub Token detector, the Azure storage key detector, and the Base64 High Entropy String detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' You can find the full list of plugins in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We deactivated keyword detectors because they were detecting commonly used words like ”password” rather than actual secret keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To remove false positives, we activated filters like UUIDs and string-like secret filtering, see the full list in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We also observed that entropy detectors sometimes detected human-readable text like paths and URLs as secrets, even when adjusting the entropy threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To address this issue, we added a gibberish8 detector filter on top of detect-secrets to verify that the detected string was actually gibberish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Additionally, we noticed that hashes were sometimes falsely detected as secret keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To mitigate this problem, we added a hash filter that verifies the size of the detected string and checks for the presence of keywords like “sha”, “md5”, “hash”, and “byte” in the neighboring context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Finally, to avoid corrupting any files, we prevent the removal of keys from files where words like “sha” or “hash” are mentioned in more than 2% of the number of lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 PERFORMANCE ANALYSIS Evaluation on PII benchmark We evaluated our PII detection pipeline on the benchmark we annotated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The 400 files contained 214 emails, 99 IP addresses and 34 secret keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Figure 1 shows the precision and recall for each PII entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Email and IP address detection perform well, with a precision and recall above 90% for emails and above 80% for IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' While key detection also achieves almost 80% precision, its recall is much lower (slightly above 50%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We found that the key detection pipeline was especially sensitive to the precision-recall trade-off, as including more plugins or disabling some filters detected more keys but also increased the number of false positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' PII detection on The Stack We run the PII pipeline on the Python, Java and JavaScript subsets of The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Table 1 shows some statistics on the number of files containing PII and the total number of secrets found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Some files containing PII are not modified if they contain only private IP addresses or popular DNS servers, as explained in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The number of files containing PII is significantly lower for JavaScript compared to Python and Java, but this could be due to the fact that JavaScript files were filtered based on line length and percentage of alphanumeric characters before running PII detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We also observe that Python and JavaScript have a higher number of secrets per file compared to Java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To better understand these results, we computed the relevant percentiles in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We can see that Java indeed has fewer secrets per file, and that almost 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1% of the files contain a large number of secrets (about 100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We found that some of these files contained multiple instances of PII, such as emails stored in some form of database, or are files containing long encodings and key-like strings 8https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/domanchi/gibberish-detector 5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 Precision Recall 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 EMAIL IP_ADDRESS KEY2M Python Java JavaScript 1M 100k EMAIL KEY IP_ADDRESSPreprint Language # files # files with PII # secrets # modified files Python 15,148,604 1,224,632 3,255,053 1,040,809 Java 25,124,914 1,588,453 2,757,169 1,506,766 JavaScript* 23,670,848 835,198 2,468,183 744,842 Table 1: Statistics from running PII detection on The Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' JavaScript files initially went through line-length filtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Modified files are those altered during PII redaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Language mean median 95th percentile 99th percentile 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9th percentile Python 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 1 6 23 135 Java 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 1 3 11 63 JavaScript 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 1 7 30 197 Table 2: Statistics of the number of detected PII per file in The Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' that are split into multiple keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Finally, we also plot the distributions of detected secrets by entity type in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' For this graph, we filtered out files with more than 100 secrets, but this did not change the distribution of PII across languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We observe that IP addresses are most often found in Python, keys in JavaScript and emails in Java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5 EXPERIMENTS 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 DATASET, MODEL, AND TRAINING DETAILS Dataset The base training dataset for the experiments in this paper contains 268 GB of Python, Java and JavaScript files from The Stack v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) after removing data from opt- out requests, near-deduplication, PII-redaction (see Section 4), and filtering based on line-length and percentage of alphanumeric characters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This dataset was also decontaminated by removing files that contained test-samples from the following benchmarks: HumanEval (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021), APPS (Hendrycks et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021), MBPP (Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) and MultiPL-E (Cassano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Tokenizer Seeing as the Santa models were the first models our community would train, our design choices for the tokenizer were modulated by a conservative approach, partly based on in- sights developed during the development of InCoder (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We train a Hugging Face Tokenizer (MOI et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) using the Byte-Pair Encoding (BPE) algorithm on raw bytes with a vocabulary size of 49,152 tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This tokenizer was trained on 600,000 rows (Around 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 GB) of data—200,000 for each language—which were pre-tokenized using a digit splitter and the default GPT-2 pre-tokenizer regex before being converted to bytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Training details Our base model is a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B-parameter decoder-only transformer with FIM and MQA trained in float16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' It has 24 layers, 16 heads and a hidden-size of 2048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The model is trained for 300K iterations with a global batch-size of 192 using Adam (Kingma & Ba, 2015) with β1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9, β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='95, ϵ = 10−8 and a weight-decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A total of 118B tokens are seen in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The learning-rate is set to 2 × 10−4 and follows a cosine decay after warming up for 2% of the training steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Each training run takes 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 days to complete on 96 Tesla V100 GPUs for a total of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='05 × 1021 FLOPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The final model described in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 uses twice the amount of compute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 ARCHITECTURE ABLATIONS We perform ablation experiments to de-risk the model architecture and training objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Specif- ically, we investigate Fill-in-the-Middle (Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) and Multi Query Attention (MQA) (Shazeer, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' FIM vs No-FIM Recent works (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) have shown that autore- gressive language-models can learn to infill code snippets by random transformation of the training 6 Preprint Language Base Stars Comments-to-code Near-dedup Tokenizer fertility Python 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 GB 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 GB 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 GB 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 GB 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5 GB Java 110 GB 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 GB 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 GB 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 GB 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5 GB JavaScript 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 GB 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 GB 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5 GB 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 GB 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 GB Table 3: Data volume after additional filtering of the Python, Java, JavaScript subsets of The Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) argue that such data transformations do not harm the left-to-right gen- erative capabilities of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Following Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022), we implement FIM as a random transformation of the input sequence and split each training document into three parts uniformly at random: prefix, middle and suffix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Each part is prepended with a corresponding sentinel token, then documents are rearranged to put the middle part at the end of the sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The autoregressive training objective is unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use context-level FIM, apply transformations at the character level, use a FIM-rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5 and SPM+PSM joint training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We compare our base model to a model that was trained with the standard left-to-right objective only (No-FIM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Multi Query Attention vs Multi Head Attention Shazeer (2019) proposes Multi Query Atten- tion (MQA), an architectural change to transformer that shares key and value embeddings across attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Compared to Multi Head Attention (MHA), this lowers the memory bandwidth requirements at generation time and results in faster inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We compare our base model to a similar model using MHA instead, with the same hyper-parameters otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that the MHA model has more parameters (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3B) than the base model in this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 DATA FILTERING ABLATIONS We experiment with a number of preprocessing methods applied to the base dataset, described in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that the filters are applied on top of the other filters such as near-deduplication, line length filtering, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' GitHub stars Do popular repositories contain good quality code?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use GitHub stars as a proxy metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We set the minimum threshold to 5 stars, as we believe that a lower number of stars would not be an indicator of popularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This filter removes more than 60% of the data (in terms of volume), see Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that more than 40% of the files do not have stars and that setting the threshold to 10 stars would remove an additional 5% of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Comment-to-code ratio Good code should be well documented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' With this assumption, we filter files with a high comments-to-code ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use the ast and tokenize modules to extract docstrings and comments from Python files, and Pygments to extract comments from Java and JavaScript files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We then analyze the comment-to-code character ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We find that about 20% of Python and Java files and 45% of JavaScript files have no comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use a minimum threshold of 1%, removing an additional 3% of files in each language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We also find that files with a ratio above 80% have poor quality, so we filter them out, eliminating 2% of data in all languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Overall, this comment-to-code filter removes 20% of the data in terms of volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' More near-deduplication Previous work (Kocetkov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) has demonstrated the effective- ness of deduplication in boosting the performance of code LLMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Based on this finding, we investi- gate whether more aggressive near-deduplication can further improve performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To this end, we conduct experiments on a 100K subset of the base dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In the original deduplication pipeline, we implemented a false positive check on top of the MinHash LSH9 output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This added processing time, but was necessary due to a high false positive rate of around 15%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To remove more duplicates while maintaining a low false positive rate and a low false negative rate, we switch to using 5-gram for min-hashing, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 for the Jaccard Similarity threshold, without any additional false positive checks after the initial near-deduplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' As a result, we see additionally 16%–20% fewer files than the original already-deduplicated base dataset (see Table 3), and a decrease in both the esti- 9https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/ekzhu/datasketch 7 Preprint Language Attention FIM HumanEval MBPP Java Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='54 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='55 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='55 JavaScript Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='64 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 Python Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='70 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='68 Table 4: Pass@100 results for the architecture ablations on HumanEval and MBPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Model Java JavaScript Python Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='61 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='42 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='54 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='57 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 Comments-to-code 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='62 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='59 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='44 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='66 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='57 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='45 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='45 Final 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='62 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='44 Table 5: Fill-in-the-middle results for the data filtering ablations on MultiPL-HumanEval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Each number reports the fraction of lines where the model exactly reproduces a single line of code that is held out from the body of a function in a held out problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' mated false positive rate (from 15% to 5%) and the estimated false negative rate for documents with high similarities (from 35% to 24%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Tokenizer fertility Can we use the tokenizer to remove low-quality files from the dataset?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We experiment with filtering files with a low character-to-token ratio10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' For each language, we find that files with a ratio below the 5th percentile are usually of poor quality, but increasing the threshold may eliminate some good-quality files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We therefore set the cutoff value for this ratio to the following values: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5 for Python, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9 for Java, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 for JavaScript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This filters out roughly 4% to 5% of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that these values depend highly on the tokenizer and the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This filter may also be biased against files with non-English comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 EVALUATION Text2code evaluation The text2code task involves generating the body of a function from a prompt that includes a function description, the function signature (its name and arguments), and optionally a handful of example inputs and outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Every problem is accompanied by a set of hidden test cases, which are used to determine if the generated function is correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use the MultiPL-E text2code benchmark Cassano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022), which is derived from HumanEval Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021) and MBPP Austin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021) (the “sanitized” subset of MBPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Whereas the latter two benchmarks target Python, MultiPL-E has a suite of compilers that translate HumanEval and MBPP to 18 other programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Since our models are only trained on Java, JavaScript, and Python, we only evaluate them on these three languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use the methodology of Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021) and we calculate pass@k rates for (k = 1, 10, 100) for every problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Intuitively, pass@1 estimates the likelihood a model will generate a correct solution in a single attempt, whereas pass@10 and pass@100 estimate the likelihood that the model will generate a correct solution given 10 and 100 attempts respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Following the literature, 10We slightly abuse the term tokenizer fertility in this work as it usually refers to the average number of subwords per token, where a token is determined by the true tokenizer of the programming language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' See e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (Rust et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) 8 Preprint Figure 3: HumanEval pass@100 performance throughout training for all models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that evalua- tion shown here is based on OpenAI Python prompts and might differ (slightly) from the MultiPL-E prompts used in the rest of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' we sample 200 completions at temperatures 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 and use 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 to estimate pass@1 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 for pass@10 and pass@100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fill-in-the-middle evaluation To evaluate fill-in-the-middle, we use the single-line exact match metric, which was introduced by Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) and also employed by Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' For every benchmark problem, we mask out a single line of text from the function body (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', not from the function description or signature), and prompt the model to fill in that line of code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We exclude blank lines and comments, and count the number of times the model produces exactly the masked out line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' This benchmark requires working solutions for problems, which MultiPL-E does not have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (A text2code benchmark like MultiPL-E only needs hidden tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=') Instead, of writing solutions by hand, we use solutions generated by a code generation model, which is the approach of Athiwaratkun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Specifically, we use working solutions produced by code-davinci-002 at temperature 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that this approach does not produce solutions to every problem, since not all problems are solvable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Moreover, for uniformity, we use this approach for Python as well, even though hand- written Python solutions exist for our benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We only report fill-in-the-middle evaluations for the data filtering ablations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 6 RESULTS 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 ABLATIONS For the architecture ablations, we report the results on text2code benchmarks in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' For the data filtering ablations, we show the text2code results in Figure 4 and report the fill-in-the middle evaluations in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We show the HumanEval performance throughout all training runs in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' You can find the full results tables of the text2code experiments are Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Slight drop in performance for MQA We see a small drop in performance for Multi Query Attention (MQA) compared to Multi Head Attention (MHA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' As shown in Table 4, the MHA model improves pass@100 with 1-4% on HumanEval and with 1-3% on MBPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We specifically observe noticeable improvements for the JavaScript versions of the text2code benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' However, it should be noted that the MHA model has more parameters (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3B) than the MQA model (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B), and a head-to-head comparison might, therefore, not be entirely fair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We think that the inference speed-ups of MQA might outweigh the small drop in performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='30 350M-theStackv1near-dedup-pass@100 Base-pass@100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='25 Arch: No Fim -pass@100 Arch: MHA -pass@100 Dataset:comments-pass@1oo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='20 Dataset:stars-pass@1oo Dataset: fertility -pass@100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='15 Dataset: near-dedup-pass@1o0 Final (near-dedup + comments)-pass@100 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 50 100 150 200 Number of tokens seen in training (B)Preprint Multi−HumanEval Pass@100 Multi−MBPP Pass@100 Multi−HumanEval Pass@10 Multi−MBPP Pass@10 Multi−HumanEval Pass@1 Multi−MBPP Pass@1 Java JavaScript Python Java JavaScript Python 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 Language Estimate Model Baseline Comments Dedup Alt Fertility Stars Final Figure 4: Pass@k rates on Multi-HumanEval and Multi-MBPP by model and language Left-to-right pass@100 Fill-in-the-middle ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' match Model Size Java JavaScript Python Java JavaScript Python InCoder 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='49 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='51 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='31 CodeGen-multi 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='39 \x17 \x17 \x17 CodeGen-mono 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B \x17 \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='57 \x17 \x17 \x17 Codex11 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5B \x17 \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='60 \x17 \x17 \x17 SantaCoder 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='49 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='62 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='44 Table 6: Comparing the performance of the final version of SantaCoder with InCoder (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), CodeGen (Nijkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), and Codex (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) on left-to-right (HumanEval pass@100) and fill-in-the-middle benchmarks (HumanEval line filling, exact match).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' FIM for cheap We observe a minor drop in performance of the FIM model compared to the No-FIM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Specifically, we see that the pass@100 performance of the FIM model is 2-4% lower on HumanEval and 1% lower on MBPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' While Bavarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) presented evidence for the existence of a FIM-for-free property (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', arguing that autoregressive models can be trained with FIM without harming left-to-right capabilities), we do find a small but consistent drop of FIM models on left-to-right text2code benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 11This is the performance of a Codex model reported by Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' It is not clear if this model is available via the OpenAI API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 10 Preprint Modest impact of near-deduplication, comments, and fertility filter On text2code benchmarks, we observe small gains for the near-deduplication and comment-to-code filters and a neutral effect of the tokenizer filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The near-deduplication filter improves HumanEval performance by 1-3% and MBPP by 1-4% across the three programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The comment-to-code filter improves HumanEval performance by 0-2% but decreases MBPP performance in certain cases (Java).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' See Appendix A for the full results table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' On fill-in-the-middle benchmarks, we see that the tokenizer fertility filter performs well, improving performance by 2-4% across the three languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The near- duplication and comments filters have a mixed effect, improving fill-in-the-middle performance for Python but deteriorating performance for JavaScript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' GitHub stars deteriorate performance Surprisingly, we find that the GitHub stars filter performs poorly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' On HumanEval and MBPP, the pass@100 performance consistently drops by 3-6% across the three languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' On the fill-in-the-middle benchmark, the performance drops by 5-11% (Table 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Note that the stars filter removes the most data (over 60%) and, therefore, raises the question whether the performance difference is due to the smaller dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' However, as can be seen in Figure 3, HumanEval pass@100 diverged early on in training, indicating that the drop in performance is not only due to data size but also data quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 FINAL MODEL Based on the insights from the architecture and dataset ablations, we train a final model, which we call SantaCoder, with MQA and FIM and the two data filters that yielded the best results: more near- deduplication and comments-to-code filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We train this model for 600K iterations (236B tokens) and keep all other hyper-parameters the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Improved text2code performance Doubling the training iterations leads to much stronger text2code performance on MultiPL-E, significantly boosting performance across all benchmarks and programming languages (see Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Looking at the performance throughout training (Figure 3), it is likely that longer training can further increase performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Surprisingly, we find that the final training run did not improve the fill-in-the-middle evaluations (see Table 5), at least on these single line infilling tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Comparison to InCoder, CodeGen, and Codex Table 6 compares our SantaCoder model to comparably-sized code generation models from previous work on the MultiPL-E benchmark, using the methodology described in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We find that our model generally outperforms previ- ous open-source multi-language code generation models despite being smaller, outperforming the InCoder 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022) model on both left-to-right generation and single line fill-in-the- middle infilling across languages, and obtaining comparable or stronger performance to CodeGen- multi 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B (Nijkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 7 CONCLUSION We described the progress of the BigCode project until December 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The community took its first steps towards redacting PII and demonstrated that regular expressions are reasonably effective at detecting emails and IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Future work should focus on increasing the precision and recall of secret keys, as well as detecting other sensitive information such as names, usernames, and pass- word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Using the PII-redacted version of The Stack, we conducted a series of architectural and data filtering ablations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' One of our main findings was that filtering for Github stars consistently decreased performance across all benchmarks and programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Using the findings of these abla- tion studies, we trained a final 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B model—dubbed SantaCoder—for 236B tokens and showed it is able to outperform previous multi-lingual code models (InCoder-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B and CodeGen-Multi-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B) on both left-to-right generation and infilling tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We anticipate that larger architectures and more training data will be able to produce stronger multilingual, infilling-capable models, and plan to continue to scale the findings from our investigations here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 11 Preprint 8 CONTRIBUTIONS Model license Carlos Munoz Ferrandis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopher Akiki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Danish Contractor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Huu Nguyen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Luis Villa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sean Hughes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yacine Jernite,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' David Lansky PII redaction Loubna Ben Allal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jia Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Paulo Villegas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro Von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopher Akiki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ian Yu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Michael Lappert,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Urvashi Bhattacharyya,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shamik Bose,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bernardo Garc´ıa del R´ıo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Francesco De Toni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Terry Yue Zhuo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Qian Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Manuel Romero Dataset Denis Kocetkov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Chenghao Mou,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Loubna Ben Allal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dmitry Ab- ulkhanov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopher Akiki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Raymond Li Tokenizer Christopher Akiki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sergey Troshin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dmitry Abulkhanov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Daniel Fried,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries Training and architecture Raymond Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Daniel Fried,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hailey Schoelkopf,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Joel Lamy Poirier,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Qian Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Niklas Muennighoff,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Loubna Ben Allal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dzmitry Bahdanau,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra Opt out Sean Hughes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Carlos Munoz Ferrandis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopher Akiki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Denis Kocetkov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Huu Nguyen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Luis Villa Evaluation Arjun Guha,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yangtian Zi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Carolyn Jane Anderson,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Loubna Ben Allal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Raymond Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Niklas Muennighoff,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Manan Dey,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Logesh Kumar Umapathi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Marco Zocca Inference Mayank Mishra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alex Gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Joel Lamy Poirier,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leandro von Werra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harm de Vries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sourab Mangrulka Acknowledgement We thank ServiceNow and HuggingFace for the provided compute resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' REFERENCES Wasi Ahmad, Saikat Chakraborty, Baishakhi Ray, and Kai-Wei Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Unified pre-training for program understanding and generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Tech- nologies, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 2655–2668, Online, June 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='aclweb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/anthology/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='naacl-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Toufique Ahmed and Premkumar Devanbu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Multilingual training for software engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 44th International Conference on Software Engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ACM, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1145/3510003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3510049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ben Athiwaratkun, Sanjay Krishna Gouda, Zijian Wang, Xiaopeng Li, Yuchen Tian, Ming Tan, Wasi Uddin Ahmad, Shiqi Wang, Qing Sun, Mingyue Shang, Sujan Kumar Gonugondla, Hantian Ding, Varun Kumar, Nathan Fulton, Arash Farahani, Siddhartha Jain, Robert Giaquinto, Haifeng Qian, Murali Krishna Ramanathan, Ramesh Nallapati, Baishakhi Ray, Parminder Bhatia, Sudipta Sengupta, Dan Roth, and Bing Xiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Multi-lingual evaluation of code generation models, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14868.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jacob Austin, Augustus Odena, Maxwell Nye, Maarten Bosma, Henryk Michalewski, David Dohan, Ellen Jiang, Carrie Cai, Michael Terry, Quoc Le, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Program synthesis with large language models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='07732, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mohammad Bavarian, Heewoo Jun, Nikolas Tezak, John Schulman, Christine McLeavey, Jerry Tworek, and Mark Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Efficient training of language models to fill in the middle, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 12 Preprint Loubna Ben Allal, Niklas Muennighoff, and Leandro Von Werra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A framework for the evaluation of code generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/bigcode-project/ bigcode-evaluation-harness, December 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Federico Cassano, John Gouwar, Daniel Nguyen, Sydney Nguyen, Luna Phipps-Costin, Donald Pinckney, Ming-Ho Yee, Yangtian Zi, Carolyn Jane Anderson, Molly Q Feldman, Arjun Guha, Michael Greenberg, and Abhinav Jangda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A scalable and extensible approach to benchmarking nl2code for 18 programming languages, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 08227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mark Chen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jerry Tworek,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Heewoo Jun,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Qiming Yuan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Henrique Ponde de Oliveira Pinto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jared Kaplan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Harri Edwards,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yuri Burda,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nicholas Joseph,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Greg Brockman,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alex Ray,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Raul Puri,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Gretchen Krueger,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Michael Petrov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Heidy Khlaaf,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Girish Sastry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Pamela Mishkin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Brooke Chan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Scott Gray,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nick Ryder,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mikhail Pavlov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alethea Power,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Lukasz Kaiser,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mohammad Bavarian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Clemens Winter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Philippe Tillet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Felipe Petroski Such,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dave Cummings,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Matthias Plappert,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fo- tios Chantzis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Elizabeth Barnes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ariel Herbert-Voss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' William Hebgen Guss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alex Nichol,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alex Paino,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nikolas Tezak,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jie Tang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Igor Babuschkin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Suchir Balaji,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shantanu Jain,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' William Saunders,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Christopher Hesse,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Andrew N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Carr, Jan Leike, Josh Achiam, Vedant Misra, Evan Morikawa, Alec Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob Mc- Grew, Dario Amodei, Sam McCandlish, Ilya Sutskever, and Wojciech Zaremba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Evaluating large language models trained on code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Aakanksha Chowdhery,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sharan Narang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jacob Devlin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Maarten Bosma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Gaurav Mishra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Adam Roberts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Paul Barham,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hyung Won Chung,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Charles Sutton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sebastian Gehrmann,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Parker Schuh,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Kensen Shi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sasha Tsvyashchenko,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Joshua Maynez,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Abhishek Rao,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Parker Barnes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yi Tay,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Noam Shazeer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Vinodkumar Prabhakaran,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Emily Reif,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Nan Du,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ben Hutchinson,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Reiner Pope,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' James Bradbury,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Jacob Austin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Michael Isard,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Guy Gur-Ari,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Pengcheng Yin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Toju Duke,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Anselm Lev- skaya,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sanjay Ghemawat,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sunipa Dev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Henryk Michalewski,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Xavier Garcia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Vedant Misra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Kevin Robinson,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Liam Fedus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Denny Zhou,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Daphne Ippolito,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' David Luan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hyeontaek Lim,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Barret Zoph,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Alexander Spiridonov,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ryan Sepassi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' David Dohan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shivani Agrawal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mark Omernick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Andrew M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dai, Thanumalayan Sankaranarayana Pillai, Marie Pellat, Aitor Lewkowycz, Er- ica Moreira, Rewon Child, Oleksandr Polozov, Katherine Lee, Zongwei Zhou, Xuezhi Wang, Brennan Saeta, Mark Diaz, Orhan Firat, Michele Catasta, Jason Wei, Kathy Meier-Hellstern, Douglas Eck, Jeff Dean, Slav Petrov, and Noah Fiedel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Palm: Scaling language model- ing with pathways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CoRR, abs/2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='02311, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='02311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='02311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fenia Christopoulou, Gerasimos Lampouras, Milan Gritta, Guchun Zhang, Yinpeng Guo, Zhongqi Li, Qi Zhang, Meng Xiao, Bo Shen, Lin Li, Hao Yu, Li Yan, Pingyi Zhou, Xin Wang, Yuchi Ma, Ignacio Iacobacci, Yasheng Wang, Guangtai Liang, Jiansheng Wei, Xin Jiang, Qianxiang Wang, and Qun Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Pangu-coder: Program synthesis with function-level language modeling, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='11280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Zhangyin Feng, Daya Guo, Duyu Tang, Nan Duan, Xiaocheng Feng, Ming Gong, Linjun Shou, Bing Qin, Ting Liu, Daxin Jiang, and Ming Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CodeBERT: A pre-trained model for pro- gramming and natural languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Findings of the Association for Computational Linguistics: EMNLP 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 1536–1547, Online, November 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Association for Computational Lin- guistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='findings-emnlp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/ 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='findings-emnlp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Zhangyin Feng, Daya Guo, Duyu Tang, Nan Duan, Xiaocheng Feng, Ming Gong, Linjun Shou, Bing Qin, Ting Liu, Daxin Jiang, and Ming Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Codebert: A pre-trained model for programming and natural languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08155, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Daniel Fried, Armen Aghajanyan, Jessy Lin, Sida Wang, Eric Wallace, Freda Shi, Ruiqi Zhong, Wen-tau Yih, Luke Zettlemoyer, and Mike Lewis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Incoder: A generative model for code infilling and synthesis, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='05999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Leo Gao, Stella Biderman, Sid Black, Laurence Golding, Travis Hoppe, Charles Foster, Jason Phang, Horace He, Anish Thite, Noa Nabeshima, Shawn Presser, and Connor Leahy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The Pile: An 800GB dataset of diverse text for language modeling, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 13 Preprint Leo Gao, Jonathan Tow, Stella Biderman, Sid Black, Anthony DiPofi, Charles Foster, Laurence Golding, Jeffrey Hsu, Kyle McDonell, Niklas Muennighoff, Jason Phang, Laria Reynolds, Eric Tang, Anish Thite, Ben Wang, Kevin Wang, and Andy Zou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A framework for few-shot lan- guage model evaluation, September 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5371628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Vincent J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hellendoorn, Christian Bird, Earl T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Barr, and Miltiadis Allamanis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Deep Learning Type Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Fse, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dan Hendrycks, Steven Basart, Saurav Kadavath, Mantas Mazeika, Akul Arora, Ethan Guo, Collin Burns, Samir Puranik, Horace He, Dawn Song, and Jacob Steinhardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Measuring coding challenge competence with APPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='09938, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 09938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='09938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CodeSearchNet challenge: Evaluating the state of semantic code search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='09436, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Srinivasan Iyer, Ioannis Konstas, Alvin Cheung, and Luke Zettlemoyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Mapping language to code in programmatic context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='09588, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Maliheh Izadi, Roberta Gismondi, and Georgios Gousios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Codefill: Multi-token code completion by jointly learning from structure and naming sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 44th International Conference on Software Engineering, ICSE ’22, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 401–412, New York, NY, USA, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Asso- ciation for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ISBN 9781450392211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1145/3510003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3510172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1145/3510003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3510172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Learning and evaluating contextual embedding of source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 37th International Conference on Machine Learning, ICML’20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' JMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Diederik P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Yoshua Bengio and Yann LeCun (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ), 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL http: //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='6980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Denis Kocetkov, Raymond Li, Loubna Ben Allal, Jia Li, Chenghao Mou, Carlos Mu˜noz Ferrandis, Yacine Jernite, Margaret Mitchell, Sean Hughes, Thomas Wolf, Dzmitry Bahdanau, Leandro von Werra, and Harm de Vries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The Stack: 3 TB of permissively licensed source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Preprint, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Sumith Kulal, Panupong Pasupat, Kartik Chandra, Mina Lee, Oded Padon, Alex Aiken, and Percy S Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Spoc: Search-based pseudocode to code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Larochelle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Beygelzimer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=" d'Alch´e-Buc, E." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fox, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Garnett (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ), Advances in Neural Information Processing Sys- tems, volume 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' cc/paper/2019/file/7298332f04ac004a0ca44cc69ecf6f6b-Paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yuhang Lai, Chengxi Li, Yiming Wang, Tianyi Zhang, Ruiqi Zhong, Luke Zettlemoyer, Scott Wen tau Yih, Daniel Fried, Sida Wang, and Tao Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ds-1000: A natural and reliable benchmark for data science code generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ArXiv, abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='11501, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yujia Li, David Choi, Junyoung Chung, Nate Kushman, Julian Schrittwieser, R´emi Leblond, Tom Eccles, James Keeling, Felix Gimeno, Agustin Dal Lago, Thomas Hubert, Peter Choy, Cyprien de Masson d’Autume, Igor Babuschkin, Xinyun Chen, Po-Sen Huang, Johannes Welbl, Sven Gowal, Alexey Cherepanov, James Molloy, Daniel Mankowitz, Esme Sutherland Robson, Push- meet Kohli, Nando de Freitas, Koray Kavukcuoglu, and Oriol Vinyals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Competition-level code generation with alphacode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='07814, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shuai Lu, Daya Guo, Shuo Ren, Junjie Huang, Alexey Svyatkovskiy, Ambrosio Blanco, Colin Clement, Dawn Drain, Daxin Jiang, Duyu Tang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Codexglue: A machine learning benchmark dataset for code understanding and generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='04664, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 14 Preprint Anthony MOI, Nicolas Patry, Pierric Cistac, Pete, Funtowicz Morgan, Sebastian P¨utz, Mishig, Bjarte Johansen, Thomas Wolf, Sylvain Gugger, Clement, Julien Chaumond, Lysandre Debut, Franc¸ois Garillot, Luc Georges, dctelus, JC Louis, MarcusGrass, Taufiquzzaman Peyash, 0xflotus, Alan deLevie, Alexander Mamaev, Arthur, Cameron, Colin Clement, Dagmawi Moges, David Hewitt, Denis Zolotukhin, and Geoffrey Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' huggingface/tokenizers: Rust 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2, November 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7298413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Erik Nijkamp, Bo Pang, Hiroaki Hayashi, Lifu Tu, Huan Wang, Yingbo Zhou, Silvio Savarese, and Caiming Xiong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A conversational paradigm for program synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Michael Pradel, Georgios Gousios, Jason Liu, and Satish Chandra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' TypeWriter: Neural Type Pre- diction with Search-Based Validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Esecfse, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Shuo Ren, Daya Guo, Shuai Lu, Long Zhou, Shujie Liu, Duyu Tang, Neel Sundaresan, Ming Zhou, Ambrosio Blanco, and Shuai Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Codebleu: a method for automatic evaluation of code synthesis, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='10297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Baptiste Roziere, Marie-Anne Lachaux, Marc Szafraniec, and Guillaume Lample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Dobf: A deob- fuscation pre-training objective for programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='07492, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Phillip Rust, Jonas Pfeiffer, Ivan Vuli´c, Sebastian Ruder, and Iryna Gurevych.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' How good is your to- kenizer?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' on the monolingual performance of multilingual language models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 3118–3135, On- line, August 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='18653/v1/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='acl-long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='acl-long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Teven Le Scao, Angela Fan, Christopher Akiki, Ellie Pavlick, Suzana Ili´c, Daniel Hesslow, Roman Castagn´e, Alexandra Sasha Luccioni, Franc¸ois Yvon, Matthias Gall´e, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Bloom: A 176b- parameter open-access multilingual language model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='05100, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Noam Shazeer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Fast transformer decoding: One write-head is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CoRR, abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='02150, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='02150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Michele Tufano, Dawn Drain, Alexey Svyatkovskiy, Shao Kun Deng, and Neel Sundaresan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Unit test case generation with transformers and focal context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' arXiv preprint arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='10297, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='05617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='05617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Advances in Neural Infor- mation Processing Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 5998–6008, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Yue Wang, Weishi Wang, Shafiq Joty, and Steven C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Hoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CodeT5: Identifier-aware unified pre-trained encoder-decoder models for code understanding and generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 8696–8708, Online and Punta Cana, Dominican Republic, November 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='18653/v1/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='emnlp-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/ 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='emnlp-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Frank F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Xu, Uri Alon, Graham Neubig, and Vincent Josua Hellendoorn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' A systematic evalua- tion of large language models of code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' In Proceedings of the 6th ACM SIGPLAN International Symposium on Machine Programming, MAPS 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 1–10, New York, NY, USA, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Asso- ciation for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ISBN 9781450392730.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1145/3520312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3534862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1145/3520312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3534862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Tao Yu, Rui Zhang, Kai Yang, Michihiro Yasunaga, Dongxu Wang, Zifan Li, James Ma, Irene Li, Qingning Yao, Shanelle Roman, Zilin Zhang, and Dragomir Radev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Spider: A large-scale human- labeled dataset for complex and cross-domain semantic parsing and text-to-sql task, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08887.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Victor Zhong, Caiming Xiong, and Richard Socher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Seq2sql: Generating structured queries from natural language using reinforcement learning, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='org/abs/ 1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='00103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 15 Preprint A FULL TEXT2CODE RESULTS We report the full results of all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Table 7 and 8 show the full results for the data filtering ablations on HumanEval and MBPP, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Table 9 and 10 reports the full results for the architecture ablations on HumanEval and MBPP, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Language Model Pass@1 Pass@10 Pass@100 Java Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 JavaScript Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='33 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 Python Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='31 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 Table 7: Full results for data filtering ablations on HumanEval 16 Preprint Language Model Pass@1 Pass@10 Pass@100 Java Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='54 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='49 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='52 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='55 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='53 JavaScript Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='43 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='64 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='59 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='66 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='43 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 Python Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 GitHub stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='63 Comments-to-code ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='69 More near deduplication 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='49 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='71 Tokenizer fertility 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='68 Table 8: Full results for data filtering ablations on MBPP Language Attention FIM Pass@1 Pass@10 Pass@100 Java Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='35 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 JavaScript Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='33 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 Python Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='36 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='39 Table 9: Full results for architecture ablations on HumanEval 17 Preprint Language Attention FIM Pass@1 Pass@10 Pass@100 Java Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='54 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='55 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='55 JavaScript Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='43 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='64 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 Python Multi Query Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 Multi Head Attention \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='49 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7 Multi Query Attention \x17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='68 Table 10: Full results for architecture ablations on MBPP Model Family Variant BLEU InCoder 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='04 CodeGen-Mono 16B 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='56 SantaCoder Baseline 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 SantaCoder No-FIM 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='71 SantaCoder MHA 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='72 SantaCoder Bf16 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67 SantaCoder GitHub Stars 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='04 SantaCoder Comments-to-code 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='81 SantaCoder More near deduplication 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='65 SantaCoder Tokenizer fertility 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='64 SantaCoder Final 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='13 Table 11: CodeXGLUE (Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) Python Docstring generation smoothed 4-gram BLEU scores using the same methodology as Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022) (L-R single).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Models are evaluated zero- shot, greedily and with a maximum generation length of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' B DOCSTRING GENERATION In addition to code completion benchmarks, we also report results on docstring generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' To this end, we evaluate our models on CodeXGLUE code-to-text Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021), which is a benchmark constructed from CodeSearchNet Husain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' We use the bigcode-evaluation-harness li- brary Ben Allal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2022), which is derived from lm-evaluation-harness Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Models are prompted with a Python function signature and asked to output a corresponding docstring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Re- sults are shown in Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Findings We find all BigCode Santa variants with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B parameters to outperform the 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B In- Coder model (Fried et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2022), which we attribute to differences in the training datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Among BigCode models, variants trained on more Python perform better: The stars variant with 32% of Python in its training corpus outperforms the tokenizer fertility variant with only 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='5% of Python (see proportions in Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' The bfloat16 is the same as the no-fim variant, except for the lat- ter being trained in float16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' There’s no notable performance difference between the two, likely because at our small scale of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1B parameters we did not face any training instabilites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Qualitative examples Below is an example prompt from CodeXGLUE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Model generations and the correct solution are in Table 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' def dailymotion_download(url, output_dir=’.’, merge=True, info_only=False, **kwargs): """ 18 Preprint Model Family Variant Generation InCoder 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='7B Download a video from Dailymotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' CodeGen-Mono 16B Downloads Dailymotion videos by URL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder Baseline Download Dailymotion videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder FIM Download a video from a dailymotion video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder MHA Download a video from a Dailymotion video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder bf16 Download video from dailymotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder GitHub stars Download media from dailymotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com SantaCoder Comments-to-code Download a video from Dailymotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder More near deduplication Download a dailymotion video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' SantaCoder Tokenizer fertility Download a video from Dailymotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Correct solution Downloads Dailymotion videos by URL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' Table 12: CodeXGLUE (Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=', 2021) Python Docstring generation examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' C PII C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 REGULAR EXPRESSIONS Email addresses We used the following regular expression to detect emails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' email_pattern = r’’’ (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='<= ˆ | [\\b\\s@,?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':)(’".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='\\p{Han}<] ) ( [ˆ\\b\\s@?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=',:)(’"<]+ @ [ˆ\\b\\s@!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=',/]* [ˆ\\b\\s@?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=',/:)(’">.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='] \\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' \\p{L} \\w{1,} ) (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='= $ | [\\b\\s@,?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':)(’".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='\\p{Han}>] ) ’’’ We replace detected emails with [random 5 character string]@example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' IP addresses We used the following regular expressions to detect IPv4 and IPv6 addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ipv4_pattern = r"(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':25[0-5]|2[0-4][0-9]|[01]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='[0-9][0-9]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=') (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':\\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':25[0-5]|2[0-4][0-9]|[01]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='[0-9][0-9]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' )){3}" ipv6_pattern = r"(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' :[0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F ]{1,4}|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':[0-9a-fA-F]{1,4}:){1,7}:|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' :[0-9a-fA-F]{1,4}:) {1,6}:[0-9a-fA-F]{1,4}|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':[0-9a-fA-F]{1,4}:){1,5}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA- F]{1,4}){1,2}|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':[0-9a-fA-F]{1,4}:){1,4}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA-F]{1,4}) {1,3}|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':[0-9a-fA-F]{1,4}:){1,3}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA-F]{1,4}) {1,4}|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':[0-9a-fA-F]{1,4}:){1,2}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA-F]{1,4}) {1,5}|[0-9a-fA-F]{1,4}:(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA-F]{1,4}){1,6}) |:(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='::[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::[0-9a-fA-F]{0,4}) {0,4}%[0-9a-zA-Z]{1,}|::(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':ffff(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ::0{1,4}){0,1}:) {0,1}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':25[0-5]|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=') {3,3}(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':25[0-5]|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':2[0-4]|1{0,1}[0-9]){0,1}[0-9])|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' :[0-9a-fA- F]{1,4}:){1,4}:(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':25[0-5]|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' :2[0-4]|1{0,1}[0-9]){0,1}[0-9]) \\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='){3,3}(25[0-5]|(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' :2[0-4]|1{0,1}[0-9]){0,1}[0-9])" ip_pattern = ( r"(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':ˆ|[\\b\\s@?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=',!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':\\’\\")(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='\\p{Han}])(" + r"|".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='join([ipv4_pattern, ipv6_pattern]) 19 Preprint + ")(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':$|[\\s@,?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':’\\"(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='\\p{Han}])" ) Data pre-filtering This is the regular expression we used to pre-filter the annotation dataset for data containing emails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' email_pattern = r’([ˆ\\s@,?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':\\’\\"=)(]+@[ˆ,\\s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='?;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=',\\’\\"=]{3,}[\\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ][ˆ\\s \\b\\’\\"@,?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='!;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=':)(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' ]+)’ For IP addresses, we used the same regular expression as the one used for PII detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='2 LIST OF PRIVATE IP ADDRESSES AND POPULAR DNS SERVERS 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='1 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='19 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='223.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='150 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='9 149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='112 208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='222 208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='220 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='26 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='20 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='14 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='15 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='3 DETECT-SECRETS FILTERS detect secrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='heuristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='is potential uuid detect secrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='heuristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='is likely id string detect secrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='heuristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='is templated secret detect secrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='heuristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='is sequential string Implementation available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/bigcode-project/ bigcode-dataset/blob/6b3f54751b6e38e1ed70f2307331d6943ba39eae/ pii/utils/keys_detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='py#L11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='4 DETECT-SECRETS PLUGINS ArtifactoryDetector AWSKeyDetector Base64HighEntropyString HexHighEntropyString AzureStorageKeyDetector CloudantDetector DiscordBotTokenDetector GitHubTokenDetector 20 Preprint IbmCloudIamDetector IbmCosHmacDetector JwtTokenDetector MailchimpDetector NpmDetector SendGridDetector SlackDetector SoftlayerDetector StripeDetector TwilioKeyDetector Implementation available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='com/bigcode-project/ bigcode-dataset/blob/6b3f54751b6e38e1ed70f2307331d6943ba39eae/ pii/utils/keys_detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content='py#L19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} +page_content=' 21' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE2T4oBgHgl3EQflgcs/content/2301.03988v1.pdf'} diff --git a/A9E2T4oBgHgl3EQfRQfr/vector_store/index.pkl b/A9E2T4oBgHgl3EQfRQfr/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..6ed3ac406d154bd3758e213f6ab89560d376a47d --- /dev/null +++ b/A9E2T4oBgHgl3EQfRQfr/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:32268138c538a94c7f4a22c8de4e6b4e96f27ec16f8831d4958dd06e7f50b272 +size 152970 diff --git a/AdE4T4oBgHgl3EQf4w7g/vector_store/index.faiss b/AdE4T4oBgHgl3EQf4w7g/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..48c39446510f2bcd35002b2b0cb8aa101e108c30 --- /dev/null +++ b/AdE4T4oBgHgl3EQf4w7g/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b028ef7e3a2f993d7e4d5d2ca773c66d6eeab3a6d27e7cbbab59e7f022ccd4c2 +size 4587565 diff --git a/CdE1T4oBgHgl3EQfWAQw/content/2301.03108v1.pdf b/CdE1T4oBgHgl3EQfWAQw/content/2301.03108v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..64420c0dc75fba816a4d0da4f5977f149686b2c1 --- /dev/null +++ b/CdE1T4oBgHgl3EQfWAQw/content/2301.03108v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4259c62df656757bd7b9aaeeddf97268192242defc2d2db0e1194f8be9589fa5 +size 100376 diff --git a/CdE1T4oBgHgl3EQfWAQw/vector_store/index.faiss b/CdE1T4oBgHgl3EQfWAQw/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..0b7299cf443f850d20ba957d3bf1efe9e98d23d3 --- /dev/null +++ b/CdE1T4oBgHgl3EQfWAQw/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a696fe9e59cafa7dbf8d11ff79dcc35614b713610e3bf5871668b968c180bdee +size 852013 diff --git a/CdE1T4oBgHgl3EQfWAQw/vector_store/index.pkl b/CdE1T4oBgHgl3EQfWAQw/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..b4d6edf82ab8ec3fb258fa866cb30a83b3e5833e --- /dev/null +++ b/CdE1T4oBgHgl3EQfWAQw/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ff332c99768aaa69c70b9a61733c12cd81f5d719e917c459956fd0e3bac1b48c +size 37990 diff --git a/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/2301.04456v1.pdf.txt b/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/2301.04456v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..86095987698c5ba97e4e0674e0cc685df3daecc8 --- /dev/null +++ b/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/2301.04456v1.pdf.txt @@ -0,0 +1,1219 @@ +A note on constructions of bent functions +Yanjun Li, Haibin Kan∗, Jie Peng, Lijing Zheng, and Changhui Chen +Abstract +Recently, Li et al. presented a generic construction of bent functions in [IEEE Trans. +Inf. Theory, vol. 68, no. 4, pp. 2735-2751, 2022]. In this paper, we give a characterization +for their construction from another perspective. This characterization enables us to obtain +another efficient construction of bent functions. Based on that, we derive several infinite +families of concrete bent functions and give their duals. Our results show that many known +bent functions are particular cases of our bent functions. +Index Terms: Bent function, duals, cryptography, Walsh-Hadamard transform, Gold function. +Mathematics Subject Classification 2020: 06E30, 94A60, 94D10. +1 +Introduction +Bent functions, introduced in [19], are those Boolean functions in an even number of variables +having the highest nonlinearity. Such functions have been extensively studied in the last four +decades, because of their closely relationship with the theory of difference sets, and their sig- +nificant applications in coding theory and cryptography [4]. Bent functions are not balanced, +however, they often act as an important and efficient ingredient for finding some balanced func- +tions with a higher nonlinearity. For instance, the authors of [25] used bent functions to construct +some disjoint spectra plateaued functions with higher nonlinearities. Their results provided a +positive answer to an open problem of [26]. The authors of [21] utilized bent functions to con- +struct balanced Boolean functions with high nonlinearity and low absolute indicator. +Their +results partially disproved a conjecture of [27]. In the past, a large amount of work was done +on the characterizations and constructions of bent functions. But until now, a complete classi- +fication is not finished and it remains elusive. Along with the deep-going of the research, the +progress on bent functions becomes more and more difficult even if a tiny progress is not easy. +For a comprehensive survey and a book on bent functions, the interested readers are referred to +[5] and [15], respectively. +In this paper, we focus our attention on the constructions of bent functions with the form +h(x) = f(x) + F ◦ φ(x), +(1) +where f is a bent function on F2n, F is a Boolean function on Fr +2, and φ = (φ1, φ2, . . . , φr) is an +(n, r)-function. In fact, the research on the bent-ness of h can be dated back to [3], where Carlet +presented a sufficient condition for a particular case (called Carlet function) of h to be bent, that +is, the case of h to be bent when r = 2, f = f1, φ1 = f1 + f2, φ2 = f1 + f3 and F(x1, x2) = x1x2 +in (1). That sufficient condition had been proved by Mesnager [13] to be necessary. Mesnager +∗Corresponding author +Y. Li is with Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, +Bengbu, Anhui 233030, China (Email: yanjlmath90@163.com). +H. Kan is with Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fu- +dan University, Shanghai 200433, China; Shanghai Engineering Research Center of Blockchain, Shanghai 200433, +China; and Yiwu Research Institute of Fudan University, Yiwu City 322000, China (E-mail: hbkan@fudan.edu.cn). +J. Peng and C. Chen are with Mathematics and Science College of Shanghai Normal University, Guilin Road +#100, Shanghai 200234, China (Emails: jpeng@shnu.edu.cn and cchxuexi@126.com). +L. Zheng is with the School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, +China (Email: zhenglijing817@163.com). +1 +arXiv:2301.04456v1 [cs.IT] 11 Jan 2023 + +[13] also studied the bent-ness of two particular cases of Carlet function. The first particular +case is to let f2(x) = f1(x) + Trn +1(ax) and f3(x) = f1(x) + Trn +1(bx) for some a, b ∈ F∗ +2n; and the +second particular case is to let f3(x) = f1(x) + Trn +1(ax) for some a ∈ F∗ +2n in Carlet function, +from which Mesnager obtained a lot of bent functions and gave their duals. Thereafter, several +papers, such as [10, 20, 22, 23, 24, 28, 30], were done for generalizing Carlet and Mesnager’s +works. The main results of those papers are listed in Table 1. +Table 1: The bent functions of the form h(x) = f(x) + F ◦ φ(x) +r +φ = (φ1, φ2, . . . , φr) +F +Condition +Ref. +2 +φ1 = f + f2, φ2 = f + f3 +F(x1, x2) = x1x2 +see Theorem 1 of +this paper +[3] +2 +φ1(x) = Trn +1(ax), +φ2(x) = Trn +1(bx) +F(x1, x2) = x1x2 +f is bent, +DaDbf ∗ = 0 +[13] +2 +φ1 = f + f2, φ2(x) = Trn +1(ax) +F(x1, x2) = x1x2 +f is bent, +Da(f + f2)∗ = 0 +[13] +3 +φi(x) = Trn +1(µix) +F(x1, x2, x3) = x1x2x3 +see [24] +[24] +r +φi(x) = Trn +1(µix) +F(x1, x2, . . . , xr) = Πr +i=1xi +see Theorem 1 of +[22] +[22] +r +φi(x) = Trn +1(µix) +any Boolean function on Fr +2 +see Theorem 2 of +this paper +[20] +r +φi(x) = Trn +1(µix) +any Boolean function on Fr +2 +f is bent, +DµiDµjf ∗ = 0 for +any i ̸= j +[28, 30] +r +φi = f + gi +any Boolean function on Fr +2 +see Theorem 4 of +this paper +[10] +r +φ +any Boolean function on Fr +2 +f satisfies Pr with φ +Thm. 5 +r +φ1 = f + g, +φi(x) = Trn +1(µix), 2 ≤ i ≤ r +any Boolean function on Fr +2 +see Corollary 5 of +this paper +Cor. 5 +r +φ1(x) = f(x) + f(x + α), +φi(x) = Trn +1(µix), 2 ≤ i ≤ r +any Boolean function on Fr +2 +α ∈ +� +µ2, . . . , µr +�⊥, +DµiDµjf ∗ = 0 for +any i ̸= j +Cor. 6 +In this paper, we continue to study the bent-ness of h defined in (1). By analysing carefully +many previous results on the constructions of bent functions in the form (1), we obtain a +framework on the constructions of bent functions, which unifies many previous constructions of +bent functions in [3, 10, 13, 20, 22, 24, 28]. This framework also enables us to find another efficient +construction of bent functions. Based on that, we obtain a number of concrete bent functions +and determine their duals. Consequently, we find that our results cover many previously known +bent functions. +2 +Preliminaries +Throughout the paper, let n = 2m be an even positive integer. Let F2n be the finite field of order +2n, F∗ +2n = F2n\{0}, and Fn +2 be the n-dimensional vector space over F2. There is a one-to-one +correspondence between F2n and Fn +2, because every a ∈ F2n can be represented uniquely by +a = a1α1 + a2α2 + · · · + anαn, where ai ∈ F2, {α1, α2, . . . , αn} is a basis of F2n over F2. So the +finite field F2n is always identified to the n-dimensional vector space Fn +2 in this paper. +For a vector ω = (ω1, ω2, . . . , ωn) ∈ Fn +2, the set suppt(ω) = {1 ≤ i ≤ n : ωi ̸= 0} is said to +be the support of ω, whose cardinality is called the (Hamming) weight of ω, denoted by wt(ω). +Namely, we have wt(ω) = |suppt(ω)|. +A mapping φ from Fn +2 to Fr +2 is called an (n, r)-function. +When n is divisible by r, the +(n, r)-function +Trn +r (x) = x + x2r + x22r + · · · + x2n−r +is called the trace function. The set of all (n, 1)-functions (namely, all Boolean functions) is +denoted by Bn. +2 + +For a given Boolean function f on Fn +2, the Walsh-Hadamard transform of f is a mapping +from Fn +2 to Z defined as +Wf(µ) = +� +x∈Fn +2 +(−1)f(x)+µ·x, +µ ∈ Fn +2, +and its inverse transform is given by +(−1)f(µ) = 2−n � +x∈Fn +2 +Wf(x)(−1)µ·x, +µ ∈ Fn +2, +where µ · x denotes the canonical inner product of µ and x (in F2n, µ · x = Trn +1(µx)). The first +derivative of f in terms of µ ∈ Fn +2 is defined as +Dµf(x) = f(x) + f(x + µ). +Definition 1. A Boolean function f over Fn +2 is called bent if n is even and Wf(µ) = ±2 +n +2 for +all µ ∈ Fn +2. +Bent functions always appear in pairs, that is, for any bent function f on Fn +2, there is always a +unique bent function f∗ such that Wf(µ) = 2 +n +2 (−1)f∗(µ) for all µ ∈ Fn +2. Hence, in the literature, +f∗ is called the dual of f. +Two Boolean functions f and g are called EA-equivalent if there is an affine automorphism +A and affine function ℓ such that f(x) = g ◦ A(x) + ℓ(x). The set of all functions which are +EA-equivalent to f is called a complete class of f. To see whether a bent function is inside a +complete class of another bent function is challenging in general. +3 +Some known results and a framework of bent functions +3.1 +Known results +In this subsection, we review some known bent functions of the form +h(x) = f(x) + F ◦ φ(x), +(2) +where f is a bent function on Fn +2, φ = (φ1, φ2, . . . , φr) is an (n, r)-function and F is a Boolean +function on Fr +2. Firstly, when r = 2, f = f1, φ1 = f1 + f2, φ2 = f1 + f3 and F(x1, x2) = x1x2, +Carlet gave the following result. +Theorem 1. [3] Let f1, f2, f3 be three bent functions on F2n such that f1 + f2 + f3 is bent as +well, and (f1 + f2 + f3)∗ = f∗ +1 + f∗ +2 + f∗ +3 . Then +h(x) = f1(x)f2(x) + f1(x)f3(x) + f2(x)f3(x) +is a bent function with dual +h∗(x) = f∗ +1 (x)f∗ +2 (x) + f∗ +1 (x)f∗ +3 (x) + f∗ +2 (x)f∗ +3 (x). +This theorem provides a general method to find new bent functions. By finding different +bent functions f1, f2 and f3 satisfying the conditions of Theorem 1, several new bent functions +have been constructed, see [7, 12, 13, 14, 16] for details. +In 2014, Mesnager [13] revisited Theorem 1, and found that the conditions of Theorem 1 is +also necessary. Then letting f1(x) = f(x), f2(x) = f(x) + Trn +1(ax) and f3(x) = f(x) + Trn +1(bx) +for some distinct a, b ∈ F∗ +2n in Theorem 1, she obtained the following result. +Corollary 1. [13] Let f be a bent function on F2n. Let a, b ∈ F∗ +2n. Then +h(x) = f(x) + Trn +1(ax)Trn +1(bx) +(3) +is bent if and only if DaDbf∗ = 0. Moreover, the dual of h is given by h∗(x) = f∗(x)f∗(x + a) + +f∗(x)f∗(x + b) + f∗(x + a)f∗(x + b). +3 + +Letting f3(x) = f1(x) + Trn +1(ax) for some a ∈ F∗ +2n in Theorem 1, Mesnager also obtained the +following result. +Corollary 2. [13] Let a ∈ F∗ +2n. Let f1, f2 be two bent functions on F2n. Then +h(x) = f1(x) + Trn +1(ax)(f1(x) + f2(x)) +is bent if and only if Da(f∗ +1 + f∗ +2 ) = 0. Moreover, the dual of h is that h∗(x) = f∗ +1 (x) + (f∗ +1 (x) + +f∗ +2 (x))f∗ +1 (x + a). +Using Corollaries 1 and 2, Mesnager found several infinite families of bent functions and +derived their duals. +After Mesnager’s work, many papers were dedicated to generalizing Corollary 1 for finding +new infinite families of bent functions. For instance, the authors of [24] generalized the function +h of Corollary 1 to the form +h(x) = f(x) + Trn +1(ax)Trn +1(bx)Trn +1(cx), +(4) +and studied its bent-ness, where f is a bent function on F2n and a, b, c ∈ F∗ +2n satisfy certain +conditions. The authors of [22] generalized the function h of Corollary 1 to the form +h(x) = f(x) + +r +� +i=1 +Trn +1(µix), +(5) +and studied its bent-ness, where f is a bent function on F2n and µ1, µ2, . . . , µr ∈ F∗ +2n satisfy +certain conditions, see [22, Theorem 1]. +The authors of [20] generalized the function h of +Corollary 1 to its extreme form. Their result is given as follows. +Theorem 2. [20] Let f be a bent function over F2n. If there exist r elements µ1, µ2, . . . , µr in +F∗ +2n and r Boolean functions g1, g2, . . . , gr on F2n such that +f∗ +� +x+ +r +� +i=1 +µiωi +� +=f∗(x)+ +r +� +i=1 +ωigi(x) +for all x ∈ F2n and all (ω1, . . . , ωr) ∈ Fr +2, then for any F ∈ Br, the Boolean function +h(x) = f(x) + F +� +Trn +1(µ1x), Trn +1(µ2x), . . . , Trn +1(µrx) +� +(6) +is bent with dual +h∗(x) = f∗(x) + F +� +g1(x), g2(x), . . . , gr(x) +� +. +Obviously, the functions h given in (3), (4), (5) and (6) are special cases of the form (2). +But the conditions of h (in (3), (4), (5) and (6)) to be bent become more and more complicated. +Therefore, a nature question is to ask that whether there is an unified simple condition such that +the function h in (2) is bent. To this end, the authors of [28] simplified Theorem 2 as follows. +Theorem 3. [28] Let f be a bent function on F2n. +Let µ1, µ2, . . . , µr ∈ F∗ +2n be such that +DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r. Then for any F ∈ Br, the function h given by (6) is bent, +whose dual is that +h∗(x) = f∗(x) + F(ϕ1(x), ϕ2(x), . . . , ϕr(x)), +where ϕi(x) = f∗(x) + f∗(x + µi) for each i ∈ {1, 2, . . . , r}. +Theorem 3 is clearly more concise than Theorem 2. But it does not contain Theorem 1 and +Corollary 2. In order to find a more general uniform, the authors of [10] presented the following +result. +4 + +Theorem 4. [10, Theorem 3] For any 1 ≤ i ≤ r, let f, gi ∈ Bn, and let φ = (φ1, φ2, . . . , φr) be +the (n, r)-function with φi = f + gi. If the sum of any odd number of functions in f, g1, . . . , gr +is a bent function, and its dual is equal to the sum of the duals of corresponding bent functions. +Then for any Boolean function F on Fr +2, the function h given by (2) is bent. Moreover, the dual +of h is given by +h∗(x) = f∗(x) + F ◦ ϕ(x), +where ϕ = (ϕ1, ϕ2, . . . , ϕr) is the (n, r)-function with ϕi(x) = f∗(x) + g∗ +i (x) for any 1 ≤ i ≤ r. +Theorem 4 reduces to Theorem 1 when r = 2 and F(x1, x2) = x1x2; and reduces to Theorems +2 and 3 when gi(x) = f(x) + Trn +1(µix) for each 1 ≤ i ≤ r. So in this sense, Theorem 4 is very +general, and it seems difficult to be generalized any more. +3.2 +A framework of bent functions +In this subsection, we try to generalize Theorem 4. By analysing carefully the conditions of h to +be bent in Theorems 1, 2, 3, and 4, respectively, we find that all conditions can be summarized +by the following property. +Definition 2 (Pr). Let f be a Boolean function over F2n. If there is an (n, r)-function φ = +(φ1, φ2, . . . , φr) such that the following two conditions are satisfied: +(i) f(x) + ω · φ(x) = f(x) + �r +i=1 ωiφi is bent for any ω = (ω1, ω2, . . . , ωr) ∈ Fr +2; +(ii) there is an (n, r)-function ϕ = (ϕ1, ϕ2, . . . , ϕr) such that +� +f(x)+ω·φ(x) +�∗ = f∗(x)+ω·ϕ(x) +for any ω ∈ Fr +2, +then we say that f satisfies Pr with respect to the (n, r)-function φ. +According to this property, we give the following framework of bent functions, which is main +result of this subsection. +Theorem 5. Let n = 2m. Let φ be an (n, r)-function, and let f be a Boolean function on F2n +satisfying Pr with respect to φ. Then for any Boolean function F on Fr +2, the function h given +by (2) is bent, and the dual of h is +h∗(x) = f∗(x) + F ◦ ϕ(x). +Proof. By the definition of the inverse Walsh-Hadamard transform, it holds that +(−1)F◦φ(x) = 2−r � +ω∈Fr +2 +WF (ω)(−1)ω·φ(x), +∀ x ∈ Fn +2. +Hence, the Walsh-Hadamard transform of h at β ∈ F2n is that +Wh(β) = +� +x∈F2n +(−1)f(x)+Trn +1 (βx)(−1)F◦φ(x) +=2−r � +x∈F2n +(−1)f(x)+Trn +1 (βx) � +ω∈Fr +2 +WF (ω)(−1)ω·φ(x) +=2−r � +ω∈Fr +2 +WF (ω) +� +x∈F2n +(−1)f(x)+Trn +1 (βx)+ω·φ(x) +=2−r � +ω∈Fr +2 +WF (ω)Wg(β), +where g(x) = f(x) + ω · φ(x). Recall that f satisfies Pr with respect to φ, that is, g is bent and +g∗(x) = f∗(x) + ω · ϕ(x) for any ω ∈ Fr +2. Hence, we have +Wh(β) = 2m−r � +ω∈Fr +2 +WF (ω)(−1)f∗(β)+ω·ϕ(β) = 2m(−1)f∗(β)+F◦ϕ(β). +The proof is completed. +5 + +According to Theorem 5, we can deduce the following corollaries. +Corollary 3. Theorem 5 reduces to that of Theorem 3 when φ = (φ1, φ2, . . . , φr) is an (n, r)- +function with φi(x) = Trn +1(µix), where µi ∈ F∗ +2n for each 1 ≤ i ≤ r. +Proof. To prove this result, by Theorem 5, it suffices to show that f satisfies Pr with respect to +φ if and only if f is bent and DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r. In fact, this fact has been +presented in [28, Lemma 3.3]. Here we provide a sketchy proof for the readers convenience. Note +that Item (i) of Pr is satisfied if and only if f is bent when φi(x) = Trn +1(µix) for each 1 ≤ i ≤ r. +Now assume that Item (ii) of Pr is satisfied, then it is easily seen that ϕi(x) = f∗(x)+f∗(x+µi) +for each 1 ≤ i ≤ r when wt(ω) = 1, and DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r when wt(ω) = 2. +Conversely, by induction on wt(ω), one can check easily that Item (ii) of Pr is also satisfied. +Corollary 4. Theorem 5 reduces to that of Theorem 4 when φ = (φ1, φ2, . . . , φr) is an (n, r)- +function with φi = f + gi, where f and gi are any Boolean functions on F2n for 1 ≤ i ≤ r. +Proof. Suppose that φ = (φ1, φ2, . . . , φr) with φi = f + gi for any 1 ≤ i ≤ r. Then for any +ω = (ω1, ω2, . . . , ωr) ∈ Fr +2, we have +f(x) + ω · φ(x) = f(x) + +r +� +i=1 +ωi(f(x) + gi(x)) = +� +Gω(x), +if wt(ω) is odd, +f(x) + Gω(x), +if wt(ω) is even, +where Gω(x) = ω1g1(x)+ω2g2(x)+· · ·+ωrgr(x). Therefore, Item (i) of Pr holds if and only if the +sum of any odd number of functions in f, g1, g2, . . . , gr is bent. Note that when suppt(ω) = {i}, +f(x) + ω · φ(x) = gi(x) and f∗(x) + ω · ϕ(x) = f∗(x) + ϕi(x). +So Item (ii) of Pr holds only if ϕi(x) = f∗(x) + g∗ +i (x) for any 1 ≤ i ≤ r. In this case, +f∗(x) + ω · ϕ(x) = f∗(x) + +r +� +i=1 +ωi(f∗(x) + g∗ +i (x)) = +� +G∗ +ω(x), +if wt(ω) is odd, +f∗(x) + G∗ +ω(x), +if wt(ω) is even, +where G∗ +ω(x) = ω1g∗ +1(x) + ω2g∗ +2(x) + · · · + ωrg∗ +r(x). Hence, Item (ii) of Pr holds if and only if +(Gω)∗ = G∗ +ω when wt(ω) is odd, and (f + Gω)∗ = f∗ + G∗ +ω when wt(ω) is even. Equivalently, +the dual of the sum of any odd number of functions in f, g1, g2, . . . , gr is equal to the sum of the +duals of corresponding bent functions. This completes the proof. +From the proof of Corollary 4, it is easily seen that for a given Boolean function f on F2n, +and an (n, r)-function φ = (φ1, φ2, . . . , φr), Pr holds if and only if the sum of any odd number +of functions in f, f + φ1, f + φ2, . . . , f + φr is bent, and its dual is equal to the sum of the duals +of corresponding bent functions. Namely, Theorem 4 is the same as Theorem 5. So in this +sense, Theorem 4 indeed cannot be generalized any more. Note that Theorem 4 was proved by +induction in [10]. Here we provide a more simple alternative proof from another perspective. +Theorem 5 also allows us to deduce the following result. +Corollary 5. Let n = 2m. Let f and g be two bent functions on F2n. Let µ2, µ3, . . . , µr ∈ F∗ +2n. +If the following two conditions are satisfied: +(A) DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r; +(B) for any ω′ = (ω2, ω3, . . . , ωr) ∈ Fr−1 +2 +, it holds that +g∗(x + +r +� +i=2 +ωiµi) = +� +g∗(x) + f∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is odd, +g∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is even, +(7) +6 + +then for any Boolean function F on Fr +2, the function h given by +h(x) = f(x) + F(f(x) + g(x), Trn +1(µ2x), Trn +1(µ3x), . . . , Trn +1(µrx)) +is bent. Moreover, the dual of h is +h∗(x) = f∗(x) + F(ϕ1, ϕ2, . . . , ϕr), +where ϕ1(x) = f∗(x) + g∗(x) and ϕi(x) = f∗(x) + f∗(x + µi) for any 2 ≤ i ≤ r. +Proof. Let φ = (φ1, φ2, . . . , φr) be the (n, r)-function with φ1(x) = f(x) + g(x) and φi(x) = +Trn +1(µix) for each 2 ≤ i ≤ r. Then for any ω = (ω1, ω2, . . . , ωr) ∈ Fr +2, it is easily seen that +f(x) + ω · φ(x) = +� +f(x) + Trn +1((ω2µ2 + ω3µ3 + · · · + ωrµr)x), +if ω1 = 0, +g(x) + Trn +1((ω2µ2 + ω3µ3 + · · · + ωrµr)x), +if ω1 = 1. +This implies that Item (i) of Pr is satisfied when f and g are bent. So we have that +� +f(x) + ω · φ(x) +�∗ = +� +f∗(x + ω2µ2 + ω3µ3 + · · · + ωrµr), +if ω1 = 0, +g∗(x + ω2µ2 + ω3µ3 + · · · + ωrµr), +if ω1 = 1. +Note that when suppt(ω) = {i}, we have +f(x) + ω · φ(x) = +� +g(x), +if i = 1, +f(x) + Trn +1(µix) +otherwise, +and f∗(x) + ω · ϕ(x) = f∗(x) + ϕi(x). +So Item (ii) of Pr holds only if ϕ1(x) = f∗(x) + g∗(x) and ϕi(x) = f∗(x) + f∗(x + µi) for any +2 ≤ i ≤ r. In this case, +f∗(x) + ω · ϕ(x) = +� +f∗(x) + �r +i=2 ωi(f∗(x) + f∗(x + µi)), +if ω1 = 0, +g∗(x) + �r +i=2 ωi(f∗(x) + f∗(x + µi)), +if ω1 = 1. +Hence, Item (ii) of Pr holds if and only if the following two relations hold: +f∗(x + ω2µ2 + · · · + ωrµr) = f∗(x) + +r +� +i=2 +ωi(f∗(x) + f∗(x + µi)) += +� +f∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is even, +�r +i=2 ωif∗(x + µi), +if wt(ω′) is odd, +(8) +and +g∗(x + ω2µ2 + · · · + ωrµr) = g∗(x) + +r +� +i=2 +ωi(f∗(x) + f∗(x + µi)) += +� +g∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is even, +g∗(x) + f∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is odd, +(9) +where ω′ = (ω2, ω3, . . . , ωr). By Corollary 3, we know that Relation (8) holds if and only if +DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r. Then the result follows from Theorem 5 immediately. +Remark 1. In Corollary 5, let φi(x) = f(x) + g(x) + Trn +1(µix) for some 1 ≤ i ≤ r, where +µi ∈ F2n. Then one can obtain a similar result as that of Corollary 5. +Remark 2. Corollary 5 is a generalization of Corollary 2, since Corollary 5 reduces to that of +Corollary 2 when r = 2 and F(x1, x2) = x1x2. +Note that Condition (B) of Corollary 5 is elusive when r > 2. In the following corollary, we +give a reduced form by applying Corollary 5 to g(x) = f(x + α) for some α ∈ F∗ +2n. +7 + +Corollary 6. Let f be a bent function on F2n. Let α ∈ F2n and µ2, µ3, . . . , µr ∈ F∗ +2n be such +that α ∈ +� +µ2, µ3, . . . , µr +�⊥ and DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r. Then for any Boolean +function F on Fr +2, the function +h(x) = f(x) + F(f(x) + f(x + α), Trn +1(µ2x), Trn +1(µ3x), . . . , Trn +1(µrx)) +is bent. Moreover, the dual of h is +h∗(x) = f∗(x) + F(ϕ1, ϕ2, . . . , ϕr), +where ϕ1(x) = Trn +1(αx) and ϕi(x) = f∗(x) + f∗(x + µi) for any 2 ≤ i ≤ r. +Proof. Let g(x) = f(x+α). Then it easily seen that g∗(x) = f∗(x)+Trn +1(αx), and then Relation +(7) becomes that +f∗(x + +r +� +i=2 +ωiµi) = +��r +i=2 ωif∗(x + µi), +if wt(ω′) is odd, +f∗(x) + �r +i=2 ωif∗(x + µi), +if wt(ω′) is even, +since α ∈ +� +µ2, µ3, . . . , µr +�⊥. +Hence, Condition (B) of Corollary 5 is satisfied if and only if +DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r by Corollary 3, and the result follows from Corollary 5 +directly. +Remark 3. Note that though the conditions of h to be bent in Corollary 6 are similar as that +of Theorem 3 (in fact, Corollary 6 reduces to Theorem 3 when α = 0), the corresponding bent +functions in Corollary 6 and Theorem 3 can be EA-inequivalent. For instance, let n = 6 and +f(x) = (x1, x2, x3) · (x4, x5, x6). +Let µ2 = (1, 0, 0, 0, 0, 0), µ3 = (0, 1, 1, 0, 0, 0). Then it is easy to check that Dµ2Dµ3f∗ = 0. +Hence, by Theorem 3, we have that +h(x) = f(x) + F(µ2 · x, µ3 · x) = f(x) + F(x1, x2 + x3) +is bent for any Boolean function F on F2 +2; and by Corollary 6, we have that +ˆh(x) = f(x) + ˆF +� +f(x) + f(x + α), µ2 · x, µ3 · x +� += f(x) + ˆF +� +f(x) + f(x + α), x1, x2 + x3 +� +is bent for any α ∈ +� +µ2, µ3 +�⊥ and any Boolean function ˆF on F3 +2. These two bent functions can +be clearly EA-inequivalent, since the algebraic degree of h is 2, while the algebraic degree of ˆh is +3 when α = µ3 and ˆF(x1, x2, x3) = x1x2x3. +Corollary 6 is efficient in producing new bent functions, since it is only required to find +some α ∈ F2n and µ2, µ3, . . . , µr ∈ F∗ +2n such that DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r and +α ∈ +� +µ2, µ3, . . . , µr +�⊥. In the next section, we will use Corollary 6 to construct a number of +concrete bent functions and compute their duals. +4 +Several concrete bent functions and their duals +The authors of [10] have found two kinds of f and φ satisfying the conditions of Theorem 4 +(that is, Pr by the previous section) for constructing new bent functions. The first kind is to +let f be a bent function and φ be a linear (n, r)-function; and the second kind is to let f and +f + φi be some self-dual bent functions for each 1 ≤ i ≤ r. They also invited the readers to find +more kinds of f and φ for obtaining more classes of bent functions in Conclusion of [10]. In the +previous section, we have shown that Theorem 5 is the same as that of Theorem 4. In addition, +we have found another new kind of f and φ satisfying Pr by Theorem 5 (see Corollary 6). In +this section, we find a number of concrete bent functions by using Corollary 6. +8 + +4.1 +New bent functions from Gold functions +In this subsection, we construct some concrete bent functions by applying Corollary 6 to Gold +function g(x) = Trn +1(λx2t+1), where t is a positive integer and λ ∈ F∗ +2n. We first recall the +following result. +Lemma 1. [6][8] Let n = 2m and d = gcd(t, n). Let g(x) = Trn +1(λx2t+1) for some λ ∈ F∗ +2n. +Then g is bent on F2n if and only if n +d is even and λ /∈ S, where S = {x2t+1 : x ∈ F2n}. +Moreover, the dual of g is that g∗(x) = Trn +1(λx2t+1 +0 +) + ( m +d mod 2), where x0 ∈ F2n satisfies that +λx0 + λ2tx22i +0 += x2t. +(10) +Note that g is explicit, but g∗ is not explicit in Lemma 1. To find some bent functions +by Corollary 6, we need to determine µ2, µ3, . . . , µr ∈ F∗ +2n such that DµiDµjf∗ = 0 for any +2 ≤ i < j ≤ r. So we take f = g∗ and present the following theorem, which is the main result +of this subsection. +Theorem 6. Take the same notations as in Lemma 1. Let λ ∈ F2n\S and µ2, µ3, . . . , µr ∈ F∗ +2n +be such that Trn +1(λ(µ2t +i µj+µiµ2t +j )) = 0 for any 2 ≤ i < j ≤ r. Then for any α ∈ +� +µ2, µ3, . . . , µr +�⊥ +and any Boolean function F on Fr +2, the function h∗ given by +h∗(x) = Trn +1(λx2t+1) + F(Trn +1(αx), ϕ2(x), ϕ3(x), . . . , ϕr(x)), +(11) +is bent, where ϕi(x) = Trn +1 +� +λ(µix2t + µ2t +i x + µ2t+1 +i +) +� +for each 2 ≤ i ≤ r. +Proof. Let f(x) = g∗(x) = Trn +1(λx2t+1 +0 +) + ( m +d mod 2), where x0 ∈ F2n satisfies (10). Then from +Lemma 1, we know that f is bent and its dual is f∗(x) = g(x) = Trn +1(λx2t+1). Hence, we have +f∗(x) + f∗(x + µi) = Trn +1 +� +λ(x2t+1 + (x + µi)2t+1) +� += Trn +1 +� +λ(µix2t + µ2t +i x + µ2t+1 +i +) +� +, ∀ µi ∈ F2n, +and +DµiDµjf∗(x) =Trn +1 +� +λ(µix2t + µ2t +i x + µ2t+1 +i +) +� ++ Trn +1 +� +λ(µi(x + µj)2t + µ2t +i (x + µj) + µ2t+1 +i +) +� +=Trn +1 +� +λ(µiµ2t +j + µ2t +i µj) +� +, +∀ µi, µj ∈ F2n. +This means that DµiDµjf∗ = 0 if Trn +1 +� +λ(µiµ2t +j + µ2t +i µj) +� += 0. Then by Corollary 6, we obtain +that +h(x) = f(x) + F(f(x) + f(x + α), Trn +1(µ2x), Trn +1(µ3x), . . . , Trn +1(µrx)) +(12) +is bent for any α ∈ +� +µ2, µ3, . . . , µr +�⊥ and any Boolean function F on Fr +2, and the dual of h is +exactly that of (11). This completes the proof. +Remark 4. When α = 0, Theorem 6 is exactly that of [28, Theorem 4.1]. +Applying Theorem 6 to t = m, we can deduce the following corollary. +Corollary 7. Let n = 2m. Let θ ∈ F∗ +2m and µ2, µ3, . . . , µr ∈ F∗ +2n be such that Trn +1(θ−1µiµ2m +j ) = 0 +for any 2 ≤ i < j ≤ r. Then for any α ∈ +� +µ2, µ3, . . . , µr +�⊥ and any F ∈ Br, the function +h(x) = Trm +1 (θx2m+1) + F +� +Trn +1(θα2mx) + Trm +1 (θα2m+1), Trn +1(µ2x), . . . , Trn +1(µrx) +� ++ 1 +is bent, whose dual is that +h∗(x) = Trm +1 (θ−1x2m+1) + F(Trn +1(αx), ϕ2(x), ϕ3(x), . . . , ϕr(x)), +where ϕi(x) = Trn +1(θ−1µ2m +i +x) + Trm +1 (θ−1µ2m+1 +i +) for each 2 ≤ i ≤ r. +9 + +Proof. Let t = m, λ ∈ F2n\F2m and θ−1 = λ+λ2m. Then it is easily checked that Trn +1(λ(µ2t +i µj + +µiµ2t +j )) = Trn +1(θ−1µiµ2m +j ). Let x0 = θx2m = (λ+λ2m)−1x2m, that is, x0 satisfies (10). Then from +Lemma 1, we obtain that f(x) = Trn +1(λx2m+1 +0 +) + 1 = Trm +1 (θx2m+1) + 1 is bent (since S = F2m +when t = m), and the dual of f is that f∗(x) = Trn +1(λx2m+1) = Trm +1 (θ−1x2m+1). The result +follows then from Theorem 6 and the calculations for (11) and (12). +Remark 5. When α = 0, Corollary 7 reduces to Theorem 12 of [20], which contains Theorem +2 of [22] (where F(x1, x2, . . . , xr) = x1x2 · · · xr), the part of bent functions in Theorem 1 of +[24] (where r = 3 and F(x1, x2, x3) = x1x2x3), and Theorem 9 of [13] (where r = 2 and +F(x1, x2) = x1x2) as special cases. +When n = 2m = 4t, the authors of [10] have given the explicit form of g∗(x) = Trn +1(λx2t+1 +0 +)+ +( m +d mod 2) by solving (10), see [10, Lemma 3], which is g∗(x) = Trn +1(P(λ)x2t+1), where P(λ) = +λ2m+1+1+λ2t+2m+23t +Trm +t (Nn +m(λ2)) +and Nn +m(λ) = λ2m+1. They have also pointed out in Remark 16 of [10] that +g∗ is self-dual if λ ∈ F2m with λ + λ2t = 1. This result enables us to give the following corollary. +Corollary 8. Let n = 2m = 4t. +Let λ ∈ F2n\S and µ2, µ3, . . . , µr ∈ F∗ +2n be such that +Trn +1(λ(µ2t +i µj + µiµ2t +j )) = 0 for any 2 ≤ i < j ≤ r, where S = {x2t+1 : x ∈ F2n}. Then for +any α ∈ +� +µ2, µ3, . . . , µr +�⊥ and any F ∈ Br, the function +h(x) = Trn +1(P(λ)x2t+1) + F +� +Trn +1(P(λ)(α2tx + αx2t + α2t+1)), Trn +1(µ2x), . . . , Trn +1(µrx) +� +(13) +is bent, whose dual is that +h∗(x) = Trn +1(λx2t+1) + F(Trn +1(αx), ϕ2(x), ϕ3(x), . . . , ϕr(x)), +where ϕi(x) = Trn +1 +� +λ(µix2t + µ2t +i x + µ2t+1 +i +) +� +for each 2 ≤ i ≤ r. In particular, for any α ∈ +� +µ2, µ3, . . . , µr +�⊥ and any Boolean function F on Fr +2, h is bent if λ ∈ F2m with λ + λ2t = 1. +Proof. Let f(x) = Trn +1(P(λ)x2t+1). Then for any α ∈ F2n, it is easily seen that f(x)+f(x+α) = +Trn +1 +� +P(λ)(αx2t +α2tx+α2t+1) +� +, and hence (12) becomes (13). Then result follows from Theorem +6 immediately. +Remark 6. When α = 0 and λ ∈ F2m with λ + λ2t = 1 (i.e., P(λ) = λ), Corollary 8 reduces to +Theorem 23 of [20], which contains Theorem 3 of [22] (where F(x1, x2, . . . , xr) = x1x2 · · · xr), +and the part of bent functions in Theorems 3 and 4 of [24] (where r = 3 and F(x1, x2x3) = +x1x2x3) as special cases. +4.2 +New bent functions from a class of bent functions inside the completed +Maiorana-MacFarland class +The authors of [10] have shown that the following function +f(x) = Trn +1(λx2tπ(x + x2m)) + g(x + x2m) +(14) +is bent if and only if λ ∈ F2n\F2m, where t is a non-negative integer, n = 2m, π is a permutation of +F2m, and g is a Boolean function on F2m. This bent function is inside the completed Maiorana- +MacFarland class, and it is a generalization of [18, Theorem 4], [29, Theorem 4.6], and [17, +Theorem 9]. In this subsection, we intend to find more bent functions by using this bent function +and Corollary 6, for which we need first to determine the dual of f. We use the technique used +in [10, Proposition 1] to complete this task. +Lemma 2. The dual of the bent function f in (14) is that +f∗(x) = Trn +1 +� +ωxπ−1(Λ−1(x + x2m)2t) +� ++ G +� +π−1(Λ−1(x + x2m)2t) +� +, +(15) +where Λ = λ + λ2m and G(z) = Trn +1 +� +λ(ωz)2tπ(z) +� ++ g(z). +10 + +Proof. Let ω ∈ F2n with ω + ω2m = 1. Then F2n can be decomposed as F2n = F2m + ωF2m, +that is, for any x ∈ F2n, there are unique y, z ∈ F2m such that x = y + ωz. This expression also +means that z = x + x2m and y = ω2mx + ωx2m. Then f can be represented by +f(x) =f(y + ωz) = Trn +1 +� +λ(y + ωz)2tπ(z) +� ++ g(z) = Trm +1 +� +Λy2tπ(z) +� ++ G(z), +where Λ = λ + λ2m and G(z) = Trn +1 +� +λ(ωz)2tπ(z) +� ++ g(z). Then for any θ = a + ωb, where +a, b ∈ F2m, we have +Wf(θ) = +� +x∈F2n +(−1)f(x)+Trn +1 (θx) += +� +y,z∈F2m +(−1)f(y+ωz)+Trn +1 ((a+ωb)(y+ωz)) += +� +z∈F2m +(−1)G(z)+Trm +1 +� +(a+b)z +� � +y∈F2m +(−1)Trm +1 +� +(Λπ(z)+b2t)y2t� +. +This implies that f is bent if and only if |{z ∈ F2m : Λπ(z) + b2t = 0}| = 1 for any b ∈ F2m. +Recall that π is a permutation of F2m. Thus, f is bent if and only if Λ = λ + λ2m ̸= 0, that is, +λ /∈ F2m. In this case, z = π−1(Λ−1b2t), and +Wf(θ) = Wf(a + bω) = 2m(−1)G(z)+Trm +1 +� +(a+b)z +� +. +This implies that +f∗(a + bω) = G(z) + Trm +1 +� +(a + b)z +� += G +� +π−1(Λ−1b2t) +� ++ Trm +1 +� +(a + b)π−1(Λ−1b2t) +� +. +Hence, the dual of f satisfies that +f∗(x) = f∗(y + zω) = G +� +π−1(Λ−1z2t) +� ++ Trm +1 +� +(y + z)π−1(Λ−1z2t) +� +. +Recall that y = ω2mx + ωx2m and z = x + x2m. Then we have +f∗(x) =G +� +π−1(Λ−1(x + x2m)2t) +� ++ Trm +1 +� +(ωx + (ωx)2m)π−1(Λ−1(x + x2m)2t) +� +=G +� +π−1(Λ−1(x + x2m)2t) +� ++ Trn +1 +� +ωxπ−1(Λ−1(x + x2m)2t) +� +. +This completes the proof. +From Lemma 2 and Corollary 6, we can deduce the following result. +Theorem 7. Take the same notations as in Lemma 2. Let f be the bent function given in (14). +Then for any µ2, µ3, . . . , µr ∈ F∗ +2m, any α ∈ +� +µ2, µ3, . . . , µr +�⊥, and any Boolean function F on +Fr +2, the function +h(x) = f(x) + F(f(x) + f(x + α), Trn +1(µ2x), Trn +1(µ3x), . . . , Trn +1(µrx)) +is bent, and the dual of h is +h∗(x) = f∗(x) + F(Trn +1(αx), ϕ2(x), ϕ3(x), . . . , ϕr(x)), +where f∗ is given by (15) and ϕi(x) = Trn +1 +� +ωµiπ−1(Λ−1(x + x2m)2t) +� +for each 2 ≤ i ≤ r. +Proof. Let T(x) = x + x2m. Then for any µi, µj ∈ F∗ +2m, it is easily seen that T(x) = T(x + µi), +which implies that f∗(x) + f∗(x + µi) = Trn +1 +� +ωµiπ−1(Λ−1(x + x2m)2t) +� +and DµiDµjf∗ = 0. The +result follows then from Corollary 6 immediately. +11 + +Similarly as that of Theorems 6 and 7, by applying Corollary 6 to the following two monomial +bent functions +f1(x) = Tr6k +1 (λx22k+2k+1) and f2(x) = Tr4k +1 (λx22k+2k+1+1) +given by [2] and [8], respectively; and to the following bent functions with Niho exponents +f3(x) = Trm +1 (x2m+1) + Trn +1 +� 2k−1−1 +� +i=1 +x(2m−1) i +2k +1 +� +given by [9], we can also obtain certain concrete bent functions, since the duals of f1, f2, f3 +have been determined in [10], [11] and [1], respectively, and hence by Corollary 6, we only need +to find some elements α ∈ F2n and µ2, µ3, . . . , µr ∈ F∗ +2n such that α ∈ +� +µ2, µ3, . . . , µr +�⊥ and +DµiDµjf∗ +e = 0 for any 2 ≤ i < j ≤ r and 1 ≤ e ≤ 3. Here, the concrete results are not unfolded +in details. +5 +Conclusion +In this paper, we gave another characterization for the generic construction of bent functions +given in [10], which enabled us to obtain another efficient construction of bent functions. Based +on this construction, we found several infinite families of bent functions and confirmed their +duals. Consequently, our results cover a lot of known bent functions. It remains to verify the +EA-equivalence of the bent functions obtained in this paper to known families. +Acknowledgments +This work was supported in part by the National Key Research and Development Program +of China under Grant 2019YFB2101703; in part by the National Natural Science Founda- +tion of China under Grants 61972258, 62272107 and U19A2066; in part by the Innovation +Action Plan of Shanghai Science and Technology under Grants 20511102200 and 21511102200; +in part by the Key Research and Development Program of Guangdong Province under Grant +2020B0101090001, in part by Scientific Research Fund of Hunan Provincial Education Depart- +ment under Grant 19B485, and in part by Open Reseach Program of Shanghai Key Lab of +Intelligent Information Processing under Grant IIPL201902. +References +[1] L. Budaghyan, C. Carlet, T. Helleseth, A. Kholosha, S. Mesnager, Further results on Niho +bent functions, IEEE Trans. Inf. Theory 58 (11) (2012) 6979-6985. 12 +[2] A. Canteaut, P. Charpin, G. M. Kyureghyan, A new class of monomial bent functions, +Finite Fields Appl. 14 (1) (2008) 221-241. 12 +[3] C. Carlet, On bent and highly nonlinear balanced/resilient functions and their algebraic +immunities, in Proc. AAECC, Berlin, Germany: Springer, vol. 3857, 2006, pp. 1-28. 1, 2, 3 +[4] C. Carlet, Boolean Functions for Cryptography and Coding Theory, Cambridge University +Press, Cambridge, 2021. 1 +[5] C. Carlet, S. Mesnager, Four decades of research on bent functions, Des. Codes Cryptogr. +78 (1) (2016) 5-50. 1 +[6] R. S. Coulter, On the evaluation of a class of Weil sums in characteristic 2, New Zealand +J. Math. 28 (2) (1999) 171-184. 9 +12 + +[7] R. S. Coulter, S. Mesnager, Bent Functions From Involutions Over F2n, IEEE Trans. Inf. +Theory 64 (4) (2018) 2979-2986. 3 +[8] N. G. Leander, Monomial Bent Functions, IEEE Trans. Inf. Theory 52 (2) (2006) 738-743. +9, 12 +[9] N. G. Leander, A. Kholosha, Bent functions with 2r Niho exponents, IEEE Trans. Inf. +Theory 52 (12) (2006) 5529-5532. 12 +[10] Y. Li, H. Kan, S. Mesnager, J. Peng, C.H. Tan, L. Zheng, Generic constructions of (Boolean +and vectorial) bent functions and their consequences, IEEE Trans. Inf. Theory 68 (4) (2022) +2735-2751. 2, 4, 5, 6, 8, 10, 12 +[11] Y. Li, H. Kan, J. Peng, C.H. Tan, B. Liu, The Explicit Dual of Leander’s Monomial Bent +Function, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E104-A (9) (2021) 1357- +1360. 12 +[12] G. Luo, X. Cao, S. Mesnager, Several new classes of self-dual bent functions derived from +involutions, Cryptogr. Commun. 11 (6) (2019) 1261-1273. 3 +[13] S. Mesnager, Several new infinite families of bent functions and their duals, IEEE Trans. +Inf. Theory 60 (7) (2014) 4397-4407. 1, 2, 3, 4, 10 +[14] S. Mesnager, Further constructions of infinite families of bent functions from new permu- +tations and their duals, Cryptogr. Commun. 8 (2) (2016) 229-246. 3 +[15] S. Mesnager, Bent Functions: Fundamentals and Results, Cham, Switzerland: Springer, +2016. 1 +[16] S. Mesnager, P. Ongan, F. Ozbudak, New bent functions from permutations and linear +translators, in Codes, Cryptology and Information Security, (Lecture Notes in Computer +Science), vol. 10194. Springer, 2017, pp. 282-297. 3 +[17] S. Mesnager, F. Zhang, C. Tang, Y. Zhou, Further study on the maximum number of bent +components of vectorial functions, Des. Codes Cryptogr. 87 (11) (2019) 2597-2610. 10 +[18] A. Pott, E. Pasalic, A. Muratovi´c-Ribi´c, S. Bajri´c, On the maximum number of bent com- +ponents of vectorial functions, IEEE Trans. Inf. Theory 64 (1) (2018) 403-411. 10 +[19] O. Rothaus, On “bent” functions, J. Combin. Theory Ser. A 20 (1976) 300-305. 1 +[20] C. Tang, Z. Zhou, Y. Qi, X. Zhang, C. Fan, T. Helleseth, Generic Construction of Bent +Functions and bent idempotents With Any Possible Algebraic Degrees, IEEE Trans. Inf. +Theory 63 (10) (2017) 6149-6157. 2, 4, 10 +[21] D. Tang, S. Maitra, Construction of n-variable (n ≡ 2 mod 4) balanced Boolean functions +with maximum absolute value in autocorrelation spectra < 2 +n +2 , IEEE Trans. Inf. Theory +64 (1) (2018) 393-402. 1 +[22] L. Wang, B. Wu, Z. Liu, D. Lin, Three new infinite families of bent functions, Sci. China +Inf. Sci. 61 (3) (2018) 032104. 2, 4, 10 +[23] X. Xie, N. Li, X. Zeng, X. Tang, Y. Yao, Several classes of bent functions over finite fields, +Des. Codes Cryptogr. 2022, https://doi.org/10.1007/s10623-022-01109-0. 2 +[24] G. Xu, X. Cao, S. Xu, Several new classes of Boolean functions with few Walsh transform +values, Appl. Algebra Eng. Commun. Comput. 28 (2) (2017) 155-176. 2, 4, 10 +[25] F. Zhang, Y. Wei, E. Pasalic, S. Xia, Large sets of disjoint spectra plateaued functions +inequivalent to partially linear functions, IEEE Trans. Inf. Theory 64 (4) (2018) 2987-2999. +1 +13 + +[26] W. Zhang, G. Xiao, Constructions of almost optimal resilient Boolean functions on large +even number of variables, IEEE Trans. Inf. Theory 55 (12) (2009) 5822-5831. 1 +[27] X.-M. Zhang and Y. Zheng, GAC-The criterion for global avalanche characteristics of cryp- +tographic functions, in J.UCS the Journal of Universal Computer Science, Berlin, Germany: +Springer, 1996, pp. 320-337. 1 +[28] L. Zheng, J. Peng, H. Kan, Y. Li, Several new infinite families of bent functions via second +order derivatives, Cryptogr. Commun. 12 (6) (2020) 1143-1160. 2, 4, 6, 9 +[29] L. Zheng, J. Peng, H. Kan, Y. Li, J. Luo, On constructions and properties of (n, m)- +functions with maximal number of bent components, Des. Codes Cryptogr. 88 (2020) 2171- +2186. 10 +[30] L. Zheng, J. Peng, H. Kan, D. Tang, Constructing vectorial bent functions via second-order +derivatives, Discret. Math. 344 (8) (2021) 112473. 2 +14 + diff --git a/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/load_file.txt b/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..1c711a531361c6687ff68d92af5262efdc0e793d --- /dev/null +++ b/D9E3T4oBgHgl3EQfVAqL/content/tmp_files/load_file.txt @@ -0,0 +1,719 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf,len=718 +page_content='A note on constructions of bent functions Yanjun Li, Haibin Kan∗, Jie Peng, Lijing Zheng, and Changhui Chen Abstract Recently, Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' presented a generic construction of bent functions in [IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2735-2751, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this paper, we give a characterization for their construction from another perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This characterization enables us to obtain another efficient construction of bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Based on that, we derive several infinite families of concrete bent functions and give their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Our results show that many known bent functions are particular cases of our bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Index Terms: Bent function, duals, cryptography, Walsh-Hadamard transform, Gold function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mathematics Subject Classification 2020: 06E30, 94A60, 94D10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 Introduction Bent functions, introduced in [19], are those Boolean functions in an even number of variables having the highest nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Such functions have been extensively studied in the last four decades, because of their closely relationship with the theory of difference sets, and their sig- nificant applications in coding theory and cryptography [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Bent functions are not balanced, however, they often act as an important and efficient ingredient for finding some balanced func- tions with a higher nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' For instance, the authors of [25] used bent functions to construct some disjoint spectra plateaued functions with higher nonlinearities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Their results provided a positive answer to an open problem of [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The authors of [21] utilized bent functions to con- struct balanced Boolean functions with high nonlinearity and low absolute indicator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Their results partially disproved a conjecture of [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In the past, a large amount of work was done on the characterizations and constructions of bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' But until now, a complete classi- fication is not finished and it remains elusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Along with the deep-going of the research, the progress on bent functions becomes more and more difficult even if a tiny progress is not easy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' For a comprehensive survey and a book on bent functions, the interested readers are referred to [5] and [15], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this paper, we focus our attention on the constructions of bent functions with the form h(x) = f(x) + F ◦ φ(x), (1) where f is a bent function on F2n, F is a Boolean function on Fr 2, and φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) is an (n, r)-function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In fact, the research on the bent-ness of h can be dated back to [3], where Carlet presented a sufficient condition for a particular case (called Carlet function) of h to be bent, that is, the case of h to be bent when r = 2, f = f1, φ1 = f1 + f2, φ2 = f1 + f3 and F(x1, x2) = x1x2 in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' That sufficient condition had been proved by Mesnager [13] to be necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager ∗Corresponding author Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li is with Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui 233030, China (Email: yanjlmath90@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan is with Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fu- dan University, Shanghai 200433, China;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Shanghai Engineering Research Center of Blockchain, Shanghai 200433, China;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and Yiwu Research Institute of Fudan University, Yiwu City 322000, China (E-mail: hbkan@fudan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='cn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Chen are with Mathematics and Science College of Shanghai Normal University, Guilin Road #100, Shanghai 200234, China (Emails: jpeng@shnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='cn and cchxuexi@126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng is with the School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China (Email: zhenglijing817@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='04456v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='IT] 11 Jan 2023 [13] also studied the bent-ness of two particular cases of Carlet function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The first particular case is to let f2(x) = f1(x) + Trn 1(ax) and f3(x) = f1(x) + Trn 1(bx) for some a, b ∈ F∗ 2n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and the second particular case is to let f3(x) = f1(x) + Trn 1(ax) for some a ∈ F∗ 2n in Carlet function, from which Mesnager obtained a lot of bent functions and gave their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Thereafter, several papers, such as [10, 20, 22, 23, 24, 28, 30], were done for generalizing Carlet and Mesnager’s works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The main results of those papers are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Table 1: The bent functions of the form h(x) = f(x) + F ◦ φ(x) r φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) F Condition Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2 φ1 = f + f2, φ2 = f + f3 F(x1, x2) = x1x2 see Theorem 1 of this paper [3] 2 φ1(x) = Trn 1(ax), φ2(x) = Trn 1(bx) F(x1, x2) = x1x2 f is bent, DaDbf ∗ = 0 [13] 2 φ1 = f + f2, φ2(x) = Trn 1(ax) F(x1, x2) = x1x2 f is bent, Da(f + f2)∗ = 0 [13] 3 φi(x) = Trn 1(µix) F(x1, x2, x3) = x1x2x3 see [24] [24] r φi(x) = Trn 1(µix) F(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , xr) = Πr i=1xi see Theorem 1 of [22] [22] r φi(x) = Trn 1(µix) any Boolean function on Fr 2 see Theorem 2 of this paper [20] r φi(x) = Trn 1(µix) any Boolean function on Fr 2 f is bent, DµiDµjf ∗ = 0 for any i ̸= j [28, 30] r φi = f + gi any Boolean function on Fr 2 see Theorem 4 of this paper [10] r φ any Boolean function on Fr 2 f satisfies Pr with φ Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 5 r φ1 = f + g, φi(x) = Trn 1(µix), 2 ≤ i ≤ r any Boolean function on Fr 2 see Corollary 5 of this paper Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 5 r φ1(x) = f(x) + f(x + α), φi(x) = Trn 1(µix), 2 ≤ i ≤ r any Boolean function on Fr 2 α ∈ � µ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥, DµiDµjf ∗ = 0 for any i ̸= j Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 6 In this paper, we continue to study the bent-ness of h defined in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' By analysing carefully many previous results on the constructions of bent functions in the form (1), we obtain a framework on the constructions of bent functions, which unifies many previous constructions of bent functions in [3, 10, 13, 20, 22, 24, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This framework also enables us to find another efficient construction of bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Based on that, we obtain a number of concrete bent functions and determine their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Consequently, we find that our results cover many previously known bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2 Preliminaries Throughout the paper, let n = 2m be an even positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let F2n be the finite field of order 2n, F∗ 2n = F2n\\{0}, and Fn 2 be the n-dimensional vector space over F2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' There is a one-to-one correspondence between F2n and Fn 2, because every a ∈ F2n can be represented uniquely by a = a1α1 + a2α2 + · · · + anαn, where ai ∈ F2, {α1, α2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , αn} is a basis of F2n over F2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So the finite field F2n is always identified to the n-dimensional vector space Fn 2 in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' For a vector ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωn) ∈ Fn 2, the set suppt(ω) = {1 ≤ i ≤ n : ωi ̸= 0} is said to be the support of ω, whose cardinality is called the (Hamming) weight of ω, denoted by wt(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Namely, we have wt(ω) = |suppt(ω)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' A mapping φ from Fn 2 to Fr 2 is called an (n, r)-function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' When n is divisible by r, the (n, r)-function Trn r (x) = x + x2r + x22r + · · · + x2n−r is called the trace function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The set of all (n, 1)-functions (namely, all Boolean functions) is denoted by Bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2 For a given Boolean function f on Fn 2, the Walsh-Hadamard transform of f is a mapping from Fn 2 to Z defined as Wf(µ) = � x∈Fn 2 (−1)f(x)+µ·x, µ ∈ Fn 2, and its inverse transform is given by (−1)f(µ) = 2−n � x∈Fn 2 Wf(x)(−1)µ·x, µ ∈ Fn 2, where µ · x denotes the canonical inner product of µ and x (in F2n, µ · x = Trn 1(µx)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The first derivative of f in terms of µ ∈ Fn 2 is defined as Dµf(x) = f(x) + f(x + µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' A Boolean function f over Fn 2 is called bent if n is even and Wf(µ) = ±2 n 2 for all µ ∈ Fn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Bent functions always appear in pairs, that is, for any bent function f on Fn 2, there is always a unique bent function f∗ such that Wf(µ) = 2 n 2 (−1)f∗(µ) for all µ ∈ Fn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, in the literature, f∗ is called the dual of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Two Boolean functions f and g are called EA-equivalent if there is an affine automorphism A and affine function ℓ such that f(x) = g ◦ A(x) + ℓ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The set of all functions which are EA-equivalent to f is called a complete class of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' To see whether a bent function is inside a complete class of another bent function is challenging in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 Some known results and a framework of bent functions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='1 Known results In this subsection, we review some known bent functions of the form h(x) = f(x) + F ◦ φ(x), (2) where f is a bent function on Fn 2, φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) is an (n, r)-function and F is a Boolean function on Fr 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Firstly, when r = 2, f = f1, φ1 = f1 + f2, φ2 = f1 + f3 and F(x1, x2) = x1x2, Carlet gave the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [3] Let f1, f2, f3 be three bent functions on F2n such that f1 + f2 + f3 is bent as well, and (f1 + f2 + f3)∗ = f∗ 1 + f∗ 2 + f∗ 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then h(x) = f1(x)f2(x) + f1(x)f3(x) + f2(x)f3(x) is a bent function with dual h∗(x) = f∗ 1 (x)f∗ 2 (x) + f∗ 1 (x)f∗ 3 (x) + f∗ 2 (x)f∗ 3 (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This theorem provides a general method to find new bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' By finding different bent functions f1, f2 and f3 satisfying the conditions of Theorem 1, several new bent functions have been constructed, see [7, 12, 13, 14, 16] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In 2014, Mesnager [13] revisited Theorem 1, and found that the conditions of Theorem 1 is also necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then letting f1(x) = f(x), f2(x) = f(x) + Trn 1(ax) and f3(x) = f(x) + Trn 1(bx) for some distinct a, b ∈ F∗ 2n in Theorem 1, she obtained the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [13] Let f be a bent function on F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let a, b ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then h(x) = f(x) + Trn 1(ax)Trn 1(bx) (3) is bent if and only if DaDbf∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of h is given by h∗(x) = f∗(x)f∗(x + a) + f∗(x)f∗(x + b) + f∗(x + a)f∗(x + b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 Letting f3(x) = f1(x) + Trn 1(ax) for some a ∈ F∗ 2n in Theorem 1, Mesnager also obtained the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [13] Let a ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f1, f2 be two bent functions on F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then h(x) = f1(x) + Trn 1(ax)(f1(x) + f2(x)) is bent if and only if Da(f∗ 1 + f∗ 2 ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of h is that h∗(x) = f∗ 1 (x) + (f∗ 1 (x) + f∗ 2 (x))f∗ 1 (x + a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Using Corollaries 1 and 2, Mesnager found several infinite families of bent functions and derived their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' After Mesnager’s work, many papers were dedicated to generalizing Corollary 1 for finding new infinite families of bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' For instance, the authors of [24] generalized the function h of Corollary 1 to the form h(x) = f(x) + Trn 1(ax)Trn 1(bx)Trn 1(cx), (4) and studied its bent-ness, where f is a bent function on F2n and a, b, c ∈ F∗ 2n satisfy certain conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The authors of [22] generalized the function h of Corollary 1 to the form h(x) = f(x) + r � i=1 Trn 1(µix), (5) and studied its bent-ness, where f is a bent function on F2n and µ1, µ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n satisfy certain conditions, see [22, Theorem 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The authors of [20] generalized the function h of Corollary 1 to its extreme form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Their result is given as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [20] Let f be a bent function over F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' If there exist r elements µ1, µ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr in F∗ 2n and r Boolean functions g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , gr on F2n such that f∗ � x+ r � i=1 µiωi � =f∗(x)+ r � i=1 ωigi(x) for all x ∈ F2n and all (ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr) ∈ Fr 2, then for any F ∈ Br, the Boolean function h(x) = f(x) + F � Trn 1(µ1x), Trn 1(µ2x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx) � (6) is bent with dual h∗(x) = f∗(x) + F � g1(x), g2(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , gr(x) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Obviously, the functions h given in (3), (4), (5) and (6) are special cases of the form (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' But the conditions of h (in (3), (4), (5) and (6)) to be bent become more and more complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Therefore, a nature question is to ask that whether there is an unified simple condition such that the function h in (2) is bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' To this end, the authors of [28] simplified Theorem 2 as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [28] Let f be a bent function on F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let µ1, µ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n be such that DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any F ∈ Br, the function h given by (6) is bent, whose dual is that h∗(x) = f∗(x) + F(ϕ1(x), ϕ2(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr(x)), where ϕi(x) = f∗(x) + f∗(x + µi) for each i ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , r}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 3 is clearly more concise than Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' But it does not contain Theorem 1 and Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In order to find a more general uniform, the authors of [10] presented the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 4 Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [10, Theorem 3] For any 1 ≤ i ≤ r, let f, gi ∈ Bn, and let φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) be the (n, r)-function with φi = f + gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' If the sum of any odd number of functions in f, g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , gr is a bent function, and its dual is equal to the sum of the duals of corresponding bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any Boolean function F on Fr 2, the function h given by (2) is bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of h is given by h∗(x) = f∗(x) + F ◦ ϕ(x), where ϕ = (ϕ1, ϕ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr) is the (n, r)-function with ϕi(x) = f∗(x) + g∗ i (x) for any 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 4 reduces to Theorem 1 when r = 2 and F(x1, x2) = x1x2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and reduces to Theorems 2 and 3 when gi(x) = f(x) + Trn 1(µix) for each 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So in this sense, Theorem 4 is very general, and it seems difficult to be generalized any more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='2 A framework of bent functions In this subsection, we try to generalize Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' By analysing carefully the conditions of h to be bent in Theorems 1, 2, 3, and 4, respectively, we find that all conditions can be summarized by the following property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Definition 2 (Pr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f be a Boolean function over F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' If there is an (n, r)-function φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) such that the following two conditions are satisfied: (i) f(x) + ω · φ(x) = f(x) + �r i=1 ωiφi is bent for any ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr) ∈ Fr 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' (ii) there is an (n, r)-function ϕ = (ϕ1, ϕ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr) such that � f(x)+ω·φ(x) �∗ = f∗(x)+ω·ϕ(x) for any ω ∈ Fr 2, then we say that f satisfies Pr with respect to the (n, r)-function φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' According to this property, we give the following framework of bent functions, which is main result of this subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let n = 2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let φ be an (n, r)-function, and let f be a Boolean function on F2n satisfying Pr with respect to φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any Boolean function F on Fr 2, the function h given by (2) is bent, and the dual of h is h∗(x) = f∗(x) + F ◦ ϕ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' By the definition of the inverse Walsh-Hadamard transform, it holds that (−1)F◦φ(x) = 2−r � ω∈Fr 2 WF (ω)(−1)ω·φ(x), ∀ x ∈ Fn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, the Walsh-Hadamard transform of h at β ∈ F2n is that Wh(β) = � x∈F2n (−1)f(x)+Trn 1 (βx)(−1)F◦φ(x) =2−r � x∈F2n (−1)f(x)+Trn 1 (βx) � ω∈Fr 2 WF (ω)(−1)ω·φ(x) =2−r � ω∈Fr 2 WF (ω) � x∈F2n (−1)f(x)+Trn 1 (βx)+ω·φ(x) =2−r � ω∈Fr 2 WF (ω)Wg(β), where g(x) = f(x) + ω · φ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Recall that f satisfies Pr with respect to φ, that is, g is bent and g∗(x) = f∗(x) + ω · ϕ(x) for any ω ∈ Fr 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, we have Wh(β) = 2m−r � ω∈Fr 2 WF (ω)(−1)f∗(β)+ω·ϕ(β) = 2m(−1)f∗(β)+F◦ϕ(β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The proof is completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 5 According to Theorem 5, we can deduce the following corollaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 5 reduces to that of Theorem 3 when φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) is an (n, r)- function with φi(x) = Trn 1(µix), where µi ∈ F∗ 2n for each 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' To prove this result, by Theorem 5, it suffices to show that f satisfies Pr with respect to φ if and only if f is bent and DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In fact, this fact has been presented in [28, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Here we provide a sketchy proof for the readers convenience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that Item (i) of Pr is satisfied if and only if f is bent when φi(x) = Trn 1(µix) for each 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Now assume that Item (ii) of Pr is satisfied, then it is easily seen that ϕi(x) = f∗(x)+f∗(x+µi) for each 1 ≤ i ≤ r when wt(ω) = 1, and DµiDµjf∗ = 0 for any 1 ≤ i < j ≤ r when wt(ω) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Conversely, by induction on wt(ω), one can check easily that Item (ii) of Pr is also satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 5 reduces to that of Theorem 4 when φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) is an (n, r)- function with φi = f + gi, where f and gi are any Boolean functions on F2n for 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Suppose that φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) with φi = f + gi for any 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr) ∈ Fr 2, we have f(x) + ω · φ(x) = f(x) + r � i=1 ωi(f(x) + gi(x)) = � Gω(x), if wt(ω) is odd, f(x) + Gω(x), if wt(ω) is even, where Gω(x) = ω1g1(x)+ω2g2(x)+· · ·+ωrgr(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Therefore, Item (i) of Pr holds if and only if the sum of any odd number of functions in f, g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , gr is bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that when suppt(ω) = {i}, f(x) + ω · φ(x) = gi(x) and f∗(x) + ω · ϕ(x) = f∗(x) + ϕi(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So Item (ii) of Pr holds only if ϕi(x) = f∗(x) + g∗ i (x) for any 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this case, f∗(x) + ω · ϕ(x) = f∗(x) + r � i=1 ωi(f∗(x) + g∗ i (x)) = � G∗ ω(x), if wt(ω) is odd, f∗(x) + G∗ ω(x), if wt(ω) is even, where G∗ ω(x) = ω1g∗ 1(x) + ω2g∗ 2(x) + · · · + ωrg∗ r(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, Item (ii) of Pr holds if and only if (Gω)∗ = G∗ ω when wt(ω) is odd, and (f + Gω)∗ = f∗ + G∗ ω when wt(ω) is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Equivalently, the dual of the sum of any odd number of functions in f, g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , gr is equal to the sum of the duals of corresponding bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' From the proof of Corollary 4, it is easily seen that for a given Boolean function f on F2n, and an (n, r)-function φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr), Pr holds if and only if the sum of any odd number of functions in f, f + φ1, f + φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , f + φr is bent, and its dual is equal to the sum of the duals of corresponding bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Namely, Theorem 4 is the same as Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So in this sense, Theorem 4 indeed cannot be generalized any more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that Theorem 4 was proved by induction in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Here we provide a more simple alternative proof from another perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 5 also allows us to deduce the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let n = 2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f and g be two bent functions on F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' If the following two conditions are satisfied: (A) DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' (B) for any ω′ = (ω2, ω3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr) ∈ Fr−1 2 , it holds that g∗(x + r � i=2 ωiµi) = � g∗(x) + f∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is odd, g∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is even, (7) 6 then for any Boolean function F on Fr 2, the function h given by h(x) = f(x) + F(f(x) + g(x), Trn 1(µ2x), Trn 1(µ3x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx)) is bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of h is h∗(x) = f∗(x) + F(ϕ1, ϕ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr), where ϕ1(x) = f∗(x) + g∗(x) and ϕi(x) = f∗(x) + f∗(x + µi) for any 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let φ = (φ1, φ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , φr) be the (n, r)-function with φ1(x) = f(x) + g(x) and φi(x) = Trn 1(µix) for each 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr) ∈ Fr 2, it is easily seen that f(x) + ω · φ(x) = � f(x) + Trn 1((ω2µ2 + ω3µ3 + · · · + ωrµr)x), if ω1 = 0, g(x) + Trn 1((ω2µ2 + ω3µ3 + · · · + ωrµr)x), if ω1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This implies that Item (i) of Pr is satisfied when f and g are bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So we have that � f(x) + ω · φ(x) �∗ = � f∗(x + ω2µ2 + ω3µ3 + · · · + ωrµr), if ω1 = 0, g∗(x + ω2µ2 + ω3µ3 + · · · + ωrµr), if ω1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that when suppt(ω) = {i}, we have f(x) + ω · φ(x) = � g(x), if i = 1, f(x) + Trn 1(µix) otherwise, and f∗(x) + ω · ϕ(x) = f∗(x) + ϕi(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So Item (ii) of Pr holds only if ϕ1(x) = f∗(x) + g∗(x) and ϕi(x) = f∗(x) + f∗(x + µi) for any 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this case, f∗(x) + ω · ϕ(x) = � f∗(x) + �r i=2 ωi(f∗(x) + f∗(x + µi)), if ω1 = 0, g∗(x) + �r i=2 ωi(f∗(x) + f∗(x + µi)), if ω1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, Item (ii) of Pr holds if and only if the following two relations hold: f∗(x + ω2µ2 + · · · + ωrµr) = f∗(x) + r � i=2 ωi(f∗(x) + f∗(x + µi)) = � f∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is even, �r i=2 ωif∗(x + µi), if wt(ω′) is odd, (8) and g∗(x + ω2µ2 + · · · + ωrµr) = g∗(x) + r � i=2 ωi(f∗(x) + f∗(x + µi)) = � g∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is even, g∗(x) + f∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is odd, (9) where ω′ = (ω2, ω3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ωr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' By Corollary 3, we know that Relation (8) holds if and only if DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then the result follows from Theorem 5 immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In Corollary 5, let φi(x) = f(x) + g(x) + Trn 1(µix) for some 1 ≤ i ≤ r, where µi ∈ F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then one can obtain a similar result as that of Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 5 is a generalization of Corollary 2, since Corollary 5 reduces to that of Corollary 2 when r = 2 and F(x1, x2) = x1x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that Condition (B) of Corollary 5 is elusive when r > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In the following corollary, we give a reduced form by applying Corollary 5 to g(x) = f(x + α) for some α ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 7 Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f be a bent function on F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let α ∈ F2n and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n be such that α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any Boolean function F on Fr 2, the function h(x) = f(x) + F(f(x) + f(x + α), Trn 1(µ2x), Trn 1(µ3x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx)) is bent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of h is h∗(x) = f∗(x) + F(ϕ1, ϕ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr), where ϕ1(x) = Trn 1(αx) and ϕi(x) = f∗(x) + f∗(x + µi) for any 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let g(x) = f(x+α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then it easily seen that g∗(x) = f∗(x)+Trn 1(αx), and then Relation (7) becomes that f∗(x + r � i=2 ωiµi) = ��r i=2 ωif∗(x + µi), if wt(ω′) is odd, f∗(x) + �r i=2 ωif∗(x + µi), if wt(ω′) is even, since α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, Condition (B) of Corollary 5 is satisfied if and only if DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r by Corollary 3, and the result follows from Corollary 5 directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Note that though the conditions of h to be bent in Corollary 6 are similar as that of Theorem 3 (in fact, Corollary 6 reduces to Theorem 3 when α = 0), the corresponding bent functions in Corollary 6 and Theorem 3 can be EA-inequivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' For instance, let n = 6 and f(x) = (x1, x2, x3) · (x4, x5, x6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let µ2 = (1, 0, 0, 0, 0, 0), µ3 = (0, 1, 1, 0, 0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then it is easy to check that Dµ2Dµ3f∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, by Theorem 3, we have that h(x) = f(x) + F(µ2 · x, µ3 · x) = f(x) + F(x1, x2 + x3) is bent for any Boolean function F on F2 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and by Corollary 6, we have that ˆh(x) = f(x) + ˆF � f(x) + f(x + α), µ2 · x, µ3 · x � = f(x) + ˆF � f(x) + f(x + α), x1, x2 + x3 � is bent for any α ∈ � µ2, µ3 �⊥ and any Boolean function ˆF on F3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' These two bent functions can be clearly EA-inequivalent, since the algebraic degree of h is 2, while the algebraic degree of ˆh is 3 when α = µ3 and ˆF(x1, x2, x3) = x1x2x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 6 is efficient in producing new bent functions, since it is only required to find some α ∈ F2n and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n such that DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r and α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In the next section, we will use Corollary 6 to construct a number of concrete bent functions and compute their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 4 Several concrete bent functions and their duals The authors of [10] have found two kinds of f and φ satisfying the conditions of Theorem 4 (that is, Pr by the previous section) for constructing new bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The first kind is to let f be a bent function and φ be a linear (n, r)-function;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and the second kind is to let f and f + φi be some self-dual bent functions for each 1 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' They also invited the readers to find more kinds of f and φ for obtaining more classes of bent functions in Conclusion of [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In the previous section, we have shown that Theorem 5 is the same as that of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In addition, we have found another new kind of f and φ satisfying Pr by Theorem 5 (see Corollary 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this section, we find a number of concrete bent functions by using Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 8 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='1 New bent functions from Gold functions In this subsection, we construct some concrete bent functions by applying Corollary 6 to Gold function g(x) = Trn 1(λx2t+1), where t is a positive integer and λ ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' We first recall the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' [6][8] Let n = 2m and d = gcd(t, n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let g(x) = Trn 1(λx2t+1) for some λ ∈ F∗ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then g is bent on F2n if and only if n d is even and λ /∈ S, where S = {x2t+1 : x ∈ F2n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Moreover, the dual of g is that g∗(x) = Trn 1(λx2t+1 0 ) + ( m d mod 2), where x0 ∈ F2n satisfies that λx0 + λ2tx22i 0 = x2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' (10) Note that g is explicit, but g∗ is not explicit in Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' To find some bent functions by Corollary 6, we need to determine µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n such that DµiDµjf∗ = 0 for any 2 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' So we take f = g∗ and present the following theorem, which is the main result of this subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Take the same notations as in Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let λ ∈ F2n\\S and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n be such that Trn 1(λ(µ2t i µj+µiµ2t j )) = 0 for any 2 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and any Boolean function F on Fr 2, the function h∗ given by h∗(x) = Trn 1(λx2t+1) + F(Trn 1(αx), ϕ2(x), ϕ3(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr(x)), (11) is bent, where ϕi(x) = Trn 1 � λ(µix2t + µ2t i x + µ2t+1 i ) � for each 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f(x) = g∗(x) = Trn 1(λx2t+1 0 ) + ( m d mod 2), where x0 ∈ F2n satisfies (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then from Lemma 1, we know that f is bent and its dual is f∗(x) = g(x) = Trn 1(λx2t+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, we have f∗(x) + f∗(x + µi) = Trn 1 � λ(x2t+1 + (x + µi)2t+1) � = Trn 1 � λ(µix2t + µ2t i x + µ2t+1 i ) � , ∀ µi ∈ F2n, and DµiDµjf∗(x) =Trn 1 � λ(µix2t + µ2t i x + µ2t+1 i ) � + Trn 1 � λ(µi(x + µj)2t + µ2t i (x + µj) + µ2t+1 i ) � =Trn 1 � λ(µiµ2t j + µ2t i µj) � , ∀ µi, µj ∈ F2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This means that DµiDµjf∗ = 0 if Trn 1 � λ(µiµ2t j + µ2t i µj) � = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then by Corollary 6, we obtain that h(x) = f(x) + F(f(x) + f(x + α), Trn 1(µ2x), Trn 1(µ3x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx)) (12) is bent for any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and any Boolean function F on Fr 2, and the dual of h is exactly that of (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' When α = 0, Theorem 6 is exactly that of [28, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Applying Theorem 6 to t = m, we can deduce the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let n = 2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let θ ∈ F∗ 2m and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n be such that Trn 1(θ−1µiµ2m j ) = 0 for any 2 ≤ i < j ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and any F ∈ Br, the function h(x) = Trm 1 (θx2m+1) + F � Trn 1(θα2mx) + Trm 1 (θα2m+1), Trn 1(µ2x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx) � + 1 is bent, whose dual is that h∗(x) = Trm 1 (θ−1x2m+1) + F(Trn 1(αx), ϕ2(x), ϕ3(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr(x)), where ϕi(x) = Trn 1(θ−1µ2m i x) + Trm 1 (θ−1µ2m+1 i ) for each 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 9 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let t = m, λ ∈ F2n\\F2m and θ−1 = λ+λ2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then it is easily checked that Trn 1(λ(µ2t i µj + µiµ2t j )) = Trn 1(θ−1µiµ2m j ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let x0 = θx2m = (λ+λ2m)−1x2m, that is, x0 satisfies (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then from Lemma 1, we obtain that f(x) = Trn 1(λx2m+1 0 ) + 1 = Trm 1 (θx2m+1) + 1 is bent (since S = F2m when t = m), and the dual of f is that f∗(x) = Trn 1(λx2m+1) = Trm 1 (θ−1x2m+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The result follows then from Theorem 6 and the calculations for (11) and (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' When α = 0, Corollary 7 reduces to Theorem 12 of [20], which contains Theorem 2 of [22] (where F(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , xr) = x1x2 · · · xr), the part of bent functions in Theorem 1 of [24] (where r = 3 and F(x1, x2, x3) = x1x2x3), and Theorem 9 of [13] (where r = 2 and F(x1, x2) = x1x2) as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' When n = 2m = 4t, the authors of [10] have given the explicit form of g∗(x) = Trn 1(λx2t+1 0 )+ ( m d mod 2) by solving (10), see [10, Lemma 3], which is g∗(x) = Trn 1(P(λ)x2t+1), where P(λ) = λ2m+1+1+λ2t+2m+23t Trm t (Nn m(λ2)) and Nn m(λ) = λ2m+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' They have also pointed out in Remark 16 of [10] that g∗ is self-dual if λ ∈ F2m with λ + λ2t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This result enables us to give the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let n = 2m = 4t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let λ ∈ F2n\\S and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n be such that Trn 1(λ(µ2t i µj + µiµ2t j )) = 0 for any 2 ≤ i < j ≤ r, where S = {x2t+1 : x ∈ F2n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and any F ∈ Br, the function h(x) = Trn 1(P(λ)x2t+1) + F � Trn 1(P(λ)(α2tx + αx2t + α2t+1)), Trn 1(µ2x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx) � (13) is bent, whose dual is that h∗(x) = Trn 1(λx2t+1) + F(Trn 1(αx), ϕ2(x), ϕ3(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr(x)), where ϕi(x) = Trn 1 � λ(µix2t + µ2t i x + µ2t+1 i ) � for each 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In particular, for any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and any Boolean function F on Fr 2, h is bent if λ ∈ F2m with λ + λ2t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f(x) = Trn 1(P(λ)x2t+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any α ∈ F2n, it is easily seen that f(x)+f(x+α) = Trn 1 � P(λ)(αx2t +α2tx+α2t+1) � , and hence (12) becomes (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then result follows from Theorem 6 immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' When α = 0 and λ ∈ F2m with λ + λ2t = 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=', P(λ) = λ), Corollary 8 reduces to Theorem 23 of [20], which contains Theorem 3 of [22] (where F(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , xr) = x1x2 · · · xr), and the part of bent functions in Theorems 3 and 4 of [24] (where r = 3 and F(x1, x2x3) = x1x2x3) as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='2 New bent functions from a class of bent functions inside the completed Maiorana-MacFarland class The authors of [10] have shown that the following function f(x) = Trn 1(λx2tπ(x + x2m)) + g(x + x2m) (14) is bent if and only if λ ∈ F2n\\F2m, where t is a non-negative integer, n = 2m, π is a permutation of F2m, and g is a Boolean function on F2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This bent function is inside the completed Maiorana- MacFarland class, and it is a generalization of [18, Theorem 4], [29, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='6], and [17, Theorem 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this subsection, we intend to find more bent functions by using this bent function and Corollary 6, for which we need first to determine the dual of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' We use the technique used in [10, Proposition 1] to complete this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The dual of the bent function f in (14) is that f∗(x) = Trn 1 � ωxπ−1(Λ−1(x + x2m)2t) � + G � π−1(Λ−1(x + x2m)2t) � , (15) where Λ = λ + λ2m and G(z) = Trn 1 � λ(ωz)2tπ(z) � + g(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 10 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let ω ∈ F2n with ω + ω2m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then F2n can be decomposed as F2n = F2m + ωF2m, that is, for any x ∈ F2n, there are unique y, z ∈ F2m such that x = y + ωz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This expression also means that z = x + x2m and y = ω2mx + ωx2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then f can be represented by f(x) =f(y + ωz) = Trn 1 � λ(y + ωz)2tπ(z) � + g(z) = Trm 1 � Λy2tπ(z) � + G(z), where Λ = λ + λ2m and G(z) = Trn 1 � λ(ωz)2tπ(z) � + g(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any θ = a + ωb, where a, b ∈ F2m, we have Wf(θ) = � x∈F2n (−1)f(x)+Trn 1 (θx) = � y,z∈F2m (−1)f(y+ωz)+Trn 1 ((a+ωb)(y+ωz)) = � z∈F2m (−1)G(z)+Trm 1 � (a+b)z � � y∈F2m (−1)Trm 1 � (Λπ(z)+b2t)y2t� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This implies that f is bent if and only if |{z ∈ F2m : Λπ(z) + b2t = 0}| = 1 for any b ∈ F2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Recall that π is a permutation of F2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Thus, f is bent if and only if Λ = λ + λ2m ̸= 0, that is, λ /∈ F2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' In this case, z = π−1(Λ−1b2t), and Wf(θ) = Wf(a + bω) = 2m(−1)G(z)+Trm 1 � (a+b)z � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This implies that f∗(a + bω) = G(z) + Trm 1 � (a + b)z � = G � π−1(Λ−1b2t) � + Trm 1 � (a + b)π−1(Λ−1b2t) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Hence, the dual of f satisfies that f∗(x) = f∗(y + zω) = G � π−1(Λ−1z2t) � + Trm 1 � (y + z)π−1(Λ−1z2t) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Recall that y = ω2mx + ωx2m and z = x + x2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then we have f∗(x) =G � π−1(Λ−1(x + x2m)2t) � + Trm 1 � (ωx + (ωx)2m)π−1(Λ−1(x + x2m)2t) � =G � π−1(Λ−1(x + x2m)2t) � + Trn 1 � ωxπ−1(Λ−1(x + x2m)2t) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' From Lemma 2 and Corollary 6, we can deduce the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Take the same notations as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let f be the bent function given in (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2m, any α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥, and any Boolean function F on Fr 2, the function h(x) = f(x) + F(f(x) + f(x + α), Trn 1(µ2x), Trn 1(µ3x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , Trn 1(µrx)) is bent, and the dual of h is h∗(x) = f∗(x) + F(Trn 1(αx), ϕ2(x), ϕ3(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , ϕr(x)), where f∗ is given by (15) and ϕi(x) = Trn 1 � ωµiπ−1(Λ−1(x + x2m)2t) � for each 2 ≤ i ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Let T(x) = x + x2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Then for any µi, µj ∈ F∗ 2m, it is easily seen that T(x) = T(x + µi), which implies that f∗(x) + f∗(x + µi) = Trn 1 � ωµiπ−1(Λ−1(x + x2m)2t) � and DµiDµjf∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' The result follows then from Corollary 6 immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 11 Similarly as that of Theorems 6 and 7, by applying Corollary 6 to the following two monomial bent functions f1(x) = Tr6k 1 (λx22k+2k+1) and f2(x) = Tr4k 1 (λx22k+2k+1+1) given by [2] and [8], respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' and to the following bent functions with Niho exponents f3(x) = Trm 1 (x2m+1) + Trn 1 � 2k−1−1 � i=1 x(2m−1) i 2k +1 � given by [9], we can also obtain certain concrete bent functions, since the duals of f1, f2, f3 have been determined in [10], [11] and [1], respectively, and hence by Corollary 6, we only need to find some elements α ∈ F2n and µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr ∈ F∗ 2n such that α ∈ � µ2, µ3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' , µr �⊥ and DµiDµjf∗ e = 0 for any 2 ≤ i < j ≤ r and 1 ≤ e ≤ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Here, the concrete results are not unfolded in details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 5 Conclusion In this paper, we gave another characterization for the generic construction of bent functions given in [10], which enabled us to obtain another efficient construction of bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Based on this construction, we found several infinite families of bent functions and confirmed their duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Consequently, our results cover a lot of known bent functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' It remains to verify the EA-equivalence of the bent functions obtained in this paper to known families.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Acknowledgments This work was supported in part by the National Key Research and Development Program of China under Grant 2019YFB2101703;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' in part by the National Natural Science Founda- tion of China under Grants 61972258, 62272107 and U19A2066;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' in part by the Innovation Action Plan of Shanghai Science and Technology under Grants 20511102200 and 21511102200;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' in part by the Key Research and Development Program of Guangdong Province under Grant 2020B0101090001, in part by Scientific Research Fund of Hunan Provincial Education Depart- ment under Grant 19B485, and in part by Open Reseach Program of Shanghai Key Lab of Intelligent Information Processing under Grant IIPL201902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' References [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Budaghyan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Carlet, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Helleseth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kholosha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Further results on Niho bent functions, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 58 (11) (2012) 6979-6985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 12 [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Canteaut, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Charpin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kyureghyan, A new class of monomial bent functions, Finite Fields Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 14 (1) (2008) 221-241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 12 [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Carlet, On bent and highly nonlinear balanced/resilient functions and their algebraic immunities, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' AAECC, Berlin, Germany: Springer, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3857, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1-28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1, 2, 3 [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Carlet, Boolean Functions for Cryptography and Coding Theory, Cambridge University Press, Cambridge, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Carlet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Four decades of research on bent functions, Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Codes Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 78 (1) (2016) 5-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [6] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Coulter, On the evaluation of a class of Weil sums in characteristic 2, New Zealand J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 28 (2) (1999) 171-184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 9 12 [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Coulter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Bent Functions From Involutions Over F2n, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 64 (4) (2018) 2979-2986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Leander, Monomial Bent Functions, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 52 (2) (2006) 738-743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 9, 12 [9] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Leander, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kholosha, Bent functions with 2r Niho exponents, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 52 (12) (2006) 5529-5532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 12 [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng, Generic constructions of (Boolean and vectorial) bent functions and their consequences, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 68 (4) (2022) 2735-2751.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2, 4, 5, 6, 8, 10, 12 [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Liu, The Explicit Dual of Leander’s Monomial Bent Function, IEICE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Fundam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' E104-A (9) (2021) 1357- 1360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 12 [12] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Luo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Cao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Several new classes of self-dual bent functions derived from involutions, Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 11 (6) (2019) 1261-1273.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Several new infinite families of bent functions and their duals, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 60 (7) (2014) 4397-4407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1, 2, 3, 4, 10 [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Further constructions of infinite families of bent functions from new permu- tations and their duals, Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 8 (2) (2016) 229-246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, Bent Functions: Fundamentals and Results, Cham, Switzerland: Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Ongan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Ozbudak, New bent functions from permutations and linear translators, in Codes, Cryptology and Information Security, (Lecture Notes in Computer Science), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 10194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Springer, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 282-297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 3 [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Mesnager, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhou, Further study on the maximum number of bent components of vectorial functions, Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Codes Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 87 (11) (2019) 2597-2610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 10 [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Pott, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Pasalic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Muratovi´c-Ribi´c, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Bajri´c, On the maximum number of bent com- ponents of vectorial functions, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 64 (1) (2018) 403-411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 10 [19] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Rothaus, On “bent” functions, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' A 20 (1976) 300-305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [20] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Qi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Fan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Helleseth, Generic Construction of Bent Functions and bent idempotents With Any Possible Algebraic Degrees, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 63 (10) (2017) 6149-6157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2, 4, 10 [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Maitra, Construction of n-variable (n ≡ 2 mod 4) balanced Boolean functions with maximum absolute value in autocorrelation spectra < 2 n 2 , IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 64 (1) (2018) 393-402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Lin, Three new infinite families of bent functions, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' China Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 61 (3) (2018) 032104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2, 4, 10 [23] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Xie, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zeng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Yao, Several classes of bent functions over finite fields, Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Codes Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2022, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='1007/s10623-022-01109-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2 [24] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Cao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Xu, Several new classes of Boolean functions with few Walsh transform values, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Algebra Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 28 (2) (2017) 155-176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2, 4, 10 [25] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Wei, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Pasalic, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Xia, Large sets of disjoint spectra plateaued functions inequivalent to partially linear functions, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 64 (4) (2018) 2987-2999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 13 [26] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Xiao, Constructions of almost optimal resilient Boolean functions on large even number of variables, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Theory 55 (12) (2009) 5822-5831.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [27] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zhang and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng, GAC-The criterion for global avalanche characteristics of cryp- tographic functions, in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content='UCS the Journal of Universal Computer Science, Berlin, Germany: Springer, 1996, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 320-337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 1 [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li, Several new infinite families of bent functions via second order derivatives, Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 12 (6) (2020) 1143-1160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2, 4, 6, 9 [29] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Luo, On constructions and properties of (n, m)- functions with maximal number of bent components, Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Codes Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 88 (2020) 2171- 2186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 10 [30] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Zheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Peng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Kan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Tang, Constructing vectorial bent functions via second-order derivatives, Discret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 344 (8) (2021) 112473.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} +page_content=' 2 14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9E3T4oBgHgl3EQfVAqL/content/2301.04456v1.pdf'} diff --git a/DNE4T4oBgHgl3EQfew0W/content/2301.05101v1.pdf b/DNE4T4oBgHgl3EQfew0W/content/2301.05101v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6eccf3efb6623dcdbdd8eab39acdc432cee010cb --- /dev/null +++ b/DNE4T4oBgHgl3EQfew0W/content/2301.05101v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c23eaaa0b326bef48c750fcbfa29f201d493b9c0720183c898361fa1a87d61a5 +size 1863845 diff --git a/E9FLT4oBgHgl3EQfFi_K/vector_store/index.pkl b/E9FLT4oBgHgl3EQfFi_K/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..ec431724125bf7a2cc042d95c9a625d2dad8a4cc --- /dev/null +++ b/E9FLT4oBgHgl3EQfFi_K/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f90d018068fada742fa7896e08f88f0f01d496c54ffbf4a2d43e46025eea19b0 +size 118501 diff --git a/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/2301.03795v1.pdf.txt b/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/2301.03795v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..3acecdd07e508990cc1fcb9a6ff3746184cf37c6 --- /dev/null +++ b/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/2301.03795v1.pdf.txt @@ -0,0 +1,1843 @@ +Wave correlations and quantum noise in cosmology +Ulf Leonhardt +Department of Physics of Complex Systems, +Weizmann Institute of Science, +Rehovot 7610001, Israel +January 11, 2023 +Abstract +Wave noise is correlated. While it may look random in space, correlations ap- +pear in space–time, because the noise is carried by wave propagation. These corre- +lations of wave noise give rise to fluctuation forces such as the Casimir force, they +are responsible for the particle creation in the dynamical Casimir effect and in the +expanding universe. This paper considers the noise correlations for light waves in +non-exponentially expanding flat space. The paper determines the high-frequency +asymptotics of the correlation spectrum in the conformal vacuum. These noise cor- +relations give rise to a nontrivial vacuum energy that may appear as the cosmological +constant. +1 +arXiv:2301.03795v1 [gr-qc] 10 Jan 2023 + +1 +Introduction +Explorers have mapped every corner of the Earth, but the time of exploration has only just +began: 95% of the current content of the universe is completely unknown. The uncharted +95% are called the “dark sector” with 25% belonging to dark matter and 70% to dark +energy [1]. While there are many ideas from particle physics on the nature of dark matter, +and several experimental programmes for detecting dark–matter particles [2] dark energy +has been an enigma [3, 4]. However, it might actually be the other way round: dark energy +could be the easier problem to solve, but not as a problem of high–energy physics. Rather, +it might belong to an area of low–energy physics, extrapolated to cosmological scales. In +this paper I will follow up on the hypothesis [5, 6, 7] that dark energy, this arcane force +that drives the universe apart, is a form of much more mundane forces, the van der Waals +and Casimir forces, that cause ordinary things to stick. These are forces of the quantum +vacuum [8, 9]. +This is not a new idea. In 1968 Zel’dovich [10] suggested that vacuum fluctuations +create Einstein’s cosmological constant Λ [11]. Einstein’s Λ is what was later called +dark energy [12]. However, Zel’dovich’s and similar suggestions [13] disagree with the +measured value of Λ by some 120 orders of magnitude. The idea that Λ comes from +the quantum vacuum is not new — and seem to have failed spectacularly. What is new +is a better theory of the quantum vacuum, inspired by precision measurements and ma- +nipulations of Casimir forces [14, 15, 16], by the analogy between dielectric media and +space–time geometries [17, 18, 19, 20, 21, 22, 23, 24] tried and tested in transformation +optics [23, 24, 25, 26] and in optical analogues of black holes [27, 28, 29, 30, 31, 32, 33], +and inspired by the person to whom this volume is dedicated: Michael Berry. Not only +did he encourage me to pursue unconventional ideas, these ideas resonate with his work +on the infinite intricacies of light [34]. +The theory [5, 6, 7] is still mostly a hypothesis, but it appears to agree with astronom- +ical data [7] and seems to resolve [7] a major inconsistency in the conventional interpreta- +tion of that data [35]: the 5σ tension between the directly measured Hubble constant [36] +and the Hubble constant inferred from the Cosmic Microwave Background [1]. There are +some 102 theories to explain the Hubble tension [37]. All of them require modifications +of known physics — changes to the standard model of particle physics, general relativ- +ity or the cosmological principle; all make some experimentally untested modifications, +with one exception. The theory advocated here is the only one in the field rooted on +experiments and relying on “new things in old things” — to quote a phrase of Michael +Berry. +These results are encouraging, but much more work needs to be done to prove or +disprove the theory on astronomical data [7], to test its physical mechanism in laboratory +analogues [38] and also to improve the theory itself. Let me explain. The renormalized +vacuum expectation value εvac of the electromagnetic energy density can be expressed +such that [5] +4πG +3c2 εvac = −αΛ∆ +(1) +in terms of the gravitational constant G, the speed of light in vacuum c and the dimen- +sionless coupling parameter αΛ. The parameter αΛ depends on the inverse squared of +the cutoff length ℓΛ with [5] αΛ = (9π)−1 if ℓΛ is the Planck length ℓp = +� +ℏG/c3 (ℏ +2 + +being the reduced Planck constant). The energy density εvac does two things: it gravitates +and it generates a trace anomaly [5, 38, 39] with energy density εΛ that appears as the +cosmological term Λ, but is no longer constant. The total vacuum energy εΛ + εvac grows +with −4εvac times the Hubble parameter [5]. The cosmological term εΛ thus accumulates +εvac during the cosmic evolution, it grows with negative εvac and falls with positive εvac. +The cosmological constant still appears in the theory, yet not as a fundamental constant +of nature but only as an integration constant [7] that depends on the initial conditions and +presumably was zero at the beginning of time. +The quantity ∆ in the vacuum energy density (1) carries the physical units of a fre- +quency squared and depends on the nature of the quantum vacuum. In the first version [5] +of the theory ∆ was found to be +∆ = ∂3 +t +1 +H + H∂2 +t +1 +H +(2) +where H denotes the Hubble parameter [40]. One sees from a scale analysis that εvac +carries the correct order of magnitude of the cosmological constant1. In the second incar- +nation [7] of the theory2 the expression +∆ = ∂3 +t +1 +H +(3) +was published and used to compare theory with data [7] assuming εvac as a perturbation +of the cosmic dynamics [7]. While Eqs. (2) and (3) agree on the leading term, they +differ in the subdominant term. The data ruled out Eq. (2) whereas Eq. (3) agrees with +the astronomical data with the precision of that data for exactly the Planck–scale value +αΛ = (9π)−1. However, this is only true within first–order perturbation theory; the full +solution of the cosmic dynamics contains oscillatory modulations, suggesting that some +vital ingredient was missing that dampens these oscillations. In this paper I hope to have +identified the missing component and to have finally deduced the correct vacuum energy. +The paper also clarifies the role the quantum vacuum plays in cosmology and it offers +an explanation why quantum electromagnetism, and quantum electromagnetism alone, is +responsible for what appears as dark energy in the current era. The heart of the problem +of explaining dark energy from vacuum fluctuations is the physics of wave noise. +Wave noise is organized. In space, it may look completely random, but in space– +time patterns of correlations are clearly visible (Fig. 1). There we see the characteristic +diagonal features of wave propagation. Waves are traveling to the left or the right with the +wave velocity c/n, and the noise they carry travels with them. If n varies the noise pattern +varies as well. The most dramatic of such modifications are reflections, for example at +obstacles where n is discontinuous. Reflected wave noise gives rise to fluctuation forces +[8, 9] such as the Casimir forces [42]. If n varies in time, waves may be reflected in time +as well [43, 44]. A reflection in space is the change of sign in the wave number, in time it +is a sign change in frequency. In the dynamical Casimir effect [45, 46, 47, 48, 49] these +negative–frequency components correspond to newly–created particles, simply because if +1The argument [5] goes as follows. According to the Friedman equation [40, 41] expression (1) gives +1 +2H2 for the realistic case of zero spatial curvature [1]. As H varies on the scale of H the energy density +εvac goes like H2 and thus plays a role in the cosmic dynamics. +2Actually, this was the result of my first, unpublished version of the theory. +3 + +Figure 1: +Wave noise. Space–time diagram of waves with Gaussian noise. Although the wave +field looks random in space {x} features appear in space–time {ct, x} following the causal cones +of wave propagation (with speed c). For this picture 128 normalized left–moving and 128 right– +moving plane waves [Eqs. (5) and (6)] with periodic boundary conditions and of random Gaussian +complex coefficients were summed up. Increasing the number of waves produces finer and finer +structures, but ultimately the noise field diverges, illustrating the divergence of the bare vacuum +noise. +part of a wave of positive frequency ω is converted to −ω the energy ℏω of the remaining +positive–frequency component must grow, particles are created. Here we focus less on the +particle aspects, but rather on the amplitude correlations of wave noise. We begin with a +brief review on a familiar example, the noise seen by accelerated observers [50, 51, 52]. +Then we show how this is related to the noise perceived by an observer at rest in an +exponentially expanding universe [53] before turning to the discussion of vacuum modes +in a universe of arbitrary expansion [54]. We confirm the extension [54] of Gibbons’ and +Hawking’s formula for the radiation temperature [53] and find a new feature not present +in exponential expansion: the Hawking partners appear as red–shifted thermal radiation. +The multiple interference of all Hawking processes in the expanding universe gives the +effective vacuum energy; to calculate it we use the Wigner function of wave noise. +2 +Uniform acceleration +Wave noise is organized, because waves can be organized in terms of modes, and the +noise appears solely in the amplitudes and phases of the mode coefficients. Consider a +simple 1+1 dimensional example: a scalar wave field ˆA in empty Minkowski space given +4 + +by the mode decomposition +�A = +� +∞ +−∞ +� +�akAk + �a† +kA∗ +k +� +dk +(4) +where the Ak are the mode functions Ak(x, t) describing how the modes propagate in +space x and time t. The �ak are the mode coefficients, and only they are subject to statistical +or quantum fluctuations. The mode functions should be normalized such that each mode +accounts for the field of exactly one particle. This is conveniently done with the help of +the scalar product [55] +(A1, A2) = i +ℏ +� +∞ +−∞ +(A∗ +1 ∂tA2 − A2 ∂tA∗ +1) dx +(5) +requiring +(A1, A2) = δ(k1 − k2) , +(A∗ +1, A2) = 0 . +(6) +For example, if the modes are plane waves Ak = A exp(ikx − iωt) with ω = c|k| we +must require A2 = ℏ/(4πω). From the canonical commutation relations between field +and momentum density then follow [55] — for Bosonic fields like the electromagnetic +field — the standard Bose commutation relations: +[�ak1,�a† +k2] = δ(k1 − k2) , +[�ak1,�ak2] = 0 . +(7) +The Minkowski vacuum |0⟩ is the quantum state annihilated by all the plane–wave oper- +ators: +�ak|0⟩ = 0 . +(8) +The Minkowski vacuum is the vacuum with respect to an observer at rest in Minkowski +space. It also appears as the vacuum to observers in uniform motion, because they per- +ceive the modes Ak as plane waves as well, Doppler–shifted of course. But this is no +longer true for accelerated observers [50, 51, 52]. +Uniform acceleration is described by the transformation to Rindler coordinates [56] +as follows. Suppose we write the Cartesian space–time coordinates in terms of hyperbolic +polar coordinates: +x = ξ cosh η , +ct = ξ sinh η . +(9) +The Rindler coordinates {ξ, η} cover the two wedges with x ≥ |η| for ξ ≥ 0 on the right +and −x ≥ |η| for ξ ≤ 0 on the left of the space–time diagram (Fig. 2). In analogy to the +regular polar coordinates {r, φ} with spatial metric dr2 + r2dφ2 we get for the hyperbolic +space–time metric +ds2 = c2dt2 − dx2 = ξ2dη2 − dξ2 . +(10) +A space–time metric measures the proper time τ with increment dτ = ds/c. In particular, +as ds = ξdη for dξ = 0, the proper time along a trajectory with fixed ξ is (ξ/c)η. We can +draw another conclusion from the analogy of the Rindler coordinates with polar coordi- +nates. In space a rotation corresponds to a shift in the angle. In Minkowski space–time, a +hyperbolic rotation corresponds to a Lorentz transformation to a frame moving with ve- +locity u. An infinitesimal Lorentz boost shifts the hyperbolic angle by du/c. A sequence +5 + +R +L ++ξ +-ξ +x +ct +η +η +Figure 2: +Accelerated observers. Space–time diagram of accelerated observers (black curves) in +Minkowski space with Cartesian coordinates x and t. The observers follow the Rindler trajectories +of Eq. (9) with fixed ξ and variable parameter η. The acceleration is given by c2/ξ while (ξ/c)η +gives the proper time of each observer. For negative ξ the parameter η needs to run backwards +(reversed arrow) as proper time always runs forwards. The observer on the right (R) is separated +from the observer on the left (L) by horizons (red). Neither left– nor right–moving light from R +can reach the shaded region in L. +of infinitesimal boosts thus draws an entire Rindler coordinate line along varying η for +ξ = const. Now, uniform acceleration is just such a sequence of infinitesimal Lorentz +transformations. We thus conclude that the Rindler line is the world line of a uniformly +accelerated observer with acceleration du/dτ = c2/ξ. +Consider such a uniformly accelerated observer. Suppose the observer is equipped +with a spectrometer. A spectrometer consists of a spectral element to decompose the field +�A into frequencies, and a detector to measure the spectral components. It is not important +what the detector is. It may be a particle detector [52] or an amplitude detector [57], +the physically important feature of the spectrometer is the ability to perform a frequency +analysis, and there the important aspect is the fact that the spectrometer responds to its +proper time τ and not to the coordinate time t. As τ = (ξ/c)η we may describe the effect +of the spectrometer as a Fourier transformation with respect to η. Note, however, that for +ξ < 0 (on the left side L of the Rindler diagram of Fig. 2) η needs to run backwards, since +proper time always runs forwards. +Imagine now a pair of accelerated observers — one with positive ξ on R and one +with the exact opposite −ξ on L. Figure 2 reveals that the two observers are separated by +horizons. The entire world line of observer L lies in the shadow of left– or right–moving +waves that touch observer R. But it turns out the two observers can and must communicate +by sharing the same noise field. To work this out, consider the spectral components they +6 + +Figure 3: +Plane wave. The accelerated observer (Fig. 2) samples noise made of plane waves +with random amplitudes and phases. Each plane wave is sampled along the Rindler trajectory of +Eq. (9) with proper time (ξ/c)η. The panel shows the real and imaginary part of the wave sampled +along the path with parameter η. Fourier analysis reveals that the positive–frequency components +for η contain negative–frequency components for t enhancing the quantum noise perceived by one +observer at +ξ by correlations with its partner at −ξ (Fig. 2). +measure: +�AR = 1 +2π +� +∞ +−∞ +�A +��� +R eiνη dη , +�AL = 1 +2π +� +∞ +−∞ +�A +��� +L e−iνη dη +(11) +in terms of the dimensionless Fourier components ν. Here the R and L indicate the space– +time trajectories of the two observers. They sample the plane–wave Minkowski modes +(Fig. 3) as oscillations with phases +ϕR = k(x ∓ ct)|R = kξ e∓η , +ϕL = k(x ∓ ct)|L = −kξ e∓η . +(12) +Now, components with positive Rindler frequencies ν may also sample negative Minkow- +ski frequencies, i.e. the complex–conjugated modes A∗ +k. In fact, moving the contour of the +Fourier integral by +iπ on R and by −iπ on L changes the sign in the phases (12) while +preserving the convergence of the Fourier integrals (11). We thus see that the Fourier +transform of the conjugate A∗ +k is exactly e−πν times the Fourier transform of Ak, on both +sides of the Rindler wedge. +Accelerated observers sample negative Minkowski frequencies. To see how this af- +fects the wave noise perceived by the accelerate observers, we introduce a set of modes +7 + +Figure 4: +Rindler modes. The figure shows examples of modes that are monochromatic for +the two accelerated observers (white hyperbolas, see also Fig. 2). For a monochromatic mode the +phase increases linearly with time, but for the observers this is proper time, not coordinate time. +Each accelerated observer comes in with asymptotically the speed of light and leaves asymptot- +ically with the speed of light. For such velocities proper time ticks exponentially slowly, and so +the phase grows only logarithmically. Near the horizon (Fig. 2) the phase diverges logarithmically +[Eq. (13)]. An exponentially small part of the wave crosses to the other side if this wave is made +of a superposition of positive–norm plane waves, describing the quantum vacuum. +that are monochromatic with respect to those observers (Fig. 4). Any mode in Minkowski +space must be a superposition of left– or right–moving waves. The left–moving waves are +functions of x− = x + ct while the right–moving modes depend on x+ = x − ct. From +x± = ξe∓η follows that the phases of monochromatic Rindler modes must be logarithmic +in x±, which means that the Rindler modes are purely imaginary powers of x±. There we +have two possibilities: x± or −x± to an imaginary power. In the first case the wave is +predominately localized on the right side of the space–time diagram (Fig. 2), in the sec- +ond case on the left side. On R we should give the Rindler wave a positive η–frequency +ν, i.e. the power ±ν of x±, while on L it should oscillate with −ν as η runs backwards +for forward–running proper time, which also corresponds to the power ±ν but this time +of −x±. We thus define +Aν = A +� +(x±)±iν +: ν > 0 +(−x±)±iν +: ν < 0 +with +x± = x ∓ ct +(13) +and represent the field as +�A = +� +± +� +∞ +−∞ +� +�aνAν + �a† +νA∗ +ν +� +dν . +(14) +8 + +ct +XIt only remains to determine the normalization factor A from Eqs. (6). We substitute the +modes (13) into the scalar product (5) with the understanding that (A1, A2) differs from +zero only when ν1 ∼ ν2. We define δ = ±(ν2 − ν1) and obtain for ν > 0: +(A1, A2) = 2cν +ℏ A2 +� +∞ +−∞ +(x ∓ ct)iδ−1 dx = 2cν +ℏ A2 � +1 − e−2πν� � ∞ +0 +ξiδ dξ +ξ . +(15) +Writing ξ as an exponential gives 2π times the standard Fourier representation of the delta +function. Defining the parameter ζ by +tanh ζ = e−πν +(16) +with cosh ζ = (1 − e−2πν)−1/2 we thus get +A = B cosh ζ , +B2 = +ℏ +4πcν . +(17) +This concludes the normalization of the Rindler modes and hence the Rindler representa- +tion of the field. Only one important, subtle point remains to be discussed. +The Rindler modes (13) are understood to be analytic on the upper half complex plane +for x+ and on the lower half plane for x− such that the left side is suppressed for ν > +0 and the right side for ν < 0. In either case, the Aν are then analytic on the lower +complex plane for the time t. From this follows that we can always close the contour +of a Fourier transformation with respect to Minkowski time t for negative frequencies +ω and get zero. In other words, the Rindler modes (13) have only positive Minkowski +frequencies. Therefore, they are superpositions of positive–norm Minkowski waves, and +so their associated annihilation operators �aν are also just superpositions of the Minkowski +�ak, which implies that both share the same vacuum state |0⟩. +Having established the vacuum in the Rindler representation, it is elementary to work +out the spectral components seen by the two accelerated observers. We obtain from +Eqs. (11) and (14) for the modes (13) with norm (17) and x± = ξe∓η the expressions +�AR = B +� +�aν cosh ζ + �a† +−ν sinh ζ +� +, +�AL = B +� +�a−ν cosh ζ + �a† +ν sinh ζ +� +. +(18) +We see here again that the observers sample negative–frequency components �a† with rel- +ative weight tanh ζ = e−πν. Representing the mode operators in terms of their real +and imaginary parts (Hermitian and anti–Hermitian parts) we see that the sampled field +amplitudes are connected — the real parts are correlated and the imaginary parts anti– +correlated. This means that the wave noise perceived by the observer on R is correlated +with the noise perceived by observer L. Observer R is influenced by some extra random- +ness that comes from this connection to observer L and vice versa. That excess noise +appears in the intensity as an additional contribution to the standard vacuum noise: +⟨ �A† +R �AR⟩ = ⟨ �A† +L �AL⟩ = B2 +�1 +2 + +1 +e2πν − 1 +� +. +(19) +As the dimensionless η is related to the proper time by the factor c/ξ, the frequencies mea- +sured in the spectrometers of the accelerated observers are related to the dimensionless ν +9 + +by the same factor. We may read the (e2πν − 1)−1 in Eq. (19) as the Planck distribution +(eℏω/kBT − 1)−1 with Unruh temperature [52] +kBT = ℏc +2πξ +(20) +where kB denotes Boltzmann’s constant. Each one of the two observers perceives the +vacuum as thermal radiation with temperature (20). Each one receives this extra noise, +because the noise is correlated. These correlations do appear when the field amplitudes +are Fourier–transformed: they are spectral correlations. In terms of particles, they appear +as entangled Einstein–Podolski–Rosen pairs [55]. When the spectrometer of observer R +detects a particle at frequency ω so does the spectrometer of observer L (provided they +are perfectly efficient). But here we are primarily concerned with amplitude noise and its +cosmological implications. +3 +Exponential expansion +Turn now from accelerated observers in static Minkowski space to an observer at rest in +the expanding universe. Consider first the conceptually simplest case: pure exponential +expansion (de Sitter space [58]). This is the phase of the cosmic evolution we are entering +at the present time and, presumably, it was the phase of inflation [59] just after the Big +Bang (although with a much higher expansion rate then in the current era). Assume +in agreement with astronomical observations [60] that the universe is homogeneous and +isotropic, and spatially flat [1]. In this case, the space–time geometry is given by the +flat–space Friedmann–Lemaitre–Robertson–Walker metric [40]: +ds2 = c2dt2 − a2dr2 +(21) +with time–dependent scale factor a(t). The scale factor describes how spatial distances +expand, as the physical distance between two points at the same time t is given by a times +the coordinate difference r. The spatial coordinates r are called comoving coordinates, +because they do not move relative to the universe. The coordinate time t is called cosmo- +logical time and, physically, it is the proper time of an observer at rest with the universe +(dr = 0). We may introduce a new time τ called conformal time, defined as +τ = +� dt +a +(22) +such that the metric becomes conformally flat: +ds2 = a2 � +c2dτ 2 − dr2� +. +(23) +For light rays (ds = 0) the conformal factor a2 is irrelevant, and so light rays travel +in conformal time and comoving space like in empty Minkowski space. As Maxwell’s +equations are conformally invariant [24] this remains true for full electromagnetic fields +and their quantum fluctuations. We assume that the quantum vacuum is carried by plane +waves in conformal time. The notation is the exact opposite as in the case of uniform +10 + +acceleration: there t is the time the vacuum propagates with and τ denotes the proper +time of the accelerated observer, whereas in the expanding universe the vacuum waves +propagate with τ while t is the proper time of the observer at rest with the universe. +Note that the gravitational field of the universe (the space–time geometry) does distin- +guish a global frame — only in this frame the metric is homogeneous and isotropic. We +can of course move this frame to any point (as the universe is homogeneous) and rotate it +(as it is isotropic) but the metric is different for an observer in uniform motion. Note also +that although the universe is spatially flat, it is curved in space–time. One obtains for the +curvature scalar [41] +R = − 6 +c2 +� +∂tH + 2H2� +(24) +in terms of the Hubble parameter +H = ∂ta +a . +(25) +In the case of exponential expansion the Hubble parameter is a constant H0 such that +a = a0 eH0t . +(26) +In this case, the space–time curvature is negative and constant3 as we also see from R = +−12H2 +0/c2. +Figure 5: +Exponential expansion. An observer at rest samples a plane wave in the exponentially +expanding universe. The wave oscillates with conformal time [Eq. (27)] that differs exponentially +from the proper time of the observer (the cosmological time t) in perfect analogy to the Minkowski +wave sampled by the accelerated observer (Fig. 3). +Suppose the observer at rest with the universe samples the plane waves of the quantum +vacuum (Fig. 5). They oscillate with frequencies Ω in the conformal time τ of Eq. (22). +3The space–time of exponential expansion (de Sitter space) is a maximally symmetric space with con- +stant Riemann tensor Rαβ +µν = −(H0/c)2 (δα +µδβ +ν − δα +ν δβ +µ). The negative prefactor indicates the negative +curvature. +11 + +de Sitter +extension +r +τ = 0 +τ +∞ +t +t +Figure 6: +Extended de Sitter space. Radial space–time diagram {cτ, r} in conformal time τ +and comoving radius r = |r|. Cosmological time t runs according to the arrows indicated and +ends (t = +∞) at the horizontal line (τ = 0).. Light travels along diagonal lines in the conformal +diagram and may cross over to the next world, the extension, for τ > 0. Light beyond the horizon +(red line) cannot reach the observer (black vertical line up until t = +∞) before this world ends +(τ = 0). Light coming in within the white area — within the horizon — leaves in the shaded area, +but cannot reach the double–shaded region in the extended world, in perfect analogy to the Rindler +horizon of uniform acceleration (Fig. 2). +We obtain for the case of exponential expansion: +τ = − 1 +aH0 +. +(27) +Note that conformal time is negative and ends at τ = 0 in the infinite future (t = +∞). +The observer samples the phase +ϕ = Ωτ = Ω +a0 +e−H0t . +(28) +This is the same phase as the one of a right–moving wave sampled by Rindler observer R +(Fig. 4). We see from Eq. (12) that Ω/a0 corresponds to kξ and H0t to the dimensionless +Rindler time η. +The observer at rest with the exponentially expanding universe thus perceives waves +in the same way as the uniformly accelerated observer in Minkowski space, including the +waves of the quantum vacuum. Like in uniform acceleration, the observer is surrounded +12 + +by a horizon (Fig. 6). Seen in conformal time and comoving space, incoming rays out- +side of the radius rH = −cτ will never arrive at the observer before the world ends in +conformal time (τ = 0). From Eq. (27) we get +rH = +c +aH . +(29) +Unlike the accelerated observer, there is no partner L to the observer R, at least in this uni- +verse. We may construct an artificial partner by extending de Sitter space to τ > 0 (simi- +lar to the Kruskal extension of the black hole [56]). For this we imagine another universe +with infinite cosmological time related to positive conformal time by τ = H−1 +0 e−H0t. In +this netherworld time runs backwards from +∞ to −∞ such that conformal time and +light smoothly passes from one world into the other (Fig. 6). The partner observer in the +netherworld is then shrouded behind a horizon (Fig. 6) from the observer in this world, +in perfect analogy to uniform acceleration. In particular, we may conclude that the de +Sitter observer perceives the vacuum as thermal radiation as well [53]. From the corre- +spondence to the case of the accelerated observer with Unruh temperature (20) we obtain +the Gibbons–Hawking temperature [53] +kBT = ℏH0 +2π . +(30) +Exponential expansion is a clear, simple, perfectly understood case of quantum noise in +cosmology, but it is largely an academic case. In reality, the universe does not expand +exponentially yet nor did it in the past. Very few papers have tackled the problem beyond +the case of de Sitter space [54, 61, 62], because it is a difficult problem of — appar- +ently — hardly any relevance, as the Gibbons–Hawking temperature of the real universe +is astronomically small (T lies in the order of 10−29K for 1/H0 of 10Gy). But if the +quantum noise of general cosmological horizons is indeed the key to understanding the +cosmological constant [5], understand it we must. +4 +Expanding flat space +Apart from exponential expansion, there is no other case when an expanding flat space +establishes a genuine event horizon [54, 63] (Fig. 7a). One sees this as follows. The cos- +mological horizon [64] is the spherical surface around a given point where the expansion +velocity reaches the speed of light. The expansion velocity u is the derivative of the proper +length ℓ = ar with respect to cosmological time t. Differentiating ℓ gives Hubble’s law, +u = Hℓ, in terms of the Hubble parameter H defined in Eq. (25). We see that u reaches +c at rH of Eq. (29). For the cosmological horizon to be an event horizon it needs to be +light–like, parallel to light rays in the {cτ, r} space–time diagram, because otherwise light +may cross it. Since +τ = +� +da +a2H +(31) +the conformal time τ does only agree with −1/(aH) for H = const, i.e. exponential +expansion, which proves that cosmological horizons are not event horizons, except in +the exponential case. In fact, the light of distant galaxies and the Cosmic Microwave +13 + +Figure 7: +Cosmological horizon. Space–time diagrams of the horizon (red curve) based on +actual cosmological data [1, 40] (plotted in units c/H0 with Hubble constant H0). a: in co– +moving spatial coordinates r and conformal time τ light (black and white lines) propagates like in +Minkowski space. The region outside the horizon is shaded in grey. Light may cross the horizon, +except when, in the final stage of cosmic evolution, the horizon becomes light–like and hence a +genuine event horizon. b: vacuum modes in analogy to the Rindler modes (Fig. 4). The modes are +defined with respect to a specific time, here τ = 0 (the present time). The figure shows the phase +pattern of the incident light only, not the outgoing light; Eq. (36) describes both. +Background reaches us from beyond our horizon [40, 63]. Therefore, it is not clear from +the outset how to generalize the Gibbons–Hawking formula (30) to the case of expanding +flat space in general.4 +Consider light in a universe with metric (21). Space shall be expanding, H > 0. For +conceptual simplicity we do not start from Maxwell’s equations, but rather describe each +polarization component by a conformally–coupled scalar field with modes satisfying the +wave equation [24, 65]: +1 +√−g ∂α +√−g gαβ∂βA − R +6 A = 0 +(32) +in terms of the metric tensor gαβ, its determinant g and matrix–inverse gαβ, and the cur- +vature scalar R of Eq. (24). Einstein’s summation convention over repeated indices is +adopted. The modes shall be normalized according to Eq. (6) with the scalar product +4This section closely follows Ref. [54] but corrects an error in the conformal factor. Despite this error, +the ideas and results of the paper [54] are correct, as we show here and in Sec. 5. +14 + +co-moving r +a +0 +conformal +-2 +-3 +0 +2r +b +0 +T +-2 +-3 +0 +1 +2[65]: +(A1, A2) = ic +ℏ +� � +A∗ +1 ∂0A2 − A2 ∂0A∗ +1 +� √−g d3x , +∂0 = g0α∂α . +(33) +One sees from the wave equation that the scalar product (33) is a conserved quantity for +arbitrary wave packets satisfying Eq. (32). Writing A as A0/a reduces the wave equation +(32) to the free wave equation for A0 with respect to the conformal time τ of Eq. (22), +which shows that light waves propagate in the expanding universe like in free Minkowski +space {cτ, r} (not just light rays). We may use the plane waves +A = (A/a) eik·r−iωτ +with +ω = c|k| , +A2 = +ℏ +16π3ω +(34) +as normalized modes. We assume that the cosmological quantum vacuum is in the vac- +uum state (8) with respect to these conformal plane waves. This cosmological vacuum +is called the conformal vacuum [65]. However, as we know from the case of exponen- +tial expansion, an observer at rest may not perceive the conformal vacuum as vacuum +fluctuations. +Imagine a point–like observer at rest with the expanding universe. We use spherical +coordinates with the origin attached to the point of the observer. Only radial waves will +matter, because all waves with higher orbital angular momentum vanish at the origin. +Write the radial modes as +A = +1 +√ +4π arAν(r, τ) . +(35) +From the wave equation (32) follows that the Aν satisfy one–dimensional wave propaga- +tion, which means that Aν consists of a superposition of incoming and outgoing waves +f(r±cτ). As A must not diverge for r → 0 we need to require Aν = f(r+cτ)−f(r−cτ), +the outgoing wave is the ingoing wave reflected at the focus. Inspired by the cases of uni- +form acceleration and exponential expansion, we wish to define modes in close analogy +to the Rindler modes of Eq. (13). These modes can only capture the cosmological hori- +zon at a given moment in time, i.e. for a given scale factor a0 and corresponding Hubble +parameter H0. We define [54] (Fig. 7b) in analogy to the Rindler modes [Eq. (13), Fig. 4]: +Aν = A +� +(η − ρ)iν − (η + ρ)iν +: ν > 0 +(ρ − η)−iν − (−η − ρ)−iν +: ν < 0 +(36) +where η (not to be confused with the Rindler η) and ρ are defined as (Fig. 8) +η = 1 + a0H0(τ0 − τ) , +ρ = a0H0 +c +r . +(37) +Like in the case of the Rindler modes, the modes (36) are analytic on the lower half τ +plane. Consequently, they consist entirely of positive–frequency plane–wave modes (34) +and share the conformal vacuum. Let us call them vacuum modes. The phase of each of +the vacuum–mode components, incoming or outgoing, is logarithmic: +ϕ = ν ln [1 + a0H0(τ0 − τ ∓ r/c)] . +(38) +15 + +ρ = 1 +0 +1 +2 +η = 1 +η = 0 +co-moving r +conformal τ +Figure 8: +Characteristic events. Space–time diagram showing a part of the actual cosmolog- +ical horizon (Fig. 7a). Vacuum modes (Fig. 7b) are established in analogy to the Rindler modes +(Fig. 4). The vacuum modes are characterized by the time parameter η and the space parameter +ρ defined in Eq. (37). The η parameter runs backwards from η = 1 when the vacuum mode is +defined (t = t0) to η = 0 when the Hawking partners arrive at the origin. At the time t0 (η = 1) +the spatial parameter reaches unity at the horizon. +Like the Rindler modes (Fig. 4) the vacuum modes (36) are not monochromatic (Fig. 7b); +the frequency ω = −∂tϕ varies in space and time. At the defining time of the modes t0 +we have +ω|t=t0 = +ω0 +1 ∓ u/c , +u = H0ℓ , +ℓ = a0r +(39) +where ω0 denotes the frequency at the origin and at t = t0. This frequency is related to +the dimensionless parameter ν by +ω0 = νH0 . +(40) +Equation (39) shows that the vacuum modes are Doppler–shifted in the expanding uni- +verse. Incoming waves propagate against the Hubble flow u and are blue–shifted, outgo- +ing waves are red–shifted. Note that the Doppler profile (39) was originally used to define +the modes (36). Here we have derived them from the analogy to the case of uniform ac- +celeration. +It remains to normalize the radial vacuum modes. For this we express the scalar +product (33) in conformal time τ and spherical coordinates {r, θ, φ} with metric tensor +gαβ = a2 diag(1, −1, −r2, −r2 sin2 θ). We obtain for the radial waves (35): +(A1, A2) = i +ℏ +� ∞ +0 +� +A∗ +ν1 ∂τAν2 − Aν2 ∂τA∗ +ν1 +� +dr . +(41) +For the vacuum modes (36) with definitions (37) we have ∂τ = −a0H0 ∂η and a0H0 dr = +16 + +c dρ and get +(A1, A2) = −ic +ℏ +� ∞ +0 +� +A∗ +ν1 ∂ηAν2 − Aν2 ∂ηA∗ +ν1 +� +dρ . +(42) +We may normalize the vacuum modes at a convenient moment (η = 0) as the scalar +product remains constant at any time. We find exactly the same norm as for the Rindler +waves, Eqs. (16) and (17). +Finally, consider the mode overlap between the vacuum modes defined at different +times. The most relevant case is the overlap between the vacuum modes at one horizon, +say at t2, with the modes at the previous horizon at t1. By this we mean that t2 is the +time when the Hawking partners generated at t1 arrive. The overlap tells how the modes +at one instant of creating Gibbons–Hawking radiation are related to the modes at the next +stage of creation. In particular, the phases between the modes are important, as the acts +of creation will interfere with each other. This is because particle creation works like +parametric amplification [55] where the phase of the incident light determines whether +particles are created or annihilated. We calculate the scalar product (A1, A2) at time t2 +where η1 = 0 (arrival of the partners) and η2 = 1 (primary Hawking radiation). We +denote the scale factors and Hubble parameters as a1, H1 and a2, H2, and use ρ = ρ2 as +integration variable with ρ1 = ρ2(a1H1)/(a2H2) from Eq. (37). In this way we get +(A1, A2) = c +ℏ (ν1 + ν2) A1A2 +�a2H2 +a1H1 +�iν1 +cosh2 ζ I12 +(43) +with definition (16) and the remaining overlap integral +I12 += +� ∞ +0 +ρ−iν1 (1 + ρ)iν2 dρ +ρ − +� 1 +0 +ρ−iν1 (1 − ρ)iν2 dρ +ρ +(44) += +Γ(−iν1) +Γ(−iν2) Γ(iν2 − iν1) − +Γ(1 + iν2) +Γ(1 − iν1 + iν2) Γ(−iν1) +(45) +in terms of Gamma functions. Note that we gave the ν an appropriate small imaginary +part such that the integrals (44) converge. The dominant contribution to the mode overlap +appears for ν1 → ν2 where Γ(iν2−iν1) ∼ 1/(iν1−iν2). In the mode expansion +� +(�aνAν + +�a† +νA∗ +ν)dν the overlap (A1, �A) picks out a single mode with ν1 = ν2 = ν by Cauchy’s +theorem. Taking into account the normalization (17) we arrive at the simple result: +�a2 ∼ +�a2H2 +a1H1 +�iν +�a1 . +(46) +Therefore, to a good approximation, the coefficients of the vacuum modes at time t2 are +given by the mode coefficients at time t1 multiplied by the characteristic logarithmic phase +factor ν(ln a2H2 − ln a1H1) of the cosmological horizons. This concludes our discussion +of the vacuum modes in the expanding universe. +5 +Radiating horizons +Consider now the noise the observer perceives. The observer, at rest with the expanding +universe at r = 0, samples the field with respect to cosmological time t, but the field +17 + +oscillates with conformal time τ. In the radial vacuum modes we have organized all the +superpositions of conformal plane waves the observer perceives, such that +�A +��� +r=0 = +� +∞ +−∞ +� +�aνA0,ν + �a† +νA∗ +0,ν +� +dν +(47) +where according to Eq. (35) the A0,ν are given by +A0,ν = +1 +√ +4π ar Aν +���� +r=0 +. +(48) +We obtain from expressions (36) and (37) for the modes: +lim +r→0 +Aν +r = ∓2iνA (±η)±iν−1 a0H0 +c +. +(49) +Consider the radiation field around two times in the cosmic evolution: near the time t0 +when particles are produced in the Gibbons–Hawking effect for the Hubble parameter +H0 and then around the time when the corresponding Hawking partners arrive, given by +the condition η = 0 (Fig. 8). The time t0 is arbitrary, but for each t0 a new system of +modes needs to be constructed according to Eqs. (36) and (37). Since any such system +is a superposition of positive–frequency plane waves, Eq. (34), the vacuum state with +respect to the mode operators �aν is the cosmic vacuum, regardless of t0. +As in the cases of uniform acceleration and exponential expansion, imagine the ob- +server as equipped with a spectrometer measuring the Fourier transformation of the field +with respect to the proper time of the observer, cosmological time. Consider the Fourier +transform near the time t0. We write for each vacuum mode +�A0,ν = +� +∞ +−∞ +A0,ν eiωt dt +(50) +with the understanding that the integration is performed near t0. There we get from +Eqs. (37) and (22): +dη = −a0H0 +a +dt , +t ∼ − 1 +H0 +ln η , +(51) +and hence from Eqs. (48) and (49): +�A0,ν = +√ +4π iνcA δ(ν − ν0) , +ν0 = ω +H0 +. +(52) +For positive frequencies ω the Fourier transform �A0,−ν of the negative–index modes van- +ishes. However, like in the case of the accelerated observer, the Fourier transform of the +complex conjugate negative–index modes A∗ +0,−ν does not disappear: +� +A∗0,−ν = e−πν �A0,ν . +(53) +From relation (16) and the normalization (17) of the vacuum modes we obtain the compact +result: +� +∞ +−∞ +�A eiωt dt +���� +r=0 += +√ +ℏν +c +i +� +�aν cosh ζ + �a† +−ν sinh ζ +� +, +ν = ω +H0 +. +(54) +18 + +The result shows that the observer, sampling the vacuum noise with respect to cosmologi- +cal time around t0, experiences the creation of Hawking particles [54], even in the case of +non–exponential expansion when the cosmological horizon is not an event horizon [63]. +Now turn to the time t1 when the Hawking partners are expected to arrive, i.e. when +η ∼ 0 (Fig. 8). It follows from Eqs. (22) and (37): +η ∼ −a0H0 +a1 +t +(55) +where a1 denotes the scale factor at t1. Defining now ν1 = (a1/a0)(ω/H0) we thus obtain +�A0,−ν = iν +√π +A +c +� +∞ +−∞ +(−η)−iν−1 e−iν1η dη ∼ i +√ +2iν A +c (ν1/ν)iν eiν +(56) +in the saddle–point approximation for ν ≫ 1. Similarly, for the negative–frequency +Fourier–transform of the complex conjugate modes with positive index ν we get +� +A∗0,+ν = e−πν �A0,−ν . +(57) +Substituting these results in the mode expansion (47) we calculate the integral over the +mode index in the saddle–point approximation as well. The phase of the integrand, ϕ = +ν ln(ν1/ν) + ν, is stationary (∂νϕ = 0) for ν = ν1. We obtain in perfect analogy to +Eq. (54): +� +∞ +−∞ +�A eiωt dt +���� +r=0 += +√ +ℏν +c +i +� +�a−ν cosh ζ + �a† +ν sinh ζ +� +, +ν = +a1 +a0H0 +ω . +(58) +Like the accelerated observer [Eq. (18)] the observer at rest with the expanding universe +measures spectral correlations expressed in the Bogoliubov transformations (54) and (58). +These correlations appear as extra noise with Planck spectrum (19). +6 +Cosmic cascade +We have thus derived the thermal radiation of cosmological horizons in expanding flat +space from the physical picture of wave noise (Fig. 1). This picture reproduces the gen- +eralization [54] of Gibbons’ and Hawking’s [53] result, Eq. (30), to arbitrary expansion. +In this general case H0 in Eq. (30) refers to the Hubble parameter (25) at any given time +t0, not required to be constant as in Gibbons’ and Hawking’s case [53] of exponential +expansion, de Sitter space (Fig. 6). In addition, we also derived a new aspect of Gibbons– +Hawking radiation not seen in de Sitter space. There the Hawking partners never arrive +before the world ends in conformal time (Fig. 6) whereas in reality they do (Fig. 8). The +light of distant galaxies and the Cosmic Microwave Background easily cross the cosmo- +logical horizon [40, 63] and so do the Hawking partners. We have found that the partners +are correlated with the primary particles, Eqs. (54) and (58), for the same dimensionless +frequency ν. For the primary particles, ν is given by the frequency ω divided by the +Hubble parameter H0, which gives in the Planck spectrum (19) the Gibbons–Hawking +temperature (30). For the Hawking partners, ν is given by ω divided by (a0/a1)H0 where +19 + +0 +1 +2 +-3 +-2 +-1 +0 +co-moving r +conformal τ +Figure 9: +Cascade of horizons. In the actual universe (Fig. 7) depicted in conformal time τ +and comoving radius r, the Gibbons–Hawking radiation at present (τ = 0) depends on a cascade +(zigzag line) of radiation generated by past cosmological horizons (red) curve. Depending on +the relative phase, radiation is created or annihilated. The multiple interference of all creation +processes gives rise to the effective Gibbons–Hawking temperature and vacuum energy density. +a1 denotes the scale factor at their time of arrival. This means that the Hawking partners +also arrive as thermal radiation, but with the red–shifted temperature +kBT1 = a0 +a1 +ℏH0 +2π . +(59) +These results are simple and intuitive, but they are still incomplete. If the present Hawk- +ing partners arrive in the future as thermal radiation, so should the Hawking partners of +the past arrive in the present. Call the scale factor and Hubble parameter of the past cos- +mological horizon a−1 and H−1. The present radiation of Hawking partners should then +have the temperature +kBT−1 = a−1 +a0 +ℏH−1 +2π +. +(60) +20 + +But neither this nor the primary temperature (30) is the effective temperature Teff of +the radiation in total, because the Hawking particles interfere with their partners. We +have worked out that they have the logarithmic phase difference (46). Like in parametric +amplification [55] the phase of the incident radiation determines whether it gets ampli- +fied or de–amplified, whether particles are created or annihilated. The Hawking partners +from the previous horizon may very well annihilate some of the Gibbons–Hawking radi- +ation at the present, depending on the relative phase. Furthermore, the horizon before the +previous horizon interferes with the particle production as well, and so does the whole +cascade of past cosmological horizons (Fig. 9). Each horizon establishes the Bogoliubov +transformation +�b±ν = �a±ν cosh ζ + �a† +∓ν sinh ζ +with +tanh ζ = e−πν . +(61) +Between horizons, the modes are phase shifted according to Eq. (46). As the frequencies +relevant to the vacuum energy much exceed the Hubble parameter, we are in the regime +of ν ≫ 1 where we get for the final �bν in terms of the initial vacuum mode operators �a±ν: +�bν ∼ �aν + �a† +−ν S e−πν +(62) +with S summing up the phase factors of the m–th previous horizons relative to the present +one: +S = +∞ +� +m=1 +�a−mH−m +a0H0 +�2iν +. +(63) +This sum is highly oscillatory, but we are interested in the net effect of the interfering +horizons, i.e. in the average. When averaged over δν ∼ 1 only an exponentially small +contribution will remain that, together with the primary e−πν, turns the Bogoliubov trans- +formation (62) into +�bν ∼ �aν + �a† +−ν eiΦ−πω/Heff +(64) +with some phase Φ that does not affect vacuum correlations. The exact expression for +Heff we shall derive in the next section, but here we can already draw some qualitative +conclusions. Since Heff depends on the history of cosmic evolution, it will introduce +a memory effect in the cosmologically relevant vacuum energy. This memory of the +past should remove the oscillations that would otherwise plague the cosmic dynamics. +Destructive interference from past cosmological horizons may also explain why first– +order perturbation theory with the primary H instead of the full Heff agrees so remarkably +well with astronomical data [7]. +It is also interesting to note that the cosmic vacuum energy vanishes within one cosmic +era and thrives in the transition periods between different eras. By era we mean a period +in the cosmic evolution dominated by one type of fluid with a characteristic equation of +state. In the radiation–dominated era [40] the Hubble parameter H goes with a−2, in the +matter–dominated era [40] H ∝ a−3/2 and during vacuum domination H would become +constant. Apart from the exponential expansion in the vacuum era, all other eras are +characterized by a power law: +H = H0 a−γ +(65) +21 + +with constant H0 and γ > 1 (where H0 denotes H at a = 1 here). The partner radiation +arriving at time t with scale factor a and Hubble parameter H originates from the past +cosmological horizon the conformal time interval τ earlier, with +τ = +� +da +a2H = +1 +γ − 1 +� 1 +aH − +1 +a−1H−1 +� += +1 +a−1H−1 +, +(66) +which gives +aH +a−1H−1 += 1 +γ . +(67) +This recurrence relation remains true for all the phases in the sum (63) such that the sum +forms a perfect harmonic series with vanishing zero–frequency component. The cycle +average of such a series vanishes: the number of particles produced is exactly zero. For +a power–law expansion, creation and annihilation thus cancels out exactly as the result of +multiple interference between past horizons (Fig. 9). +7 +Wigner function +The interferences in the cosmic cascade of creation and annihilation at horizons (Fig. 9) +are captured in the sum (63). Yet this sum is difficult to evaluate and mathematically ill– +defined. Let us therefore try to deduce a better formula for the effective Gibbons–Hawking +temperature. The principal problem of our previous approach (Sec. 5) is the Fourier trans- +formation. We wish to deduce the radiation spectrum as it evolves in time, and there we +are interested in spectral features ∼ exp(−2π/H) that would require an integration time +in the order of 1/H for their accurate resolution. However, the universe also evolves on +a time scale of 1/H and with it the Gibbons–Hawking spectrum. The two aspects, spec- +tral accuracy and temporal resolution, appear to be mutually exclusive. Frequency and +time are as mutually exclusive as position and momentum in quantum mechanics (being +Fourier transforms of each other). Fortunately, there are good compromises. To give a +simple example, music sheets describe tones – frequencies — in time; to give a sophis- +ticated example, quantum quasiprobability distributions [55, 66, 67, 68] describe both +position and momentum. Probably the best compromise is the Wigner function [66]. In +quantum mechanics, the Wigner function is a partial Fourier transformation of the density +matrix [55]. The density matrix is a correlation function of two variables, for example +two positions. The Wigner function performs a Fourier transformation with respect to +the position difference as a function of the position average. In this way the Wigner +function captures the momentum spectrum as a function of position. The marginal dis- +tributions (reduced probability distributions) all give the correct probability distributions +of either position or momentum, or of any linear combination of the two, with perfect +accuracy. This property defines the Wigner function uniquely [69] and explains why the +Wigner function describes conjugate variables (position and momentum, time and fre- +quency) with the highest possible precision. Here we employ the time–frequency Wigner +function: +W = 1 +2π +� +∞ +−∞ +K(t + θ/2, t − θ/2) eiωθ dθ +(68) +22 + +of the two–time field correlation function K defined as the vacuum expectation value +K = ⟨ �A1 �A2 + �A2 �A1⟩ +(69) +with the indices indicating the two times and positions {t1, r1} and {t2, r2}. In the con- +formal vacuum, the electromagnetic field fluctuations propagate like in empty Minkowski +space of the conformal times τ and comoving positions r. We may thus use the well– +known expression of the Minkowski vacuum correlations [8]: +K = +1 +(2π)2s2 , +s2 = a1a2 +� +c2(τ2 − τ1)2 − (r2 − r1)2� +(70) +in terms of the Minkowski metric s with reciprocal conformal factor a1a2. Here we are +interested in the spectrum measured with respect to the cosmological times t1 and t2 at a +given point comoving with the universe: +r2 = r1 , +t2 = t + θ/2 , +t1 = t − θ/2 . +(71) +There are several ways to derive Eq. (70) — we may expand the field in terms of the +plane–wave modes (34) and integrate, or we may use the fact that K is the real part of +the analytic function ⟨ �A1 �A2⟩ with imaginary part given by the difference between retarded +and advanced Green function, and derive K in one line from the Kramers–Kronig relation +[5].5 Note that these vacuum correlations exist outside of the causal cone (s < 0) as +has been recently measured in quantum optics [70]. The correlations peak at s = 0, +because electromagnetic waves propagate along light cones, including electromagnetic +noise. Space–time points on the light cone (s = 0) are thus strongly correlated. Wave +noise is organized (Fig. 1). +Cosmology adds one subtle complication to the definition (68) of the Wigner function: +there was a beginning of time (say at t = 0). For a given cosmological time t the Fourier +time θ runs only from −2t to +2t in the real world. Close to the beginning, the expansion +factor a develops a branch point [41] such that a becomes complex in the time before, +which explains [41] why there was nothing real before the beginning of reality. The +conformal time τ, being defined as the integral of the inverse of a, inherits the branch +point and ceases to be real for |θ| > 2t as well. The branch points of τ are harmless in the +integrand (70), but a goes to zero with some fractional power [41]. We might be inclined +to run the integral in the definition (68) of the Wigner function from −2t to +2t, but +the branch points of a1 or a2 at ±2t in the integrand (70) would then create oscillations +with period π/t in the spectrum. The spectral oscillations average out for frequencies ω +much larger than the inverse cosmic age, but like the oscillations in the cosmic cascade +(Sec. 6) they obscure the subtle thermal spectrum of Gibbons–Hawking radiation. It is +therefore wise to analytically continue a around the beginning of time. If we lead the +integral (68) slightly above the branch points ±2t for ω > 0 and slightly below for ω < 0 +the oscillations are gone, because if we approximate a(t) by some root for t ∼ 0 we could +close the integration contour on the upper half plane for ω > 0 and on the lower half plane +for ω < 0 (due to the Fourier factor eiωt) and get zero. +5There is a sign error in Eq. (50) of Ref. [5] and subsequent expressions, because the wrong half plane +was taken in closing the integration contour. Fortunately — thanks to another sign error — the result (80) +carries the correct sign. +23 + +Having cleared the way we are now ready to calculate the Wigner function. It is wise +not to use the explicit expression (70) of the correlation function, but rather our experience +with Rindler modes in expanding flat space (Sec. 4). We expand [Eq. (47)] the radiation +field �A in terms of the vacuum modes (36) defined at some arbitrary time t0 ≥ t. The +value of t0 is not important, as the modes capture the conformal vacuum for all times. +In the vacuum expectation value (69) of K the ⟨�a† and �a⟩ vanish while the ⟨�aν and �a† +ν′⟩ +produce delta functions δ(ν − ν′). For the modes at r = |r2 − r1| = 0 we apply Eqs. (48) +and (49) with the normalization (16) and (17), note that the negative–ν modes are reduced +by the factor e−πν, and obtain the expression +K = +a2 +0H2 +0 +(2π)2c2a1η1a2η2 +� ∞ +0 +2ν +�1 +2 + +1 +e2πν − 1 +� +cos +� +ν ln η2 +η1 +� +dν . +(72) +Let us check that this formula agrees with the standard result (70) for K. Formula (72) +contains the typical Planck term ν(e2πν − 1)−1 plus the contribution ν/2 of the vacuum +energy. We express these terms in a geometrical series: +ν +2 + ν +�1 +2 + +1 +e2πν − 1 +� += ν +∞ +� +m=0 +′ +e−2πmν +(73) +where the prime should indicate that the zeroth term is meant to be divided by 2. As +1 +4 sinh2(z/2) = ++∞ +� +m=−∞ +1 +(z − 2πmi)2 = −∂z ++∞ +� +m=−∞ +1 +z − 2πmi +(74) +we see that the term (73) is the Fourier transform of [4 sinh2(z/2)]−1 for ν > 0 where +we can close the integration contour on the upper half plane. Running through the pole at +zero (instead of surrounding it) produces the factor 1/2 in the vacuum term. For ν < 0 +we close the contour on the lower half plane and get the same expression with ν replaced +by |ν|. From the inverse Fourier transformation then follows +� ∞ +0 +ν +�1 +2 + +1 +e2πν − 1 +� +cos νz dν = +1 +4 sinh2(z/2) +(75) +and from this — and definition (37) for η — we obtain Eq. (70). We have thus reproduced +the known vacuum correlation, but only for times less than t0. In the Wigner function (68) +we must integrate from −∞ to +∞. Therefore we should move t0 to +∞. In the infinite +future the expansion a0 goes to infinity and H0 to a finite value, and so [Eq. (37)] the ratio +η2/η1 goes to (τ∞ − τ2)/(τ∞ − τ1) while the factors (a0H0)/(aη) go to 1/(τ∞ − τ). In +Eq. (72) we may thus replace η by +η = τ∞ − τ = +� ∞ +a +da +a2H +(76) +and remove the a0H0 altogether. We thus obtain for the thermal part of the Wigner func- +tion +Wth = +1 +(2π)2c2 +� ∞ +0 +ν +e2πν − 1 D(ν, ω) dν +(77) +24 + +with the kernel +D = 1 +π e−ωσ +� +∞ +−∞ +1 +a1η1a2η2 +cos +� +ν ln η2 +η1 +� +eiωϑ dϑ +(78) +where we have lifted the integration line in expression (68) by the constant positive imag- +inary time σ, assuming positive frequencies where, as we know, we should lead the inte- +gration contour above the branch points at the origin of physical time: +θ = ϑ + iσ +with +σ > 0 +for +ω > 0 . +(79) +Consider de–Sitter space as a test case of our formula. In this case, a grows exponentially +with constant H0, τ = −(H0a)−1 with τ∞ = 0, and ln(τ2/τ1) = −H0(ϑ + iσ). We get +D = H2 +0δ(ω − H0ν) +(80) +and hence a perfect Planck spectrum with Gibbons–Hawking temperature (30). Formula +(78) thus reproduces Gibbons’ and Hawking’s classic result [53]. Consider now the realis- +tic case of cosmic evolution, which deviates from pure exponential expansion. The kernel +D is of course independent of the integration contour (unless singularities or branch cuts +are crossed) but for any given real time t there will be only one imaginary time σ when +D does approach the defining integral of a delta function in the asymptotic limit of large +frequencies ω (whereas for de–Sitter space all σ do). In the following we work out the +condition when this is the case. +But first we need to consider some realistic cosmology in order to estimate the validity +of the approximation we are going to make. In the spatially flat, isotropic and homoge- +neous universe the square of the Hubble parameter is proportional to the energy density +(by Friedman’s equations [40, 41]). For radiation (photons and neutrinos) the energy +density goes with the inverse fourth power of the expansion factor a, because the energy +falls with the inverse wavelength and hence with a−1 and the density falls with a−3. For +matter (baryonic and dark) the energy density is essentially the rest–mass mass density +multiplied by c2 and a−3. Dark energy Λ — being the cosmological constant — remains +constant. This gives the Λ Cold Dark Matter (ΛCDM) model: +H2 = H2 +0 +�ΩR +a4 + ΩM +a3 + ΩΛ +� +(81) +where H0 denotes the Hubble constant at the present time (a = 1) and the Ωm describe +the weights of the various contributions to the energy density with all Ωm summing up to +unity. The cosmic parameters are retrieved from the fluctuations of the Cosmic Microwave +Background [1] and are listed in Ref. [40]. For a ≫ ΩR/ΩM ≈ 0.3 × 10−3 we can +ignore the radiation contribution and enter a stage of cosmic evolution entirely dominated +by matter and Λ. For describing this matter–vacuum era in the simplest possible way we +change the scale of a and the units of time replacing (ΩM/ΩΛ)1/3a → a and H0 +√ΩΛt → t +such that +H2 = a−3 + 1 . +(82) +From t being the integral of 1/(aH) with respect to a we obtain +a = +� +sinh 3t +2 +�2/3 +and +H = coth 3t +2 . +(83) +25 + +We get the conformal time +τ = +� a +0 +da +a2H = 2√a 2F1 +� +1/6, 1/2, 7/6, −a3� +, +τ∞ = Γ(1/3) Γ(7/6) +Γ(3/2) +(84) +in terms of the hypergeometric function 2F1 and the Gamma function Γ, and from the +relationship (e.6) [71] of the hypergeometric function: +η = τ∞ − τ = a−1 +2F1 +� +1/3, 1/2, 4/3, −a−3� +. +(85) +Consider now the curves in the complex a–plane where the Hubble parameter is real. +For the Λ–matter model (82) we get three curves where H2 is real: straight lines going +through the origin with angles {0, π/3, −π/3}. The Hubble parameter itself is real for +∞ > H2 > 0. So the curves come in from ∞ and end at the points where H = ∞ +or H = 0, which is {0, eiπ/3, e−iπ/3} for the Λ–matter stage (82). The positive real axis +corresponds to the real world with real time t, the π/3–line in the upper half plane corre- +sponds to the line with positive imaginary part π/3 in the complex plane of cosmological +time. In terms of the time t + θ/2 in the Wigner function (68) it draws a line (79) parallel +to the real axis with σ = 2π/3. This is the line we are going to need in our integral +(78). The ΛCDM model (81) has four roots of H2 = 0 we can calculate from Ferrari’s +formula for the roots of quartic equations, two are real and negative, the other two com- +plex conjugate to each other; we take the root a+ on the upper half plane, for which +|a+| = 0.775 and arg a+ = π/3 − 1.09 × 10−4. Calculating η according to Eq. (76) we +find arg η+ = −π/3 + 1.34 × 10−4. We see that a+η+ is real to an accuracy in the order +of 10−5. +This has consequences if we calculate the integral (78) in the saddle–point approxima- +tion for large ω, because we get for the first and second derivatives of the phase ln(η2/η1) +in the cosine: +∂θ ln η2 +η1 +���� +iσ += −Re 1 +aη +���� +iσ +, +∂2 +θ ln η2 +η1 +���� +iσ += 1 +2 Im +� H +aη − +1 +(aη)2 +����� +iσ +(86) +and so the second derivative vanishes: the integral (78) gives a delta function. In fact, +for large ω only ϑ ∼ 0 matters where we may approximate ln(η2/η1) ∼ −i�σ − �Hϑ and +(a1η1a2η2)−1 ∼ �H2 with the definitions +�H = 1 +aη +���� +iσ +, +�σ = 2 arg a|iσ . +(87) +We thus obtain from Eq. (78): +D = e−(ωσ−ν�σ) �H2δ(ω − �Hν) . +(88) +For the matter–vacuum universe in our scaled units we have in particular +�H = 2F1 +� +1/3, 1/2, 4/3, sech2(3t/2) +� +, +�σ = σ = 2π/3 . +(89) +From Eq. (88) follows that, in the full ΛCDM model, the thermal part (77) of the Wigner +function (68) approaches the high–frequency asymptotics: +Wth ∼ +ω +(2π)2c2 e−2πω/Heff +for +ω ≫ �H +(90) +26 + +expressed in terms of the effective Hubble parameter +Heff = +�H +1 + +1 +2π(σ �H − �σ) +. +(91) +The problem is solved. +8 +Summary and outlook +We have derived the Gibbons–Hawking temperature for the standard cosmological model +— the Λ Cold Dark Matter model — from the physical picture of wave noise (Fig. 1). +The resulting temperature, +kBT = ℏHeff +2π +, +(92) +depends on the effective Hubble parameter Heff of Eq. (91) with +1 +Heff += 1 +�H ++ σ +2π − +�σ +2π �H +. +(93) +The effective Hubble parameter sums up the multiple interferences in the cascade of cre- +ation and annihilation at cosmological horizons (Fig. 9). It does it by analytic continuation +of the cosmic dynamics to complex times. The parameter �H is given by +�H = +1 +a(τ∞ − τ) +���� +t+iσ/2 +(94) +in terms of the scale factor a and the conformal time τ evaluated at infinity and at a +certain complex time t + iσ/2 on the upper half plane. The real part of this complex time +is the cosmological time at which Gibbons–Hawking radiation is acting at the moment, +the imaginary part σ/2 needs to be determined from the requirement +Im �H +��� +t+iσ/2 = 0 . +(95) +The parameter �σ is given by twice the argument of a at the complex time: +�σ = 2 arg a|t+iσ/2 . +(96) +Expression (94) generalizes the Gibbons–Hawking formula (30) for de–Sitter space [53]. +In de–Sitter space [58] the scale factor a grows exponentially as a = eH0t while the +conformal time τ falls as −H−1 +0 e−H0t approaching τ∞ = 0 in the infinite future. The +product a(τ∞ − τ) = H−1 +0 +clearly is constant and real for all imaginary times. In a +realistic cosmological model σ needs to be calculated. For example, in the most relevant +case, the matter–vacuum dominated period of cosmic evolution, we get σ = 2π/3 for all +times t (in appropriate units6). +6Here time is measured in the inverse units of √ΩΛH0 where ΩΛH2 +0 describes the contribution of the +cosmological constant Λ to the square of the Hubble parameter at the present time (a = 1). +27 + +The temperature (92) lies in the order of 10−29K (at the present cosmological time) +and so the particles of Gibbons–Hawking radiation are completely negligible, but the +amplitude fluctuations are not — according to Lifshitz theory [5]. They are predicted to +produce the contribution (1) to the renormalized vacuum energy proportional to +∆ = ∂3 +t +1 +Heff +. +(97) +This contribution drives the cosmological term εΛ [5, 6, 7] (but is not proportional to +εΛ itself). Expression (97) with effective Hubble parameter (93) hopefully is the final +formula in a series of attempts [5, 7] to determine the correct vacuum energy of expanding +flat space. For the matter–vacuum dominated period we obtain in our units +∆ = 1 +�H4 +� +4 − 8H �H − +� +4 − 26 +3 H2 +� +�H2 + +� +6 − 20 +3 H2 +� +H �H3 +� +(98) +in terms of expression (94) at the complex time t + iπ/3 where �H is real — with �H +given by Eq. (89) — and the Hubble parameter [Eq. (83)] that is real as well — with +H = tanh(3t/2). Figure 10 compares this result with the previous attempts for the +vacuum energy, Eqs. (2) and (3). +t +0.0 +0.5 +1.0 +1.5 +2.0 +-2.0 +-1.5 +-1.0 +-0.5 +0.0 +0.5 +1.0 +Figure 10: Comparison. Black curve: Heff for the matter–vacuum dominated period of cosmic +evolution in scaled units. We see that Heff gently falls from 1.24 to unity for t → ∞ (de Sitter +space in the far future). Red curves: ∆ (proportional to −εvac) in scaled units. Solid curve: result +of this paper, Eq. (98). Dashed curve: 1 +6∆ obtained from Eq. (3) and used, in perturbation theory, +in the comparison [7] with astronomical data. Dashed–and–dotted curve: result of Eq. (2), ruled +out by the data [7]. The factor 1 +6 was chosen such that the curves have the same asymptotics for +t → ∞. The curves are similar, but with a different prefactor that would correspond to a different +cutoff [5]. The cutoff is a parameter of the theory, because it is not precisely known (only in its +order of magnitude). It remains to be seen how the solid curve compares with astronomical data. +Formula (93) depends on the history of cosmic expansion — being determined by +analytic continuation of the entire expansion. As the vacuum energy acts back on the +28 + +cosmic evolution due to its gravity, it has the tendency of developing oscillations in the +Hubble parameter if ∆ depends on just the local values of a. It is hoped that the memory +effect in the vacuum energy derived here will eliminate such artefacts. The multiple +interference of cosmic creation and annihilation (Fig. 9) summed up in Heff may also +explain why first–order perturbation theory is remarkably good at fitting the cosmological +data [7] while the full theory with the previous expressions would fail. +We obtained our result (93) assuming that the electromagnetic vacuum noise consists +of modes oscillating with conformal time (22) whereas an observer at rest with the uni- +verse counts time as cosmological time. Furthermore we assumed, inspired by optical +analogues of gravity [17, 18, 19, 20, 21, 22, 23, 24], that the “medium” of space behaves +like a medium, comoving with the universe like the observer at rest. We therefore re- +quired that the spectrum of vacuum fluctuations perceived by space is the spectrum with +respect to cosmological time. As the two times differ the spectrum becomes nontrivial +and, as it turned out, thermal. We used the physical picture of wave noise (Fig. 1) and the +asymptology [34] of Wigner functions [68] to work out the temperature. +We can draw another conclusion from the picture of wave noise (Fig. 1). Our analy- +sis has been entirely local: we picked an arbitrary point in the spatially flat universe and +considered the vacuum fluctuations at this point evolving in time. Nevertheless, the quan- +tum vacuum is arriving from long distances away, in particular the noise of the Hawking +partners. For sustaining the correlations responsible for the Gibbons–Hawking effect and +hence the vacuum energy εvac, perfect vacuum modes need to be formed according to +Eq. (36). These are superpositions of perfect, non–dispersive plane waves (34) sustaining +correlations across vast distances in space. Such long–range correlations cannot exist in +massive fields, even for energies at the Planck scale where mass is almost irrelevant. Let +us estimate the requirement for maintaining correlations. A field with particles of mass m +obeys the dispersion relation +ℏ2ω2 = ℏ2c2k2 + m2c4 . +(99) +Assuming λ = 2πc/ω = ℓp with Planck length ℓp we get for the deviation of the phase +from the cosmological horizon to the point of observation: +δϕ = rHδk ∼ −πrH +ℓP +λ2 +C +, +λC = 2πℏ +mc +(100) +where λC denotes the Compton wavelength. We obtain that for rH ∼ 1010ly the mass m +must not exceed 10−2eV for not ruining the noise correlations. There is only one field +with particles of such low mass, the electromagnetic field. Gluons are massless like the +electromagnetic photons, but they are short–range due to interactions with themselves. +Neutrinos have masses ≲ 0.8eV [72] and are therefore probably too heavy as well. More- +over, neutrinos are fermions, and it seems questionable whether fermions can create vac- +uum forces. The standard vacuum fluctuations acting in the Casimir or van der Waals +forces [42] are not fluctuations of particles and antiparticles, but field fluctuations. What +are the physically relevant field fluctuations of fermions in the vacuum state? The need +for massless bosonic fields to sustain wave correlation across cosmological distances may +thus explain why only the electromagnetic field seems to contribute to the cosmological +vacuum energy, as the comparison with astronomical data suggests [7]. +29 + +Finally, we found that for cosmological eras dominated by only one type of matter +or energy the effective Gibbons–Hawking temperature is strictly zero or constant. These +eras are the radiation–dominated era at the youth of the universe (a ≪ 10−3), the matter– +dominated era in its middle age, and the vacuum–dominated era for the eternity to follow +(a ≫ 1). We found this by summing up the cosmic interferences, but we also see it in one +glance from our analytic theory. Pure eras are described by power laws with H = H0 a−γ, +γ > 1 or exponential expansion with γ = 0. For a power law the conformal time τ +grows with aγ−1 and hence is analytic. We may close the integration contour of the +Wigner function (68) of the vacuum correlations (70) at infinity, get the vacuum term by +integrating through the double pole at τ2 = τ1 but zero thermal contribution. Formula (94) +also indicates that power laws in H generate zero Gibbons–Hawking temperature, because +τ tends to infinity for a → ∞, but the formula requires a finite τ∞. For exponential +expansion, the Gibbons–Hawking temperature (92) is constant, and so its contribution +(97) to the dynamical vacuum energy density (1) vanishes as well. As the cosmological +term is driven by the dynamical vacuum energy it remains constant. The vacuum energy +acts only in transitions. +This is a typical feature of the Casimir effect. In dielectrics [8, 9], the Casimir energy +thrives on differences in the dielectric properties of a medium causing forces at interfaces +and boundaries. In Casimir cosmology [40], the vacuum energy arises in the transitions +between cosmic eras, changing the cosmological constant there [5, 6, 7]. The current +era is such a transition period — the transition from matter to vacuum domination — +and so the cosmological constant varies, which affects the Hubble constant (the Hubble +parameter at the present time). The predicted variation of the Hubble constant [7] appears +to agree with the astronomical data [36], giving some empirical support to the theory +presented here. Wave noise (Fig. 1) may thus not only explain the mundane, the stickiness +of the microworld, but perhaps also the arcane, the force of the macroworld that drives +the universe apart. +Acknowledgements +Two and a half decades ago Michael Berry’s work on the optical Aharonov Bohm effect +inspired me to look for connections between quantum optics and general relativity, and +he has been an inspiration ever since. I am most grateful to him and wish him a happy +anniversary. I would also like to thank Dror Berechya, David Bermudez, Nikolay Ebel, +Jonathan Kogman, Amaury Micheli, and Scott Robertson for discussions and comments +on this paper. The paper has been supported by the Israel Science Foundation and the +Murray B. Koffler Professorial Chair. +References +[1] Planck Collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. & +Astrophys. 641, A6 (2020). +[2] Proceedings of the Les Houches Summer School 2021 on Dark Matter (to be pub- +lished). +30 + +[3] C. Burrage, A brief introduction to extended gravity and connections to dark energy: +Illustrated with scalar field examples, in Ref. [2]. +[4] L. Amendola and S. Tsujikawa, Dark Energy: Theory and Observations (Cambridge +University Press, Cambridge, 2010). +[5] U. Leonhardt, Lifshitz theory of the cosmological constant, Ann. Phys. (New York) +411, 167973 (2019). +[6] U. Leonhardt, The case for a Casimir cosmology, Phil. Trans. R. Soc. A 378, +20190229 (2020). +[7] D. Berechya and U. Leonhardt, Lifshitz cosmology: quantum vacuum and Hubble +tension, Month. Not. Roy. Astron. Soc. 507, 3473 (2021). +[8] S. Y. Buhmann, Dispersion Forces (Springer, Heidelberg, 2013). +[9] W. M. R. Simpson and U. Leonhardt (eds.) Forces of the quantum vacuum (World +Scientific, Singapore, 2015). +[10] Ya. B. Zel’dovich, The cosmological constant and the theory of elementary particles, +Usp. Fiz. Nauk 95, 209 (1968) [English translation: Sov. Phys. Uspekhi 11, 381 +(1968)]. +[11] A. Einstein, Kosmologische Betrachtungen zur allgemeinen Relativit¨atstheorie, +Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl. 142 (1917) [English Translation +in The Principle of Relativity (Dover, Mineola, 2013)]. +[12] D. Huterer and M. S. Turner, Prospects for probing the dark energy via supernova +distance measurements, Phys. Rev. D 60, 081301 (1999). +[13] S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61, 1 (1989). +[14] S. K. Lamoreaux, Demonstration of the Casimir Force in the 0.6 to 6µm Range, +Phys. Rev. Lett. 78, 5 (1997). +[15] J. N. Munday, F. Capasso, and V. A. Parsegian, Measured long–range repulsive +Casimir–Lifshitz forces, Nature 457, 170 (2009). +[16] R. Zhao, L. Li, S. Yang, W. Bao, Y. Xia, P. Ashby, Y. Wang, and X. Zhang, Stable +Casimir equilibria and quantum trapping, Science 364, 984 (2019). +[17] W. Gordon, Zur Lichtfortpflanzung nach der Relativit¨atstheorie, Ann. Phys. +(Leipzig) 72, 421 (1923). +[18] P. M. Quan, Sur les ´equations de l’´electromagn´etisme dans la mati`ere, C. R. Acad. +Sci. (Paris) 242, 465 (1956). +[19] P. M. Quan, Inductions ´electromagn´etiques en relativit´e g´en´erale et principe de Fer- +mat, Arch. Ration. Mech. Anal. 1, 54 (1957). +31 + +[20] J. Plebanski, Electromagnetic Waves in Gravitational Fields, Phys. Rev. 118, 1396 +(1960). +[21] W. Schleich and M. O. Scully, General relativity and modern optics, in New trends +in atomic physics: Les Houches, session XXXVIII, 1982 by G. Grynberg and R. Stora +(eds.) (Elsevier, Amsterdam, 1984). +[22] U. Leonhardt and P. Piwnicki, Optics of nonuniformly moving media, Phys. Rev. A +60, 4301 (1999). +[23] U. Leonhardt and T. G. Philbin, General relativity in electrical engineering, New J. +Phys. 8, 247 (2006). +[24] U. Leonhardt and T. G. Philbin, Geometry and Light: the Science of Invisibility, +(Dover, Mineola, 2010). +[25] U. Leonhardt, Optical Conformal Mapping, Science 312, 1777 (2006). +[26] J. B. Pendry, D. Schurig, and D. R. Smith, Controlling Electromagnetic Fields, Sci- +ence 312, 1780 (2006). +[27] T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. K¨onig, and U. Leonhardt, +Science 319, 1367 (2008). +[28] F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Ru- +bino, V. G. Sala, and D. Faccio, Hawking Radiation from Ultrashort Laser Pulse +Filaments, Phys. Rev. Lett. 105, 203901 (2010). +[29] E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C.E. +Kuklewicz, U. Leonhardt, F. K¨onig, and D. Faccio, Negative-Frequency Resonant +Radiation, Phys. Rev. Lett. 108, 253901 (2012). +[30] C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, Trapping light by mimicking +gravitational lensing, Nat. Photonics 7, 902 (2013). +[31] R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, Optical simula- +tions of gravitational effects in the Newton–Schr¨odinger system, Nat. Phys. 11, 872 +(2015). +[32] R. Bekenstein, Y. Kabessa, Y. Sharabi, O. Tal, N. Engheta, G. Eisenstein, A. J. +Agranat, and M. Segev, Control of light by curved space in nanophotonic structures, +Nat. Photonics 11, 664 (2017). +[33] J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Observation +of Stimulated Hawking Radiation in an Optical Analogue, Phys. Rev. Lett. 122, +010404 (2019). +[34] M. V. Berry, https://michaelberryphysics.wordpress.com/publications/ +32 + +[35] E. Di Valentino, A combined analysis of the H0 late time direct measurements and +the impact on the Dark Energy sector. Month. Not. Roy. Astron. Soc. 502, 2065 +(2021). +[36] A. Riess et al., A Comprehensive Measurement of the Local Value of the Hubble +Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the +SH0ES Team, Astrophys. J. Lett. 934, L7 (2022). +[37] E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, +A. G. Riess, and J. Silk, In the Realm of the Hubble tension — a Review of Solutions, +Class. Quant. Grav. 38, 153001 (2021). +[38] I. Y. Efrat and U. Leonhardt, Van der Waals anomaly: Analog of dark energy with +ultracold atoms, Phys. Rev. B 104, 235432 (2021). +[39] R. M. Wald, Trace anomaly of a conformally invariant quantum field in curved +spacetime, Phys. Rev. D 17, 1477 (1978). +[40] U. Leonhardt, Casimir cosmology, Int. J. Mod. Phys. 37, 2241006 (2022). +[41] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth- +Heinemann, Amsterdam, 2003). +[42] A. W. Rodriguez, F. Capasso, and S. G. Johnson, The Casimir effect in microstruc- +tured geometries, Nat. Photon. 5, 211 (2011). +[43] J. T. Mendonc¸a, Theory of photon acceleration (CRC Press, Bristol, 2000). +[44] J. T. Mendonc¸a and A. Guerreiro, Time refraction and the quantum properties of +vacuum, Phys. Rev. A 72, 063805 (2005). +[45] J. Schwinger, Casimir energy for dielectrics, Proc. Natl. Acad. Sci. USA 89, 4091 +(1992). +[46] V. V. Dodonov, Current status of the dynamical Casimir effect, Phys. Scr. 82, 038105 +(2010). +[47] C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, +F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a supercon- +ducting circuit, Nature 479, 376 (2011). +[48] P. L¨ahteenm¨aki, G. S. Paraoanu, J. Hassel, and P. J. Hakonen, Dynamical casimir +effect in a Josephson metamaterial, Proc. Natl. Acad. Sci. USA 110, 4234 (2013). +[49] S. Vezzoli, A. Mussot, N. Westerberg, A. Kudlinski, H. Dinparasti Saleh, A. Prain, +F. Biancalana, E. Lantz, and D. Faccio, Optical analogue of the dynamical Casimir +effect in a dispersion-oscillating fibre, Commun. Phys. 2, 84 (2019). +[50] S. A. Fulling, Nonuniqueness of Canonical Field Quantization in Riemannian +Space-Time, Phys. Rev. D 7, 2850 (1973). +33 + +[51] P. C. W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A +8, 609 (1975). +[52] W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976). +[53] G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, +and particle creation, Phys. Rev. D 15, 2738 (1977). +[54] U. Leonhardt, Cosmological horizons radiate, Europhys. Lett. 135, 10002 (2021). +[55] U. Leonhardt, Essential Quantum Optics: From Quantum Measurements to Black +Holes, (Cambridge University Press, Cambridge, 2010). +[56] W. Rindler, Kruskal Space and the Uniformly Accelerated Frame, Am. J. Phys. 34, +1174 (1966). +[57] U. Leonhardt, I. Griniasty, S. Wildeman, E. Fort, and M. Fink, Classical analog of +the Unruh effect, Phys. Rev. A 98, 022118 (2018). +[58] W. de Sitter, On Einstein’s Theory of Gravitation and its Astronomical Conse- +quences. Third Paper, Month. Not. Roy. Astron. Soc. 78, 3 (1917). +[59] A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large–Scale Structure +(Cambridge University Press, Cambridge, 2000). +[60] J. R. Gott III, M. Juri´c, D. Schlegel, F. Hoyle, M. Vogeley, M. Tegmark, N. Bahcall, +and J. Brinkmann, A Map of the Universe, Astrophys. J. 624, 463 (2005). +[61] P. C. W. Davies and T. M. Davies, How Far Can the Generalized Second Law Be +Generalized? Found. Phys. 32, 1877 (2002). +[62] R.-G. Cai and S. P. Kim, First law of thermodynamics and Friedmann equations of +Friedmann–Robertson–Walker universe, J. High. E. Phys. 2, 50 (2005). +[63] T. M. Davis and C. H. Lineweaver, Expanding Confusion: Common Misconceptions +of Cosmological Horizons and the Superluminal Expansion of the Universe, Publ. +Astron. Soc. Australia 21, 97 (2004). +[64] E. Harrison, Cosmology: the science of the universe (Cambridge University Press, +Cambridge, 2000). +[65] N. D. Birrell and P. C. W. Davies. Quantum fields in curved space (Cambridge Uni- +versity Press, Cambridge, 1984). +[66] E. P. Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Phys. +Rev. 40, 749 (1932). +[67] K. E. Cahill and R. J. Glauber, Density Operators and Quasiprobability Distribu- +tions, Phys. Rev. 177, 1882 (1969). +[68] W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Weinheim, 2001). +34 + +[69] U. Leonhardt, Measuring the Quantum State of Light, (Cambridge University Press, +Cambridge, 1997). +[70] F. F. Settembrini, F. Lindel, A. M. Herter, S. Y. Buhmann. and J. Faist, Detection of +quantum-vacuum field correlations outside the light cone, Nat. Commun. 13, 3383 +(2022). +[71] L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1977). +[72] KATRIN Collaboration, Direct neutrino-mass measurement with sub-electronvolt +sensitivity, Nat. Phys. 18, 160 (2022). +35 + diff --git a/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/load_file.txt b/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f4a71e2e34a72bd362e1f06616934d9ba8e211a2 --- /dev/null +++ b/EtE2T4oBgHgl3EQfSwcw/content/tmp_files/load_file.txt @@ -0,0 +1,1147 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf,len=1146 +page_content='Wave correlations and quantum noise in cosmology Ulf Leonhardt Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel January 11, 2023 Abstract Wave noise is correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' While it may look random in space, correlations ap- pear in space–time, because the noise is carried by wave propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These corre- lations of wave noise give rise to fluctuation forces such as the Casimir force, they are responsible for the particle creation in the dynamical Casimir effect and in the expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This paper considers the noise correlations for light waves in non-exponentially expanding flat space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The paper determines the high-frequency asymptotics of the correlation spectrum in the conformal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These noise cor- relations give rise to a nontrivial vacuum energy that may appear as the cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='03795v1 [gr-qc] 10 Jan 2023 1 Introduction Explorers have mapped every corner of the Earth, but the time of exploration has only just began: 95% of the current content of the universe is completely unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The uncharted 95% are called the “dark sector” with 25% belonging to dark matter and 70% to dark energy [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' While there are many ideas from particle physics on the nature of dark matter, and several experimental programmes for detecting dark–matter particles [2] dark energy has been an enigma [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, it might actually be the other way round: dark energy could be the easier problem to solve, but not as a problem of high–energy physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rather, it might belong to an area of low–energy physics, extrapolated to cosmological scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this paper I will follow up on the hypothesis [5, 6, 7] that dark energy, this arcane force that drives the universe apart, is a form of much more mundane forces, the van der Waals and Casimir forces, that cause ordinary things to stick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These are forces of the quantum vacuum [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is not a new idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In 1968 Zel’dovich [10] suggested that vacuum fluctuations create Einstein’s cosmological constant Λ [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Einstein’s Λ is what was later called dark energy [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, Zel’dovich’s and similar suggestions [13] disagree with the measured value of Λ by some 120 orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The idea that Λ comes from the quantum vacuum is not new — and seem to have failed spectacularly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' What is new is a better theory of the quantum vacuum, inspired by precision measurements and ma- nipulations of Casimir forces [14, 15, 16], by the analogy between dielectric media and space–time geometries [17, 18, 19, 20, 21, 22, 23, 24] tried and tested in transformation optics [23, 24, 25, 26] and in optical analogues of black holes [27, 28, 29, 30, 31, 32, 33], and inspired by the person to whom this volume is dedicated: Michael Berry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Not only did he encourage me to pursue unconventional ideas, these ideas resonate with his work on the infinite intricacies of light [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The theory [5, 6, 7] is still mostly a hypothesis, but it appears to agree with astronom- ical data [7] and seems to resolve [7] a major inconsistency in the conventional interpreta- tion of that data [35]: the 5σ tension between the directly measured Hubble constant [36] and the Hubble constant inferred from the Cosmic Microwave Background [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There are some 102 theories to explain the Hubble tension [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' All of them require modifications of known physics — changes to the standard model of particle physics, general relativ- ity or the cosmological principle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' all make some experimentally untested modifications, with one exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The theory advocated here is the only one in the field rooted on experiments and relying on “new things in old things” — to quote a phrase of Michael Berry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These results are encouraging, but much more work needs to be done to prove or disprove the theory on astronomical data [7], to test its physical mechanism in laboratory analogues [38] and also to improve the theory itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Let me explain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The renormalized vacuum expectation value εvac of the electromagnetic energy density can be expressed such that [5] 4πG 3c2 εvac = −αΛ∆ (1) in terms of the gravitational constant G, the speed of light in vacuum c and the dimen- sionless coupling parameter αΛ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The parameter αΛ depends on the inverse squared of the cutoff length ℓΛ with [5] αΛ = (9π)−1 if ℓΛ is the Planck length ℓp = � ℏG/c3 (ℏ 2 being the reduced Planck constant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The energy density εvac does two things: it gravitates and it generates a trace anomaly [5, 38, 39] with energy density εΛ that appears as the cosmological term Λ, but is no longer constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The total vacuum energy εΛ + εvac grows with −4εvac times the Hubble parameter [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cosmological term εΛ thus accumulates εvac during the cosmic evolution, it grows with negative εvac and falls with positive εvac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cosmological constant still appears in the theory, yet not as a fundamental constant of nature but only as an integration constant [7] that depends on the initial conditions and presumably was zero at the beginning of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The quantity ∆ in the vacuum energy density (1) carries the physical units of a fre- quency squared and depends on the nature of the quantum vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the first version [5] of the theory ∆ was found to be ∆ = ∂3 t 1 H + H∂2 t 1 H (2) where H denotes the Hubble parameter [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' One sees from a scale analysis that εvac carries the correct order of magnitude of the cosmological constant1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the second incar- nation [7] of the theory2 the expression ∆ = ∂3 t 1 H (3) was published and used to compare theory with data [7] assuming εvac as a perturbation of the cosmic dynamics [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' While Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (2) and (3) agree on the leading term, they differ in the subdominant term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The data ruled out Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (2) whereas Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (3) agrees with the astronomical data with the precision of that data for exactly the Planck–scale value αΛ = (9π)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, this is only true within first–order perturbation theory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' the full solution of the cosmic dynamics contains oscillatory modulations, suggesting that some vital ingredient was missing that dampens these oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this paper I hope to have identified the missing component and to have finally deduced the correct vacuum energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The paper also clarifies the role the quantum vacuum plays in cosmology and it offers an explanation why quantum electromagnetism, and quantum electromagnetism alone, is responsible for what appears as dark energy in the current era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The heart of the problem of explaining dark energy from vacuum fluctuations is the physics of wave noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wave noise is organized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In space, it may look completely random, but in space– time patterns of correlations are clearly visible (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There we see the characteristic diagonal features of wave propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Waves are traveling to the left or the right with the wave velocity c/n, and the noise they carry travels with them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' If n varies the noise pattern varies as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The most dramatic of such modifications are reflections, for example at obstacles where n is discontinuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Reflected wave noise gives rise to fluctuation forces [8, 9] such as the Casimir forces [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' If n varies in time, waves may be reflected in time as well [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A reflection in space is the change of sign in the wave number, in time it is a sign change in frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the dynamical Casimir effect [45, 46, 47, 48, 49] these negative–frequency components correspond to newly–created particles, simply because if 1The argument [5] goes as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' According to the Friedman equation [40, 41] expression (1) gives 1 2H2 for the realistic case of zero spatial curvature [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As H varies on the scale of H the energy density εvac goes like H2 and thus plays a role in the cosmic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2Actually, this was the result of my first, unpublished version of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 3 Figure 1: Wave noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space–time diagram of waves with Gaussian noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Although the wave field looks random in space {x} features appear in space–time {ct, x} following the causal cones of wave propagation (with speed c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For this picture 128 normalized left–moving and 128 right– moving plane waves [Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (5) and (6)] with periodic boundary conditions and of random Gaussian complex coefficients were summed up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Increasing the number of waves produces finer and finer structures, but ultimately the noise field diverges, illustrating the divergence of the bare vacuum noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' part of a wave of positive frequency ω is converted to −ω the energy ℏω of the remaining positive–frequency component must grow, particles are created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Here we focus less on the particle aspects, but rather on the amplitude correlations of wave noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We begin with a brief review on a familiar example, the noise seen by accelerated observers [50, 51, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Then we show how this is related to the noise perceived by an observer at rest in an exponentially expanding universe [53] before turning to the discussion of vacuum modes in a universe of arbitrary expansion [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We confirm the extension [54] of Gibbons’ and Hawking’s formula for the radiation temperature [53] and find a new feature not present in exponential expansion: the Hawking partners appear as red–shifted thermal radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The multiple interference of all Hawking processes in the expanding universe gives the effective vacuum energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' to calculate it we use the Wigner function of wave noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2 Uniform acceleration Wave noise is organized, because waves can be organized in terms of modes, and the noise appears solely in the amplitudes and phases of the mode coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consider a simple 1+1 dimensional example: a scalar wave field ˆA in empty Minkowski space given 4 by the mode decomposition �A = � +∞ −∞ � �akAk + �a† kA∗ k � dk (4) where the Ak are the mode functions Ak(x, t) describing how the modes propagate in space x and time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The �ak are the mode coefficients, and only they are subject to statistical or quantum fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The mode functions should be normalized such that each mode accounts for the field of exactly one particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is conveniently done with the help of the scalar product [55] (A1, A2) = i ℏ � +∞ −∞ (A∗ 1 ∂tA2 − A2 ∂tA∗ 1) dx (5) requiring (A1, A2) = δ(k1 − k2) , (A∗ 1, A2) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (6) For example, if the modes are plane waves Ak = A exp(ikx − iωt) with ω = c|k| we must require A2 = ℏ/(4πω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From the canonical commutation relations between field and momentum density then follow [55] — for Bosonic fields like the electromagnetic field — the standard Bose commutation relations: [�ak1,�a† k2] = δ(k1 − k2) , [�ak1,�ak2] = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (7) The Minkowski vacuum |0⟩ is the quantum state annihilated by all the plane–wave oper- ators: �ak|0⟩ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (8) The Minkowski vacuum is the vacuum with respect to an observer at rest in Minkowski space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It also appears as the vacuum to observers in uniform motion, because they per- ceive the modes Ak as plane waves as well, Doppler–shifted of course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' But this is no longer true for accelerated observers [50, 51, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Uniform acceleration is described by the transformation to Rindler coordinates [56] as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Suppose we write the Cartesian space–time coordinates in terms of hyperbolic polar coordinates: x = ξ cosh η , ct = ξ sinh η .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (9) The Rindler coordinates {ξ, η} cover the two wedges with x ≥ |η| for ξ ≥ 0 on the right and −x ≥ |η| for ξ ≤ 0 on the left of the space–time diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In analogy to the regular polar coordinates {r, φ} with spatial metric dr2 + r2dφ2 we get for the hyperbolic space–time metric ds2 = c2dt2 − dx2 = ξ2dη2 − dξ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (10) A space–time metric measures the proper time τ with increment dτ = ds/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In particular, as ds = ξdη for dξ = 0, the proper time along a trajectory with fixed ξ is (ξ/c)η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We can draw another conclusion from the analogy of the Rindler coordinates with polar coordi- nates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In space a rotation corresponds to a shift in the angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In Minkowski space–time, a hyperbolic rotation corresponds to a Lorentz transformation to a frame moving with ve- locity u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' An infinitesimal Lorentz boost shifts the hyperbolic angle by du/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A sequence 5 R L +ξ ξ x ct η η Figure 2: Accelerated observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space–time diagram of accelerated observers (black curves) in Minkowski space with Cartesian coordinates x and t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The observers follow the Rindler trajectories of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (9) with fixed ξ and variable parameter η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The acceleration is given by c2/ξ while (ξ/c)η gives the proper time of each observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For negative ξ the parameter η needs to run backwards (reversed arrow) as proper time always runs forwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The observer on the right (R) is separated from the observer on the left (L) by horizons (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Neither left– nor right–moving light from R can reach the shaded region in L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' of infinitesimal boosts thus draws an entire Rindler coordinate line along varying η for ξ = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Now, uniform acceleration is just such a sequence of infinitesimal Lorentz transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We thus conclude that the Rindler line is the world line of a uniformly accelerated observer with acceleration du/dτ = c2/ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consider such a uniformly accelerated observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Suppose the observer is equipped with a spectrometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A spectrometer consists of a spectral element to decompose the field �A into frequencies, and a detector to measure the spectral components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It is not important what the detector is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It may be a particle detector [52] or an amplitude detector [57], the physically important feature of the spectrometer is the ability to perform a frequency analysis, and there the important aspect is the fact that the spectrometer responds to its proper time τ and not to the coordinate time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As τ = (ξ/c)η we may describe the effect of the spectrometer as a Fourier transformation with respect to η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Note, however, that for ξ < 0 (on the left side L of the Rindler diagram of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2) η needs to run backwards, since proper time always runs forwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Imagine now a pair of accelerated observers — one with positive ξ on R and one with the exact opposite −ξ on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Figure 2 reveals that the two observers are separated by horizons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The entire world line of observer L lies in the shadow of left– or right–moving waves that touch observer R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' But it turns out the two observers can and must communicate by sharing the same noise field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' To work this out, consider the spectral components they 6 Figure 3: Plane wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The accelerated observer (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2) samples noise made of plane waves with random amplitudes and phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Each plane wave is sampled along the Rindler trajectory of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (9) with proper time (ξ/c)η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The panel shows the real and imaginary part of the wave sampled along the path with parameter η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fourier analysis reveals that the positive–frequency components for η contain negative–frequency components for t enhancing the quantum noise perceived by one observer at +ξ by correlations with its partner at −ξ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' measure: �AR = 1 2π � +∞ −∞ �A ��� R eiνη dη , �AL = 1 2π � +∞ −∞ �A ��� L e−iνη dη (11) in terms of the dimensionless Fourier components ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Here the R and L indicate the space– time trajectories of the two observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' They sample the plane–wave Minkowski modes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 3) as oscillations with phases ϕR = k(x ∓ ct)|R = kξ e∓η , ϕL = k(x ∓ ct)|L = −kξ e∓η .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (12) Now, components with positive Rindler frequencies ν may also sample negative Minkow- ski frequencies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' the complex–conjugated modes A∗ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In fact, moving the contour of the Fourier integral by +iπ on R and by −iπ on L changes the sign in the phases (12) while preserving the convergence of the Fourier integrals (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We thus see that the Fourier transform of the conjugate A∗ k is exactly e−πν times the Fourier transform of Ak, on both sides of the Rindler wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Accelerated observers sample negative Minkowski frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' To see how this af- fects the wave noise perceived by the accelerate observers, we introduce a set of modes 7 Figure 4: Rindler modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The figure shows examples of modes that are monochromatic for the two accelerated observers (white hyperbolas, see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For a monochromatic mode the phase increases linearly with time, but for the observers this is proper time, not coordinate time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Each accelerated observer comes in with asymptotically the speed of light and leaves asymptot- ically with the speed of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For such velocities proper time ticks exponentially slowly, and so the phase grows only logarithmically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Near the horizon (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2) the phase diverges logarithmically [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (13)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' An exponentially small part of the wave crosses to the other side if this wave is made of a superposition of positive–norm plane waves, describing the quantum vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' that are monochromatic with respect to those observers (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Any mode in Minkowski space must be a superposition of left– or right–moving waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The left–moving waves are functions of x− = x + ct while the right–moving modes depend on x+ = x − ct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From x± = ξe∓η follows that the phases of monochromatic Rindler modes must be logarithmic in x±, which means that the Rindler modes are purely imaginary powers of x±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There we have two possibilities: x± or −x± to an imaginary power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the first case the wave is predominately localized on the right side of the space–time diagram (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2), in the sec- ond case on the left side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' On R we should give the Rindler wave a positive η–frequency ν, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' the power ±ν of x±, while on L it should oscillate with −ν as η runs backwards for forward–running proper time, which also corresponds to the power ±ν but this time of −x±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We thus define Aν = A � (x±)±iν : ν > 0 (−x±)±iν : ν < 0 with x± = x ∓ ct (13) and represent the field as �A = � ± � +∞ −∞ � �aνAν + �a† νA∗ ν � dν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (14) 8 ct XIt only remains to determine the normalization factor A from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We substitute the modes (13) into the scalar product (5) with the understanding that (A1, A2) differs from zero only when ν1 ∼ ν2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We define δ = ±(ν2 − ν1) and obtain for ν > 0: (A1, A2) = 2cν ℏ A2 � +∞ −∞ (x ∓ ct)iδ−1 dx = 2cν ℏ A2 � 1 − e−2πν� � ∞ 0 ξiδ dξ ξ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (15) Writing ξ as an exponential gives 2π times the standard Fourier representation of the delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Defining the parameter ζ by tanh ζ = e−πν (16) with cosh ζ = (1 − e−2πν)−1/2 we thus get A = B cosh ζ , B2 = ℏ 4πcν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (17) This concludes the normalization of the Rindler modes and hence the Rindler representa- tion of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Only one important, subtle point remains to be discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The Rindler modes (13) are understood to be analytic on the upper half complex plane for x+ and on the lower half plane for x− such that the left side is suppressed for ν > 0 and the right side for ν < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In either case, the Aν are then analytic on the lower complex plane for the time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From this follows that we can always close the contour of a Fourier transformation with respect to Minkowski time t for negative frequencies ω and get zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In other words, the Rindler modes (13) have only positive Minkowski frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Therefore, they are superpositions of positive–norm Minkowski waves, and so their associated annihilation operators �aν are also just superpositions of the Minkowski �ak, which implies that both share the same vacuum state |0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Having established the vacuum in the Rindler representation, it is elementary to work out the spectral components seen by the two accelerated observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtain from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (11) and (14) for the modes (13) with norm (17) and x± = ξe∓η the expressions �AR = B � �aν cosh ζ + �a† −ν sinh ζ � , �AL = B � �a−ν cosh ζ + �a† ν sinh ζ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (18) We see here again that the observers sample negative–frequency components �a† with rel- ative weight tanh ζ = e−πν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Representing the mode operators in terms of their real and imaginary parts (Hermitian and anti–Hermitian parts) we see that the sampled field amplitudes are connected — the real parts are correlated and the imaginary parts anti– correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This means that the wave noise perceived by the observer on R is correlated with the noise perceived by observer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Observer R is influenced by some extra random- ness that comes from this connection to observer L and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' That excess noise appears in the intensity as an additional contribution to the standard vacuum noise: ⟨ �A† R �AR⟩ = ⟨ �A† L �AL⟩ = B2 �1 2 + 1 e2πν − 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (19) As the dimensionless η is related to the proper time by the factor c/ξ, the frequencies mea- sured in the spectrometers of the accelerated observers are related to the dimensionless ν 9 by the same factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may read the (e2πν − 1)−1 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (19) as the Planck distribution (eℏω/kBT − 1)−1 with Unruh temperature [52] kBT = ℏc 2πξ (20) where kB denotes Boltzmann’s constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Each one of the two observers perceives the vacuum as thermal radiation with temperature (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Each one receives this extra noise, because the noise is correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These correlations do appear when the field amplitudes are Fourier–transformed: they are spectral correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In terms of particles, they appear as entangled Einstein–Podolski–Rosen pairs [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' When the spectrometer of observer R detects a particle at frequency ω so does the spectrometer of observer L (provided they are perfectly efficient).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' But here we are primarily concerned with amplitude noise and its cosmological implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 3 Exponential expansion Turn now from accelerated observers in static Minkowski space to an observer at rest in the expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consider first the conceptually simplest case: pure exponential expansion (de Sitter space [58]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is the phase of the cosmic evolution we are entering at the present time and, presumably, it was the phase of inflation [59] just after the Big Bang (although with a much higher expansion rate then in the current era).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Assume in agreement with astronomical observations [60] that the universe is homogeneous and isotropic, and spatially flat [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this case, the space–time geometry is given by the flat–space Friedmann–Lemaitre–Robertson–Walker metric [40]: ds2 = c2dt2 − a2dr2 (21) with time–dependent scale factor a(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The scale factor describes how spatial distances expand, as the physical distance between two points at the same time t is given by a times the coordinate difference r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The spatial coordinates r are called comoving coordinates, because they do not move relative to the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The coordinate time t is called cosmo- logical time and, physically, it is the proper time of an observer at rest with the universe (dr = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may introduce a new time τ called conformal time, defined as τ = � dt a (22) such that the metric becomes conformally flat: ds2 = a2 � c2dτ 2 − dr2� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (23) For light rays (ds = 0) the conformal factor a2 is irrelevant, and so light rays travel in conformal time and comoving space like in empty Minkowski space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As Maxwell’s equations are conformally invariant [24] this remains true for full electromagnetic fields and their quantum fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We assume that the quantum vacuum is carried by plane waves in conformal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The notation is the exact opposite as in the case of uniform 10 acceleration: there t is the time the vacuum propagates with and τ denotes the proper time of the accelerated observer, whereas in the expanding universe the vacuum waves propagate with τ while t is the proper time of the observer at rest with the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Note that the gravitational field of the universe (the space–time geometry) does distin- guish a global frame — only in this frame the metric is homogeneous and isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We can of course move this frame to any point (as the universe is homogeneous) and rotate it (as it is isotropic) but the metric is different for an observer in uniform motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Note also that although the universe is spatially flat, it is curved in space–time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' One obtains for the curvature scalar [41] R = − 6 c2 � ∂tH + 2H2� (24) in terms of the Hubble parameter H = ∂ta a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (25) In the case of exponential expansion the Hubble parameter is a constant H0 such that a = a0 eH0t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (26) In this case, the space–time curvature is negative and constant3 as we also see from R = −12H2 0/c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Figure 5: Exponential expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' An observer at rest samples a plane wave in the exponentially expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The wave oscillates with conformal time [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (27)] that differs exponentially from the proper time of the observer (the cosmological time t) in perfect analogy to the Minkowski wave sampled by the accelerated observer (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Suppose the observer at rest with the universe samples the plane waves of the quantum vacuum (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' They oscillate with frequencies Ω in the conformal time τ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 3The space–time of exponential expansion (de Sitter space) is a maximally symmetric space with con- stant Riemann tensor Rαβ µν = −(H0/c)2 (δα µδβ ν − δα ν δβ µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The negative prefactor indicates the negative curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 11 de Sitter extension r τ = 0 τ ∞ t t Figure 6: Extended de Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Radial space–time diagram {cτ, r} in conformal time τ and comoving radius r = |r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cosmological time t runs according to the arrows indicated and ends (t = +∞) at the horizontal line (τ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='. Light travels along diagonal lines in the conformal diagram and may cross over to the next world, the extension, for τ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Light beyond the horizon (red line) cannot reach the observer (black vertical line up until t = +∞) before this world ends (τ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Light coming in within the white area — within the horizon — leaves in the shaded area, but cannot reach the double–shaded region in the extended world, in perfect analogy to the Rindler horizon of uniform acceleration (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtain for the case of exponential expansion: τ = − 1 aH0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (27) Note that conformal time is negative and ends at τ = 0 in the infinite future (t = +∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The observer samples the phase ϕ = Ωτ = Ω a0 e−H0t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (28) This is the same phase as the one of a right–moving wave sampled by Rindler observer R (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We see from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (12) that Ω/a0 corresponds to kξ and H0t to the dimensionless Rindler time η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The observer at rest with the exponentially expanding universe thus perceives waves in the same way as the uniformly accelerated observer in Minkowski space, including the waves of the quantum vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Like in uniform acceleration, the observer is surrounded 12 by a horizon (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Seen in conformal time and comoving space, incoming rays out- side of the radius rH = −cτ will never arrive at the observer before the world ends in conformal time (τ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (27) we get rH = c aH .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (29) Unlike the accelerated observer, there is no partner L to the observer R, at least in this uni- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may construct an artificial partner by extending de Sitter space to τ > 0 (simi- lar to the Kruskal extension of the black hole [56]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For this we imagine another universe with infinite cosmological time related to positive conformal time by τ = H−1 0 e−H0t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this netherworld time runs backwards from +∞ to −∞ such that conformal time and light smoothly passes from one world into the other (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The partner observer in the netherworld is then shrouded behind a horizon (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6) from the observer in this world, in perfect analogy to uniform acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In particular, we may conclude that the de Sitter observer perceives the vacuum as thermal radiation as well [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From the corre- spondence to the case of the accelerated observer with Unruh temperature (20) we obtain the Gibbons–Hawking temperature [53] kBT = ℏH0 2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (30) Exponential expansion is a clear, simple, perfectly understood case of quantum noise in cosmology, but it is largely an academic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In reality, the universe does not expand exponentially yet nor did it in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Very few papers have tackled the problem beyond the case of de Sitter space [54, 61, 62], because it is a difficult problem of — appar- ently — hardly any relevance, as the Gibbons–Hawking temperature of the real universe is astronomically small (T lies in the order of 10−29K for 1/H0 of 10Gy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' But if the quantum noise of general cosmological horizons is indeed the key to understanding the cosmological constant [5], understand it we must.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4 Expanding flat space Apart from exponential expansion, there is no other case when an expanding flat space establishes a genuine event horizon [54, 63] (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' One sees this as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cos- mological horizon [64] is the spherical surface around a given point where the expansion velocity reaches the speed of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The expansion velocity u is the derivative of the proper length ℓ = ar with respect to cosmological time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Differentiating ℓ gives Hubble’s law, u = Hℓ, in terms of the Hubble parameter H defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We see that u reaches c at rH of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the cosmological horizon to be an event horizon it needs to be light–like, parallel to light rays in the {cτ, r} space–time diagram, because otherwise light may cross it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Since τ = � da a2H (31) the conformal time τ does only agree with −1/(aH) for H = const, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' exponential expansion, which proves that cosmological horizons are not event horizons, except in the exponential case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In fact, the light of distant galaxies and the Cosmic Microwave 13 Figure 7: Cosmological horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space–time diagrams of the horizon (red curve) based on actual cosmological data [1, 40] (plotted in units c/H0 with Hubble constant H0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' a: in co– moving spatial coordinates r and conformal time τ light (black and white lines) propagates like in Minkowski space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The region outside the horizon is shaded in grey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Light may cross the horizon, except when, in the final stage of cosmic evolution, the horizon becomes light–like and hence a genuine event horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' b: vacuum modes in analogy to the Rindler modes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The modes are defined with respect to a specific time, here τ = 0 (the present time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The figure shows the phase pattern of the incident light only, not the outgoing light;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (36) describes both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Background reaches us from beyond our horizon [40, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Therefore, it is not clear from the outset how to generalize the Gibbons–Hawking formula (30) to the case of expanding flat space in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='4 Consider light in a universe with metric (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space shall be expanding, H > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For conceptual simplicity we do not start from Maxwell’s equations, but rather describe each polarization component by a conformally–coupled scalar field with modes satisfying the wave equation [24, 65]: 1 √−g ∂α √−g gαβ∂βA − R 6 A = 0 (32) in terms of the metric tensor gαβ, its determinant g and matrix–inverse gαβ, and the cur- vature scalar R of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Einstein’s summation convention over repeated indices is adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The modes shall be normalized according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (6) with the scalar product 4This section closely follows Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [54] but corrects an error in the conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Despite this error, the ideas and results of the paper [54] are correct, as we show here and in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 14 co-moving r a 0 conformal 2 3 0 2r b 0 T 2 3 0 1 2[65]: (A1, A2) = ic ℏ � � A∗ 1 ∂0A2 − A2 ∂0A∗ 1 � √−g d3x , ∂0 = g0α∂α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (33) One sees from the wave equation that the scalar product (33) is a conserved quantity for arbitrary wave packets satisfying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Writing A as A0/a reduces the wave equation (32) to the free wave equation for A0 with respect to the conformal time τ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (22), which shows that light waves propagate in the expanding universe like in free Minkowski space {cτ, r} (not just light rays).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may use the plane waves A = (A/a) eik·r−iωτ with ω = c|k| , A2 = ℏ 16π3ω (34) as normalized modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We assume that the cosmological quantum vacuum is in the vac- uum state (8) with respect to these conformal plane waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This cosmological vacuum is called the conformal vacuum [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, as we know from the case of exponen- tial expansion, an observer at rest may not perceive the conformal vacuum as vacuum fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Imagine a point–like observer at rest with the expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We use spherical coordinates with the origin attached to the point of the observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Only radial waves will matter, because all waves with higher orbital angular momentum vanish at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Write the radial modes as A = 1 √ 4π arAν(r, τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (35) From the wave equation (32) follows that the Aν satisfy one–dimensional wave propaga- tion, which means that Aν consists of a superposition of incoming and outgoing waves f(r±cτ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As A must not diverge for r → 0 we need to require Aν = f(r+cτ)−f(r−cτ), the outgoing wave is the ingoing wave reflected at the focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Inspired by the cases of uni- form acceleration and exponential expansion, we wish to define modes in close analogy to the Rindler modes of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These modes can only capture the cosmological hori- zon at a given moment in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' for a given scale factor a0 and corresponding Hubble parameter H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We define [54] (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7b) in analogy to the Rindler modes [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (13), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4]: Aν = A � (η − ρ)iν − (η + ρ)iν : ν > 0 (ρ − η)−iν − (−η − ρ)−iν : ν < 0 (36) where η (not to be confused with the Rindler η) and ρ are defined as (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8) η = 1 + a0H0(τ0 − τ) , ρ = a0H0 c r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (37) Like in the case of the Rindler modes, the modes (36) are analytic on the lower half τ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consequently, they consist entirely of positive–frequency plane–wave modes (34) and share the conformal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Let us call them vacuum modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The phase of each of the vacuum–mode components, incoming or outgoing, is logarithmic: ϕ = ν ln [1 + a0H0(τ0 − τ ∓ r/c)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (38) 15 ρ = 1 0 1 2 η = 1 η = 0 co-moving r conformal τ Figure 8: Characteristic events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space–time diagram showing a part of the actual cosmolog- ical horizon (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Vacuum modes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7b) are established in analogy to the Rindler modes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The vacuum modes are characterized by the time parameter η and the space parameter ρ defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The η parameter runs backwards from η = 1 when the vacuum mode is defined (t = t0) to η = 0 when the Hawking partners arrive at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' At the time t0 (η = 1) the spatial parameter reaches unity at the horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Like the Rindler modes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4) the vacuum modes (36) are not monochromatic (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' the frequency ω = −∂tϕ varies in space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' At the defining time of the modes t0 we have ω|t=t0 = ω0 1 ∓ u/c , u = H0ℓ , ℓ = a0r (39) where ω0 denotes the frequency at the origin and at t = t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This frequency is related to the dimensionless parameter ν by ω0 = νH0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (40) Equation (39) shows that the vacuum modes are Doppler–shifted in the expanding uni- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Incoming waves propagate against the Hubble flow u and are blue–shifted, outgo- ing waves are red–shifted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Note that the Doppler profile (39) was originally used to define the modes (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Here we have derived them from the analogy to the case of uniform ac- celeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It remains to normalize the radial vacuum modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For this we express the scalar product (33) in conformal time τ and spherical coordinates {r, θ, φ} with metric tensor gαβ = a2 diag(1, −1, −r2, −r2 sin2 θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtain for the radial waves (35): (A1, A2) = i ℏ � ∞ 0 � A∗ ν1 ∂τAν2 − Aν2 ∂τA∗ ν1 � dr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (41) For the vacuum modes (36) with definitions (37) we have ∂τ = −a0H0 ∂η and a0H0 dr = 16 c dρ and get (A1, A2) = −ic ℏ � ∞ 0 � A∗ ν1 ∂ηAν2 − Aν2 ∂ηA∗ ν1 � dρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (42) We may normalize the vacuum modes at a convenient moment (η = 0) as the scalar product remains constant at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We find exactly the same norm as for the Rindler waves, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (16) and (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Finally, consider the mode overlap between the vacuum modes defined at different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The most relevant case is the overlap between the vacuum modes at one horizon, say at t2, with the modes at the previous horizon at t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' By this we mean that t2 is the time when the Hawking partners generated at t1 arrive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The overlap tells how the modes at one instant of creating Gibbons–Hawking radiation are related to the modes at the next stage of creation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In particular, the phases between the modes are important, as the acts of creation will interfere with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is because particle creation works like parametric amplification [55] where the phase of the incident light determines whether particles are created or annihilated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We calculate the scalar product (A1, A2) at time t2 where η1 = 0 (arrival of the partners) and η2 = 1 (primary Hawking radiation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We denote the scale factors and Hubble parameters as a1, H1 and a2, H2, and use ρ = ρ2 as integration variable with ρ1 = ρ2(a1H1)/(a2H2) from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this way we get (A1, A2) = c ℏ (ν1 + ν2) A1A2 �a2H2 a1H1 �iν1 cosh2 ζ I12 (43) with definition (16) and the remaining overlap integral I12 = � ∞ 0 ρ−iν1 (1 + ρ)iν2 dρ ρ − � 1 0 ρ−iν1 (1 − ρ)iν2 dρ ρ (44) = Γ(−iν1) Γ(−iν2) Γ(iν2 − iν1) − Γ(1 + iν2) Γ(1 − iν1 + iν2) Γ(−iν1) (45) in terms of Gamma functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Note that we gave the ν an appropriate small imaginary part such that the integrals (44) converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The dominant contribution to the mode overlap appears for ν1 → ν2 where Γ(iν2−iν1) ∼ 1/(iν1−iν2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the mode expansion � (�aνAν + �a† νA∗ ν)dν the overlap (A1, �A) picks out a single mode with ν1 = ν2 = ν by Cauchy’s theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Taking into account the normalization (17) we arrive at the simple result: �a2 ∼ �a2H2 a1H1 �iν �a1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (46) Therefore, to a good approximation, the coefficients of the vacuum modes at time t2 are given by the mode coefficients at time t1 multiplied by the characteristic logarithmic phase factor ν(ln a2H2 − ln a1H1) of the cosmological horizons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This concludes our discussion of the vacuum modes in the expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5 Radiating horizons Consider now the noise the observer perceives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The observer, at rest with the expanding universe at r = 0, samples the field with respect to cosmological time t, but the field 17 oscillates with conformal time τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the radial vacuum modes we have organized all the superpositions of conformal plane waves the observer perceives, such that �A ��� r=0 = � +∞ −∞ � �aνA0,ν + �a† νA∗ 0,ν � dν (47) where according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (35) the A0,ν are given by A0,ν = 1 √ 4π ar Aν ���� r=0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (48) We obtain from expressions (36) and (37) for the modes: lim r→0 Aν r = ∓2iνA (±η)±iν−1 a0H0 c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (49) Consider the radiation field around two times in the cosmic evolution: near the time t0 when particles are produced in the Gibbons–Hawking effect for the Hubble parameter H0 and then around the time when the corresponding Hawking partners arrive, given by the condition η = 0 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The time t0 is arbitrary, but for each t0 a new system of modes needs to be constructed according to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (36) and (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Since any such system is a superposition of positive–frequency plane waves, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (34), the vacuum state with respect to the mode operators �aν is the cosmic vacuum, regardless of t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As in the cases of uniform acceleration and exponential expansion, imagine the ob- server as equipped with a spectrometer measuring the Fourier transformation of the field with respect to the proper time of the observer, cosmological time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consider the Fourier transform near the time t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We write for each vacuum mode �A0,ν = � +∞ −∞ A0,ν eiωt dt (50) with the understanding that the integration is performed near t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There we get from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (37) and (22): dη = −a0H0 a dt , t ∼ − 1 H0 ln η , (51) and hence from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (48) and (49): �A0,ν = √ 4π iνcA δ(ν − ν0) , ν0 = ω H0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (52) For positive frequencies ω the Fourier transform �A0,−ν of the negative–index modes van- ishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, like in the case of the accelerated observer, the Fourier transform of the complex conjugate negative–index modes A∗ 0,−ν does not disappear: � A∗0,−ν = e−πν �A0,ν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (53) From relation (16) and the normalization (17) of the vacuum modes we obtain the compact result: � +∞ −∞ �A eiωt dt ���� r=0 = √ ℏν c i � �aν cosh ζ + �a† −ν sinh ζ � , ν = ω H0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (54) 18 The result shows that the observer, sampling the vacuum noise with respect to cosmologi- cal time around t0, experiences the creation of Hawking particles [54], even in the case of non–exponential expansion when the cosmological horizon is not an event horizon [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Now turn to the time t1 when the Hawking partners are expected to arrive, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' when η ∼ 0 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It follows from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (22) and (37): η ∼ −a0H0 a1 t (55) where a1 denotes the scale factor at t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Defining now ν1 = (a1/a0)(ω/H0) we thus obtain �A0,−ν = iν √π A c � +∞ −∞ (−η)−iν−1 e−iν1η dη ∼ i √ 2iν A c (ν1/ν)iν eiν (56) in the saddle–point approximation for ν ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Similarly, for the negative–frequency Fourier–transform of the complex conjugate modes with positive index ν we get � A∗0,+ν = e−πν �A0,−ν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (57) Substituting these results in the mode expansion (47) we calculate the integral over the mode index in the saddle–point approximation as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The phase of the integrand, ϕ = ν ln(ν1/ν) + ν, is stationary (∂νϕ = 0) for ν = ν1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtain in perfect analogy to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (54): � +∞ −∞ �A eiωt dt ���� r=0 = √ ℏν c i � �a−ν cosh ζ + �a† ν sinh ζ � , ν = a1 a0H0 ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (58) Like the accelerated observer [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (18)] the observer at rest with the expanding universe measures spectral correlations expressed in the Bogoliubov transformations (54) and (58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These correlations appear as extra noise with Planck spectrum (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6 Cosmic cascade We have thus derived the thermal radiation of cosmological horizons in expanding flat space from the physical picture of wave noise (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This picture reproduces the gen- eralization [54] of Gibbons’ and Hawking’s [53] result, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (30), to arbitrary expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this general case H0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (30) refers to the Hubble parameter (25) at any given time t0, not required to be constant as in Gibbons’ and Hawking’s case [53] of exponential expansion, de Sitter space (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In addition, we also derived a new aspect of Gibbons– Hawking radiation not seen in de Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There the Hawking partners never arrive before the world ends in conformal time (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6) whereas in reality they do (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The light of distant galaxies and the Cosmic Microwave Background easily cross the cosmo- logical horizon [40, 63] and so do the Hawking partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We have found that the partners are correlated with the primary particles, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (54) and (58), for the same dimensionless frequency ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the primary particles, ν is given by the frequency ω divided by the Hubble parameter H0, which gives in the Planck spectrum (19) the Gibbons–Hawking temperature (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the Hawking partners, ν is given by ω divided by (a0/a1)H0 where 19 0 1 2 3 2 1 0 co-moving r conformal τ Figure 9: Cascade of horizons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the actual universe (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7) depicted in conformal time τ and comoving radius r, the Gibbons–Hawking radiation at present (τ = 0) depends on a cascade (zigzag line) of radiation generated by past cosmological horizons (red) curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Depending on the relative phase, radiation is created or annihilated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The multiple interference of all creation processes gives rise to the effective Gibbons–Hawking temperature and vacuum energy density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' a1 denotes the scale factor at their time of arrival.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This means that the Hawking partners also arrive as thermal radiation, but with the red–shifted temperature kBT1 = a0 a1 ℏH0 2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (59) These results are simple and intuitive, but they are still incomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' If the present Hawk- ing partners arrive in the future as thermal radiation, so should the Hawking partners of the past arrive in the present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Call the scale factor and Hubble parameter of the past cos- mological horizon a−1 and H−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The present radiation of Hawking partners should then have the temperature kBT−1 = a−1 a0 ℏH−1 2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (60) 20 But neither this nor the primary temperature (30) is the effective temperature Teff of the radiation in total, because the Hawking particles interfere with their partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We have worked out that they have the logarithmic phase difference (46).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Like in parametric amplification [55] the phase of the incident radiation determines whether it gets ampli- fied or de–amplified, whether particles are created or annihilated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The Hawking partners from the previous horizon may very well annihilate some of the Gibbons–Hawking radi- ation at the present, depending on the relative phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Furthermore, the horizon before the previous horizon interferes with the particle production as well, and so does the whole cascade of past cosmological horizons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Each horizon establishes the Bogoliubov transformation �b±ν = �a±ν cosh ζ + �a† ∓ν sinh ζ with tanh ζ = e−πν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (61) Between horizons, the modes are phase shifted according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (46).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As the frequencies relevant to the vacuum energy much exceed the Hubble parameter, we are in the regime of ν ≫ 1 where we get for the final �bν in terms of the initial vacuum mode operators �a±ν: �bν ∼ �aν + �a† −ν S e−πν (62) with S summing up the phase factors of the m–th previous horizons relative to the present one: S = ∞ � m=1 �a−mH−m a0H0 �2iν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (63) This sum is highly oscillatory, but we are interested in the net effect of the interfering horizons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' in the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' When averaged over δν ∼ 1 only an exponentially small contribution will remain that, together with the primary e−πν, turns the Bogoliubov trans- formation (62) into �bν ∼ �aν + �a† −ν eiΦ−πω/Heff (64) with some phase Φ that does not affect vacuum correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The exact expression for Heff we shall derive in the next section, but here we can already draw some qualitative conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Since Heff depends on the history of cosmic evolution, it will introduce a memory effect in the cosmologically relevant vacuum energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This memory of the past should remove the oscillations that would otherwise plague the cosmic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Destructive interference from past cosmological horizons may also explain why first– order perturbation theory with the primary H instead of the full Heff agrees so remarkably well with astronomical data [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It is also interesting to note that the cosmic vacuum energy vanishes within one cosmic era and thrives in the transition periods between different eras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' By era we mean a period in the cosmic evolution dominated by one type of fluid with a characteristic equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the radiation–dominated era [40] the Hubble parameter H goes with a−2, in the matter–dominated era [40] H ∝ a−3/2 and during vacuum domination H would become constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Apart from the exponential expansion in the vacuum era, all other eras are characterized by a power law: H = H0 a−γ (65) 21 with constant H0 and γ > 1 (where H0 denotes H at a = 1 here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The partner radiation arriving at time t with scale factor a and Hubble parameter H originates from the past cosmological horizon the conformal time interval τ earlier, with τ = � da a2H = 1 γ − 1 � 1 aH − 1 a−1H−1 � = 1 a−1H−1 , (66) which gives aH a−1H−1 = 1 γ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (67) This recurrence relation remains true for all the phases in the sum (63) such that the sum forms a perfect harmonic series with vanishing zero–frequency component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cycle average of such a series vanishes: the number of particles produced is exactly zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For a power–law expansion, creation and annihilation thus cancels out exactly as the result of multiple interference between past horizons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 7 Wigner function The interferences in the cosmic cascade of creation and annihilation at horizons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 9) are captured in the sum (63).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Yet this sum is difficult to evaluate and mathematically ill– defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Let us therefore try to deduce a better formula for the effective Gibbons–Hawking temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The principal problem of our previous approach (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5) is the Fourier trans- formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We wish to deduce the radiation spectrum as it evolves in time, and there we are interested in spectral features ∼ exp(−2π/H) that would require an integration time in the order of 1/H for their accurate resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' However, the universe also evolves on a time scale of 1/H and with it the Gibbons–Hawking spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The two aspects, spec- tral accuracy and temporal resolution, appear to be mutually exclusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Frequency and time are as mutually exclusive as position and momentum in quantum mechanics (being Fourier transforms of each other).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fortunately, there are good compromises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' To give a simple example, music sheets describe tones – frequencies — in time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' to give a sophis- ticated example, quantum quasiprobability distributions [55, 66, 67, 68] describe both position and momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Probably the best compromise is the Wigner function [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In quantum mechanics, the Wigner function is a partial Fourier transformation of the density matrix [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The density matrix is a correlation function of two variables, for example two positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The Wigner function performs a Fourier transformation with respect to the position difference as a function of the position average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this way the Wigner function captures the momentum spectrum as a function of position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The marginal dis- tributions (reduced probability distributions) all give the correct probability distributions of either position or momentum, or of any linear combination of the two, with perfect accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This property defines the Wigner function uniquely [69] and explains why the Wigner function describes conjugate variables (position and momentum, time and fre- quency) with the highest possible precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Here we employ the time–frequency Wigner function: W = 1 2π � +∞ −∞ K(t + θ/2, t − θ/2) eiωθ dθ (68) 22 of the two–time field correlation function K defined as the vacuum expectation value K = ⟨ �A1 �A2 + �A2 �A1⟩ (69) with the indices indicating the two times and positions {t1, r1} and {t2, r2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the con- formal vacuum, the electromagnetic field fluctuations propagate like in empty Minkowski space of the conformal times τ and comoving positions r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may thus use the well– known expression of the Minkowski vacuum correlations [8]: K = 1 (2π)2s2 , s2 = a1a2 � c2(τ2 − τ1)2 − (r2 − r1)2� (70) in terms of the Minkowski metric s with reciprocal conformal factor a1a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Here we are interested in the spectrum measured with respect to the cosmological times t1 and t2 at a given point comoving with the universe: r2 = r1 , t2 = t + θ/2 , t1 = t − θ/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (71) There are several ways to derive Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (70) — we may expand the field in terms of the plane–wave modes (34) and integrate, or we may use the fact that K is the real part of the analytic function ⟨ �A1 �A2⟩ with imaginary part given by the difference between retarded and advanced Green function, and derive K in one line from the Kramers–Kronig relation [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 Note that these vacuum correlations exist outside of the causal cone (s < 0) as has been recently measured in quantum optics [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The correlations peak at s = 0, because electromagnetic waves propagate along light cones, including electromagnetic noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Space–time points on the light cone (s = 0) are thus strongly correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wave noise is organized (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cosmology adds one subtle complication to the definition (68) of the Wigner function: there was a beginning of time (say at t = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For a given cosmological time t the Fourier time θ runs only from −2t to +2t in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Close to the beginning, the expansion factor a develops a branch point [41] such that a becomes complex in the time before, which explains [41] why there was nothing real before the beginning of reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The conformal time τ, being defined as the integral of the inverse of a, inherits the branch point and ceases to be real for |θ| > 2t as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The branch points of τ are harmless in the integrand (70), but a goes to zero with some fractional power [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We might be inclined to run the integral in the definition (68) of the Wigner function from −2t to +2t, but the branch points of a1 or a2 at ±2t in the integrand (70) would then create oscillations with period π/t in the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The spectral oscillations average out for frequencies ω much larger than the inverse cosmic age, but like the oscillations in the cosmic cascade (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6) they obscure the subtle thermal spectrum of Gibbons–Hawking radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It is therefore wise to analytically continue a around the beginning of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' If we lead the integral (68) slightly above the branch points ±2t for ω > 0 and slightly below for ω < 0 the oscillations are gone, because if we approximate a(t) by some root for t ∼ 0 we could close the integration contour on the upper half plane for ω > 0 and on the lower half plane for ω < 0 (due to the Fourier factor eiωt) and get zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5There is a sign error in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (50) of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [5] and subsequent expressions, because the wrong half plane was taken in closing the integration contour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fortunately — thanks to another sign error — the result (80) carries the correct sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 23 Having cleared the way we are now ready to calculate the Wigner function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It is wise not to use the explicit expression (70) of the correlation function, but rather our experience with Rindler modes in expanding flat space (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We expand [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (47)] the radiation field �A in terms of the vacuum modes (36) defined at some arbitrary time t0 ≥ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The value of t0 is not important, as the modes capture the conformal vacuum for all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the vacuum expectation value (69) of K the ⟨�a† and �a⟩ vanish while the ⟨�aν and �a† ν′⟩ produce delta functions δ(ν − ν′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the modes at r = |r2 − r1| = 0 we apply Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (48) and (49) with the normalization (16) and (17), note that the negative–ν modes are reduced by the factor e−πν, and obtain the expression K = a2 0H2 0 (2π)2c2a1η1a2η2 � ∞ 0 2ν �1 2 + 1 e2πν − 1 � cos � ν ln η2 η1 � dν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (72) Let us check that this formula agrees with the standard result (70) for K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Formula (72) contains the typical Planck term ν(e2πν − 1)−1 plus the contribution ν/2 of the vacuum energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We express these terms in a geometrical series: ν 2 + ν �1 2 + 1 e2πν − 1 � = ν ∞ � m=0 ′ e−2πmν (73) where the prime should indicate that the zeroth term is meant to be divided by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As 1 4 sinh2(z/2) = +∞ � m=−∞ 1 (z − 2πmi)2 = −∂z +∞ � m=−∞ 1 z − 2πmi (74) we see that the term (73) is the Fourier transform of [4 sinh2(z/2)]−1 for ν > 0 where we can close the integration contour on the upper half plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Running through the pole at zero (instead of surrounding it) produces the factor 1/2 in the vacuum term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For ν < 0 we close the contour on the lower half plane and get the same expression with ν replaced by |ν|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' From the inverse Fourier transformation then follows � ∞ 0 ν �1 2 + 1 e2πν − 1 � cos νz dν = 1 4 sinh2(z/2) (75) and from this — and definition (37) for η — we obtain Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (70).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We have thus reproduced the known vacuum correlation, but only for times less than t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the Wigner function (68) we must integrate from −∞ to +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Therefore we should move t0 to +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the infinite future the expansion a0 goes to infinity and H0 to a finite value, and so [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (37)] the ratio η2/η1 goes to (τ∞ − τ2)/(τ∞ − τ1) while the factors (a0H0)/(aη) go to 1/(τ∞ − τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (72) we may thus replace η by η = τ∞ − τ = � ∞ a da a2H (76) and remove the a0H0 altogether.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We thus obtain for the thermal part of the Wigner func- tion Wth = 1 (2π)2c2 � ∞ 0 ν e2πν − 1 D(ν,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' ω) dν (77) 24 with the kernel D = 1 π e−ωσ � +∞ −∞ 1 a1η1a2η2 cos � ν ln η2 η1 � eiωϑ dϑ (78) where we have lifted the integration line in expression (68) by the constant positive imag- inary time σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' assuming positive frequencies where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' as we know,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' we should lead the inte- gration contour above the branch points at the origin of physical time: θ = ϑ + iσ with σ > 0 for ω > 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (79) Consider de–Sitter space as a test case of our formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In this case, a grows exponentially with constant H0, τ = −(H0a)−1 with τ∞ = 0, and ln(τ2/τ1) = −H0(ϑ + iσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We get D = H2 0δ(ω − H0ν) (80) and hence a perfect Planck spectrum with Gibbons–Hawking temperature (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Formula (78) thus reproduces Gibbons’ and Hawking’s classic result [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Consider now the realis- tic case of cosmic evolution, which deviates from pure exponential expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The kernel D is of course independent of the integration contour (unless singularities or branch cuts are crossed) but for any given real time t there will be only one imaginary time σ when D does approach the defining integral of a delta function in the asymptotic limit of large frequencies ω (whereas for de–Sitter space all σ do).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the following we work out the condition when this is the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' But first we need to consider some realistic cosmology in order to estimate the validity of the approximation we are going to make.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In the spatially flat, isotropic and homoge- neous universe the square of the Hubble parameter is proportional to the energy density (by Friedman’s equations [40, 41]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For radiation (photons and neutrinos) the energy density goes with the inverse fourth power of the expansion factor a, because the energy falls with the inverse wavelength and hence with a−1 and the density falls with a−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For matter (baryonic and dark) the energy density is essentially the rest–mass mass density multiplied by c2 and a−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Dark energy Λ — being the cosmological constant — remains constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This gives the Λ Cold Dark Matter (ΛCDM) model: H2 = H2 0 �ΩR a4 + ΩM a3 + ΩΛ � (81) where H0 denotes the Hubble constant at the present time (a = 1) and the Ωm describe the weights of the various contributions to the energy density with all Ωm summing up to unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cosmic parameters are retrieved from the fluctuations of the Cosmic Microwave Background [1] and are listed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For a ≫ ΩR/ΩM ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='3 × 10−3 we can ignore the radiation contribution and enter a stage of cosmic evolution entirely dominated by matter and Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For describing this matter–vacuum era in the simplest possible way we change the scale of a and the units of time replacing (ΩM/ΩΛ)1/3a → a and H0 √ΩΛt → t such that H2 = a−3 + 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (82) From t being the integral of 1/(aH) with respect to a we obtain a = � sinh 3t 2 �2/3 and H = coth 3t 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (83) 25 We get the conformal time τ = � a 0 da a2H = 2√a 2F1 � 1/6, 1/2, 7/6, −a3� , τ∞ = Γ(1/3) Γ(7/6) Γ(3/2) (84) in terms of the hypergeometric function 2F1 and the Gamma function Γ, and from the relationship (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='6) [71] of the hypergeometric function: η = τ∞ − τ = a−1 2F1 � 1/3, 1/2, 4/3, −a−3� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (85) Consider now the curves in the complex a–plane where the Hubble parameter is real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the Λ–matter model (82) we get three curves where H2 is real: straight lines going through the origin with angles {0, π/3, −π/3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The Hubble parameter itself is real for ∞ > H2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' So the curves come in from ∞ and end at the points where H = ∞ or H = 0, which is {0, eiπ/3, e−iπ/3} for the Λ–matter stage (82).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The positive real axis corresponds to the real world with real time t, the π/3–line in the upper half plane corre- sponds to the line with positive imaginary part π/3 in the complex plane of cosmological time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In terms of the time t + θ/2 in the Wigner function (68) it draws a line (79) parallel to the real axis with σ = 2π/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is the line we are going to need in our integral (78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The ΛCDM model (81) has four roots of H2 = 0 we can calculate from Ferrari’s formula for the roots of quartic equations, two are real and negative, the other two com- plex conjugate to each other;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' we take the root a+ on the upper half plane, for which |a+| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='775 and arg a+ = π/3 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='09 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Calculating η according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (76) we find arg η+ = −π/3 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='34 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We see that a+η+ is real to an accuracy in the order of 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This has consequences if we calculate the integral (78) in the saddle–point approxima- tion for large ω, because we get for the first and second derivatives of the phase ln(η2/η1) in the cosine: ∂θ ln η2 η1 ���� iσ = −Re 1 aη ���� iσ , ∂2 θ ln η2 η1 ���� iσ = 1 2 Im � H aη − 1 (aη)2 ����� iσ (86) and so the second derivative vanishes: the integral (78) gives a delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In fact, for large ω only ϑ ∼ 0 matters where we may approximate ln(η2/η1) ∼ −i�σ − �Hϑ and (a1η1a2η2)−1 ∼ �H2 with the definitions �H = 1 aη ���� iσ , �σ = 2 arg a|iσ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (87) We thus obtain from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (78): D = e−(ωσ−ν�σ) �H2δ(ω − �Hν) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (88) For the matter–vacuum universe in our scaled units we have in particular �H = 2F1 � 1/3, 1/2, 4/3, sech2(3t/2) � , �σ = σ = 2π/3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (89) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (88) follows that, in the full ΛCDM model, the thermal part (77) of the Wigner function (68) approaches the high–frequency asymptotics: Wth ∼ ω (2π)2c2 e−2πω/Heff for ω ≫ �H (90) 26 expressed in terms of the effective Hubble parameter Heff = �H 1 + 1 2π(σ �H − �σ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (91) The problem is solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8 Summary and outlook We have derived the Gibbons–Hawking temperature for the standard cosmological model — the Λ Cold Dark Matter model — from the physical picture of wave noise (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The resulting temperature, kBT = ℏHeff 2π , (92) depends on the effective Hubble parameter Heff of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (91) with 1 Heff = 1 �H + σ 2π − �σ 2π �H .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (93) The effective Hubble parameter sums up the multiple interferences in the cascade of cre- ation and annihilation at cosmological horizons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It does it by analytic continuation of the cosmic dynamics to complex times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The parameter �H is given by �H = 1 a(τ∞ − τ) ���� t+iσ/2 (94) in terms of the scale factor a and the conformal time τ evaluated at infinity and at a certain complex time t + iσ/2 on the upper half plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The real part of this complex time is the cosmological time at which Gibbons–Hawking radiation is acting at the moment, the imaginary part σ/2 needs to be determined from the requirement Im �H ��� t+iσ/2 = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (95) The parameter �σ is given by twice the argument of a at the complex time: �σ = 2 arg a|t+iσ/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (96) Expression (94) generalizes the Gibbons–Hawking formula (30) for de–Sitter space [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In de–Sitter space [58] the scale factor a grows exponentially as a = eH0t while the conformal time τ falls as −H−1 0 e−H0t approaching τ∞ = 0 in the infinite future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The product a(τ∞ − τ) = H−1 0 clearly is constant and real for all imaginary times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In a realistic cosmological model σ needs to be calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For example, in the most relevant case, the matter–vacuum dominated period of cosmic evolution, we get σ = 2π/3 for all times t (in appropriate units6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 6Here time is measured in the inverse units of √ΩΛH0 where ΩΛH2 0 describes the contribution of the cosmological constant Λ to the square of the Hubble parameter at the present time (a = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 27 The temperature (92) lies in the order of 10−29K (at the present cosmological time) and so the particles of Gibbons–Hawking radiation are completely negligible, but the amplitude fluctuations are not — according to Lifshitz theory [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' They are predicted to produce the contribution (1) to the renormalized vacuum energy proportional to ∆ = ∂3 t 1 Heff .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (97) This contribution drives the cosmological term εΛ [5, 6, 7] (but is not proportional to εΛ itself).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Expression (97) with effective Hubble parameter (93) hopefully is the final formula in a series of attempts [5, 7] to determine the correct vacuum energy of expanding flat space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For the matter–vacuum dominated period we obtain in our units ∆ = 1 �H4 � 4 − 8H �H − � 4 − 26 3 H2 � �H2 + � 6 − 20 3 H2 � H �H3 � (98) in terms of expression (94) at the complex time t + iπ/3 where �H is real — with �H given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (89) — and the Hubble parameter [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (83)] that is real as well — with H = tanh(3t/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Figure 10 compares this result with the previous attempts for the vacuum energy, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (2) and (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='0 Figure 10: Comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Black curve: Heff for the matter–vacuum dominated period of cosmic evolution in scaled units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We see that Heff gently falls from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='24 to unity for t → ∞ (de Sitter space in the far future).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Red curves: ∆ (proportional to −εvac) in scaled units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Solid curve: result of this paper, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (98).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Dashed curve: 1 6∆ obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (3) and used, in perturbation theory, in the comparison [7] with astronomical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Dashed–and–dotted curve: result of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (2), ruled out by the data [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The factor 1 6 was chosen such that the curves have the same asymptotics for t → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The curves are similar, but with a different prefactor that would correspond to a different cutoff [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The cutoff is a parameter of the theory, because it is not precisely known (only in its order of magnitude).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It remains to be seen how the solid curve compares with astronomical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Formula (93) depends on the history of cosmic expansion — being determined by analytic continuation of the entire expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As the vacuum energy acts back on the 28 cosmic evolution due to its gravity, it has the tendency of developing oscillations in the Hubble parameter if ∆ depends on just the local values of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' It is hoped that the memory effect in the vacuum energy derived here will eliminate such artefacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The multiple interference of cosmic creation and annihilation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 9) summed up in Heff may also explain why first–order perturbation theory is remarkably good at fitting the cosmological data [7] while the full theory with the previous expressions would fail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtained our result (93) assuming that the electromagnetic vacuum noise consists of modes oscillating with conformal time (22) whereas an observer at rest with the uni- verse counts time as cosmological time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Furthermore we assumed, inspired by optical analogues of gravity [17, 18, 19, 20, 21, 22, 23, 24], that the “medium” of space behaves like a medium, comoving with the universe like the observer at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We therefore re- quired that the spectrum of vacuum fluctuations perceived by space is the spectrum with respect to cosmological time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As the two times differ the spectrum becomes nontrivial and, as it turned out, thermal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We used the physical picture of wave noise (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1) and the asymptology [34] of Wigner functions [68] to work out the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We can draw another conclusion from the picture of wave noise (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Our analy- sis has been entirely local: we picked an arbitrary point in the spatially flat universe and considered the vacuum fluctuations at this point evolving in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Nevertheless, the quan- tum vacuum is arriving from long distances away, in particular the noise of the Hawking partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For sustaining the correlations responsible for the Gibbons–Hawking effect and hence the vacuum energy εvac, perfect vacuum modes need to be formed according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These are superpositions of perfect, non–dispersive plane waves (34) sustaining correlations across vast distances in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Such long–range correlations cannot exist in massive fields, even for energies at the Planck scale where mass is almost irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Let us estimate the requirement for maintaining correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A field with particles of mass m obeys the dispersion relation ℏ2ω2 = ℏ2c2k2 + m2c4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (99) Assuming λ = 2πc/ω = ℓp with Planck length ℓp we get for the deviation of the phase from the cosmological horizon to the point of observation: δϕ = rHδk ∼ −πrH ℓP λ2 C , λC = 2πℏ mc (100) where λC denotes the Compton wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We obtain that for rH ∼ 1010ly the mass m must not exceed 10−2eV for not ruining the noise correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' There is only one field with particles of such low mass, the electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Gluons are massless like the electromagnetic photons, but they are short–range due to interactions with themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Neutrinos have masses ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='8eV [72] and are therefore probably too heavy as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' More- over, neutrinos are fermions, and it seems questionable whether fermions can create vac- uum forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The standard vacuum fluctuations acting in the Casimir or van der Waals forces [42] are not fluctuations of particles and antiparticles, but field fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' What are the physically relevant field fluctuations of fermions in the vacuum state?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The need for massless bosonic fields to sustain wave correlation across cosmological distances may thus explain why only the electromagnetic field seems to contribute to the cosmological vacuum energy, as the comparison with astronomical data suggests [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 29 Finally, we found that for cosmological eras dominated by only one type of matter or energy the effective Gibbons–Hawking temperature is strictly zero or constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' These eras are the radiation–dominated era at the youth of the universe (a ≪ 10−3), the matter– dominated era in its middle age, and the vacuum–dominated era for the eternity to follow (a ≫ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We found this by summing up the cosmic interferences, but we also see it in one glance from our analytic theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Pure eras are described by power laws with H = H0 a−γ, γ > 1 or exponential expansion with γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For a power law the conformal time τ grows with aγ−1 and hence is analytic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' We may close the integration contour of the Wigner function (68) of the vacuum correlations (70) at infinity, get the vacuum term by integrating through the double pole at τ2 = τ1 but zero thermal contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Formula (94) also indicates that power laws in H generate zero Gibbons–Hawking temperature, because τ tends to infinity for a → ∞, but the formula requires a finite τ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' For exponential expansion, the Gibbons–Hawking temperature (92) is constant, and so its contribution (97) to the dynamical vacuum energy density (1) vanishes as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' As the cosmological term is driven by the dynamical vacuum energy it remains constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The vacuum energy acts only in transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' This is a typical feature of the Casimir effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In dielectrics [8, 9], the Casimir energy thrives on differences in the dielectric properties of a medium causing forces at interfaces and boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' In Casimir cosmology [40], the vacuum energy arises in the transitions between cosmic eras, changing the cosmological constant there [5, 6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The current era is such a transition period — the transition from matter to vacuum domination — and so the cosmological constant varies, which affects the Hubble constant (the Hubble parameter at the present time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The predicted variation of the Hubble constant [7] appears to agree with the astronomical data [36], giving some empirical support to the theory presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wave noise (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1) may thus not only explain the mundane, the stickiness of the microworld, but perhaps also the arcane, the force of the macroworld that drives the universe apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Acknowledgements Two and a half decades ago Michael Berry’s work on the optical Aharonov Bohm effect inspired me to look for connections between quantum optics and general relativity, and he has been an inspiration ever since.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' I am most grateful to him and wish him a happy anniversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' I would also like to thank Dror Berechya, David Bermudez, Nikolay Ebel, Jonathan Kogman, Amaury Micheli, and Scott Robertson for discussions and comments on this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' The paper has been supported by the Israel Science Foundation and the Murray B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Koffler Professorial Chair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' References [1] Planck Collaboration, Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cosmological parameters, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' & Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 641, A6 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [2] Proceedings of the Les Houches Summer School 2021 on Dark Matter (to be pub- lished).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 30 [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Burrage, A brief introduction to extended gravity and connections to dark energy: Illustrated with scalar field examples, in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [4] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Amendola and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Tsujikawa, Dark Energy: Theory and Observations (Cambridge University Press, Cambridge, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [5] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Lifshitz theory of the cosmological constant, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (New York) 411, 167973 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [6] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, The case for a Casimir cosmology, Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A 378, 20190229 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Berechya and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Lifshitz cosmology: quantum vacuum and Hubble tension, Month.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 507, 3473 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Buhmann, Dispersion Forces (Springer, Heidelberg, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Simpson and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=') Forces of the quantum vacuum (World Scientific, Singapore, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [10] Ya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Zel’dovich, The cosmological constant and the theory of elementary particles, Usp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Nauk 95, 209 (1968) [English translation: Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Uspekhi 11, 381 (1968)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Einstein, Kosmologische Betrachtungen zur allgemeinen Relativit¨atstheorie, Sitzungsber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Preuss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Akad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wiss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='-Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 142 (1917) [English Translation in The Principle of Relativity (Dover, Mineola, 2013)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Huterer and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Turner, Prospects for probing the dark energy via supernova distance measurements, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D 60, 081301 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Weinberg, The cosmological constant problem, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 61, 1 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lamoreaux, Demonstration of the Casimir Force in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='6 to 6µm Range, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 78, 5 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Munday, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Capasso, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Parsegian, Measured long–range repulsive Casimir–Lifshitz forces, Nature 457, 170 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Yang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Bao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Xia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Ashby, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Zhang, Stable Casimir equilibria and quantum trapping, Science 364, 984 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [17] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Gordon, Zur Lichtfortpflanzung nach der Relativit¨atstheorie, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (Leipzig) 72, 421 (1923).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Quan, Sur les ´equations de l’´electromagn´etisme dans la mati`ere, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' (Paris) 242, 465 (1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Quan, Inductions ´electromagn´etiques en relativit´e g´en´erale et principe de Fer- mat, Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 1, 54 (1957).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 31 [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Plebanski, Electromagnetic Waves in Gravitational Fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 118, 1396 (1960).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [21] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schleich and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Scully, General relativity and modern optics, in New trends in atomic physics: Les Houches, session XXXVIII, 1982 by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Grynberg and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Stora (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=') (Elsevier, Amsterdam, 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [22] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Piwnicki, Optics of nonuniformly moving media, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A 60, 4301 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [23] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Philbin, General relativity in electrical engineering, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 8, 247 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [24] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Philbin, Geometry and Light: the Science of Invisibility, (Dover, Mineola, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [25] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Optical Conformal Mapping, Science 312, 1777 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Pendry, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schurig, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Smith, Controlling Electromagnetic Fields, Sci- ence 312, 1780 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Philbin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kuklewicz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Robertson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Hill, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' K¨onig, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Science 319, 1367 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [28] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Belgiorno, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cacciatori, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Clerici, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Gorini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Ortenzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rizzi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Ru- bino, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sala, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Faccio, Hawking Radiation from Ultrashort Laser Pulse Filaments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 105, 203901 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [29] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rubino, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' McLenaghan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kehr, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Belgiorno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Townsend, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rohr, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kuklewicz, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' K¨onig, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Faccio, Negative-Frequency Resonant Radiation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 108, 253901 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Zhu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Genov, Trapping light by mimicking gravitational lensing, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Photonics 7, 902 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [31] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Bekenstein, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mutzafi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rotschild, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Segev, Optical simula- tions of gravitational effects in the Newton–Schr¨odinger system, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 11, 872 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [32] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Bekenstein, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kabessa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sharabi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Tal, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Engheta, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Eisenstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Agranat, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Segev, Control of light by curved space in nanophotonic structures, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Photonics 11, 664 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [33] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Drori, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rosenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Bermudez, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Silberberg, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Observation of Stimulated Hawking Radiation in an Optical Analogue, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 122, 010404 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [34] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Berry, https://michaelberryphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='wordpress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='com/publications/ 32 [35] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Di Valentino, A combined analysis of the H0 late time direct measurements and the impact on the Dark Energy sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Month.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 502, 2065 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=', A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 934, L7 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [37] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Di Valentino, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Pan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Visinelli, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Melchiorri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mota, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Riess, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Silk, In the Realm of the Hubble tension — a Review of Solutions, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 38, 153001 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [38] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Efrat and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Van der Waals anomaly: Analog of dark energy with ultracold atoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' B 104, 235432 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [39] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wald, Trace anomaly of a conformally invariant quantum field in curved spacetime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D 17, 1477 (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [40] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Casimir cosmology, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 37, 2241006 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [41] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Landau and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lifshitz, The Classical Theory of Fields (Butterworth- Heinemann, Amsterdam, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rodriguez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Capasso, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Johnson, The Casimir effect in microstruc- tured geometries, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 5, 211 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mendonc¸a, Theory of photon acceleration (CRC Press, Bristol, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [44] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mendonc¸a and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Guerreiro, Time refraction and the quantum properties of vacuum, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A 72, 063805 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [45] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schwinger, Casimir energy for dielectrics, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' USA 89, 4091 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [46] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Dodonov, Current status of the dynamical Casimir effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Scr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 82, 038105 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [47] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wilson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Johansson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Pourkabirian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Simoen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Johansson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Duty, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Nori, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Delsing, Observation of the dynamical Casimir effect in a supercon- ducting circuit, Nature 479, 376 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [48] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' L¨ahteenm¨aki, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Paraoanu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Hassel, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Hakonen, Dynamical casimir effect in a Josephson metamaterial, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' USA 110, 4234 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [49] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Vezzoli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Mussot, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Westerberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kudlinski, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Dinparasti Saleh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Prain, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Biancalana, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lantz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Faccio, Optical analogue of the dynamical Casimir effect in a dispersion-oscillating fibre, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2, 84 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [50] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fulling, Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D 7, 2850 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 33 [51] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Davies, Scalar production in Schwarzschild and Rindler metrics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A 8, 609 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [52] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Unruh, Notes on black-hole evaporation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D 14, 870 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Gibbons and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D 15, 2738 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [54] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Cosmological horizons radiate, Europhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 135, 10002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [55] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Essential Quantum Optics: From Quantum Measurements to Black Holes, (Cambridge University Press, Cambridge, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [56] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rindler, Kruskal Space and the Uniformly Accelerated Frame, Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 34, 1174 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [57] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Griniasty, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wildeman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fort, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Fink, Classical analog of the Unruh effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' A 98, 022118 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [58] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' de Sitter, On Einstein’s Theory of Gravitation and its Astronomical Conse- quences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Third Paper, Month.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 78, 3 (1917).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Liddle and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lyth, Cosmological Inflation and Large–Scale Structure (Cambridge University Press, Cambridge, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [60] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Gott III, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Juri´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schlegel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Hoyle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Vogeley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Tegmark, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Bahcall, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Brinkmann, A Map of the Universe, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 624, 463 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [61] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Davies and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Davies, How Far Can the Generalized Second Law Be Generalized?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 32, 1877 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [62] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cai and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Kim, First law of thermodynamics and Friedmann equations of Friedmann–Robertson–Walker universe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' High.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 2, 50 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [63] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Davis and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lineweaver, Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Australia 21, 97 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [64] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Harrison, Cosmology: the science of the universe (Cambridge University Press, Cambridge, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [65] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Birrell and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Davies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Quantum fields in curved space (Cambridge Uni- versity Press, Cambridge, 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [66] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 40, 749 (1932).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [67] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Cahill and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Glauber, Density Operators and Quasiprobability Distribu- tions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 177, 1882 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [68] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Schleich, Quantum Optics in Phase Space (Wiley-VCH, Weinheim, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 34 [69] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Leonhardt, Measuring the Quantum State of Light, (Cambridge University Press, Cambridge, 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [70] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Settembrini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lindel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Herter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Buhmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Faist, Detection of quantum-vacuum field correlations outside the light cone, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 13, 3383 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [71] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Landau and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' [72] KATRIN Collaboration, Direct neutrino-mass measurement with sub-electronvolt sensitivity, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 18, 160 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} +page_content=' 35' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE2T4oBgHgl3EQfSwcw/content/2301.03795v1.pdf'} diff --git a/F9E0T4oBgHgl3EQfhQEq/vector_store/index.faiss b/F9E0T4oBgHgl3EQfhQEq/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..3b87dc305a9b58f6e08ad121048fbccd9b671ac1 --- /dev/null +++ b/F9E0T4oBgHgl3EQfhQEq/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:374d3db6805df9417adf057a1e387e610b0707b89ddd1acc1614200c3c69fcb3 +size 2490413 diff --git a/FNE0T4oBgHgl3EQfhAFe/vector_store/index.faiss b/FNE0T4oBgHgl3EQfhAFe/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..5cb584d6d39f437c1754b3bc2e20f8913a85501e --- /dev/null +++ b/FNE0T4oBgHgl3EQfhAFe/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed586d865902911d4ce74e9873c0bff065abbda834150ece511199347fb45043 +size 786477 diff --git a/FNE0T4oBgHgl3EQfhAFe/vector_store/index.pkl b/FNE0T4oBgHgl3EQfhAFe/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..087fceb1aa27ea6c20d784919a54b8bb9df73e88 --- /dev/null +++ b/FNE0T4oBgHgl3EQfhAFe/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8be24d953d4524a07e289dddcbe796b7c6c7a14b4d817ebed34ef241c62114b4 +size 27250 diff --git a/FNE2T4oBgHgl3EQfSwf4/vector_store/index.faiss b/FNE2T4oBgHgl3EQfSwf4/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..2bd39add9e8b286452538e63913f2ff7ed6d9f22 --- /dev/null +++ b/FNE2T4oBgHgl3EQfSwf4/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:94d136f84c9ff815a52125e5cb905d3ba7e4263950b58f35d56dd35f2684aa50 +size 6619181 diff --git a/GdFIT4oBgHgl3EQfWysJ/vector_store/index.faiss b/GdFIT4oBgHgl3EQfWysJ/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..20b701919437e65cef4ceadd6e17581565aaf56c --- /dev/null +++ b/GdFIT4oBgHgl3EQfWysJ/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:563445c292e4c8c098b3adac69a5bbae7acf65d7dbd8f7d0bcfe03e69680abf8 +size 5505069 diff --git a/GdFIT4oBgHgl3EQfWysJ/vector_store/index.pkl b/GdFIT4oBgHgl3EQfWysJ/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..2a4fec150c5f9a102e29ed46f0119ccb25bf1c0a --- /dev/null +++ b/GdFIT4oBgHgl3EQfWysJ/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cd6eaed437998f95b0fb5f8c531ce200c6a5356723ec9712403721698371a394 +size 171364 diff --git a/H9AyT4oBgHgl3EQf5vo1/vector_store/index.faiss b/H9AyT4oBgHgl3EQf5vo1/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..5e275416646a9cc5eb0a8e3135c13f31406e71ce --- /dev/null +++ b/H9AyT4oBgHgl3EQf5vo1/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7a5583464e0959074c1a3f37b1ec4737ceda43489208682b3f9d1a0cb9493b14 +size 5242925 diff --git a/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/2301.01517v1.pdf.txt b/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/2301.01517v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..04a8e9d6eaafb3d29660c7f65baf351ea462e88a --- /dev/null +++ b/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/2301.01517v1.pdf.txt @@ -0,0 +1,1898 @@ +Tuning a two-impurity Kondo system by a moir´e superstructure +Sergey Trishin,1 Christian Lotze,1 Friedemann Lohss,1 Giada Franceschi,1 +Leonid I. Glazman,2 Felix von Oppen,3 and Katharina J. Franke1 +1Fachbereich Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany +2Department of Physics, Yale University, New Haven, Connecticut 06520, USA +3Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany +Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems. Working with +Mn atoms on Au(111) covered by a monolayer of MoS2, we tune the inter-adatom exchange via the +adatom distance and the adatom-substrate exchange via the location relative to a moir´e structure of +the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with +heights depending on the adatom location relative to the moir´e structure. Mn dimers spaced by a few +atomic lattice sites exhibit split Kondo resonances. In contrast, adatoms in closely spaced dimers +couple antiferromagnetically, resulting in a molecular-singlet ground state. +Exciting the singlet- +triplet transition by tunneling electrons, we find that the singlet-triplet splitting is surprisingly +sensitive to the moir´e structure. We interpret our results theoretically by relating the variations in +the singlet-triplet splitting to the heights of the Kondo peaks of single adatoms, finding evidence +for coupling of the adatom spin to multiple conduction electron channels. +Exchange interactions between magnetic adatoms and +itinerant electrons of a substrate can induce correla- +tion effects. For strong exchange coupling, the adatom +spin becomes Kondo screened [1, 2]. +For intermedi- +ate coupling, where the Kondo temperature is compa- +rable to temperature or other competing couplings, the +Kondo renormalizations remain in the perturbative do- +main [3]. +When the exchange coupling is weak, com- +peting couplings such as single-ion anisotropy can dom- +inate, in which case Kondo screening can be neglected +and spin excitations can be probed [4]. The panorama +becomes yet broader when exchange coupling the adatom +to a second magnetic atom in its vicinity. +The na- +ture of this coupling depends on the interatomic spacing. +In close proximity, direct exchange tends to dominate, +while larger separations favor substrate-mediated cou- +plings such as the oscillatory Rudermann-Kittel-Kasuya- +Yosida (RKKY) [5–7] and Dzyaloshinskii-Moriya (DM) +[8, 9] interactions. The resulting ground states may be +ferromagnetic [10, 11], antiferromagnetic [10, 11], or non- +collinear [12]. +The competition between inter-adatom and adatom- +substrate exchange leads to a rich phase diagram with +multiple correlated ground states. Theoretically, the two- +impurity Kondo problem has been treated extensively +[13, 14], and motivated numerous experiments [10, 15– +18]. The parameter space can be most directly explored +by scanning-tunneling-microscope (STM) experiments. +Atom manipulation with the STM tip admits manoev- +ering the atoms into lattice sites at various distances +and thus investigating different interatomic interaction +strengths [19]. Tuning of the exchange coupling to the +surface is somewhat less straightforward. An early ap- +proach used strain-induced changes in the band gap of +a decoupling interlayer [20]. +A more controlled strat- +egy would exploit well-defined superstructures. +Prime +candidates to impose a spatially periodic modulation of +the atom–substrate interaction strength are interlayers +which form moir´e structures with the underlying metal +substrate [21–23]. Most notably, monolayers of MoS2 on +Au(111) have been successfully employed for tuning the +exchange coupling of single magnetic Fe atoms from es- +sentially uncoupled to strongly Kondo screened [23]. +Here, +we +exploit +the +moir´e +pattern +formed +by +monolayer-MoS2 on Au(111) to tune the exchange cou- +pling of Mn dimers with the substrate, thereby probing +the competition between interatomic and atom-substrate +exchange. We find that the direct exchange coupling be- +tween closely-spaced Mn atoms leads to a singlet ground +state and study the remarkably strong variations of the +singlet-triplet splitting across the moir´e pattern. We in- +troduce a new experimental signature of multi-channel +Kondo coupling by exploiting a theoretical relation be- +tween the singlet-triplet excitation energy of the dimer +and the Kondo renormalizations of individual adatoms +and find evidence that the Mn adatoms are coupled to +several conduction-electron channels. +We use the previously established moir´e-patterned de- +coupling layer MoS2 on Au(111) [23], grown by deposit- +ing Mo atoms and subsequent annealing to 800 K in H2S +gas at a pressure p = 10−5 mbar [24, 25]. A moir´e struc- +ture forms as a result of the lattice mismatch between +adlayer and substrate, easily seen in the STM images as +a modulation of the apparent height with a periodicity +of ≈ 3.3 nm (Fig. 1a) [24–26]. Deposition of Mn atoms +at low temperatures (< 10 K) leads to isolated atoms ob- +servable as round protrusions with an apparent height of +≈ 300 pm. Some round protrusions with smaller appar- +ent height are attributed to Mn atoms attached to defects +and excluded from further analysis. We also find some +oval protrusions. As discussed in more detail below, we +attribute these to Mn dimers. +We start by characterizing individual Mn atoms. +These exhibit a narrow zero-bias resonance in differential- +arXiv:2301.01517v1 [cond-mat.mes-hall] 4 Jan 2023 + +2 +conductance (dI/dV ) spectra as shown for two examples +in Fig. 1b. At our experimental temperature of 1.1 K, the +lineshape is well reproduced by a temperature-broadened +logarithmic peak. The peak splits when applying a mag- +netic field (Fig. 1c). At 3 T, the Zeeman split amounts +to 600 µV. This behavior is reminiscent of a weakly cou- +pled Kondo impurity, with the experimental temperature +larger than or of the order of the Kondo temperature +[3]. Mn atoms at different positions with respect to the +moir´e lattice exhibit lineshapes with small variations in +intensity, but the same broadening (see Fig. 1b for two +extremal cases). The intensity modulations can be un- +derstood as modulations of Jν0, where J is the strength +of the exchange coupling to the conduction electrons and +ν0 the density of states (DoS) at the Fermi level as dis- +cussed in more detail below. The observed variations are +consistent with the DoS modulations due to the adatoms’ +position on the moir´e structure (Fig. 1d). +Next, we characterize dimer structures formed by two +adatoms in close proximity to each other. +Density- +functional calculations suggest that isolated atoms sit in +hollow sites of the terminating S layer [28]. Starting with +this assumption, we can tentatively assign model struc- +tures to the most commonly found dimer arrangements +on the surface by evaluating the separation and orienta- +tion in the STM images. Figure 2a,b shows an arrange- +ment, where two Mn atoms are separated by three lattice +sites of the MoS2 substrate. At this separation, the atoms +show a Kondo resonance as previously described for in- +dividual adatoms (Fig. 2c), indicating that interatomic +interactions are negligible. At a distance of two atomic +lattice sites (Fig. 2d,e), the Kondo resonance develops a +dip at the Fermi level (Fig. 2f). The spectrum is reminis- +cent of a Zeeman-split Kondo resonance, indicating mag- +netic interactions between the atoms, presumably result- +ing from substrate-mediated RKKY interactions. When +the atoms are in even closer proximity, their shapes are +no longer individually resolved in the STM image (Fig. +2g,h). While a definite assignment of the adsorption sites +is thus difficult, the oval shape and its orientation with +respect to the underlying lattice suggest that the atoms +lie in nearest-neighbor hollow sites (for details and STM +manipulations, see section S2 in Supplementary Material +(SM) [29]). +Differential-conductance spectra measured +on this type of dimer are radically different from those +of individual atoms or weakly interacting dimers. The +Kondo resonance is now replaced by pronounced inelas- +tic steps at ±10 mV (Fig. 2i). +It is rather surprising to detect inelastic excitations +of a relatively large energy, considering that individ- +ual atoms do not show a noticeable magnetocrystalline +anisotropy. +Instead of a change in magnetocrystalline +anisotropy energy, we suggest that the threshold energy +is associated with a spin-changing transition of the dimer. +Such excitations have been observed for Mn dimers on +CuN [30]. +The close proximity of the atoms may al- +3 nm +4.2 +3.8 +3.4 +dI/dV (G0) x 10-3 +dI/dV (G0) x 10-3 +-10 +-5 +0 +5 +10 +bias voltage (mV) +a) +d) +c) +b) +0.20 +0.15 +0.10 +0.05 +Jν0 +1.6 +1.2 +0.8 +0.4 +distance (nm) +moiré min. +moiré max.. +0 T +3 T +3.6 +3.2 +2.8 +2.4 +-15 -10 -5 +0 +5 +10 +15 +bias voltage (mV) +moiré maximum +moiré minimum +Figure 1. Variation of the Kondo coupling across the moir´e +structure. +a) STM topography of Mn atoms on the moir´e +structure of MoS2 on Au(111) (recorded at 100 mV, 20 pA). b) +dI/dV spectra taken on Mn atoms adsorbed close to a moir´e +maximum (black) and a moir´e minimum (red). The dashed +lines show fits using a code based on Ref. [27]. The fits yield +a (dimensionless) adatom-substrate exchange Jν0 of -0.080 +(red) and -0.049 (black). c) dI/dV spectra on a Mn atom at 0 +T (black) and 3 T (orange). The zero-bias resonance splits at +3 T (fit: dashed line). [Spectra were recorded at a setpoint of +15 mV, 3 nA (panel b) and 10 mV, 3 nA (panel c)]. d) Values +of Jν0 obtained from fitting dI/dV spectra (keeping T 2 +0 = +0.000415 constant, as obtained from a best fit with B-field) +on atoms at various positions within the moir´e superstructure +(distance to the moir´e maximum). Symbols indicate different +measurement sets. The black dashed line is a linear guide to +the eye through the data points. The red dashed lines are +corresponding lines obtained from fits using different tunnel +couplings T 2 +0 . The upper line corresponds T 2 +0 = 2.635×10−4 +and the lower line to T 2 +0 = 5.6×10−4. These boundary values +have been determined from error margins of fits at 3 T. +low for direct exchange as a result of finite overlap of +the atomic d orbitals. Mn atoms are indeed likely cou- +pled antiferromagnetically when interacting via direct ex- +change [31]. This would lead to a singlet ground state +|Stot = 0, M = 0⟩. +Magnetic excitations must then in- +volve a spin-changing transition such as the singlet-triplet +transition and the excitation energy directly reflects the +exchange coupling JD (for details, see below). To further +corroborate the antiferromagnetic nature of the exchange +coupling, we apply an external magnetic field of 3 T to +the dimer. The inelastic steps become slightly broader +(Fig. 2k). This is consistent with a singlet-triplet transi- + +3 +2a +5.5Å +1a +i)3.0 +2.8 +2.6 +2.4 +2.2 +-15 -10 -5 +0 +5 +10 +15 +bias voltage (mV) +a) +b) +c) +d) +e) +f) +g) +h) +0T +3T +S=0 +S=1 +Energy +B field +gμBB +~J D +|S,M> +|1,0> +|1,+1> +|1,-1> +|0,0> +j) +k) +4.0 +3.5 +3.0 +-10 +-5 +0 +5 +10 +bias voltage (mV) +5.1Å +3a +5.6Å +4.2 +4.0 +3.8 +3.6 +-10 +-5 +0 +5 +10 +bias voltage (mV) +4.0 +3.0 +2.0 +20 +-10 +0 +10 +20 +bias voltage (mV) +5.5Å +dI/dV (G ) x 10 +0 +-3 +dI/dV (G ) x 10 +0 +-3 +dI/dV (G ) x 10 +0 +-3 +dI/dV (G ) x 10 +0 +-3 +Figure 2. Various dimer structures. a), d), g) Structure mod- +els and b), e), f) corresponding STM topographies of Mn +dimers on MoS2with various interatom spacings. Yellow, gray, +and purple spheres represent S, Mo, and Mn, respectively. +The Mn atoms, sitting in MoS2 hollow sites, are separated +by three lattice sites (panels a,b), two lattice sites (panels +d,e), and one lattice site (panels g,h). c), f), i) dI/dV spectra +recorded at the locations indicated by the black crosses in +(b,e,h). The spectra drastically depend on the dimer separa- +tion, exhibiting a Kondo resonance (panel c), a split Kondo +resonance (panel f), and a step-like increase in the differen- +tial conductance (panel i). j) Energy-level diagram of the ob- +served spin excitation in (i). The degeneracy of the M = 0, ±1 +sublevels of the excited state is lifted by a magnetic field. k) +dI/dV spectra of a dimer with Mn in nearest-neighbor sites +with and without magnetic field and respective fits with sym- +metric step functions (dashed). For our measurement condi- +tions at 1.1 K, a magnetic field of 3 T is not sufficient to fully +resolve the splitting, but the excitation appears broadened by +110 µV. STM topographies were recorded at 100 mV, 20 pA, +the setpoint of the dI/dV spectra was 10 mV, 3 nA (c,f), 15 +mV, 3 nA (i), and 20 mV, 3 nA (k). +tion to |Stot = 1, M⟩, where the excited state is Zeeman +split in the magnetic field, but the sublevels are not in- +dividually resolved at the experimental temperature of +1.1 K (Fig. 2j). +Importantly, we do not observe addi- +tional excitations around zero bias, which would indicate +a higher-spin ground state as favored by ferromagnetic +coupling of the atoms. +As discussed above, the moir´e superstructure weakly +affects the height of the Kondo resonance of individual +atoms reflecting the modulation of the dimensionless ex- +change coupling Jν0. As the dimer is in a singlet ground +state, one may naively expect that the moir´e structure +does not influence the inelastic excitations. Remarkably, +we observe strong variations of the singlet–triplet tran- +sition by several meV as the dimer’s adsorption site is +varied with respect to the moir´e lattice (Fig. 3). Dimers +located on maxima of the moir´e structure (Fig. 3a,e) +exhibit the smallest excitation energy (7.5 meV), while +those on minima (Fig. 3d,e) show the largest excitation +energy (10 meV). +To understand these variations, we compute the shift +of the singlet-triplet splitting ∆ due to the hybridiza- +tion of the adatom d orbitals with the substrate and +relate it to the exchange coupling between the adatom +and conduction-electron spins. As we do not observe in- +elastic excitations on single adatoms indicating negligible +single-ion anisotropy, we assume that the Mn atoms are +only weakly perturbed by the surrounding and retain the +half-filled d-shell when placed on the substrate. Accord- +ing to Hund’s rule, this implies a high-spin configuration +with S = 5/2 and suggests that spin-orbit coupling will +be weak, so that the inter-adatom exchange can be mod- +eled by isotropic Heisenberg exchange, Hex = JDSA ·SB. +Here, SA,B denotes the spins of adatom A,B. +In the absence of hybridization with the substrate, +states with magnitude Stot of the total spin Stot = +SA + SB will have direct exchange energy +Eex(SA, SB; Stot) = JD +2 [Stot(Stot +1)− +� +j∈{A,B} +Sj(Sj +1)]. +(1) +Evaluating the singlet-triplet splitting for SA, SB = +5 +2, +we find +∆ = Eex(5 +2, 5 +2; 1) − Eex(5 +2, 5 +2; 0) = JD. +(2) +This splitting is reduced by the hybridization of the +adatom d orbitals with the conduction electrons. In gen- +eral, the d orbitals hybridize with 2S = 5 (symmetry- +adapted) conduction-electron channels [32]. +Since the +substrate breaks rotational symmetry, the strength of +hybridization Vm depends on the channel m. +The en- +ergies of the singlet and triplet states are then shifted by +virtual excitation processes, in which a d electron hops +into the substrate or a substrate electron hops into the +d shell. Physically, these processes reduce the effective +adatom spin, which results in a smaller direct exchange. +A detailed calculation in second-order perturbation the- +ory (see section S1 in SM for details [29]) gives a renor- +malized singlet-triplet splitting +∆ = JD +� +1 − 2 +5 +� +m +ν0|Vm|2 +� 1 +|ϵd| + +1 +ϵd + U +�� +. +(3) +Here, −ϵd > 0 is the energy to remove an electron from +the filled d-shell and ϵd+U the energy to add an electron. +The factor 2 in front of the sum over channels accounts + +84 +1nm +1nm +a) +b) +c) +d) +e) ++ ++ ++ ++ +1.1 +1.0 +0.9 +0.8 +0.7 +0.6 +normalized dI/dV +-15 +-10 +-5 +0 +5 +10 +15 +bias voltage (mV) +1nm +1nm +Figure 3. +Antiferromagnetically coupled Mn dimers (oval +structures), which are identical apart from their location rela- +tive to the moir´e structure. a-d) STM topographies of dimers +(a) on the maximum, (b) close to the maximum, (c) further +from the maximum, and (d) at the minimum of the moir´e +structure. e) dI/dV spectra acquired on the dimers shown in +(a-d), with colors matched to the crosses in (a-d). Topogra- +phies recorded at 100 mV, 20 pA, setpoints of the recorded +spectra were 20 mV, 1 nA (b), 20 mV, 3 nA (a) and 15 mV, +3 nA (c), (d). Spectra are normalized for clarity. +for the fact that both adatoms can be excited. The factor +1/5 results from angular-momentum coupling. +The singlet-triplet spacing can be directly related to +experimentally measurable quantities by noting that the +exchange coupling between the conduction electrons and +the spin-S adatom is given by [32] +Jm = ν0|Vm|2 +2S +� 1 +|ϵd| + +1 +ϵd + U +� +, +(4) +so that we can express the singlet-triplet splitting of the +S = 5 +2 Mn dimer as +∆ = JD +� +1 − 2 +� +m +ν0Jm +� +. +(5) +For weak coupling (ν0Jm ≪ 1), the relative change +in the singlet-triplet spacing between minimum (∆min) +and maximum (∆max) is approximately equal to δ ≃ +(∆min − ∆max)/JD. +Equation (5) relates this directly +to the corresponding change in the sum of the dimen- +sionless exchange couplings � +m ν0Jm to the substrate. +Since information on the exchange couplings ν0Jm can +be extracted from the Kondo data on a single adatom, +applying this relation to the data in Fig. 3e gives direct +information on the number of conduction-electron chan- +nels coupled to the adatom spins. +For analyzing the number of participating channels, we +first assume that the adatom spin is coupled to a single +channel. With this assumption, we can extract the di- +mensionless adatom-substrate exchange coupling ν0J of +the single channel by fitting the Kondo peak of the iso- +lated atoms using a program based on Ref. [27]. Showcas- +ing the variation between extremal positions with respect +to the moir´e pattern, we extracted a value of ν0J = 0.049 +for the adatom on the moir´e minimum and ν0J = 0.080 +for an atom on the maximum from fitting the Kondo +data in Fig. 1b. Equation 5 (specified to a single chan- +nel) then predicts a relative change δ of the singlet-triplet +splitting from minimum to maximum by ≈ 6%. This is +clearly smaller than the experimentally observed varia- +tion of ≈ 25% (Fig. 3e). We have extracted ν0J for sev- +eral dozen isolated atoms in various positions across the +moir´e structure. In all cases, ν0J decreases with increas- +ing distance from the maxima of the moir´e pattern (Fig. +1d). The variations of ν0J for similar distances from the +moir´e maxima partially derive from the lack of rotational +symmetry, so that the distance to the moir´e maximum +does not uniquely specify the adsorption site. Moreover, +the fitting procedure contains some uncertainty, as the +strength of tunneling T 2 +0 and ν0J both affect the peak +height. We first determined T 2 +0 from a spectrum of an +atom subject to a magnetic field (for which the uncer- +tainty is reduced due to the additional magnetic-field in- +duced structure). +We then fitted all spectra with the +extracted value of T 2 +0 . To indicate the error margins of +the fits, we reran all fits taking extremal values of T 2 +0 +consistent with the B-field data with sufficient accuracy. +The black dashed line in Fig. 1d shows a linear guide- +to-the-eye for the best fit results, while the red dashed +lines indicate the scalings obtained when using the ex- +tremal values of T 2 +0 . We find that with the assumption +of a single channel, only the largest variation in ν0J (up- +per red dashed line) would explain the variation of the +singlet-triplet splitting. +We can also apply Eq. (5), when assuming that all five +channels are equally coupled. Since each channel renor- +malizes independently, the value of ν0Jm for any m is +equal to that extracted with the single-channel assump- +tion. (In the leading-logarithm approximation underly- +ing the Kondo fits, the number of channels enters only +as an overall prefactor, which can be absorbed into T 2 +0 .) +With this assumption, Eq. (5) predicts a variation in the +singlet-triplet spacing, which is larger by a factor of five +than in the single-channel case. We then find that the +observed variation in the singlet-triplet spacing across +the moir´e structure (Fig. 3e) would only be consistent +with the opposite extreme case (lower red dashed line +in Fig. 1d). Thus, while the uncertainties of the fitting +procedure preclude a fully quantitative analysis, our re- +sults strongly suggest that the Mn atoms have substan- +tial coupling to several conduction-electron channels in +the Au(111) substrate. +In conclusion, we varied the adatom-substrate ex- +change of Mn monomers and dimers by exploiting the + +:5 +moir´e pattern of a MoS2 layer on Au(111). The moir´e +structure imprints density-of-states modulations, which +in turn affect the Kondo resonance of the monomer and +the singlet-triplet splitting of antiferromagnetically cou- +pled dimers. Relating these variations through a theo- +retical analysis, we find evidence that the adatoms are +coupled to multiple conduction-electron channels. This +constrasts with the commonly made assumption that +adatoms couple only to a single channel of a metallic +substrate. Our results show that this assumption is vi- +olated in the perturbative limit. +For the fully devel- +oped Kondo effect, relatively small differences in ν0Jm +between channels result in large differences in the asso- +ciated Kondo temperatures TK,m ∝ e−1/ν0Jm. Then, the +single-channel approximation can still be adequate pro- +vided that only the first stage of the resulting multistage +Kondo screening is accessible in experiment. +Interest- +ingly, coupling to multiple conduction-electron channels +has previously been invoked to explain the appearance of +multiple Yu-Shiba-Rusinov states induced by magnetic +adatoms on superconductors [33, 34]. Our results em- +phasize that adatom dimers realize a rich two-impurity +problem. While theoretical studies have focused on spin- +1 +2 impurities, adatom dimers typically have higher spins +and couple to multiple conduction-electron channels. +We acknowledge financial support by the Deutsche +Forschungsgemeinschaft (DFG, German Research Foun- +dation) through project numbers 328545488 (CRC 227, +project B05) and 277101999 (CRC 183, project C02 and +a Mercator professorship), as well as by the National Sci- +ence Foundation through grant NSF DMR-2002275. +[1] V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, +and N. S. Wingreen, Tunneling into a single magnetic +atom: Spectroscopic evidence of the kondo resonance, Sci- +ence 280, 567 (1998). +[2] J. Li, W.-D. Schneider, R. Berndt, and B. Delley, Kondo +scattering observed at a single magnetic impurity, Phys. +Rev. Lett. 80, 2893 (1998). +[3] Y.-H. Zhang, S. Kahle, T. Herden, C. Stroh, M. Mayor, +U. Schlickum, M. Ternes, P. Wahl, and K. Kern, Temper- +ature and magnetic field dependence of a Kondo system +in the weak coupling regime, Nature Commun. 4, 2110 +(2013). +[4] A. J. Heinrich, J. A. Gupta, C. P. Lutz, and D. M. Ei- +gler, Single-atom spin-flip spectroscopy, Science 306, 466 +(2004). +[5] M. A. Ruderman and C. Kittel, Indirect Exchange Cou- +pling of Nuclear Magnetic Moments by Conduction Elec- +trons, Phys. Rev. 96, 99 (1954). +[6] T. Kasuya, A Theory of Metallic Ferro- and Antiferro- +magnetism on Zener’s Model, Prog. Theor. Phys. 16, 45 +(1956). +[7] K. Yosida, Magnetic Properties of Cu-Mn Alloys, Phys. +Rev. 106, 893 (1957). +[8] I. Dzyaloshinsky, A thermodynamic theory of weak ferro- +magnetism of antiferromagnetics, J. Phys. Chem. Solids +4, 241 (1958). +[9] T. Moriya, Anisotropic Superexchange Interaction and +Weak Ferromagnetism, Phys. Rev. 120, 91 (1960). +[10] P. Wahl, P. Simon, L. Diekh¨oner, V. S. Stepanyuk, +P. Bruno, M. A. Schneider, and K. Kern, Exchange inter- +action between single magnetic adatoms, Phys. Rev. Lett. +98, 056601 (2007). +[11] F. Meier, L. Zhou, J. Wiebe, and R. Wiesendanger, Re- +vealing Magnetic Interactions from Single-Atom Magneti- +zation Curves, Science 320, 82 (2008). +[12] A. +Khajetoorians, +M. +Steinbrecher, +M. +Ternes, +M. +Bouhassoune, +M. +dos +Santos +Dias, +S. +Lounis, +J. Wiebe, and R. Wiesendanger, Tailoring the chiral +magnetic +interaction +between +two +individual +atoms, +Nature Commun. 7, 10620 (2016). +[13] C. Jayaprakash, +H. R. Krishna-murthy, and J. W. +Wilkins, Two-Impurity Kondo Problem, Phys. Rev. Lett. +47, 737 (1981). +[14] B. A. Jones, C. M. Varma, and J. W. Wilkins, Low- +Temperature Properties of the Two-Impurity Kondo +Hamiltonian, Phys. Rev. Lett. 61, 125 (1988). +[15] N. Tsukahara, S. Shiraki, S. Itou, N. Ohta, N. Takagi, +and M. Kawai, Evolution of Kondo Resonance from a Sin- +gle Impurity Molecule to the Two-Dimensional Lattice, +Phys. Rev. Lett. 106, 187201 (2011). +[16] H. Pr¨user, +P. E. Dargel, +M. Bouhassoune, +R. G. +Ulbrich, T. Pruschke, S. Lounis, and M. Wenderoth, +Interplay between the Kondo effect and the Ruder- +man–Kittel–Kasuya–Yosida interaction, Nature Commun. +5, 5417 (2014). +[17] A. +Spinelli, +M. +Gerrits, +R. +Toskovic, +B. +Bryant, +M. Ternes, and A. F. Otte, Exploring the phase diagram +of the two-impurity Kondo problem, Nature Commun. 6, +10046 (2015). +[18] M. Moro Lagares, R. Korytar, M. Piantek, R. Robles, +N. Lorente, J. Pascual, M. Ibarra, and D. Serrate, Real +space manifestations of coherent screening in atomic scale +Kondo lattices, Nature Commun. 10, 2211 (2019). +[19] A. A. Khajetoorians, D. Wegner, A. F. Otte, and +I. Swart, Creating designer quantum states of matter +atom-by-atom, Nature Rev. Phys. 1, 703 (2019). +[20] J. C. Oberg, M. R. Calvo, F. Delgado, M. Moro-Lagares, +D. Serrate, J. Fernandez-Rossier, and C. F. Hirjibehedin, +Control of single-spin magnetic anisotropy by exchange +coupling, Nat. Nanotech. 9, 64 (2014). +[21] J. Ren, H. Guo, J. Pan, Y. Y. Zhang, X. Wu, H.-G. +Luo, S. Du, S. T. Pantelides, and H.-J. Gao, Kondo effect +of cobalt adatoms on a graphene monolayer controlled by +substrate-induced ripples, Nano Lett. 14, 4011 (2014). +[22] P. +Jacobson, +T. +Herden, +M. +Muenks, +G. +Laskin, +O. Brovko, V. Stepanyuk, M. Ternes, and K. Kern, Quan- +tum engineering of spin and anisotropy in magnetic molec- +ular junctions, Nature Commun. 6, 8536 (2015). +[23] S. Trishin, C. Lotze, N. Bogdanoff, F. von Oppen, and +K. J. Franke, Moir´e Tuning of Spin Excitations: Individual +Fe Atoms on MoS2/Au(111), Phys. Rev. Lett. 127, 236801 +(2021). +[24] S. S. Grønborg, S. Ulstrup, M. Bianchi, M. Dendzik, +C. E. Sanders, J. V. Lauritsen, P. Hofmann, and J. A. +Miwa, Synthesis of epitaxial single-layer MoS2 on Au +(111), Langmuir 31, 9700 (2015). +[25] N. Krane, C. Lotze, and K. J. Franke, Moir´e structure of +MoS2 on Au(111): Local structural and electronic prop- + +6 +erties, Surf. Sci. 678, 136 (2018). +[26] H. Bana, E. Travaglia, L. Bignardi, P. Lacovig, C. E. +Sanders, M. Dendzik, M. Michiardi, M. Bianchi, D. Lizzit, +F. Presel, D. D. Angelis, N. Apostol, P. K. Das, J. Fu- +jii, I. Vobornik, R. Larciprete, A. Baraldi, P. Hofmann, +and S. Lizzit, Epitaxial growth of single-orientation high- +quality MoS2 monolayers, 2D Materials 5, 035012 (2018). +[27] M. Ternes, Spin excitations and correlations in scanning +tunneling spectroscopy, New J. Phys. 17, 063016 (2015). +[28] Y. Wang, B. Wang, R. Huang, B. Gao, F. Kong, +and Q. Zhang, First-principles study of transition-metal +atoms adsorption on MoS2 monolayer, Physica E: Low- +dimensional Systems and Nanostructures 63, 276 (2014). +[29] Supporting Information. +[30] C. F. Hirjibehedin, C. P. Lutz, and A. J. Heinrich, Spin +coupling in engineered atomic structures, Science 312, +1021 (2006). +[31] Y. Mokrousov, G. Bihlmayer, S. Bl¨ugel, and S. Heinze, +Magnetic order and exchange interactions in monoatomic +3d transition-metal chains, Phys. Rev. B 75, 104413 +(2007). +[32] J. R. Schrieffer, The Kondo Effect − The Link Be- +tween Magnetic and Nonmagnetic Impurities in Metals?, +J. Appl. Phys. 38, 1143 (1967). +[33] M. Ruby, Y. Peng, F. von Oppen, B. W. Heinrich, and +K. J. Franke, Orbital Picture of Yu-Shiba-Rusinov Multi- +plets, Phys. Rev. Lett. 117, 186801 (2016). +[34] D.-J. Choi, C. Rubio-Verd´u, J. De Bruijckere, M. M. +Ugeda, N. Lorente, and J. I. Pascual, Mapping the orbital +structure of impurity bound states in a superconductor, +Nature Commun. 8, 15175 (2017). + +7 +SUPPLEMENTARY MATERIAL +I. +THEORETICAL CONSIDERATIONS +We provide details concerning the theoretical considerations in the main text. We assume that Mn retains its half- +filled d shell in the presence of the weak coupling to the substrate. The uncoupled state of Mn is thus fully rotationally +symmetric and coupled to five conduction-electron channels. As the rotational symmetry is broken by the coupling to +the substrate, their hybridization Vm with the various conduction-electron channels will be different. In the following, +we compute the singlet-triplet splitting perturbatively, focusing on one channel (m = 0 for definiteness). The general +result is obtained by adding the independent corrections for all five channels. +A. +Spin states of monomer +First consider the spin states of a single Mn adatom. We can generate the spin states | 5 +2, Sz⟩ by applying the spin +lowering operator S− = �2 +m=−2 c† +m,↓cm,↑ to +|5 +2, 5 +2⟩ = +� +m +c† +m,↑|vac⟩. +(1) +Then, we have +|5 +2, 5 +2⟩ = | ↑↑↑↑↑⟩ +|5 +2, 3 +2⟩ = +� +1 +5 +� +|states with one flipped spin⟩ +|5 +2, 1 +2⟩ = +� +1 +10 +� +|states with two flipped spins⟩ +|5 +2, −1 +2⟩ = +� +1 +10 +� +|states with three flipped spins⟩ +|5 +2, −3 +2⟩ = +� +1 +5 +� +|states with four flipped spins⟩ +|5 +2, −5 +2⟩ = | ↓↓↓↓↓⟩. +(2) +Similarly, we can derive the states with one less electron, say in the m = 0 state. One finds +|2, 2⟩ = | ↑↑↑↑⟩ +|2, 1⟩ = +� +1 +4 +� +|states with one flipped spin⟩ +|2, 0⟩ = +� +1 +6 +� +|states with two flipped spins⟩ +|2, −1⟩ = +� +1 +4 +� +|states with three flipped spins⟩ +|2, −2⟩ = | ↓↓↓↓⟩. +(3) + +8 +Applying c0,↑ to the S = 5 +2 states, one finds +c0,↑|5 +2, 5 +2⟩ = |2, 2⟩ +c0,↑|5 +2, 3 +2⟩ = +� +4 +5|2, 1⟩ +c0,↑|5 +2, 1 +2⟩ = +� +6 +10|2, 0⟩ +c0,↑|5 +2, −1 +2⟩ = +� +4 +10|2, −1⟩ +c0,↑|5 +2, −3 +2⟩ = +� +1 +5|2, −2⟩ +c0,↑|5 +2, −5 +2⟩ = 0. +(4) +Applying c0,↓ to the S = 5 +2 states, one finds +c0,↓|5 +2, 5 +2⟩ = 0 +c0,↓|5 +2, 3 +2⟩ = +� +1 +5|2, 2⟩ +c0,↓|5 +2, 1 +2⟩ = +� +4 +10|2, 1⟩ +c0,↓|5 +2, −1 +2⟩ = +� +6 +10|2, 0⟩ +c0,↓|5 +2, −3 +2⟩ = +� +4 +5|2, −1⟩ +c0,↓|5 +2, −5 +2⟩ = |2, −2⟩. +(5) +B. +Singlet state of dimer – tunneling out +The spin state of the dimer can either be expanded in product states |S1, M1⟩ ⊗ |S2, M2⟩ of the two adatoms, or +according to magnitude Stot and projection Mtot of the total angular momentum Stot = S1 +S2 as |S1, S2; Stot, Mtot⟩. +First consider the singlet state of the dimer. Using Clebsch-Gordan coefficients, we can expand it into product states +as +|5 +2, 5 +2; 0, 0⟩ = +� +1 +6 +� +|5 +2, 5 +2⟩ ⊗ |5 +2, −5 +2⟩ − |5 +2, 3 +2⟩ ⊗ |5 +2, −3 +2⟩ + |5 +2, 1 +2⟩ ⊗ |5 +2, −1 +2⟩ +−|5 +2, −1 +2⟩ ⊗ |5 +2, 1 +2⟩ + |5 +2, −3 +2⟩ ⊗ |5 +2, 3 +2⟩ − |5 +2, −5 +2⟩ ⊗ |5 +2, 5 +2⟩ +� +. +(6) +Applying cL,0,↑ for the left adatom gives +cL,0,↑|5 +2, 5 +2; 0, 0⟩ = +� +1 +6 +� +|2, 2⟩ ⊗ |5 +2, −5 +2⟩ − +� +4 +5|2, 1⟩ ⊗ |5 +2, −3 +2⟩ + +� +6 +10|2, 0⟩ ⊗ |5 +2, −1 +2⟩ +− +� +4 +10|2, −1⟩ ⊗ |5 +2, 1 +2⟩ + +� +1 +5|2, −2⟩ ⊗ |5 +2, 3 +2⟩ +� +(7) +Similarly, we have +cL,0,↓|5 +2, 5 +2; 0, 0⟩ = +� +1 +6 +� +− +� +1 +5|2, 2⟩ ⊗ |5 +2, −3 +2⟩ + +� +4 +10|2, 1⟩ ⊗ |5 +2, −1 +2⟩ − +� +6 +10|2, 0⟩ ⊗ |5 +2, 1 +2⟩ ++ +� +4 +5|2, −1⟩ ⊗ |5 +2, 3 +2⟩ − |2, −2⟩ ⊗ |5 +2, 5 +2⟩ +� +(8) + +9 +We can compare these states to +|2, 5 +2; 1 +2, 1 +2⟩ = +� +1 +15|2, 2⟩ ⊗ |5 +2, −3 +2⟩ − +� +2 +15|2, 1⟩ ⊗ |5 +2, −1 +2⟩ + +� +1 +5|2, 0⟩ ⊗ |5 +2, 1 +2⟩ +− +� +4 +15|2, −1⟩ ⊗ |5 +2, 3 +2⟩ + +� +1 +3|2, −2⟩ ⊗ |5 +2, 5 +2⟩ +(9) +|2, 5 +2; 1 +2, −1 +2⟩ = +� +1 +3|2, 2⟩ ⊗ |5 +2, −5 +2⟩ − +� +4 +15|2, 1⟩ ⊗ |5 +2, −3 +2⟩ + +� +1 +5|2, 0⟩ ⊗ |5 +2, −1 +2⟩ +− +� +2 +15|2, −1⟩ ⊗ |5 +2, 1 +2⟩ + +� +1 +15|2, −2⟩ ⊗ |5 +2, 3 +2⟩, +(10) +so that we identify +cL,0,↑|5 +2, 5 +2; 0, 0⟩ = − +� +1 +2|2, 5 +2; 1 +2, −1 +2⟩ +; +cL,0,↓|5 +2, 5 +2; 0, 0⟩ = +� +1 +2|2, 5 +2; 1 +2, 1 +2⟩. +(11) +C. +Singlet state of dimer – tunneling in +Now consider tunneling in of an electron. We can follow the same steps. Now, the m = 0 state of one of the atoms +will be doubly occupied rather than empty, but this is also a zero-spin state. Thus, all the Clebsch-Gordan coefficients +remain the same and one finds +c† +L,0,↑|5 +2, 5 +2; 0, 0⟩ = +� +1 +2|2, 5 +2; 1 +2, 1 +2⟩ +; +c† +L,0,↓|5 +2, 5 +2; 0, 0⟩ = − +� +1 +2|2, 5 +2; 1 +2, −1 +2⟩. +(12) +D. +Triplet state of dimer – tunneling out +We expand the triplet state of the dimer into product states of the two monomers. Due to rotational invariance, +we can consider the M = 1 state without loss of generality, +|5 +2, 5 +2; 1, 1⟩ = +� +1 +7|5 +2, 5 +2⟩ ⊗ |5 +2, −3 +2⟩ − +� +8 +35|5 +2, 3 +2⟩ ⊗ |5 +2, −1 +2⟩ + +� +9 +35|5 +2, 1 +2⟩ ⊗ |5 +2, 1 +2⟩ +− +� +8 +35|5 +2, −1 +2⟩ ⊗ |5 +2, 3 +2⟩ + +� +1 +7|5 +2, −3 +2⟩ ⊗ |5 +2, 5 +2⟩. +(13) +Applying cL,0,↑ for the left adatom gives +cL,0,↑|5 +2, 5 +2; 1, 1⟩ = +� +1 +7|2, 2⟩ ⊗ |5 +2, −3 +2⟩ − +� +8 +35 +� +4 +5|2, 1⟩ ⊗ |5 +2, −1 +2⟩ + +� +9 +35 +� +6 +10|2, 0⟩ ⊗ |5 +2, 1 +2⟩ +− +� +8 +35 +� +4 +10|2, −1⟩ ⊗ |5 +2, 3 +2⟩ + +� +1 +7 +� +1 +5|2, −2⟩ ⊗ |5 +2, 5 +2⟩. +(14) +Similarly, +cL,0,↓|5 +2, 5 +2; 1, 1⟩ = − +� +8 +35 +� +1 +5|2, 2⟩ ⊗ |5 +2, −1 +2⟩ + +� +9 +35 +� +4 +10|2, 1⟩ ⊗ |5 +2, 1 +2⟩ − +� +8 +35 +� +6 +10|2, 0⟩ ⊗ |5 +2, 3 +2⟩ ++ +� +1 +7 +� +4 +5|2, −1⟩ ⊗ |5 +2, 5 +2⟩. +(15) + +10 +We can compare this to +|2, 5 +2; 1 +2, 1 +2⟩ = +� +1 +15|2, 2⟩ ⊗ |5 +2, −3 +2⟩ − +� +2 +15|2, 1⟩ ⊗ |5 +2, −1 +2⟩ + +� +1 +5|2, 0⟩ ⊗ |5 +2, 1 +2⟩ +− +� +4 +15|2, −1⟩ ⊗ |5 +2, 3 +2⟩ + +� +1 +3|2, −2⟩ ⊗ |5 +2, 5 +2⟩ +|2, 5 +2; 3 +2, 1 +2⟩ = +� +32 +105|2, 2⟩ ⊗ |5 +2, −3 +2⟩ − +� +5 +21|2, 1⟩ ⊗ |5 +2, −1 +2⟩ + +� +2 +35|2, 0⟩ ⊗ |5 +2, 1 +2⟩ ++ +� +2 +105|2, −1⟩ ⊗ |5 +2, 3 +2⟩ − +� +8 +21|2, −2⟩ ⊗ |5 +2, 5 +2⟩ +|2, 5 +2; 3 +2, 3 +2⟩ = +� +4 +35|2, 2⟩ ⊗ |5 +2, −1 +2⟩ − +� +9 +35|2, 1⟩ ⊗ |5 +2, 1 +2⟩ + +� +12 +35|2, 0⟩ ⊗ |5 +2, 3 +2⟩ − +� +2 +7|2, −1⟩ ⊗ |5 +2, 5 +2⟩, +(16) +so that we identify +cL,0,↑|5 +2, 5 +2; 1, 1⟩ = +� +7 +15|2, 5 +2; 1 +2, 1 +2⟩ + +� +2 +15|2, 5 +2; 3 +2, 1 +2⟩ +; +cL,0,↓|5 +2, 5 +2; 1, 1⟩ = − +� +2 +5|2, 5 +2; 3 +2, 3 +2⟩ +(17) +E. +Triplet state of dimer – tunneling in +This follows again by analogy with the tunneling-out terms, so that +c† +L,0,↓|5 +2, 5 +2; 1, 1⟩ = +� +7 +15|2, 5 +2; 1 +2, 1 +2⟩ + +� +2 +15|2, 5 +2; 3 +2, 1 +2⟩ +; +c† +L,0,↑|5 +2, 5 +2; 1, 1⟩ = − +� +2 +5|2, 5 +2; 3 +2, 3 +2⟩ +(18) +F. +Singlet-triplet splitting +In the absence of coupling to the substrate, the impurity spins S1 and S2 of the two Mn adatoms are subject to +antiferromagnetic exchange coupling of the dimer, Hex = JDS1 · S2 with JD > 0. Depending on the total spin Stot, +the coupling energy is +Eex(S1, S2; Stot) = JD +2 [Stot(Stot + 1) − S1(S1 + 1) − S2(S2 + 1)]. +(19) +For Mn adatoms with S1 = S2 = 5 +2, the splitting between the triplet (S = 1) excited state and the singlet (S = 0) +ground state is equal to ∆E(0) +st = JD. +The singlet-triplet splitting is renormalized due the coupling of the adatoms to the substrate electrons. Tunneling +of electrons between adatom d orbitals and substrate couples the singlet to the intermediate states |2, 5 +2; 1 +2, ± 1 +2⟩. The +singlet state has exchange energy +Eex(5 +2, 5 +2; 0) = −35JD +4 +, +(20) +while the intermediate states have exchange energy +Eex(2, 5 +2; 1 +2) = −7JD. +(21) +In the absense of hybridization, we can then write the energy of of singlet state as +E(0) +s += 2EMn + EFS + Eex(5 +2, 5 +2; 0), +(22) +where EMn denotes the energy of the uncoupled Mn adatom and EFS the energy of the unperturbed Fermi sea. +Similarly, the intermediate state has energy +E(0) +s,out = 2EMn + |ϵd| + EFS + ξk + Eex(2, 5 +2; 1 +2) +(23) + +11 +for tunneling out and +E(0) +s,in = 2EMn + ϵd + U + EFS − ξk + Eex(2, 5 +2; 1 +2) +(24) +for tunneling in. Here, −ϵd > 0 is the energy to remove an electron from the filled d-shell and ϵd + U the energy to +add an electron. We can then compute the perturbative shift of the singlet state as +∆Es = 2|V0|2 +� +� +� +� +ξk>0 +1 +[2EMn + EFS + Eex( 5 +2, 5 +2; 0)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 +2; 1 +2)] ++ +� +ξk<0 +1 +[2EMn + EFS + Eex( 5 +2, 5 +2; 0)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 +2; 1 +2)] +� +� +� . +(25) +Note that the two intermediate states |2, 5 +2; 1 +2, ± 1 +2⟩ give the same contributions, each with a factor 1/2 due to the +matrix elements. Note also that the overall factor of two appears, since electrons can tunnel from either Mn adatom +of the dimer. We can then simplify +∆Es = −2ν0|V0|2 +ˆ ∞ +0 +dξ +� +1 +|ϵd| + ξ + Eex(2, 5 +2; 1 +2) − Eex( 5 +2, 5 +2; 0) + +1 +ϵd + U + ξ + Eex(2, 5 +2; 1 +2) − Eex( 5 +2, 5 +2; 0) +� +(26) +or +∆Es = −2ν0|V0|2 +ˆ ∞ +0 +dξ +� +1 +|ϵd| + ξ + 7 +4JD ++ +1 +ϵd + U + ξ + 7 +4JD +� +. +(27) +Here, we introduced the density of states ν0. Assuming the dimer coupling JD to be small compared to the atomic- +physics scales |ϵd| and U, we find +∆Es = const + 7JD +4 2ν0|V0|2 +� 1 +|ϵd| + +1 +ϵd + U +� +, +(28) +where the constant is a contribution that is independent of the exchange couplings and that cancels out in the +singlet-triplet spacing against a similar contribution to the shift of the triplet state. +Now consider the shift of the triplet state. There are intermediate states with different energies, which have to be +incorporated with the appropriate matrix elements. This yields +∆Et = 2|V0|2 +� +� +� +� +ξk>0 +7 +15 +[2EMn + EFS + Eex( 5 +2, 5 +2; 1)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 +2; 1 +2)] ++ +� +ξk<0 +7 +15 +[2EMn + EFS + Eex( 5 +2, 5 +2; 1)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 +2; 1 +2)] ++ +� +ξk>0 +8 +15 +[2EMn + EFS + Eex( 5 +2, 5 +2; 1)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 +2; 3 +2)] ++ +� +ξk<0 +8 +15 +[2EMn + EFS + Eex( 5 +2, 5 +2; 1)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 +2; 3 +2)] +� +� +� . +(29) +Using the energies +Eex(5 +2, 5 +2; 1) = −31JD +4 +(30) +Eex(2, 5 +2; 1 +2) = −7JD +(31) +Eex(2, 5 +2; 3 +2) = −11JD +2 +, +(32) +we find, by the same steps as for the singlet shift, +∆Et = const + +� 7 +15 +3JD +4 ++ 8 +15 +9JD +4 +� +2ν0|V0|2 +� 1 +|ϵd| + +1 +ϵd + U +� += const + 31JD +20 2ν0|V0|2 +� 1 +|ϵd| + +1 +ϵd + U +� +. +(33) + +12 +Combining results, we obtain the singlet-triplet splitting +∆ = JD + ∆Et − ∆Es = JD +� +1 − 1 +52ν0|V0|2 +� 1 +|ϵd| + +1 +ϵd + U +�� +. +(34) +Schrieffer [1] has derived the sd exchange coupling J between adatom spins (magnitude S) and conduction electrons +and finds +J = |V0|2 +2S +� 1 +|ϵd| + +1 +ϵd + U +� +(35) +(assuming dominant coupling to a single channel). Thus, we can express the renormalized singlet-triplet splitting as +∆ = JD + ∆Et − ∆Es = JD(1 − 2ν0J). +(36) +Accounting for the coupling of the adatom to all five conduction electron channels m, this result generalizes to +∆ = JD(1 − 2 +� +m +ν0Jm). +(37) +This equation is quoted in the main text. +II. +ADDITIONAL EXPERIMENTAL DATA +A. +Adsorption structure of Mn atoms on MoS2 +Figure 1a shows an overview topography image of a monolayer-island of MoS2 decorated with a large number of +Mn atoms. A close-up view confirms that the individual atoms appear as round protrusions throughout a bias voltage +range of -1 to 1 V (Fig. 1b). Owing to the convolution with the tip shape, the atoms appear with a large width +(∼ 0.9 nm), impeding the determination of the exact adsorption site on the atomic lattice constant of MoS2. The +similarity of apparent heights and spectroscopic signatures suggests that all atoms adsorb in equivalent lattice sites. +This is in agreement the observation of unique adsorption sites of Fe on MoS2 [2]. DFT calculations further suggest +hollow sites to be the energetically most favorable positions [3, 4]. Occasionally, we find elongated protrusions (see +also lineprofiles in Fig. 1c), which we ascribe to dimers. +10 nm +3 nm +a) +b) +c) +300 +200 +100 +0 +apparent height (pm) +3.0 +2.5 +2.0 +1.5 +1.0 +0.5 +0.0 +distance (nm) +Supplementary Figure 1. a) Large-scale STM image of a monolayer-island of MoS2 on Au(111) after adsorption of Mn atoms +at low temperature. Recorded at 1 V and 100 pA. b) Close-up view showing individual atoms as round protrusions and some +elongated structures most probably being Mn dimers. Some point defects can be observed in the MoS2 layer. Recorded at 100 +mV and 20 pA. c) Height profiles along the black and red lines shown in b. + +13 +B. +Manipulation of Mn atoms +We mainly investigated Mn dimers statistically distributed over the surface. In rare cases, we were able to manip- +ulate the Mn atoms in a controlled manner. Fig. 2 shows an example of consecutive manipulation events and the +dI/dV spectra recorded on the obtained structures. In Fig. 2a two Mn atoms are separated at sufficiently far distance +such that they exhibit a Kondo resonance (spectrum shown in 2d). At closer distance (b), the Kondo resonance is +split (Fig. 2e). When the atoms are pushed into adjacent lattice sites as in Fig. 2c, the singlet-triplet excitation is +observed (Fig. 2f). +2.80 +2.70 +2.60 +-15 +-10 +-5 +0 +5 +10 +15 +bias voltage (mV) +dI/dV (G0) x 10 +-3 +2.8 +2.6 +2.4 +2.2 +-15 +-10 +-5 +0 +5 +10 +15 +bias voltage (mV) +dI/dV (G0) x 10 +-3 +b) ++ +c) ++ +a) +d) ++ +5.0 +4.0 +3.0 +2.0 +dI/dV (G0) x 10 +-3 +-15 +-10 +-5 +0 +5 +10 +15 +bias voltage (mV) +e) +f) +5 Å +5 Å +5 Å +Supplementary Figure 2. Manipulation of two Mn atoms into dimer structures. a-c) STM topographies of the same atoms +before and after successive manipulation events. The atom at the bottom of figure (a) was pushed closer towards the other +upper atom, as seen in (b). Here the atoms are still distinguishable. In (c) the lower atom was pushed even closer to the upper +atom, resulting in a dimer. d-f) dI/dV spectra performed on the upper atom in (a), (b) and (c) respectively. The topographies +were recorded at 100 mV and 20 pA, the setpoint of the recorded spectra was 15 mV and 3 nA (f) and 10 mV and 3 nA (g). +Fig. 3a shows one dimer where two Mn atoms are two lattice sites apart. The Kondo resonance is split (red line in +Fig. 3c). Removing one of the atoms leads to an unperturbed Kondo resonance (green line in Fig. 2c). +An unambiguous assignment of the adsorption sites of the Mn atoms within the dimer structures is challenging +as the Mn atoms appear very large and cannot be separately resolved. Analyzing the orientation of the dimers on +the surface, we observed only three orientations, suggesting the registry with the threefold atomic lattice structure +of MoS2. While attempting to remove one of the Mn atoms from the densely-packed dimer structures by a voltage +pulse, we often observed effectively a rotation of the dimers. Also the resulting dimers follow the main axes (Fig. 4). + +14 ++ ++ +a) +b) +4.5 +4.0 +3.5 +3.0 +dI/dV (G0) x 10 +-3 +-10 +-5 +0 +5 +10 +bias voltage (mV) +c) +5 Å +5 Å +Supplementary Figure 3. Disassembly of a Mn dimer. a,b) STM topographies of a Mn dimer before and after the removal of +one atom. Here the right atom in (a) was removed, leading to a single Mn atom as shown in (b). c) dI/dV spectra performed +on the left atom in (a) and on the same (remaining) atom (b) respectively. The topographies were recorded at 100 mV and 20 +pA, the setpoint of the recorded spectra was 10 mV and 3 nA (g). +1 +1 +2 +2 +3 +3 +a) +b) +1 nm +1 nm +Supplementary Figure 4. +Rotation of Mn dimers. a), b) STM topographies of single Mn dimers before (a) and after (b) +applying a high bias voltage. In (a) the dimers 1 and 3 show the same orientation, whereas dimer 2 is rotated by roughly 120◦ +with respect to 1 and 3. After a bias voltage of 1.5 V was applied to the dimers in (a), dimer 1 and 2 appear rotated by 120◦. +The topographies were recorded at 100 mV and 20 pA. +C. +RKKY coupled dimers in different moir´e sites +In the main text, we showed the variation of singlet-triplet excitations along the moir´e superstructure. To probe +whether RKKY-coupled Mn dimers are equally affected by the moir´e structure, we investigate Mn dimers with a +spacing of two substrate lattice sites (Fig. 5). As described in the main text, substrate-mediated interactions lead to +small excitation gaps around the Fermi level on top of the Kondo resonance (red lines in Fig. 5c,f). Various dimers +in different moir´e sites display similar gap sizes while the height of the Kondo resonance varies. The same height +modulation of the Kondo resonance is found on the isolated atoms in the same adsorption sites. This is shown by +spectra taken on the same atoms after the neighbor has been removed by STM manipulation (black lines in Fig. 5c,f). +Hence, once Kondo correlations of the individual atoms dominate the spectra and the coupling enters through a small +perturbation, we hardly observe any moir´e induced modulations in the coupling. +[1] J. R. Schrieffer, J. Appl. Phys. 38, 1143 (1967). +[2] S. Trishin, C. Lotze, N. Bogdanoff, F. von Oppen, and K. J. Franke, Phys. Rev. Lett. 127, 236801 (2021). +[3] X. Chen, L. Zhong, X. Li, and J. Qi, Nanoscale 9, 2188 (2017). +[4] Y. Wang, B. Wang, R. Huang, B. Gao, F. Kong, and Q. Zhang, Physica E: Low-dimensional Systems and Nanostructures +63, 276 (2014). + +. +.: +.15 +4.5 +4.0 +3.5 +3.0 +dI/dV (G0) x 10 +-3 +-10 +-5 +0 +5 +10 +bias voltage (mV) +2.8 +2.4 +2.0 +1.6 +dI/dV (G0) x 10 +-3 +-10 +-5 +0 +5 +10 +bias voltage (mV) ++ +a) ++ ++ ++ +b) +d) +e) +c) +f) +5 Å +5 Å +5 Å +5 Å +Supplementary Figure 5. Moir´e effect on RKKY-coupled Mn dimers. a), d) STM topographies of Mn dimers. Whereas in +(a) the dimer is adsorbed close to the moir´e maximum, in (d) the dimer is adsorbed in the moir´e valley. c), f) dI/dV spectra +performed at the crosses in (a) and (d). b),e) show the same scan frame, after one atom has been removed from the dimer. +The black spectra in (c) and (f) show the spectra of the respective monomer. The topographies were recorded at 100 mV and +20 pA, the setpoint of the recorded spectra was 15 mV and 3 nA (c) and 10 mV and 3 nA (f). + diff --git a/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/load_file.txt b/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a15ed0fbd9eb7321cbc43f145ad3d690b9886291 --- /dev/null +++ b/H9AzT4oBgHgl3EQfjf2C/content/tmp_files/load_file.txt @@ -0,0 +1,803 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf,len=802 +page_content='Tuning a two-impurity Kondo system by a moir´e superstructure Sergey Trishin,1 Christian Lotze,1 Friedemann Lohss,1 Giada Franceschi,1 Leonid I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Glazman,2 Felix von Oppen,3 and Katharina J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Franke1 1Fachbereich Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany 2Department of Physics, Yale University, New Haven, Connecticut 06520, USA 3Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Working with Mn atoms on Au(111) covered by a monolayer of MoS2, we tune the inter-adatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moir´e structure of the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Mn dimers spaced by a few atomic lattice sites exhibit split Kondo resonances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In contrast, adatoms in closely spaced dimers couple antiferromagnetically, resulting in a molecular-singlet ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Exciting the singlet- triplet transition by tunneling electrons, we find that the singlet-triplet splitting is surprisingly sensitive to the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We interpret our results theoretically by relating the variations in the singlet-triplet splitting to the heights of the Kondo peaks of single adatoms, finding evidence for coupling of the adatom spin to multiple conduction electron channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Exchange interactions between magnetic adatoms and itinerant electrons of a substrate can induce correla- tion effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' For strong exchange coupling, the adatom spin becomes Kondo screened [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' For intermedi- ate coupling, where the Kondo temperature is compa- rable to temperature or other competing couplings, the Kondo renormalizations remain in the perturbative do- main [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' When the exchange coupling is weak, com- peting couplings such as single-ion anisotropy can dom- inate, in which case Kondo screening can be neglected and spin excitations can be probed [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The panorama becomes yet broader when exchange coupling the adatom to a second magnetic atom in its vicinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The na- ture of this coupling depends on the interatomic spacing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In close proximity, direct exchange tends to dominate, while larger separations favor substrate-mediated cou- plings such as the oscillatory Rudermann-Kittel-Kasuya- Yosida (RKKY) [5–7] and Dzyaloshinskii-Moriya (DM) [8, 9] interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The resulting ground states may be ferromagnetic [10, 11], antiferromagnetic [10, 11], or non- collinear [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The competition between inter-adatom and adatom- substrate exchange leads to a rich phase diagram with multiple correlated ground states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Theoretically, the two- impurity Kondo problem has been treated extensively [13, 14], and motivated numerous experiments [10, 15– 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The parameter space can be most directly explored by scanning-tunneling-microscope (STM) experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Atom manipulation with the STM tip admits manoev- ering the atoms into lattice sites at various distances and thus investigating different interatomic interaction strengths [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Tuning of the exchange coupling to the surface is somewhat less straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' An early ap- proach used strain-induced changes in the band gap of a decoupling interlayer [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A more controlled strat- egy would exploit well-defined superstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Prime candidates to impose a spatially periodic modulation of the atom–substrate interaction strength are interlayers which form moir´e structures with the underlying metal substrate [21–23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Most notably, monolayers of MoS2 on Au(111) have been successfully employed for tuning the exchange coupling of single magnetic Fe atoms from es- sentially uncoupled to strongly Kondo screened [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Here, we exploit the moir´e pattern formed by monolayer-MoS2 on Au(111) to tune the exchange cou- pling of Mn dimers with the substrate, thereby probing the competition between interatomic and atom-substrate exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We find that the direct exchange coupling be- tween closely-spaced Mn atoms leads to a singlet ground state and study the remarkably strong variations of the singlet-triplet splitting across the moir´e pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We in- troduce a new experimental signature of multi-channel Kondo coupling by exploiting a theoretical relation be- tween the singlet-triplet excitation energy of the dimer and the Kondo renormalizations of individual adatoms and find evidence that the Mn adatoms are coupled to several conduction-electron channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We use the previously established moir´e-patterned de- coupling layer MoS2 on Au(111) [23], grown by deposit- ing Mo atoms and subsequent annealing to 800 K in H2S gas at a pressure p = 10−5 mbar [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A moir´e struc- ture forms as a result of the lattice mismatch between adlayer and substrate, easily seen in the STM images as a modulation of the apparent height with a periodicity of ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='3 nm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1a) [24–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Deposition of Mn atoms at low temperatures (< 10 K) leads to isolated atoms ob- servable as round protrusions with an apparent height of ≈ 300 pm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Some round protrusions with smaller appar- ent height are attributed to Mn atoms attached to defects and excluded from further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We also find some oval protrusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As discussed in more detail below, we attribute these to Mn dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We start by characterizing individual Mn atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' These exhibit a narrow zero-bias resonance in differential- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='01517v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='mes-hall] 4 Jan 2023 2 conductance (dI/dV ) spectra as shown for two examples in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' At our experimental temperature of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='1 K, the lineshape is well reproduced by a temperature-broadened logarithmic peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The peak splits when applying a mag- netic field (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' At 3 T, the Zeeman split amounts to 600 µV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This behavior is reminiscent of a weakly cou- pled Kondo impurity, with the experimental temperature larger than or of the order of the Kondo temperature [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Mn atoms at different positions with respect to the moir´e lattice exhibit lineshapes with small variations in intensity, but the same broadening (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1b for two extremal cases).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The intensity modulations can be un- derstood as modulations of Jν0, where J is the strength of the exchange coupling to the conduction electrons and ν0 the density of states (DoS) at the Fermi level as dis- cussed in more detail below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The observed variations are consistent with the DoS modulations due to the adatoms’ position on the moir´e structure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Next, we characterize dimer structures formed by two adatoms in close proximity to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Density- functional calculations suggest that isolated atoms sit in hollow sites of the terminating S layer [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Starting with this assumption, we can tentatively assign model struc- tures to the most commonly found dimer arrangements on the surface by evaluating the separation and orienta- tion in the STM images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Figure 2a,b shows an arrange- ment, where two Mn atoms are separated by three lattice sites of the MoS2 substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' At this separation, the atoms show a Kondo resonance as previously described for in- dividual adatoms (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2c), indicating that interatomic interactions are negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' At a distance of two atomic lattice sites (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2d,e), the Kondo resonance develops a dip at the Fermi level (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The spectrum is reminis- cent of a Zeeman-split Kondo resonance, indicating mag- netic interactions between the atoms, presumably result- ing from substrate-mediated RKKY interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' When the atoms are in even closer proximity, their shapes are no longer individually resolved in the STM image (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2g,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' While a definite assignment of the adsorption sites is thus difficult, the oval shape and its orientation with respect to the underlying lattice suggest that the atoms lie in nearest-neighbor hollow sites (for details and STM manipulations, see section S2 in Supplementary Material (SM) [29]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Differential-conductance spectra measured on this type of dimer are radically different from those of individual atoms or weakly interacting dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The Kondo resonance is now replaced by pronounced inelas- tic steps at ±10 mV (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' It is rather surprising to detect inelastic excitations of a relatively large energy, considering that individ- ual atoms do not show a noticeable magnetocrystalline anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Instead of a change in magnetocrystalline anisotropy energy, we suggest that the threshold energy is associated with a spin-changing transition of the dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Such excitations have been observed for Mn dimers on CuN [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The close proximity of the atoms may al- 3 nm 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 dI/dV (G0) x 10-3 dI/dV (G0) x 10-3 10 5 0 5 10 bias voltage (mV) a) d) c) b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='05 Jν0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 distance (nm) moiré min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' moiré max.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='. 0 T 3 T 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 15 -10 -5 0 5 10 15 bias voltage (mV) moiré maximum moiré minimum Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Variation of the Kondo coupling across the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a) STM topography of Mn atoms on the moir´e structure of MoS2 on Au(111) (recorded at 100 mV, 20 pA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' b) dI/dV spectra taken on Mn atoms adsorbed close to a moir´e maximum (black) and a moir´e minimum (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The dashed lines show fits using a code based on Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The fits yield a (dimensionless) adatom-substrate exchange Jν0 of -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='080 (red) and -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='049 (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c) dI/dV spectra on a Mn atom at 0 T (black) and 3 T (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The zero-bias resonance splits at 3 T (fit: dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [Spectra were recorded at a setpoint of 15 mV, 3 nA (panel b) and 10 mV, 3 nA (panel c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' d) Values of Jν0 obtained from fitting dI/dV spectra (keeping T 2 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='000415 constant, as obtained from a best fit with B-field) on atoms at various positions within the moir´e superstructure (distance to the moir´e maximum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Symbols indicate different measurement sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The black dashed line is a linear guide to the eye through the data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The red dashed lines are corresponding lines obtained from fits using different tunnel couplings T 2 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The upper line corresponds T 2 0 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='635×10−4 and the lower line to T 2 0 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6×10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' These boundary values have been determined from error margins of fits at 3 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' low for direct exchange as a result of finite overlap of the atomic d orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Mn atoms are indeed likely cou- pled antiferromagnetically when interacting via direct ex- change [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This would lead to a singlet ground state |Stot = 0, M = 0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Magnetic excitations must then in- volve a spin-changing transition such as the singlet-triplet transition and the excitation energy directly reflects the exchange coupling JD (for details, see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' To further corroborate the antiferromagnetic nature of the exchange coupling, we apply an external magnetic field of 3 T to the dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The inelastic steps become slightly broader (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This is consistent with a singlet-triplet transi- 3 2a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5Å 1a i)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 15 -10 -5 0 5 10 15 bias voltage (mV) a) b) c) d) e) f) g) h) 0T 3T S=0 S=1 Energy B field gμBB ~J D |S,M> |1,0> |1,+1> |1,-1> |0,0> j) k) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 10 5 0 5 10 bias voltage (mV) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='1Å 3a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6Å 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 10 5 0 5 10 bias voltage (mV) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 20 10 0 10 20 bias voltage (mV) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5Å dI/dV (G ) x 10 0 3 dI/dV (G ) x 10 0 3 dI/dV (G ) x 10 0 3 dI/dV (G ) x 10 0 3 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Various dimer structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a), d), g) Structure mod- els and b), e), f) corresponding STM topographies of Mn dimers on MoS2with various interatom spacings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Yellow, gray, and purple spheres represent S, Mo, and Mn, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The Mn atoms, sitting in MoS2 hollow sites, are separated by three lattice sites (panels a,b), two lattice sites (panels d,e), and one lattice site (panels g,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c), f), i) dI/dV spectra recorded at the locations indicated by the black crosses in (b,e,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The spectra drastically depend on the dimer separa- tion, exhibiting a Kondo resonance (panel c), a split Kondo resonance (panel f), and a step-like increase in the differen- tial conductance (panel i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' j) Energy-level diagram of the ob- served spin excitation in (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The degeneracy of the M = 0, ±1 sublevels of the excited state is lifted by a magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' k) dI/dV spectra of a dimer with Mn in nearest-neighbor sites with and without magnetic field and respective fits with sym- metric step functions (dashed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' For our measurement condi- tions at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='1 K, a magnetic field of 3 T is not sufficient to fully resolve the splitting, but the excitation appears broadened by 110 µV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' STM topographies were recorded at 100 mV, 20 pA, the setpoint of the dI/dV spectra was 10 mV, 3 nA (c,f), 15 mV, 3 nA (i), and 20 mV, 3 nA (k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' tion to |Stot = 1, M⟩, where the excited state is Zeeman split in the magnetic field, but the sublevels are not in- dividually resolved at the experimental temperature of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='1 K (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Importantly, we do not observe addi- tional excitations around zero bias, which would indicate a higher-spin ground state as favored by ferromagnetic coupling of the atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As discussed above, the moir´e superstructure weakly affects the height of the Kondo resonance of individual atoms reflecting the modulation of the dimensionless ex- change coupling Jν0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As the dimer is in a singlet ground state, one may naively expect that the moir´e structure does not influence the inelastic excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Remarkably, we observe strong variations of the singlet–triplet tran- sition by several meV as the dimer’s adsorption site is varied with respect to the moir´e lattice (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Dimers located on maxima of the moir´e structure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3a,e) exhibit the smallest excitation energy (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 meV), while those on minima (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3d,e) show the largest excitation energy (10 meV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' To understand these variations, we compute the shift of the singlet-triplet splitting ∆ due to the hybridiza- tion of the adatom d orbitals with the substrate and relate it to the exchange coupling between the adatom and conduction-electron spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As we do not observe in- elastic excitations on single adatoms indicating negligible single-ion anisotropy, we assume that the Mn atoms are only weakly perturbed by the surrounding and retain the half-filled d-shell when placed on the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Accord- ing to Hund’s rule, this implies a high-spin configuration with S = 5/2 and suggests that spin-orbit coupling will be weak, so that the inter-adatom exchange can be mod- eled by isotropic Heisenberg exchange, Hex = JDSA ·SB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Here, SA,B denotes the spins of adatom A,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In the absence of hybridization with the substrate, states with magnitude Stot of the total spin Stot = SA + SB will have direct exchange energy Eex(SA, SB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stot) = JD 2 [Stot(Stot +1)− � j∈{A,B} Sj(Sj +1)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (1) Evaluating the singlet-triplet splitting for SA, SB = 5 2, we find ∆ = Eex(5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1) − Eex(5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0) = JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (2) This splitting is reduced by the hybridization of the adatom d orbitals with the conduction electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In gen- eral, the d orbitals hybridize with 2S = 5 (symmetry- adapted) conduction-electron channels [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Since the substrate breaks rotational symmetry, the strength of hybridization Vm depends on the channel m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The en- ergies of the singlet and triplet states are then shifted by virtual excitation processes, in which a d electron hops into the substrate or a substrate electron hops into the d shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Physically, these processes reduce the effective adatom spin, which results in a smaller direct exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A detailed calculation in second-order perturbation the- ory (see section S1 in SM for details [29]) gives a renor- malized singlet-triplet splitting ∆ = JD � 1 − 2 5 � m ν0|Vm|2 � 1 |ϵd| + 1 ϵd + U �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (3) Here, −ϵd > 0 is the energy to remove an electron from the filled d-shell and ϵd+U the energy to add an electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The factor 2 in front of the sum over channels accounts 84 1nm 1nm a) b) c) d) e) + + + + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 normalized dI/dV 15 10 5 0 5 10 15 bias voltage (mV) 1nm 1nm Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Antiferromagnetically coupled Mn dimers (oval structures), which are identical apart from their location rela- tive to the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a-d) STM topographies of dimers (a) on the maximum, (b) close to the maximum, (c) further from the maximum, and (d) at the minimum of the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' e) dI/dV spectra acquired on the dimers shown in (a-d), with colors matched to the crosses in (a-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Topogra- phies recorded at 100 mV, 20 pA, setpoints of the recorded spectra were 20 mV, 1 nA (b), 20 mV, 3 nA (a) and 15 mV, 3 nA (c), (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Spectra are normalized for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' for the fact that both adatoms can be excited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The factor 1/5 results from angular-momentum coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The singlet-triplet spacing can be directly related to experimentally measurable quantities by noting that the exchange coupling between the conduction electrons and the spin-S adatom is given by [32] Jm = ν0|Vm|2 2S � 1 |ϵd| + 1 ϵd + U � , (4) so that we can express the singlet-triplet splitting of the S = 5 2 Mn dimer as ∆ = JD � 1 − 2 � m ν0Jm � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (5) For weak coupling (ν0Jm ≪ 1), the relative change in the singlet-triplet spacing between minimum (∆min) and maximum (∆max) is approximately equal to δ ≃ (∆min − ∆max)/JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Equation (5) relates this directly to the corresponding change in the sum of the dimen- sionless exchange couplings � m ν0Jm to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Since information on the exchange couplings ν0Jm can be extracted from the Kondo data on a single adatom, applying this relation to the data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3e gives direct information on the number of conduction-electron chan- nels coupled to the adatom spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' For analyzing the number of participating channels, we first assume that the adatom spin is coupled to a single channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' With this assumption, we can extract the di- mensionless adatom-substrate exchange coupling ν0J of the single channel by fitting the Kondo peak of the iso- lated atoms using a program based on Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Showcas- ing the variation between extremal positions with respect to the moir´e pattern, we extracted a value of ν0J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='049 for the adatom on the moir´e minimum and ν0J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='080 for an atom on the maximum from fitting the Kondo data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Equation 5 (specified to a single chan- nel) then predicts a relative change δ of the singlet-triplet splitting from minimum to maximum by ≈ 6%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This is clearly smaller than the experimentally observed varia- tion of ≈ 25% (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We have extracted ν0J for sev- eral dozen isolated atoms in various positions across the moir´e structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In all cases, ν0J decreases with increas- ing distance from the maxima of the moir´e pattern (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The variations of ν0J for similar distances from the moir´e maxima partially derive from the lack of rotational symmetry, so that the distance to the moir´e maximum does not uniquely specify the adsorption site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Moreover, the fitting procedure contains some uncertainty, as the strength of tunneling T 2 0 and ν0J both affect the peak height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We first determined T 2 0 from a spectrum of an atom subject to a magnetic field (for which the uncer- tainty is reduced due to the additional magnetic-field in- duced structure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We then fitted all spectra with the extracted value of T 2 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' To indicate the error margins of the fits, we reran all fits taking extremal values of T 2 0 consistent with the B-field data with sufficient accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The black dashed line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1d shows a linear guide- to-the-eye for the best fit results, while the red dashed lines indicate the scalings obtained when using the ex- tremal values of T 2 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We find that with the assumption of a single channel, only the largest variation in ν0J (up- per red dashed line) would explain the variation of the singlet-triplet splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We can also apply Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (5), when assuming that all five channels are equally coupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Since each channel renor- malizes independently, the value of ν0Jm for any m is equal to that extracted with the single-channel assump- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (In the leading-logarithm approximation underly- ing the Kondo fits, the number of channels enters only as an overall prefactor, which can be absorbed into T 2 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=') With this assumption, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (5) predicts a variation in the singlet-triplet spacing, which is larger by a factor of five than in the single-channel case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We then find that the observed variation in the singlet-triplet spacing across the moir´e structure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3e) would only be consistent with the opposite extreme case (lower red dashed line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Thus, while the uncertainties of the fitting procedure preclude a fully quantitative analysis, our re- sults strongly suggest that the Mn atoms have substan- tial coupling to several conduction-electron channels in the Au(111) substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In conclusion, we varied the adatom-substrate ex- change of Mn monomers and dimers by exploiting the :5 moir´e pattern of a MoS2 layer on Au(111).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The moir´e structure imprints density-of-states modulations, which in turn affect the Kondo resonance of the monomer and the singlet-triplet splitting of antiferromagnetically cou- pled dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Relating these variations through a theo- retical analysis, we find evidence that the adatoms are coupled to multiple conduction-electron channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This constrasts with the commonly made assumption that adatoms couple only to a single channel of a metallic substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Our results show that this assumption is vi- olated in the perturbative limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' For the fully devel- oped Kondo effect, relatively small differences in ν0Jm between channels result in large differences in the asso- ciated Kondo temperatures TK,m ∝ e−1/ν0Jm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Then, the single-channel approximation can still be adequate pro- vided that only the first stage of the resulting multistage Kondo screening is accessible in experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Interest- ingly, coupling to multiple conduction-electron channels has previously been invoked to explain the appearance of multiple Yu-Shiba-Rusinov states induced by magnetic adatoms on superconductors [33, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Our results em- phasize that adatom dimers realize a rich two-impurity problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' While theoretical studies have focused on spin- 1 2 impurities, adatom dimers typically have higher spins and couple to multiple conduction-electron channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foun- dation) through project numbers 328545488 (CRC 227, project B05) and 277101999 (CRC 183, project C02 and a Mercator professorship), as well as by the National Sci- ence Foundation through grant NSF DMR-2002275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Madhavan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Jamneala, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Crommie, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wingreen, Tunneling into a single magnetic atom: Spectroscopic evidence of the kondo resonance, Sci- ence 280, 567 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Schneider, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Berndt, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Delley, Kondo scattering observed at a single magnetic impurity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 80, 2893 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [3] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kahle, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Herden, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stroh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Mayor, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Schlickum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ternes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wahl, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kern, Temper- ature and magnetic field dependence of a Kondo system in the weak coupling regime, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 4, 2110 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Heinrich, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Gupta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lutz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ei- gler, Single-atom spin-flip spectroscopy, Science 306, 466 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ruderman and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kittel, Indirect Exchange Cou- pling of Nuclear Magnetic Moments by Conduction Elec- trons, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 96, 99 (1954).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kasuya, A Theory of Metallic Ferro- and Antiferro- magnetism on Zener’s Model, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 16, 45 (1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [7] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Yosida, Magnetic Properties of Cu-Mn Alloys, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 106, 893 (1957).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [8] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Dzyaloshinsky, A thermodynamic theory of weak ferro- magnetism of antiferromagnetics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Solids 4, 241 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [9] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 120, 91 (1960).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wahl, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Simon, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Diekh¨oner, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stepanyuk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bruno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Schneider, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kern, Exchange inter- action between single magnetic adatoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 98, 056601 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Meier, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wiebe, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wiesendanger, Re- vealing Magnetic Interactions from Single-Atom Magneti- zation Curves, Science 320, 82 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Khajetoorians, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Steinbrecher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ternes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bouhassoune, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' dos Santos Dias, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lounis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wiebe, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wiesendanger, Tailoring the chiral magnetic interaction between two individual atoms, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 7, 10620 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [13] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Jayaprakash, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Krishna-murthy, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wilkins, Two-Impurity Kondo Problem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 47, 737 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [14] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Jones, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Varma, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wilkins, Low- Temperature Properties of the Two-Impurity Kondo Hamiltonian, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 61, 125 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [15] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Tsukahara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Shiraki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Itou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ohta, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Takagi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kawai, Evolution of Kondo Resonance from a Sin- gle Impurity Molecule to the Two-Dimensional Lattice, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 106, 187201 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pr¨user, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Dargel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bouhassoune, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ulbrich, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pruschke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lounis, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wenderoth, Interplay between the Kondo effect and the Ruder- man–Kittel–Kasuya–Yosida interaction, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 5, 5417 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Spinelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Gerrits, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Toskovic, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bryant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ternes, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Otte, Exploring the phase diagram of the two-impurity Kondo problem, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 6, 10046 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Moro Lagares, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Korytar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Piantek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Robles, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lorente, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pascual, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ibarra, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Serrate, Real space manifestations of coherent screening in atomic scale Kondo lattices, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 10, 2211 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Khajetoorians, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wegner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Otte, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Swart, Creating designer quantum states of matter atom-by-atom, Nature Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 703 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Oberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Calvo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Delgado, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Moro-Lagares, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Serrate, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Fernandez-Rossier, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Hirjibehedin, Control of single-spin magnetic anisotropy by exchange coupling, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Nanotech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 9, 64 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ren, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pantelides, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Gao, Kondo effect of cobalt adatoms on a graphene monolayer controlled by substrate-induced ripples, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 14, 4011 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [22] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Jacobson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Herden, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Muenks, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Laskin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Brovko, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stepanyuk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ternes, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kern, Quan- tum engineering of spin and anisotropy in magnetic molec- ular junctions, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 6, 8536 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Trishin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lotze, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bogdanoff, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' von Oppen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Franke, Moir´e Tuning of Spin Excitations: Individual Fe Atoms on MoS2/Au(111), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 127, 236801 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Grønborg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ulstrup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bianchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Dendzik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Sanders, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lauritsen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Hofmann, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Miwa, Synthesis of epitaxial single-layer MoS2 on Au (111), Langmuir 31, 9700 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [25] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Krane, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lotze, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Franke, Moir´e structure of MoS2 on Au(111): Local structural and electronic prop- 6 erties, Surf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 678, 136 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [26] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bana, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Travaglia, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bignardi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lacovig, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Sanders, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Dendzik, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Michiardi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bianchi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lizzit, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Presel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Angelis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Apostol, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Das, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Fu- jii, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Vobornik, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Larciprete, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Baraldi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Hofmann, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lizzit, Epitaxial growth of single-orientation high- quality MoS2 monolayers, 2D Materials 5, 035012 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ternes, Spin excitations and correlations in scanning tunneling spectroscopy, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 17, 063016 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Gao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kong, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhang, First-principles study of transition-metal atoms adsorption on MoS2 monolayer, Physica E: Low- dimensional Systems and Nanostructures 63, 276 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [29] Supporting Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Hirjibehedin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lutz, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Heinrich, Spin coupling in engineered atomic structures, Science 312, 1021 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [31] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Mokrousov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bihlmayer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bl¨ugel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Heinze, Magnetic order and exchange interactions in monoatomic 3d transition-metal chains, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' B 75, 104413 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Schrieffer, The Kondo Effect − The Link Be- tween Magnetic and Nonmagnetic Impurities in Metals?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 38, 1143 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ruby, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Peng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' von Oppen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Heinrich, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Franke, Orbital Picture of Yu-Shiba-Rusinov Multi- plets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 117, 186801 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [34] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Choi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rubio-Verd´u, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' De Bruijckere, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Ugeda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lorente, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Pascual, Mapping the orbital structure of impurity bound states in a superconductor, Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 8, 15175 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 7 SUPPLEMENTARY MATERIAL I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' THEORETICAL CONSIDERATIONS We provide details concerning the theoretical considerations in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We assume that Mn retains its half- filled d shell in the presence of the weak coupling to the substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The uncoupled state of Mn is thus fully rotationally symmetric and coupled to five conduction-electron channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As the rotational symmetry is broken by the coupling to the substrate, their hybridization Vm with the various conduction-electron channels will be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In the following, we compute the singlet-triplet splitting perturbatively, focusing on one channel (m = 0 for definiteness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The general result is obtained by adding the independent corrections for all five channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Spin states of monomer First consider the spin states of a single Mn adatom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We can generate the spin states | 5 2, Sz⟩ by applying the spin lowering operator S− = �2 m=−2 c† m,↓cm,↑ to |5 2, 5 2⟩ = � m c† m,↑|vac⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (1) Then, we have |5 2, 5 2⟩ = | ↑↑↑↑↑⟩ |5 2, 3 2⟩ = � 1 5 � |states with one flipped spin⟩ |5 2, 1 2⟩ = � 1 10 � |states with two flipped spins⟩ |5 2, −1 2⟩ = � 1 10 � |states with three flipped spins⟩ |5 2, −3 2⟩ = � 1 5 � |states with four flipped spins⟩ |5 2, −5 2⟩ = | ↓↓↓↓↓⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (2) Similarly, we can derive the states with one less electron, say in the m = 0 state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' One finds |2, 2⟩ = | ↑↑↑↑⟩ |2, 1⟩ = � 1 4 � |states with one flipped spin⟩ |2, 0⟩ = � 1 6 � |states with two flipped spins⟩ |2, −1⟩ = � 1 4 � |states with three flipped spins⟩ |2, −2⟩ = | ↓↓↓↓⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (3) 8 Applying c0,↑ to the S = 5 2 states, one finds c0,↑|5 2, 5 2⟩ = |2, 2⟩ c0,↑|5 2, 3 2⟩ = � 4 5|2, 1⟩ c0,↑|5 2, 1 2⟩ = � 6 10|2, 0⟩ c0,↑|5 2, −1 2⟩ = � 4 10|2, −1⟩ c0,↑|5 2, −3 2⟩ = � 1 5|2, −2⟩ c0,↑|5 2, −5 2⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (4) Applying c0,↓ to the S = 5 2 states, one finds c0,↓|5 2, 5 2⟩ = 0 c0,↓|5 2, 3 2⟩ = � 1 5|2, 2⟩ c0,↓|5 2, 1 2⟩ = � 4 10|2, 1⟩ c0,↓|5 2, −1 2⟩ = � 6 10|2, 0⟩ c0,↓|5 2, −3 2⟩ = � 4 5|2, −1⟩ c0,↓|5 2, −5 2⟩ = |2, −2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (5) B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Singlet state of dimer – tunneling out The spin state of the dimer can either be expanded in product states |S1, M1⟩ ⊗ |S2, M2⟩ of the two adatoms, or according to magnitude Stot and projection Mtot of the total angular momentum Stot = S1 +S2 as |S1, S2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stot, Mtot⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' First consider the singlet state of the dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Using Clebsch-Gordan coefficients, we can expand it into product states as |5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = � 1 6 � |5 2, 5 2⟩ ⊗ |5 2, −5 2⟩ − |5 2, 3 2⟩ ⊗ |5 2, −3 2⟩ + |5 2, 1 2⟩ ⊗ |5 2, −1 2⟩ −|5 2, −1 2⟩ ⊗ |5 2, 1 2⟩ + |5 2, −3 2⟩ ⊗ |5 2, 3 2⟩ − |5 2, −5 2⟩ ⊗ |5 2, 5 2⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (6) Applying cL,0,↑ for the left adatom gives cL,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = � 1 6 � |2, 2⟩ ⊗ |5 2, −5 2⟩ − � 4 5|2, 1⟩ ⊗ |5 2, −3 2⟩ + � 6 10|2, 0⟩ ⊗ |5 2, −1 2⟩ − � 4 10|2, −1⟩ ⊗ |5 2, 1 2⟩ + � 1 5|2, −2⟩ ⊗ |5 2, 3 2⟩ � (7) Similarly, we have cL,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = � 1 6 � − � 1 5|2, 2⟩ ⊗ |5 2, −3 2⟩ + � 4 10|2, 1⟩ ⊗ |5 2, −1 2⟩ − � 6 10|2, 0⟩ ⊗ |5 2, 1 2⟩ + � 4 5|2, −1⟩ ⊗ |5 2, 3 2⟩ − |2, −2⟩ ⊗ |5 2, 5 2⟩ � (8) 9 We can compare these states to |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩ = � 1 15|2, 2⟩ ⊗ |5 2, −3 2⟩ − � 2 15|2, 1⟩ ⊗ |5 2, −1 2⟩ + � 1 5|2, 0⟩ ⊗ |5 2, 1 2⟩ − � 4 15|2, −1⟩ ⊗ |5 2, 3 2⟩ + � 1 3|2, −2⟩ ⊗ |5 2, 5 2⟩ (9) |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, −1 2⟩ = � 1 3|2, 2⟩ ⊗ |5 2, −5 2⟩ − � 4 15|2, 1⟩ ⊗ |5 2, −3 2⟩ + � 1 5|2, 0⟩ ⊗ |5 2, −1 2⟩ − � 2 15|2, −1⟩ ⊗ |5 2, 1 2⟩ + � 1 15|2, −2⟩ ⊗ |5 2, 3 2⟩, (10) so that we identify cL,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = − � 1 2|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, −1 2⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' cL,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = � 1 2|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (11) C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Singlet state of dimer – tunneling in Now consider tunneling in of an electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We can follow the same steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Now, the m = 0 state of one of the atoms will be doubly occupied rather than empty, but this is also a zero-spin state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Thus, all the Clebsch-Gordan coefficients remain the same and one finds c† L,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = � 1 2|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c† L,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0, 0⟩ = − � 1 2|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, −1 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (12) D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Triplet state of dimer – tunneling out We expand the triplet state of the dimer into product states of the two monomers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Due to rotational invariance, we can consider the M = 1 state without loss of generality, |5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = � 1 7|5 2, 5 2⟩ ⊗ |5 2, −3 2⟩ − � 8 35|5 2, 3 2⟩ ⊗ |5 2, −1 2⟩ + � 9 35|5 2, 1 2⟩ ⊗ |5 2, 1 2⟩ − � 8 35|5 2, −1 2⟩ ⊗ |5 2, 3 2⟩ + � 1 7|5 2, −3 2⟩ ⊗ |5 2, 5 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (13) Applying cL,0,↑ for the left adatom gives cL,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = � 1 7|2, 2⟩ ⊗ |5 2, −3 2⟩ − � 8 35 � 4 5|2, 1⟩ ⊗ |5 2, −1 2⟩ + � 9 35 � 6 10|2, 0⟩ ⊗ |5 2, 1 2⟩ − � 8 35 � 4 10|2, −1⟩ ⊗ |5 2, 3 2⟩ + � 1 7 � 1 5|2, −2⟩ ⊗ |5 2, 5 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (14) Similarly, cL,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = − � 8 35 � 1 5|2, 2⟩ ⊗ |5 2, −1 2⟩ + � 9 35 � 4 10|2, 1⟩ ⊗ |5 2, 1 2⟩ − � 8 35 � 6 10|2, 0⟩ ⊗ |5 2, 3 2⟩ + � 1 7 � 4 5|2, −1⟩ ⊗ |5 2, 5 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (15) 10 We can compare this to |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩ = � 1 15|2, 2⟩ ⊗ |5 2, −3 2⟩ − � 2 15|2, 1⟩ ⊗ |5 2, −1 2⟩ + � 1 5|2, 0⟩ ⊗ |5 2, 1 2⟩ − � 4 15|2, −1⟩ ⊗ |5 2, 3 2⟩ + � 1 3|2, −2⟩ ⊗ |5 2, 5 2⟩ |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 1 2⟩ = � 32 105|2, 2⟩ ⊗ |5 2, −3 2⟩ − � 5 21|2, 1⟩ ⊗ |5 2, −1 2⟩ + � 2 35|2, 0⟩ ⊗ |5 2, 1 2⟩ + � 2 105|2, −1⟩ ⊗ |5 2, 3 2⟩ − � 8 21|2, −2⟩ ⊗ |5 2, 5 2⟩ |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 3 2⟩ = � 4 35|2, 2⟩ ⊗ |5 2, −1 2⟩ − � 9 35|2, 1⟩ ⊗ |5 2, 1 2⟩ + � 12 35|2, 0⟩ ⊗ |5 2, 3 2⟩ − � 2 7|2, −1⟩ ⊗ |5 2, 5 2⟩, (16) so that we identify cL,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = � 7 15|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩ + � 2 15|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 1 2⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' cL,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = − � 2 5|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 3 2⟩ (17) E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Triplet state of dimer – tunneling in This follows again by analogy with the tunneling-out terms, so that c† L,0,↓|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = � 7 15|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, 1 2⟩ + � 2 15|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 1 2⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c† L,0,↑|5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1, 1⟩ = − � 2 5|2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2, 3 2⟩ (18) F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Singlet-triplet splitting In the absence of coupling to the substrate, the impurity spins S1 and S2 of the two Mn adatoms are subject to antiferromagnetic exchange coupling of the dimer, Hex = JDS1 · S2 with JD > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Depending on the total spin Stot, the coupling energy is Eex(S1, S2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Stot) = JD 2 [Stot(Stot + 1) − S1(S1 + 1) − S2(S2 + 1)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (19) For Mn adatoms with S1 = S2 = 5 2, the splitting between the triplet (S = 1) excited state and the singlet (S = 0) ground state is equal to ∆E(0) st = JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The singlet-triplet splitting is renormalized due the coupling of the adatoms to the substrate electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Tunneling of electrons between adatom d orbitals and substrate couples the singlet to the intermediate states |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, ± 1 2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The singlet state has exchange energy Eex(5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0) = −35JD 4 , (20) while the intermediate states have exchange energy Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) = −7JD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (21) In the absense of hybridization, we can then write the energy of of singlet state as E(0) s = 2EMn + EFS + Eex(5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0), (22) where EMn denotes the energy of the uncoupled Mn adatom and EFS the energy of the unperturbed Fermi sea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Similarly, the intermediate state has energy E(0) s,out = 2EMn + |ϵd| + EFS + ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) (23) 11 for tunneling out and E(0) s,in = 2EMn + ϵd + U + EFS − ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) (24) for tunneling in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Here, −ϵd > 0 is the energy to remove an electron from the filled d-shell and ϵd + U the energy to add an electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We can then compute the perturbative shift of the singlet state as ∆Es = 2|V0|2 � � � � ξk>0 1 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2)] + � ξk<0 1 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2)] � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (25) Note that the two intermediate states |2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2, ± 1 2⟩ give the same contributions, each with a factor 1/2 due to the matrix elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Note also that the overall factor of two appears, since electrons can tunnel from either Mn adatom of the dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' We can then simplify ∆Es = −2ν0|V0|2 ˆ ∞ 0 dξ � 1 |ϵd| + ξ + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) − Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0) + 1 ϵd + U + ξ + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) − Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 0) � (26) or ∆Es = −2ν0|V0|2 ˆ ∞ 0 dξ � 1 |ϵd| + ξ + 7 4JD + 1 ϵd + U + ξ + 7 4JD � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (27) Here, we introduced the density of states ν0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Assuming the dimer coupling JD to be small compared to the atomic- physics scales |ϵd| and U, we find ∆Es = const + 7JD 4 2ν0|V0|2 � 1 |ϵd| + 1 ϵd + U � , (28) where the constant is a contribution that is independent of the exchange couplings and that cancels out in the singlet-triplet spacing against a similar contribution to the shift of the triplet state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Now consider the shift of the triplet state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' There are intermediate states with different energies, which have to be incorporated with the appropriate matrix elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This yields ∆Et = 2|V0|2 � � � � ξk>0 7 15 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2)] + � ξk<0 7 15 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2)] + � ξk>0 8 15 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1)] − [2EMn + |ϵd| + EFS + ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2)] + � ξk<0 8 15 [2EMn + EFS + Eex( 5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1)] − [2EMn + ϵd + U + EFS − ξk + Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2)] � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (29) Using the energies Eex(5 2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1) = −31JD 4 (30) Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 2) = −7JD (31) Eex(2, 5 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3 2) = −11JD 2 , (32) we find, by the same steps as for the singlet shift, ∆Et = const + � 7 15 3JD 4 + 8 15 9JD 4 � 2ν0|V0|2 � 1 |ϵd| + 1 ϵd + U � = const + 31JD 20 2ν0|V0|2 � 1 |ϵd| + 1 ϵd + U � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (33) 12 Combining results, we obtain the singlet-triplet splitting ∆ = JD + ∆Et − ∆Es = JD � 1 − 1 52ν0|V0|2 � 1 |ϵd| + 1 ϵd + U �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (34) Schrieffer [1] has derived the sd exchange coupling J between adatom spins (magnitude S) and conduction electrons and finds J = |V0|2 2S � 1 |ϵd| + 1 ϵd + U � (35) (assuming dominant coupling to a single channel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Thus, we can express the renormalized singlet-triplet splitting as ∆ = JD + ∆Et − ∆Es = JD(1 − 2ν0J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (36) Accounting for the coupling of the adatom to all five conduction electron channels m, this result generalizes to ∆ = JD(1 − 2 � m ν0Jm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' (37) This equation is quoted in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' ADDITIONAL EXPERIMENTAL DATA A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Adsorption structure of Mn atoms on MoS2 Figure 1a shows an overview topography image of a monolayer-island of MoS2 decorated with a large number of Mn atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' A close-up view confirms that the individual atoms appear as round protrusions throughout a bias voltage range of -1 to 1 V (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Owing to the convolution with the tip shape, the atoms appear with a large width (∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='9 nm), impeding the determination of the exact adsorption site on the atomic lattice constant of MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The similarity of apparent heights and spectroscopic signatures suggests that all atoms adsorb in equivalent lattice sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This is in agreement the observation of unique adsorption sites of Fe on MoS2 [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' DFT calculations further suggest hollow sites to be the energetically most favorable positions [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Occasionally, we find elongated protrusions (see also lineprofiles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1c), which we ascribe to dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 10 nm 3 nm a) b) c) 300 200 100 0 apparent height (pm) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 distance (nm) Supplementary Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a) Large-scale STM image of a monolayer-island of MoS2 on Au(111) after adsorption of Mn atoms at low temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Recorded at 1 V and 100 pA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' b) Close-up view showing individual atoms as round protrusions and some elongated structures most probably being Mn dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Some point defects can be observed in the MoS2 layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Recorded at 100 mV and 20 pA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c) Height profiles along the black and red lines shown in b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 13 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Manipulation of Mn atoms We mainly investigated Mn dimers statistically distributed over the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In rare cases, we were able to manip- ulate the Mn atoms in a controlled manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2 shows an example of consecutive manipulation events and the dI/dV spectra recorded on the obtained structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2a two Mn atoms are separated at sufficiently far distance such that they exhibit a Kondo resonance (spectrum shown in 2d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' At closer distance (b), the Kondo resonance is split (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' When the atoms are pushed into adjacent lattice sites as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2c, the singlet-triplet excitation is observed (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='80 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='70 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='60 15 10 5 0 5 10 15 bias voltage (mV) dI/dV (G0) x 10 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='2 15 10 5 0 5 10 15 bias voltage (mV) dI/dV (G0) x 10 3 b) + c) + a) d) + 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 dI/dV (G0) x 10 3 15 10 5 0 5 10 15 bias voltage (mV) e) f) 5 Å 5 Å 5 Å Supplementary Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Manipulation of two Mn atoms into dimer structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a-c) STM topographies of the same atoms before and after successive manipulation events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The atom at the bottom of figure (a) was pushed closer towards the other upper atom, as seen in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Here the atoms are still distinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In (c) the lower atom was pushed even closer to the upper atom, resulting in a dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' d-f) dI/dV spectra performed on the upper atom in (a), (b) and (c) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The topographies were recorded at 100 mV and 20 pA, the setpoint of the recorded spectra was 15 mV and 3 nA (f) and 10 mV and 3 nA (g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3a shows one dimer where two Mn atoms are two lattice sites apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The Kondo resonance is split (red line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 3c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Removing one of the atoms leads to an unperturbed Kondo resonance (green line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' An unambiguous assignment of the adsorption sites of the Mn atoms within the dimer structures is challenging as the Mn atoms appear very large and cannot be separately resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Analyzing the orientation of the dimers on the surface, we observed only three orientations, suggesting the registry with the threefold atomic lattice structure of MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' While attempting to remove one of the Mn atoms from the densely-packed dimer structures by a voltage pulse, we often observed effectively a rotation of the dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Also the resulting dimers follow the main axes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 14 + + a) b) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 dI/dV (G0) x 10 3 10 5 0 5 10 bias voltage (mV) c) 5 Å 5 Å Supplementary Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Disassembly of a Mn dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a,b) STM topographies of a Mn dimer before and after the removal of one atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Here the right atom in (a) was removed, leading to a single Mn atom as shown in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c) dI/dV spectra performed on the left atom in (a) and on the same (remaining) atom (b) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The topographies were recorded at 100 mV and 20 pA, the setpoint of the recorded spectra was 10 mV and 3 nA (g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 1 1 2 2 3 3 a) b) 1 nm 1 nm Supplementary Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rotation of Mn dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a), b) STM topographies of single Mn dimers before (a) and after (b) applying a high bias voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' In (a) the dimers 1 and 3 show the same orientation, whereas dimer 2 is rotated by roughly 120◦ with respect to 1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' After a bias voltage of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 V was applied to the dimers in (a), dimer 1 and 2 appear rotated by 120◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The topographies were recorded at 100 mV and 20 pA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' RKKY coupled dimers in different moir´e sites In the main text, we showed the variation of singlet-triplet excitations along the moir´e superstructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' To probe whether RKKY-coupled Mn dimers are equally affected by the moir´e structure, we investigate Mn dimers with a spacing of two substrate lattice sites (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' As described in the main text, substrate-mediated interactions lead to small excitation gaps around the Fermi level on top of the Kondo resonance (red lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 5c,f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Various dimers in different moir´e sites display similar gap sizes while the height of the Kondo resonance varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The same height modulation of the Kondo resonance is found on the isolated atoms in the same adsorption sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' This is shown by spectra taken on the same atoms after the neighbor has been removed by STM manipulation (black lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 5c,f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Hence, once Kondo correlations of the individual atoms dominate the spectra and the coupling enters through a small perturbation, we hardly observe any moir´e induced modulations in the coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Schrieffer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 38, 1143 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Trishin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lotze, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Bogdanoff, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' von Oppen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Franke, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' 127, 236801 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [3] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Qi, Nanoscale 9, 2188 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Gao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Kong, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Zhang, Physica E: Low-dimensional Systems and Nanostructures 63, 276 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' : .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='15 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 dI/dV (G0) x 10 3 10 5 0 5 10 bias voltage (mV) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content='6 dI/dV (G0) x 10 3 10 5 0 5 10 bias voltage (mV) + a) + + + b) d) e) c) f) 5 Å 5 Å 5 Å 5 Å Supplementary Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Moir´e effect on RKKY-coupled Mn dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' a), d) STM topographies of Mn dimers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' Whereas in (a) the dimer is adsorbed close to the moir´e maximum, in (d) the dimer is adsorbed in the moir´e valley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' c), f) dI/dV spectra performed at the crosses in (a) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' b),e) show the same scan frame, after one atom has been removed from the dimer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The black spectra in (c) and (f) show the spectra of the respective monomer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} +page_content=' The topographies were recorded at 100 mV and 20 pA, the setpoint of the recorded spectra was 15 mV and 3 nA (c) and 10 mV and 3 nA (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AzT4oBgHgl3EQfjf2C/content/2301.01517v1.pdf'} diff --git a/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/2301.01273v1.pdf.txt b/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/2301.01273v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..45744f71f3bff95221e7e802838e4549224c2c85 --- /dev/null +++ b/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/2301.01273v1.pdf.txt @@ -0,0 +1,2051 @@ +1 + +Design of dye-sensitized TiO2 materials for photocatalytic hydrogen production: +light and shadow +Lorenzo Zani,a Michele Melchionna,b Tiziano Montini,b Paolo Fornasiero b,* +a Institute of Chemistry of Organometallic Compounds (CNR-ICCOM), Sesto Fiorentino 50019, Italy. +b Department of Chemical and Pharmaceutical Sciences, CNR-ICCOM Trieste Research Unit and INSTM +Research Unit, University of Trieste, Trieste 34127, Italy; email: pfornasiero@units.it. + +Table of Contents +1. +Introduction: visible light absorption and the relationship with DSSCs +2. +How to properly compare data +3. +Charge transfer processes in DSP +4. +Design of dye scaffold for application in DSP +5. +Hydrophobicity vs. hydrophilicity of the photocatalyst surface +6. +Effect of dye loading on photocatalytic performances +7. +Impact of TiO2 crystal structure: which phase is the best? +8. +Approaches to improve stability +9. +Nature of the hydrogen evolution catalyst +10. Sustainability of the sacrificial donor +11. Perspectives +12. References + +Abstract: +Visible light-driven production of fuels and value-added chemicals is currently one of the most intensely +investigated research topics across various scientific disciplines, due to its potential to ease the World’s +dependence on fossil fuels. In this perspective, we recapitulate some of the main features of dye-sensitized +photocatalytic systems aimed at solar H2 production, focusing in particular on TiO2-based three-component +assemblies with organic sensitizers. Relevant aspects include the structural and electronic properties of the +sensitizers, the nature of the semiconductor and the hydrogen evolution catalysts, the role of the sacrificial +donor and the effect of the reaction parameters on H2 production rate and stability. Besides presenting the most +significant recent developments of the field, we also analyse some of its common practices in terms of +experimental design, laboratory procedures and data presentation, trying to highlight their weaknesses and +suggesting possible improvements. We then conclude with a short paragraph discussing the possible future +development of this exciting research area. + +2 + +1. Introduction: visible light absorption and the relationship with DSSCs +Due to the urgent need to replace fossil fuels as the World’s main energy source, the conversion of solar +radiation into chemical energy in the form of so-called “solar fuels”, often referred to as “artificial +photosynthesis”,[1] is currently of utmost scientific and technological relevance.[2] Among the different +artificial photocatalytic processes, H2 production through water splitting (WS) has probably been the most +intensely studied, since H2 is endowed with high volumetric energy density, no carbon footprint and can be +either directly burned or used in fuel cells to produce electricity, thus constituting an almost ideal energy +carrier.[3,4] +In 1972, the pioneering work of Honda and Fujishima demonstrated that WS into H2 and O2 could be +achieved by irradiating a TiO2 photoanode connected to a platinum cathode in an electrochemical cell.[5] The +main drawback of such system was the use of a wide band-gap (≥ 3.0 eV) semiconductor (SC) as the light- +harvesting material, which hampered absorption and conversion of visible light (λ > 400 nm) and made it +necessary to use UV radiation to drive the reaction forward. +To solve such an issue, several possible approaches to modify inorganic heterogeneous photocatalysts have +been investigated,[6] including the use of narrow band-gap semiconductors[7,8] the chemical modification of +large band-gap materials to impart them the ability to absorb visible light,[9] or the application of more +complex photocatalytic assemblies such as Z-schemes.[10,11] Besides, another effective strategy has been the +sensitization of semiconductors with molecular dyes, able to harvest light in the desired wavelength range and +inject the resulting photogenerated electrons into the SC conduction band.[12] This concept was first +established in Dye-Sensitized Solar Cells (DSSC), in which, after excitation and charge injection, electrons +are collected at a TiO2 photoanode while holes are transferred to the reduced form of a suitable redox mediator +(typically I3−/I−), which is then regenerated at the cathode to close the cycle and produce an electric current +(Figure 1a).[13] Due to the analogy with DSSCs, such photocatalytic systems are usually called Dye-Sensitized +Photocatalysts (DSP). +DSSC and DSP share the same dye/semiconductor interface but, in the latter, photogenerated electrons in +the conduction band are transferred to an electrocatalyst (such as Pt) for solar fuel production, instead of being +used for electricity generation. Accordingly, in DSP the oxidized dye molecules must be reduced by a suitable +hole scavenger to allow the process to continue (Figure 1b). In a proper WS procedure, electrons would be +supplied by water itself, allowing coupling of H2 production with O2 evolution without formation of any other +by-product. However, water oxidation demands combining the sensitizers with appropriate catalysts, often a +synthetically demanding operation,[14] and is usually affected by significant drawbacks, such as the need for +a large overpotential,[15] the quick recombination of photogenerated charge carriers, and the rapid back +reaction between H2 and O2.[16] Consequently, to achieve a high yield of H2 production, but also to better +determine the photocatalyst intrinsic activity, dye regeneration is more commonly carried out by means of a +sacrificial electron donor, usually abbreviated as SED (see below).[17] From the above discussion it is clear +that, despite the similarities between the two systems, the materials used in DSSC or DSP, such as dyes and + +3 + +semiconductors, must work under different conditions and thus will need to be developed independently to +provide optimal performances in each application. + + + + + + + + + + + +Figure 1. Schematic representation of the working mechanisms of (a) a DSSC and (b) a DSP. +In this perspective, the main features of selected DSP systems especially developed for H2 production will +be critically presented, trying to highlight their strengths as well as the areas where there is still room for +improvement. Although the concept of dye-sensitization has been applied to different kinds of materials,[18] +inorganic[19] as well as organic,[20,21] we will focus on TiO2-based systems, since they are by far the most +investigated in the literature and thus can be more easily compared. In the majority of such systems, TiO2 is +used as the anatase crystalline form, or as the commercially available 80:20 anatase/rutile mixture known as +P25,[22] but alternatives have also been described. +Before starting the discussion, we will briefly introduce the topic of the correct presentation and comparison +of photocatalytic data, as the adoption of a more homogeneous and shared standard will be of crucial +importance for the future development of the field. +2. How to properly compare data +The criticality of correctly evaluating the merits of a new proposed photocatalyst is one of the contemporary +topics of discussions within the photocatalysis community.[23,24] In this respect, the importance of +introducing more comprehensive and diligent practices when assessing and comparing photocatalysts +performances has been recently highlighted.[25] As an example, for heterogeneous photocatalysts it is very +common to report the rate of evolved product per mass of photocatalyst, which gives also an idea of how stable +it is, but does not take into account the contribution of its textural features. Hence, adding a rate normalized +by the material surface area provides a more thorough screening and is therefore recommended.[26] +Turnover numbers (TON), or in alternative turnover frequency (TOF), are two other classic catalytic +parameters, which in the specific case of DSP are calculated over the number of moles of dye covering the +semiconductor nanoparticles. Hence, the catalytic sites are assumed to be equal to the number of molecules of + +Load +(a) +(b) +e +W +@" +Pt on Tco +(reduction +TCO +hy +hv +catalyst) +e +2H* +Dye +e +CB +SED* +Ered +Dye +TiO2 +H2 +@ +Sed +Reduction +catalyst +M/M +SeD = Sacrificial Electron Donor +. dye +M = redox mediator4 + +dyes, which may in principle lead to underestimated TON or TOF, if not all the dye molecules are in the right +spatial configuration for electron transfer to the SC (e.g. formation of aggregates, intermolecular charge +transfer). Moreover, apart from depending on several conditions such as temperature and pH, TOF is a kinetic- +dependent parameter, so that it should be evaluated at low conversions (or at least the reactant or product +concentrations should be provided), or ideally as an instantaneous value measured at specified product (or +reactant) concentrations.[27] Most studies on heterogeneous photocatalysts, however, compare them in terms +of quantum yield (QY), quantum efficiency (QE), or photonic efficiencies, where instead of the number of +catalytic sites (which for DSP is assumed to be the number of dye molecules), the number of incident photons +is considered.[23] While the adoption of this parameter seems to remove the uncertainty on the effectiveness +of the adsorbed dye to transfer electrons, it also introduces an element of ambiguity related to the +heterogeneous nature of the photocatalyst. In fact, for heterogeneous systems, not all the incident photons are +necessarily absorbed, with scattering phenomena taking place and decreasing the amount of utilized photons. +For heterogeneous photocatalysts, the term apparent quantum yield (AQY) is therefore more sensible.[28] As +a result, the AQY is almost always an underestimation of the real QY. Moreover, as the AQY is a function of +the excitation wavelength,[29] a fact that is at times ignored, the comparison between DSP with different +absorption characteristics may be affected by inaccuracies, causing false esteems. A good practice will +therefore be to plot the wavelength-dependent AQY profile by measuring it at successively increasing +wavelengths, and then verify that the pattern follows that of the photocatalyst or sensitizer absorption spectrum. +3. Charge transfer processes in DSP +As shown in Figure 1, the photocatalytic cycle in DSP is initiated by the two steps of light absorption and +charge separation, which are of pivotal importance to determine the efficiency of H2 generation. Two main +mechanisms have been proposed for the charge separation process involving a photoexcited dye, the +semiconductor (most commonly TiO2) and the SED, classified as reductive quenching and oxidative +quenching, respectively.[30] Following light absorption (eq. 1), the reductive quenching mechanism proceeds +with an electron transfer from the SED to the excited dye, which is thus converted into a radical anion (D•−, +eq. 2). Subsequent electron injection into the semiconductor conduction band restores the dye in its ground +state and completes charge separation (eq. 3). In the oxidative quenching mechanism, on the other hand, the +first electron transfer step involves charge injection from the excited dye to the semiconductor, with +concomitant formation of a dye radical cation (D•+, eq. 4). The latter is then reduced by the SED, and the same +charge separation state is reached (eq. 5). Finally, the electrons in the conduction band of the semiconductor +will be used for H2 generation by proton reduction (eq. 6). Besides these productive electron transfer events, +however, it must be pointed out that detrimental, reverse charge transfer processes can also take place, such as +charge recombination between injected electrons and the dye cation or the oxidized SED. The ratio between +the rates of forward and backward electron transfer processes is what ultimately dictates the efficiency of the +photocatalytic system.[12] + +5 + +Photoexcitation: + +Pt/TiO2/D + hν → Pt/TiO2/D* + + + + +(1) +Reductive quenching: +Pt/TiO2/D* + SED → Pt/TiO2/D•− + SED+ + + + +(2) + + + + +Pt/TiO2/D•− → Pt/TiO2 (e−)/D + + + + +(3) +Oxidative quenching: +Pt/TiO2/D* → Pt/TiO2 (e−)/D•+ + + + + +(4) + + + + +Pt/TiO2 (e−)/D•+ + SED → Pt/TiO2 (e−)/D + SED+ + + +(5) +Proton reduction: +Pt/TiO2 (e−)/D + H+ → Pt/TiO2/D + 1/2 H2 + + + +(6) +In general, the oxidative quenching mechanism is considered to be predominant for almost all dye classes +(see below), in analogy with what happens in DSSCs. The reductive quenching mechanism is probably relevant +only in the case of poorly reducing, cationic dyes (e. g. thionine, methylene blue, nile blue A), and has been +suggested to provide inferior results in terms of H2 production.[30] The efficiency of the charge transfer +process between the dye and the semiconductor is usually assessed by means of photoluminescence decay +studies: by comparing the excited state lifetime of the dye in solution to that of the dye/semiconductor assembly +the rate constant for electron transfer can be calculated with good approximation.[31] +4. Design of dye scaffold for application in DSP +Dye design is certainly one of the most important factors affecting light harvesting and charge transfer +efficiency in DSP systems. As mentioned in the introduction, the concept of dye-sensitization in DSP was +originally derived from that of DSSCs. Consequently, the main classes of dyes employed in photocatalysis +resemble those already applied in solar cells, namely (i) metalorganic complexes, especially based on +ruthenium with bi- o terpyridine ligands; (ii) porphyrins and phthalocyanines bearing different central metals; +(iii) metal-free organic dyes. This latter class of dyes has been the subject of the largest number of studies in +recent years,[32,33] and can be further divided into sub-categories, such as emissive dyes traditionally used in +chemical biology, or donor (D)-acceptor (A) structures, where electron-donating groups are connected to +electron-accepting units via conjugated sections of various nature. Such an arrangement allows extending and +strengthening the absorption spectra of the resulting compounds, improving their light-harvesting ability. In +their simplest form, these compounds are usually denoted as D-π-A dyes, with the electron acceptor also +fulfilling the role of anchoring group to the semiconductor;[34] from them, more complex architectures such +as D-A-π-A, D-D-π-A and others[35] have been derived by the insertion of additional donor or acceptor units +in various parts of the structure. +A comprehensive review on the use of all the above classes of sensitizers in DSP is beyond the scope of +this manuscript, and has already been presented elsewhere.[12] Here, we will focus our attention on the +employment of organic dyes, since they have provided the best results in DSP systems. Moreover, the fact that +they do not contain precious or toxic heavy metals makes them more sustainable than metalorganic complexes, +which is particularly relevant in the field of renewable energy technologies. Finally, they are usually accessible + +6 + +through simple and modular synthetic processes, allowing to efficiently tune their stereoelectronic properties. +Accordingly, they constitute an ideal platform to analyse how their structural and compositional changes can +affect the overall performances of the DSP systems. +Despite their similarities, organic dyes used in DSP have evolved independently from those employed in +DSSCs, due to the different conditions in which they must operate. For example, they have to work efficiently +in the aqueous environment used in DSP, while DSSC usually contain organic solvents and are moisture- +sensitive. In addition, they must be regenerated by SED molecules, which are different from the redox couples +commonly used in DSSCs, thus requiring a different alignment of their energy levels (especially the HOMO +level). Finally, the fact that DSSCs are self-contained devices in which the photo- and electroactive materials +are supported onto electrodes while DSPs operate in heterogeneous suspension bears different requirements in +terms of dyes molar absorptivity and loading onto the semiconductor. For the above reasons, although DSP +and DSSC dyes usually have similar light harvesting properties, they can present significant differences in the +way they are attached to the SC surface, in the balance of their hydrophobic and hydrophilic characteristics, +and in their electrochemical properties. Some of these features will be discussed below. +To work efficiently in a DSP system, any sensitizer has to fulfil two obvious requirements: (i) it should be +able to absorb light efficiently in the visible region of the spectrum (where solar radiation is maximized); (ii) +it should transfer easily the photogenerated electrons to the conduction band of the semiconductor. Thanks to +the extensive experience accumulated in the field of DSSC, it has been relatively straightforward to build a +library of organic photosensitizers for DSP applications having both these properties.[12,32] By changing the +nature of the main chromophore and adjusting the length of the conjugated section, compounds have been +reported with the main absorption band going from around 400 nm (as in the case of simple D-A structures, +Figure 2, 1)[36,37] to almost 700 nm, close to the near-IR region (as in the case of porphyrin- or BODIPY- +containing species, Figure 2, 2).[31,38,39] On the other hand, insertion in the structure of additional electron- +donating or accepting fragments can serve to modulate the frontier orbitals energy levels and thus alter the rate +of the intermolecular charge transfer processes.[40,41] It should be noted that all such properties can be +efficiently modelled by means of DFT calculations.[42] + +Figure 2. Structures of organic dyes having very different UV-Vis absorption maxima in solution. +Nevertheless, there are other characteristics the sensitizers must possess to boost the activity of a three- +component photocatalytic system. First, to be able to transfer electrons quickly to the semiconductor, they +should have a robust anchoring to its surface. Due to the analogy with DSSC dyes, most compounds bind the + +113 +CN +OH +2 +O +NC +OH += 391 nm (THF) +max7 + +semiconductor through a carboxylic acid group (either simple or as a part of a cyanoacrylic function).[43] +However, the aqueous conditions employed for H2 production and the different pH levels associated with +different hole scavengers (see below) motivate the look for alternatives. A systematic study was conducted by +Reisner and co-workers, who compared the performances of perylene monoimide (PMI) dyes endowed with +different anchoring groups (Figure 3a, Table 1) in acidic, neutral and basic conditions, using two hole +scavengers (triethanolamine and ascorbic acid).[44] Their main finding was that while a dye bearing the +carboxylic group was very active and sufficiently stable under acidic conditions, moving towards higher pH +the use of a phosphonic acid anchor became clearly preferable; interestingly, a dye with a hydroxyquinoline +anchoring group (PMI-HQui) proved also very efficient under acidic conditions, but underwent fast +deactivation as a result of detachment from TiO2 surface. + +Figure 3. Structures of organic dyes with different anchoring groups. +Table 1. H2 generation efficiency of PMI dyes with different anchoring groups.[44] +Dye +Dye loading +[μmol/g] +Conditions +(SED, pH)a +H2 produced +[μmol] (24 h) +TON +(24 h) +Retained activity +after 24 hb + + +AA, pH 4.5 +53.7 ± 6.2 +6461 ± 749 +78% +PMI- +CO2H +13.3 +TEOA, pH 7.0 +3.9 ± 0.5 +471 ± 63 +33% + + +TEOA, pH 8.5 +4.1 ± 1.4 +490 ± 170 +35% + + +AA, pH 4.5 +21.7 ± 2.2 +2146 ± 203 +80% +PMI-AcAc +16.2 +TEOA, pH 7.0 +1.3 ± 0.1 +133 ± 13 +51% + + +TEOA, pH 8.5 +3.0 ± 0.7 +294 ± 67 +52% + + +AA, pH 4.5 +42.5 ± 6.3 +3546 ± 523 +70% +PMI- +PO3H2 +19.3 +TEOA, pH 7.0 +3.6 ± 0.4 +303 ± 30 +46% + + +TEOA, pH 8.5 +8.5 ± 1.3 +708 ± 107 +48% + + +AA, pH 4.5 +53.3 ± 5.9 +4928 ± 549 +44% +PMI- +HQui +17.3 +TEOA, pH 7.0 +2.5 ± 0.5 +232 ± 26 +38% + + +TEOA, pH 8.5 +2.8 ± 0.4 +262 ± 36 +41% + +(a) +PM.COHRA +COOH +(b) +BO +PMI-AcAc, R= +Buo +Heos! +-R +PM-POM,R? +POM +A +tB +O +PmhQu,R? +Ho- +C.H +DpP-cA R-CoOoH +N +DDP-CN.RACN +tBu +GOOH +PMHDPA RE! +COOH8 + + + +AA, pH 4.5 +41.4 ± 2.9 +3943 ± 394 +54% +PMI-DPA +16.8 +TEOA, pH 7.0 +3.8 ± 0.2 +366 ± 37 +55% + + +TEOA, pH 8.5 +4.7 ± 0.7 +444 ± 62 +56% +a 1.25 mg Dye/TiO2/Pt in 3 mL 0.1 M SED solution, UV-filltered simulated solar irradiation (AM 1.5 G, 100 mW +cm−2, λ > 420 nm, 25 °C). b Calculated by comparing TOF values after 1 h and after 24 h. +A peculiar result was reported by Singh et al., who compared the efficiency of two photocatalytic systems +obtained with analogous dyes bearing a cyanoacrylic or a malononitrile anchoring group (Figure 3b). +Surprisingly, it was the latter (DPP-CN) that produced the better result in terms of H2 production in typical +conditions (dye loading 25 μmol/g, TEOA 10% vol. in H2O, pH 7, 2.0 Sun irradiation, λ> 400 nm), with a +TON of 9664 in 10 h (corresponding to 1208 μmol of evolved H2) compared to 6720 recorded for DPP-CA +(840 μmol of evolved H2).[45] Although the authors did not provide details on the anchoring mode of +malononitrile to TiO2, it is supposedly similar to that of dicyanomethylene compounds reported as sensitizers +for DSSC.[46,47] Nevertheless, the latter were used as Type-II sensitizers and have a much simpler molecular +structure, and therefore the working mechanism is hardly comparable in the two cases: given the excellent +results reported, it seems that a deeper investigation of dyes with malononitrile or related anchoring groups +could be useful to shed light on their behavior and further improve their performances. +Another key point is that the sensitizer, after photoexcitation and charge injection, should be readily +regenerated by the reductant present in solution (either water in WS processes or a SED). Once again, this +process has been thoroughly characterized in DSSC, and the main properties that a dye must possess to undergo +efficient regeneration by a certain redox mediator are known in sufficient detail (driving force of the reaction +i.e. dye HOMO position,[48] presence of certain functional groups on the donor section[49]). In the case of +DSP systems, the situation is much less clear: an obvious requirement is for the sensitizer to have a more +positive ground-state oxidation potential (ES+/S*) than the standard redox potential of the reducing agent. +However, this condition is not met in every case: for example, TEOA redox potential is reported to be +0.82- +1.07 V vs. Normal Hydrogen Electrode (NHE),[17] but an efficient H2 production was found also when +employing it as a SED in combination with dyes having oxidation potentials in the +0.64-0.74 range.[45,50] +Conversely, despite an apparently appropriate driving force for regeneration, many organic dyes with +triphenylamine donors were found inactive when used together with ethanol as a hole scavenger.[51] Such +apparent contradiction is probably due to two main reasons: first, dyes ES+/S* values are usually measured on +diluted organic solutions in CH2Cl2 or CH3CN, a very different environment compared to that in which they +are actually used (adsorbed on TiO2 in aqueous environment); second, different hole scavengers may work +according to different reaction mechanisms and their redox potentials usually vary with pH,[17] which affects +dye regeneration rates and thus photocatalytic turnover frequencies. In addition, the relative dye +hydrophobicity/hydrophilicity could also influence its regeneration process (see below). To better evaluate the +ability of organic dyes to work in DSP systems, it would be therefore advisable to investigate their +electrochemical properties in more detail and in conditions more relevant to their actual application. + +9 + +Furthermore, the reference electrode against which potentials are measured and the formalism used to convert +such values to orbital energies (vs. vacuum) should be clearly indicated, as incomplete information often +hinders comparison of data reported in different studies. +As a final point of this paragraph, spatial organization of dye molecules on the semiconductor surface +should also be precisely controlled, to maximize the photocatalyst light absorption ability and reduce losses +due to energy dissipation. Such a parameter has also often been associated with the relative +hydrophobicity/hydrophilicity of the dyes, controlling their interactions with the solvent and the semiconductor +surface (see below). Ahn, Son and co-workers found that by decorating phenothiazine dyes with alkyl chains +of different length (Figure 4, P1-P5) a macroscopic effect on H2 production efficiency could be observed, with +the best result provided by dye P5 featuring the largest substituent (TON after 5 h increasing from 380 for P1 +to 1026 for P5); the authors claimed that “alkyl groups on nitrogen can induce a favorable orientation of dyes +on TiO2, which may result in the efficient electron injection from excited dyes to TiO2”.[52] +Such a concept was further developed by Abbotto, Fornasiero and co-workers, who modified the same class +of dyes and placed different hydrophobic and hydrophilic chains on the nitrogen atom (Figure 4).[53] They +found that dye PTZ-ALK, featuring an n-octyl chain, showed a much higher H2 production efficiency +compared to its hydrophilic counterparts (PTZ-TEG and PTZ-GLU) at low dye loading, but such a difference +was largely reduced when the loading was increased up to 30 μmol g–1 (Table 2). According to the authors, at +high loadings the organization of PTZ-GLU is “similar to that of PTZ-ALK, with the PTZ units interacting +with the Pt/TiO2 surface and the bulky lateral chains avoiding intermolecular quenching”; when the loading +is decreased, though, “the glucose unit could interact directly with the TiO2 surface through the remaining OH +groups and it might change the orientation of the PTZ scaffold affecting the electron transfer to TiO2”.[53] + + + + + + + + + + +Figure 4. (a) Structures of phenothiazine-based photosensitizers and GLUA additive; (b) DFT computational analysis +showing the H-bond interaction between dye PTZ-GLU and GLUA (in the red circle). Reprinted with permission from +reference [54] (© 2018, American Chemical Society). +The importance of having a correct disposition of sensitizers molecules on the semiconductor surface was +later confirmed when the same group studied the effect of combining PTZ-GLU with different co-adsorbents, +including in particular glucoronic acid (GLUA, Figure 4).[54] It was found that using the sensitizer and GLUA + +(a) +(b) +ONI +ONT +P. rhch. +GN +HooG +COOHI +Pizalk Ra coh? +Hood +PTZTEGLRS +HO +OH +PTZGLU,RE +oMe +glucoronfic acid (GLUA) +OH +OHI10 + +in a 1:1 ratio clearly increased the TON of the photocatalyst; remarkably, this was not the case when a different +and more hydrophobic co-adsorbent (chenodeoxycholic acid, CDCA) was used (Table 2). By employing DFT +computational analysis, the authors found that a “directional and selective” interaction was established +between PTZ-GLU and GLUA, which helped stabilizing the dye-semiconductor assembly and was effective +in hindering dye-dye intramolecular interactions, minimizing unproductive energy transfer phenomena. This +was confirmed by the fact that, when PTZ-ALK was combined with either CDCA or GLUA in the same ratio, +no improvement was observed, since no selective interaction could be established between the coadsorbents +and the bare alkyl chain. +Table 2. Photocatalytic data for PTZ dyes in combination with different coadsorbents.[53,54]a +In summary, although dye design principles for DSSC and DSP may be similar, sensitizers for the latter +application should be developed in response to specific requirements to allow performance improvements. +While maintaining a wide and intense light absorption in the visible spectrum, charge injection rates into the +SC should be improved, for example by investigating new anchoring groups exploiting unusual charge transfer +mechanisms. Dye regeneration rates should also be enhanced by exact tuning of the sensitizers HOMO levels +towards use with a specific electron donor; this operation should be assisted by measuring the dyes +electrochemical properties under more realistic conditions, and by performing time-resolved spectroscopic +analysis of dye regeneration by different species, as already done in DSSC.[55] Finally, dye organization on +the SC surface should be optimized by exploiting the formation of ordered supramolecular structures, either +using the dyes alone or by interaction with co-adsorbent species, not limited to those traditionally employed +in DSSCs. + +Dye +Dye loading +[μmol/g] +Coadsorbent +H2 produced +[mmol/g] (20 h) +TON (20 +h) +LFE20 [%]b +AQY [%]c +PTZ- +GLU +1 +- +- +678 +0.008 +- +30 +- +0.88 +59 +0.024 +0.071 +30 +GLUA (1:1) +1.37 +91 +0.037 +0.139 +30 +CDCA (1:1) +0.73 +48 +0.020 +0.077 +PTZ- +ALK +1 +- +- +1232 +0.017 +- +30 +- +0.96 +64 +0.026 +0.081 +30 +GLUA (1:1) +0.66 +44 +0.018 +0.062 +30 +CDCA (1:1) +0.84 +56 +0.023 +0.073 +PTZ- +TEG +1 +- +- +396 +0.005 +- +30 +- +0.421 +29 +0.013 +- +a Conditions: TEOA 10% v/v solution in H2O, pH 7.0, 20 h irradiation, visible light (λ > 420 nm). b LFE20: light-to- +fuel efficiency after 20 h; for details on its calculation, see ref. [32]; c obtained with light irradiation at 450 nm. + +11 + +5. Hydrophobicity vs. hydrophilicity of the photocatalyst surface +Variation of the dyes relative hydrophobicity and hydrophilicity can have a significant impact on the +photocatalyst performances. However, the simple question if it is better, in terms of H2 production efficiency, +to use a more hydrophobic or hydrophilic sensitizer has not yet been definitively answered. Clearly, dye +optimization should not only aim at improving the individual properties of the molecules (structural, +spectroscopic, electrochemical), but should also take into account the specific conditions in which the +photocatalytic reaction is conducted, including solvent, pH, presence and nature of a hole scavenger, type of +illumination and so on; in this regard, it is then possible that the optimal sensitizer in one case will be +outperformed by a different compound in another, if the reaction conditions are not the same. +As mentioned above, some early studies examined the effect of placing alkyl chains of different lengths on +the donor section of the sensitizers, usually finding that photocatalysts based on dyes with long (up to C16) +substituents provided the best results.[52,56,57] In a further refinement, the issue of where it is best to place +such hydrophobic groups has also been recently investigated. Although comparing reports on different classes +of dyes is not always straightforward, it has emerged that putting alkyl chains on the middle part of the organic +dye structures can also be advantageous,[58,59] and even lead to enhanced results, as shown in Figure 5a, +where the TON values for dyes MB25 and AD418 are compared to that obtained for dye DF15 (TEOA as +SED, pH 7).[51] Such an effect was attributed to a more efficient shielding of TiO2 coupled with a higher dye +regeneration rate, due to the lack of steric bulk on the donor group. Indeed, further increase of the dyes +hydrophobicity by installation of alkyl chains both on their donor and intermediate sections can even be +detrimental, as exemplified by the data collected for Pt@TiO2/OB1-3 photocatalysts (Figure 5b): after an +initial improvement going from OB1 to OB2, performances with the OB3-based system were almost back to +the initial level, probably as a consequence of an excessive steric bulk and non-optimal interaction with the +hole scavenger.[60] + + +HCo +OH +300 +DF15 +MB25 +AD418 +250 +DF15 +GSH +200 +HsCo +可 +OHI +150 : +- +er +100 +1. +MB25 +50 +TON=474 +ToN=569 +TON=872 +T +5 +10 +15 +20 +5 +101 +15 +20 +5 +10 +15 +20 +tme(h) +time(h) +time (h) +AD418 +CsH +(b) +TON-510 ++ +R +NC +TON= 251 +SH +OBTRECH.ROH +TON=210 +OB2.RE(CH2)/CH.R-=H12 + +Figure 5. Structures of (a) dyes DF15, MB25, AD418 and (b) OB1-3, and the H2 production curves of the +corresponding Pt/TiO2 dye-sensitized photocatalysts in the presence of TEOA as hole scavenger. Adapted with permission +from references [51] (© 2018, Wiley-VCH) and [60] (© 2019, American Chemical Society). +Moving to the opposite direction in terms of dye polarity, Kang and co-workers investigated the impact of +changing the hydrophilic and steric properties of a series of organic dyes in sensitized H2 generation using +Pt/TiO2 photocatalysts (Figure 6).[61,62] When using EDTA as sacrificial donor at acidic pH, it was found +that hydrophilic methoxymethyl substituents at the 4,4′-positions of the diphenylamino end group enhanced +the photocatalytic activity compared to both the parent compound (without substituents) and a hydrophobic +counterpart. Differently from what seen above for hydrophobic chains, introduction of hydrophilic substituents +also in the middle conjugated section of the molecules did not bring any further improvement. By applying +both transient spectroscopy techniques and DFT calculations, the authors concluded that the different +performances of the photocatalysts were due to a different organization of solvent molecules around the +hydrophilic or hydrophobic substituents, coupled with steric effects that determined the amount of dye +adsorbed on the semiconductor surface, which collectively influenced the kinetics of charge transfer processes +across the SED/dye/semiconductor interfaces. For the best sensitizer, MOD, an AQY value of 0.27 ± 0.03% +was measured under monochromatic light irradiation at 436 nm. + + + + + + + + + + + + + + + +Figure 6. (top) Structures of the hydrophilic sensitizers designed by Kang and co-workers, and of the corresponding +hydrophobic dye. (bottom) TON of the H2 production reaction of the corresponding Pt/TiO2 DSP in the presence of EDTA +as a hole scavenger. Reproduced with permission from ref. [62] (© 2012, Wiley-VCH). +Despite their obvious interest, the above results turned out to be quite specific, as shown by the previously +mentioned work by Abbotto, Fornasiero and co-workers on phenothiazine dyes,[53] in which they reported + +OH +R +HD, R1 = R?= H +MOD,R=-CH,OCH3,R?=H +PD, R1 = -(CH2),CH3, R? = H +MO4D, R1 = R? = -CH,OCH3 +18 +MOD +16 +MO4D +14 +HD +PD +12 +10- +NOI +8. +6. +4. +2 +0 +0 +50 +100 +150 +200 +250 +Time (min)13 + +that dyes with hydrophilic substituents on the donor section were actually less efficient than that featuring a +simple alkyl chain; it should be noted that their experiments were conducted in water at neutral pH and using +TEOA as SED, thus in very different conditions compared to those performed by Kang et al. +The importance of correctly matching the sensitizers structure with the actual reaction conditions was +further demonstrated in a recent study, in which a series of ten organic dyes based on the benzothiadiaziole +(BTD) core and featuring a different number of hydrophobic and hydrophilic chains were used as sensitizers +for Pt/TiO2 in H2 production experiments with three different hole scavengers (TEOA, ascorbic acid, EtOH), +at different pH levels (Figure 7).[63] The best performances with TEOA at pH 7 were obtained with highly +hydrophobic dyes BB2a and BB2d (TON up to 295), whereas introduction of hydrophilic substituents on the +donor section did not bring any improvement. Remarkably, when employing ascorbic acid as SED at pH 4, +the situation was significantly changed, with the highest H2 amount produced by the photocatalysts based on +hydrophilic dyes BB2e and BB3e (TON up to 2266). Although the exact reason for the reversal in relative +performances is not known, the improved interaction of the hydrophilic dyes with the polar SED molecules, +coupled with a better matching of their ground-state oxidation potentials (compared to TEOA) and the easier +proton reduction at lower pH clearly contributed to the observed outcome. + + + + + + + + + + + + + + +Figure 7. (top) Structures of the hydrophobic and hydrophilic sensitizers of the BB2 and BB3 series; (bottom) TON +values obtained in combination with different SEDs at different pH (dye@P25/Pt photocatalysts, dye loading 10 μmol/g, +λ> 420 nm, irradiation time 15 h). +In general, the results of all the above-mentioned studies suggest that no such thing as an “ideal dye” for +DSP generation of H2 exists, and that optimization of sensitizers properties must always be assessed in relation +to the specific reaction conditions applied. In particular, choice of the sacrificial donor and of the pH level at +which the reactions are conducted appear especially decisive in determining the H2 production efficiency. In +this context, it will be imperative in future years to improve dye design by introducing on the donor section + +HiCs +CHi +HnCsCsHt +R +OH +BB2a. RHi +BB2e,R= +BB3.Ria +Sensitizer +TON Values +BB2a +BB2d +BB2e +IBB3e +SED +TEOa(pHz) +295 +238 +126 +147 +AA(pH4) +1231 +780 +2266 +19.1714 + +functional groups able to interact efficiently with the selected SED molecule, which, together with appropriate +tuning of the energy levels (see previous section), should help increase regeneration rate constants. To this +end, we think that investigation of dyes with combined hydrophobic/hydrophilic sections should be continued, +trying to favor structures able to provide a significant hydrophobic barrier against recombination near the SC +surface, while at the same time bearing hydrophilic groups of carefully tuned steric bulk near the region where +interaction with SED is thought to happen. +6. Effect of dye loading on photocatalytic performances +The effect of dye loading on photocatalyst performances is usually evaluated in two different ways, either +by saturation of the semiconductor surface with dye molecules or by adsorption of a precise amount of +sensitizers. In the first approach, the semiconductor nanoparticles are suspended in a solution containing a +large amount of dye, so that adsorption is maximized: as a consequence, different sensitizers will be adsorbed +in different amounts, depending mostly on their size and on their geometrical properties. In this way, it is +possible to evaluate the relative H2 production abilities of the corresponding photocatalysts, but no precise +information on the individual dye efficiency and on its optimal loading can be obtained. +For example, this was the case in the above-cited work by Liu et al.,[59] where the maximum possible +amount of “starbust” dyes DH1-4 was loaded on Pt/mc-TiO2 (an especially-developed anatase cubic +“microcage” TiO2 material). The TONs registered after 20 hours for dyes DH3-4 were higher than that +obtained for dye DH2, but the latter had a much higher adsorption density on the semiconductor surface, and +thus the corresponding photocatalyst produced a higher H2 amount (Figure 8 and Table 3). + + + + + + + + + + + + +Figure 8. Structures of dyes DH1-4.[59] + + + + +COOH +spacer +CN +CN +DH1-3 +COOH +DH4 +spacer: +DH1 +Dh2 +DH315 + +Table 3. Photocatalytic data for DH1-4/Pt/mc-TiO2 three-component systems.[59]a +Dye +Dye loading +[μmol/g] +H2 produced +[mmol/g] (20 h)b +TON (20 h)b +DH1 +47.18 +46.42 +984 +DH2 +59.11 +84.75 +1434 +DH3 +47.80 +75.68 +1583 +DH4 +32.77 +74.88 +2285 +a Conditions: 50 mg of dye/Pt/mc-TiO2 in 100 mL of a 10% TEOA solution in H2O. +Irradiation with a 300W Xe lamp equipped with a cut-off filter (λ > 420 nm). b Experiments +were run in triplicate, only the best result is shown. +In the second approach, a solution containing a precise quantity of sensitizer is used to stain the +semiconductor, so that after sensitization a colorless supernatant solution is obtained. In this way, a precise +amount of dye can be loaded on the photocatalyst, allowing to determine the effect of different dye loadings +and to assess the relative TON values of the dyes at the same level of superficial concentration. A common +finding in this kind of experiments is that the overall amount of generated H2 initially increases with the +increasing dye loading, but then reaches a maximum and starts decreasing again above a certain dye +concentration. For example, such an effect was observed in several studies by Pal et al. examining organic +sensitizers with different structures and anchoring groups,[45,50,57,64] and was attributed to the fact that +initially the fraction of incident light absorbed by the dye increases with increasing dye loading, but then the +photocatalytic activity starts to decline due to dye aggregation (accompanied by unproductive intermolecular +energy transfer) and shielding effects reducing the penetration depth of incident light. +Clearly, since the maximization of dye loading on the semiconductor surface does not always lead to +improved performances, this second approach appears preferable and a screening of the effect of dye +concentration is recommended to obtain photocatalysts with optimized efficiency. +7. Impact of TiO2 crystal structure: which phase is the best? +In the case of DSP, the semiconductor basically acts as an electron transporter from the sensitizer to the +catalytically active site, so that, as mentioned above, one of the main requirements to be met by the sensitizer +is that the injection of the excited electron into the semiconductor conduction band (CB) is allowed. Usually, +such thermodynamic restriction is condensed into the need for “correct band alignment”, namely the potential +energy of the LUMO level of the dye must be more negative than that of the semiconductor CB. The +widespread prominence of TiO2 is often jeopardized by critical factors that compromise its performance, and +decrease it to an unacceptable level. From the point of view of the semiconductor, some of the setbacks, +particularly pronounced for first row transition metal oxides, include a fast charge recombination, poor charge +mobility, surface effects, size of the band-gap and others.[65,66] One additional aspect is the relationship +between the metal oxide crystal structure and the performance, which can be usefully exploited for better + +16 + +photocatalyst design. TiO2, which is stable under ambient conditions in the three polymorphs rutile, anatase +and brookite, is the best case study to fathom such a relationship. The three phases exhibit different +photocatalysis-relevant properties such as charge recombination rate, band gap, density if states (DOS) and +mode of charge carrier transport. Although such differences have been correlated to variations of photocatalytic +efficiency,[67] establishing an univocal trend is a complex matter, because there is a strong dependence on the +nature of the catalyst, being a single crystal, a thin film or a powder.[68] For example, while a recent study +conducted on different anatase, brookite, and rutile single-crystal wafers with only one exposed surface showed +that the anatase surfaces are generally more active than those of rutile and brookite for methanol +photooxidation,[69] investigation of composite materials for alcohol photoreforming revealed that the +hydrogen production relative to the surface area increased with brookite content, suggesting that brookite facets +were more active for proton reduction under those conditions.[70] +Based on the catalyst nature, the presence, type and distribution of defects plays a very important role, +whereby conduction band electrons can be trapped and stabilized to different extents, with the specific TiO2 +crystal structure being a powerful determinant.[71] Furthermore, additional factors come into play as well, +such as complex charge transport kinetics within TiO2[72] or varying particle size distribution,[73] making it +difficult to shape a comprehensive and reliable paradigm related to predicted activity of each material. +Despite such a complexity, the built knowledge on TiO2 crystal structure/photocatalytic dependence has +resulted in very interesting new outputs, arising from the wise exploitation of advanced techniques. For +instance, the once overlooked brookite, long considered an inactive phase, has recently gained attention due to +its peculiar physico-chemical properties,[74,75] whose assessment was made possible by the emergence of +new strategies for its synthesis in a pure form.[76] In the context of DSP, it was recently demonstrated that +photocatalysts obtained by sensitization of nanocrystalline brookite/Pt with the above-mentioned sensitizer +OB2 (Figure 5) provided better performances in H2 production experiments compared to their P25-based +counterparts (Figure 9a), being also characterized by a remarkable stability (Figure 9b).[60] This result was +attributed to a reduction in charge recombination rate due to the lower reactivity of conduction band electrons +of brookite compared to anatase,[71] in agreement with previous studies conducted on DSSCs.[77] +In addition, the morphology of the TiO2 is to be taken into careful consideration. Several groups have +reported the use of anatase-based semiconductors with tailor-made morphology for use in DSP systems, such +as cubic “microcage” materials[59] or hierarchical porous structures,[31,39,50] showing enhanced +performances compared to the commercial TiO2 sources, owing to improved electronic features or larger +surface area. Cargnello et al. demonstrated how the geometrical anisotropy of brookite nanorods was +instrumental for improving charge separation, with the possibility to tune the photocatalytic activity for H2 +evolution by controlling the nanorods length.[78] + +17 + + +Figure 9. (a) H2 production per photocatalyst surface area of OB2-sensitized P25/Pt (red circles) and brookite/Pt +(black hollow circles) over 20 h visible light irradiation (λ > 420 nm, dye loading, 10 μmol·g–1); (b) H2 production relative +to surface area of OB2@brookite/Pt photocatalyst over 170 h of visible light irradiation. All experiments were performed +with TEOA as SED. Reproduced with permission from ref. [60] (© 2019, American Chemical Society). +In view of the interesting results already obtained, investigations on the combination of dyes with different +TiO2-based materials should be continued. In particular, studies should concentrate on the development of +semiconductors with tailored morphology to speed up charge transport and transfer to the HEC, while +minimizing charge recombination rates. In addition, studies should be conducted on the sensitization of +polymorph mixtures other than the common P25, such as for example brookite/anatase mixtures, to take +advantage of both the higher reactivity towards hydrogen reduction and the enhanced degree of charge +separation thanks to the presence of phase boundaries. +8. Approaches to improve stability +Being as important as activity, the photocatalyst stability requires attention, and when optimizing a system +for H2 production all possible phenomena contributing to its deactivation should be investigated. In the specific +case of DSP, the typical deactivation mechanisms observed in non-sensitized SC photocatalysts, such as +surface passivation or photocorrosion processes,[79] can be accompanied by additional sensitizer-related +degradation pathways, which can be related both to the strength of their bond with the SC and their intrinsic +chemical and photochemical stability. +First, photocatalyst deactivation can occur due to partial or complete detachment of the dye from the +semiconductor surface, which clearly depends on the kind of anchoring group placed on the sensitizer structure. +We have already alluded to this aspect when discussing the work of Reisner et al. on PMI dyes endowed with +different anchoring groups (see above),[44] although there we mostly focused on photocatalytic performances. +In general, it has been reported that the carboxylate linkage may not be an optimal choice when employing +dye-sensitized photocatalysts in aqueous environment, due to accelerated hydrolysis of the titanate ester +linkage, especially at basic pH. For this reason, the use of more robust anchors, such as phosphonate +derivatives, has become increasingly popular, although it is still more common for Ru-based organometallic + +(a) +(b) +80 +0B2@brookite +OB2@P25 +400 +0-0B2@Brookite +60 +0 +300 +TON=549 +40 +TON=4201 +200 +TON=510 +20 +100 +dye loading 10 μmol g-1 +dyeloading7.5μmolg1 +0 +0 +0 +5 +10 +15 +20 +0 +25 +50 +75 +100 +125 +150175 +Time (h) +Time (h)18 + +dyes [80,81] than for metal-free organic structures.[82] In this regard, an interesting alternative could be +represented by the use of a silane coupling reagent to covalently anchor the sensitizer to TiO2: such approach +was demonstrated in a seminal paper by Arakawa and co-workers, who reported that chemical fixation of Eosin +Y through amide coupling with Pt/TiO2 functionalized with γ-aminopropyl-triethoxysilane yielded a stable +and efficient photocatalytst for H2 production from TEOA (Figure 10).[83] To the best of our knowledge, such +strategy has not been applied further in DSP systems, although dyes with silane and silatrane anchors were +later used to sensitize metal oxide electrodes for photoelectrochemical cells,[84,85] and were shown to give +DSSCs with high power conversion efficiencies.[86] Further studies could help establish how the siloxane +anchoring group should be connected to the sensitizer structure to provide optimal charge transfer rates, a +matter that has undergone in-depth scrutiny in the field of DSSC.[87] + + + + + + + + +Figure 10. (a) Eosin Y anchored to TiO2 through an aminosiloxane linker; (b) stable H2 production along consecutive +photocatalytic experiments. Reproduced with permission from ref. [83] (© 2000, Elsevier B. V.). +Furthermore, the anchoring stability of the dye can be improved by increasing the number of anchoring +groups as studied in detail by Park and co-workers, who prepared three triphenylamine-based sensitizers, D1- +3 bearing one, two or three cyanoacrylic anchoring groups, respectively, and studied their possible binding +modes on TiO2 (Figure 11a).[88] Although in situ IR studies suggested that simultaneous binding of all three +carboxylic acids was hardly possible, dyes D2 was observed to give both mono- and bis-coordinated complexes +on TiO2, while D3 was bound mostly in bis-coordinated fashion. Consequently, in photocatalytic experiments +dyes D2-3 gave better efficiency and stability compared to D1 probably as an effect of their more robust +anchoring on TiO2 (Figure 11a). Similar observations were made in the already-cited work by Son et al., who +observed that bidentate phenothiazine dyes yielded consistently better performances compared to their +analogues with only one anchoring unit (Figure 11b),[52] as well as in a study by Watanabe, Tani and co- +workers, investigating porphyrin derivatives with mono- or multi-pyridyl anchoring groups.[89] + +(a) +(b) +ChangeTEOAaq.solution +(Centritugation) +Br +Br +2500 +1st +2 nd +3rd +HO +2000 +Br +Br +(umol) +1500 +TiO2 +Si +1000 +500 +0 +7 +14 +21 +Time (h)19 + + +Figure 11. (a) mono-, bis- and tris-cyanoacrylic dyes D1-3, and the performances of the corresponding photocatalysts +in H2 evolution experiments with TEOA and EDTA as sacrificial donors. Reproduced with permission from ref. [88] (© +Elsevier B. V., 2012); (b) Photocatalytic data for mono- and bis-coordinating phenothiazine dyes. Reproduced with +permission from ref. [52] (© 2012, Royal Society of Chemistry). +Another key aspect to consider to enhance photocatalyst stability is preventing the intermolecular +quenching that follows agglomeration of the dye molecules. A common approach to solve the issue, often an +indispensable requirement, is to endow the dye molecule with an encumbered steric environment; indeed, it +has been repeatedly demonstrated that placing alkyl chains of sufficient length in the intermediate section of +the sensitizers can provide the necessary steric bulk to avoid dye aggregation.[51,59,60,64,90] A remarkable +example was provided by Abbotto, Fornasiero and co-workers, in their work on H2 production by DSP +featuring phenothiazine dyes (Figure 12).[91] +They found that, at the beginning of the photocatalytic experiment dye PTZ1 provided a better performance +than all other analogues named PTZ2-6; however, after a prolonged period of time, the overall amount of gas +produced by dye PTZ5 was higher, as a result of a superior photocatalytic stability, as visible by its constant +H2 evolution rate. Although the reasons for this result are not completely clear, the presence of n-butyl chains +in the middle part of PTZ5 surely helped to reduce dye agglomeration and limit undesired energy transfer +processes between dye molecules. As mentioned above, another strategy to optimize the dye geometry on the +SC surface and hinder dye-dye interactions is to use co-adsorbents, especially by exploiting the formation of + +(a): +R +20 +136 +21. +CN +20 +COOH +: +DL.RIaREH +30 +260 +30 +N +tmmh) +HOOD +TEOA. +EDTA +N +D3.R=Re +(a) +ECN +NC +COOH +P.51 +2001 +Hooc +CN +ON +Hooo. +C16H33 +iP2 +100 +50 +HOOC +CN +Q +21 +3 +Time (h) +HooCr +CNI20 + +directional hydrogen bonds with the sensitizer molecules,[54] but a definite effect on DSP stability for such +systems has not been reported. + + + + + + + + + + + + + + + +Figure 12. (a) Structures of sensitizers PTZ1 and PTZ5; (b) H2 production rates measured using the dye/Pt/TiO2 +materials suspended in TEOA 10% v/v solution at pH 7.0 under irradiation with visible light (λ>420 nm); (c) Degradation +plots of the dye-sensitized Pt/TiO2 photocatalysts under visible irradiation in the same conditions of H2 production +experiments. Reproduced with permission from ref. [91] (© 2015, Wiley-VCH). +The instability of DSP can also derive from the degradation of the dye over time by reaction with chemical +quenchers present in solution or reactive species formed during photocatalysis, such as H2 itself. Indeed, it was +observed early,[83] and confirmed subsequently,[92] that emissive dyes such as Eosin Y can undergo +irreversible hydrogenation by H2 in the reaction conditions, giving species characterized by a lower degree of +conjugation and as such less able to absorb visible light, thus hindering photocatalytic activity. +The different stability of the above-mentioned dyes MB25 and AD418 was interpreted in terms of their +different resistance to degradation during photocatalysis. MB25 presented an electron-donating +propilenedioxythiophene (ProDOT) ring next to a double bond, which activated a decomposition pathway +starting with dye protonation and nucleophilic attack by water; AD418, in which the double bond was +substituted by a thiophene ring, could not undergo the same side reaction and therefore gave rise to a much +more stable photocatalytic system, resulting in a far higher TON.[51] Finally, in a recent paper Lai et al. studied +the degradation process of multicarbazole-based organic dyes to understand the issues related to stability of +Pt/TiO2 photocatalysts for H2 evolution. Supported by combined UV–Vis, FT-IR, 1H and 13C NMR, and MS +techniques, it was suggested that the decline of activity matched the progressive removal of the electron +acceptor unit (consisting of cyanoacrylate moiety), via initial decarboxylation reaction followed by removal +of the CN− group, a mechanism previously unreported for DSP systems.[93] + +(a) +1F +HC4@ +ON +NG +COOH +GN +NO +Iza +Hood +PTZ3 +COOH +PTZ5 +(6) +(c) +PTZ1 +PTZ5 +10 +350 +1:0. +3300元 +60 +0.4 +0.2 +PTZ1 +14 +0.0 +2 +4 +6 +18 +20 +si +20 +Irradiation time./h +(rradiation time dh21 + +Thanks to the advances in dye design and in the investigation of photocatalyst deactivation pathways, +several DSP systems, including some of those cited above, have been demonstrated to achieve prolonged +stability in H2 production experiments, with the best examples being still noticeably active after more than 100 +h under continuous illumination (Table 4). Unfortunately, setup of such experiments is nontrivial, especially +for those groups having access to only one photochemical reaction apparatus, and thus extended stability +studies (at least > 48 h) are still lacking in some of the recently published works. Given the importance of the +photocatalyst stability parameters, however, they appear indispensable for a complete and fair assessment of +new DSP systems and should be always included whenever possible. +Table 4. Stability data of some selected DSP systems. + +In view of the above discussion, improvement of DSP stability should be first pursued by making the +dye/semiconductor assembly more robust. Accordingly, a more thorough exploration of structures with +multiple binding sites to TiO2 should be carried out. On the other hand, care shall also be placed in designing +dyes not incorporating labile functional groups in their central section. In this regard, it will be preferable to +prepare compounds with directly connected (hetero)aromatic rings, without the presence of multiple +(double/triple) bonds, and without excessively electron-donating moieties, as they could be progressively +oxidized during the H2 evolution reaction. + +9. Nature of the hydrogen evolution catalyst (HEC) +Usually, in dye-sensitized photocatalytic systems for H2 production, proton reduction is carried out by metal +nanoparticles adsorbed on the semiconductor surface, with platinum being by far the most common choice.[12] +Dye +Reaction +Time (h) +Dye loading +[μmol/g] +H2 produced +[mmol/g] +TON +SED (pH) +Ref. +Alizarin +80 +2.5 +7.91a +6326 +TEOA (9) +[92] +Alizarin +Red +92 +2.5 +7.93a +6342 +TEOA (9) +[92] +PTZ5 +90 +59.6 +-b +-b +TEOA (7) +[91] +S1 +48 +6.25 +63.75 +10200 +AA (4) +[40] +Dimer 2 +83 +28.3 +84.91 +2860 +AA (4) +[89] +OB2 +170 +7.5 +15.75 +4201 +TEOA (7) +[60] +Calix-3 +50 +37.3 +630.97 +16927 +TEOA +(11.8) +[94] +DH4 +105 +32.8 +547.22 +16699 +TEOA +(n.d.c) +[59] +BB3e +72 +2.5 +29.11 +23285 +AA (4) +[63] +a Calculated based on the TON and dye loading data presented in the original paper. b Exact values were not +provided; Figure S9 in the supporting information of the original publication shows a constant H2 production rate +of approx. 250 μmol g−1 h−1 for the entire experiment. c The authors report that the solution pH was adjusted by +addition of perchloric acid. + +22 + +Clearly, this is due to the excellent properties of platinum as a heterogeneous catalyst for H2 evolution, +guaranteeing high activity and stability, but also to the fact that most of the studies focus on the investigation +of other components of the system (such as the dye or the semiconductor) and therefore need to use the same +catalyst to obtain results comparable with those already reported in the literature. +Nevertheless, several studies have focused on finding more readily available and cheaper catalysts than +platinum, in the perspective of an industrial scale-up of the system. Indeed, it has even been shown that H2 +production with dye-sensitized TiO2 can proceed also in the absence of adsorbed metals,[95] but usually gas +evolution rates were not sufficient for practical purposes. In addition, the possibility to use dissolved +homogenous metal catalysts, not anchored to TiO2, has also been explored: for example, Kruth et al. reported +the employment of commercially available PdCl2(CH3CN)2 and Pd(PPh3)2Cl2 as catalysts in combination with +polymer-capped titania nanoparticles sensitized with ruthenium complex N3.[96] Although a moderate and +stable H2 evolution was obtained, the authors mention that the results were inferior to those previously reported +for other composite TiO2 photocatalysts. +More commonly, transition metal or metal salt nanoparticles adsorbed on the semiconductor surface have +been reported as catalysts for DSP systems. Although this has been done more often for purely inorganic +photocatalytic assemblies,[97–99] several examples exist also in the dye-sensitized field. Already in 2007, Lu +and co-workers described the use of an Eosin Y-sensitized CuO/TiO2 nanocomposite, in which cuprous oxide +played the double role of semiconductor and catalyst for water reduction, being able to collect electrons directly +by injection from the sensitizer or through electron transfer from titania; its employment allowed to obtain a +much higher H2 production rate compared to that observed in its absence.[100] More recently, the use of +elemental Co was also reported in a similar system, in which Rhodamine B was used as the sensitizer; +remarkably, the authors reported the possibility to achieve a full water splitting process, avoiding the use of +any sacrificial donor, thanks to the synergistic effect of the sensitizer and the neighbouring cobalt atoms. The +fact that the reaction proceeded through the desired mechanism was supported by the production of nearly +stoichiometric amounts of the two gases (H2:O2 ratio was approximately 2.3).[101] Du and co-workers +examined several first-row transition metal-based oxide/hydroxide materials, such as cobalt oxide (CoOx), +cobalt hydroxide (Co(OH)2), nickel oxide (NiOx), nickel hydroxide (Ni(OH)2), ferric hydroxide (Fe(OH)3) and +copper hydroxide (Cu(OH)2), as catalysts in a three-component photocatalytic system with TiO2 as the +semiconductor, Eosin Y as the sensitizer and TEOA as SED (Figure 13). They found that Ni(OH)2 exhibited +the best performance, which was about 90 times higher than that of pure TiO2 under the same conditions and +was kept stable for several hours through repeated illumination/evacuation cycles.[102] + +23 + + +Figure 13. (a) Mechanism of Eosin Y-sensitized H2 production with Ni(OH)2/TiO2 nanoparticles; (b) comparison +between different transition metal oxides/hydroxides used as HEC. Reproduced with permission from ref. [102] (© 2014, +Elsevier B. V.). +A series of studies was published by Patir and co-workers on the use of Cu2WS4 nanocubes as HEC in +combination with TiO2 sensitized by a variety of different metal-free organic sensitizers.[41,103–105] The +new catalyst was synthesized by a hot injection method that produced nanocubic structures with 100-500 nm- +long edges and characterized by a single crystalline phase. Photocatalytic studies revealed that use of Cu2WS4 +caused an increase in the H2 production rate compared to the catalyst-free dye-sensitized semiconductor, but +its performances were lower than those of Pt nanospheres. The system was also sufficiently stable under +irradiation, although XPS measurements conducted both before and after the experiments indicated a partial +hydrogenation of the Cu2WS4 structure during the photocatalytic reaction. +Finally, it should be mentioned that several examples of supported molecular catalysts have also been +reported in DSP systems for H2 production. Many of these studies have been conducted by Reisner’s group, +who focused especially on the development of Co- and Ni-based complexes (Figure 14), used in combination +with both Ru-containing sensitizers and metal-free organic dyes. Earlier work concerned the employment of +cobaloxime complexes such as CoP1,[106,107] whose attachment to the semiconductor was allowed only by +an axial pyridine ligand endowed with a phosphonate anchoring group. Later, the catalyst design was improved +by preparing complex CoP3, featuring a single ligand incorporating both the diamine-dioxime equatorial unit +and the axial pyridine:[108] accordingly, the authors reported that “CoP3 displays significant advantages over +previously reported immobilized Co catalysts as it shows a higher catalytic proton reduction activity and +provides a strong and more stable anchoring to metal oxides surfaces”. At the same time, DuBois-type +[Ni(P2R’N2R’’)2]2+ complexes were also investigated in combination with Ru tris(bipyridine) dyes, and it was +shown that they could work in water reduction reactions both in homogenous phase or adsorbed on a +semiconductor, albeit with different electron transfer mechanisms.[109] In general, the performances provided +by these molecular catalysts were good, but inferior to those obtained with Pt nanoparticles.[44,82] + + +(a) +(b) +Ni(OH)2 +40- +Ni(OH) +Visible +Light +Hydrogen evolution (μmol) +H2 +Cu(OH), +30 +CB +e' +e +H,O +Co(OH), +e +20 +TiO2 +00 +10 +Coo, +EY +Fe(OH), +VB +Blank +Nio, +024 + + +Figure 14. Structures of molecular complexes used as HEC in dye-sensitized systems. +Despite that, we consider studies on alternative HECs of high relevance in the perspective of a potential +future large-scale deployment of DSP technology, and recommend that they will be expanded in the future +also by other research groups. Finding reliable catalytic species based on cheaper and more available metals +than Pt could significantly reduce the projected cost of DSP systems, while at the same time eliminate (or +largely reduce) the risk of shortages of critical materials in the long term. +10. Sustainability of the sacrificial donor +As explained in the introduction, during photocatalysis on DSP (not differently from purely SC-based +photocatalysts), charge separation following light irradiation generates two reactive sites, where the newly +formed holes and electrons can promote oxidation and reduction reactions, respectively. The development of +new photocatalysts is heavily based on the detailed understanding of its intrinsic activity. Hence, it is +convenient to simplify the investigation of the photocatalysts features by focusing on one half-reaction only, +relying on the use of sacrificial electron donors or acceptors (SED or SEA respectively) that readily react with +the photogenerated charge carriers, thus not placing kinetic restrictions that would affect the half-reaction of +interest.[110] For example, such a practice is common in the photocatalytic water splitting field, where most +studies focus on either the H2 evolution or on the water oxidation, using sacrificial agents for the other half- +reaction. Focusing on the H2 evolution process, obviously the choice of the SED is subject to stringent +thermodynamic requirements for the reaction to proceed efficiently. Among them, the most important is that +the HOMO of the dye must suitably match the redox potential of the SEDred/SEDox couple to ensure the rapid +regeneration of the oxidized dye (i.e. the HOMO of dye must be more positive than the oxidation potential of +the SED). Typical SED include triethylamine (TEA), triethanolamine (TEOA), ethylenediaminetetraacetic +acid (EDTA), ascorbic acid (AA), S2–, I- and others.[17] +However, while alleviating the complexity demands of photocatalyst developments from fundamental +perspective, this approach does not match sustainability concepts. To address this aspect of photocatalysis, an +increasing load of research has moved towards more useful SED, whose oxidation can be associated with other +processes relevant for sustainability.[111] For example, alcohols can act as efficient donors for many inorganic +semiconductor photocatalysts including TiO2,[112] with potential oxidation to industrially relevant +compounds, as recently demonstrated for ethanol and glycerol.[113] Despite that, the use of alcohols as hole + +H2O3 +PO3H2 +Ph +PO3H2 +Br +Cop1 +Cop3 +H,O3P +PO3H2 +Du Bois-type25 + +scavengers in DSP systems is still in its infancy, and has been reported only in a handful of studies, +investigating the employment of MeOH,[114] EtOH[51,63] or glycerol.[50] Unfortunately, the performances +obtained with such sacrificial donors are generally lower than those registered with TEOA or AA, and the +structural and electronic requirements of the dyes to work efficiently with them have not yet been fully +clarified. Probably, one key issue is that small alcohol molecules can adsorb on the SC surface, reducing the +H+ reduction rate and enhancing charge recombination;[115] therefore, they should be used in combination +with dyes able to efficiently shield the photocatalyst surface but at the same time small and hydrophilic enough +to allow good interaction with the SED. Achieving such a structural design is nontrivial and therefore studies +on sensitizer optimization are still in progress. In addition, alcohol oxidation could be promoted by combining +the dyes with appropriate molecular catalysts,[116] also in an integrated dyad design, as already demonstrated +in photoelectrochemical cells.[117] +Another promising research direction would be to explore the photoreforming (PR) of biomass-derived +materials, such as lignin and lignocellulose, as hole scavengers, opening the way to the production of clean +fuels from abundant and cheap raw materials, or even waste.[118] Despite their favourable thermodynamics, +however, such raw materials are often characterized by limited solubility, brown-dark colour and slow +oxidation kinetics, making it necessary to apply pre-digestion procedures and use appropriate catalysts for their +efficient photoconversion. Due to such issues, no DSP system for lignocellulose PR has been reported as of +yet, but given its great potential such approach should definitely be pursued in the future. +11. Perspectives +In this article, we have highlighted some key aspects of the visible light-driven H2 production mediated by +heterogeneous dye-sensitized photocatalysts. Compared to the other two main technologies currently +employed for the production of solar H2, namely tandem photovoltaic-electrolysis systems and +photoelectrochemical cells, the photocatalytic approach is still characterized by an inferior solar-to-hydrogen +(STH) efficiency, but at the same time is comparatively simpler, less expensive and easier to scale-up.[4] +However, to be able to replace, at least partially, H2 generation methods based on more mature technologies +(such as hydrocarbon reforming or water electrolysis), photocatalytic processes still need to overcome some +serious obstacles. In general, the major factors currently restricting large-scale application of DSP systems +towards a possible industrialization can be traced back to their insufficient efficiency and stability and their +excessive cost. +Focusing on the first aspect, it will be mandatory to improve the performances of DSP systems by further +optimization of their active materials. In terms of dyes, although a picture is starting to emerge regarding the +need to precisely control their lipophilicity/hydrophilicity balance, as well as the precise position of their +energy levels, more detailed design principles are required to develop structures able to work efficiently in the +aqueous environment typical of DSP applications. Crucial aspects to be considered are the development of +improved anchoring groups, able to ensure a rapid charge injection rate into the conduction band of the +sensitizer, the use of panchromatic chromophores, to enhance light harvesting in the entirety of the visible + +26 + +spectrum, the attainment of a precise organization of dye molecules on the SC surface (also by the use of co- +adsorbents), as well as the establishment of more efficient interactions with hole scavenger species present in +solution, beyond the simple manipulation of orbital levels. +In parallel with the discovery of more efficient dye sensitizers, improvements are also required concerning +the semiconductor structure. Significant results have already been obtained by exploring different TiO2 +polymorphs (either in pure form or as mixed phases) as well as precisely controlled titania nanostructures. +Despite that, several problems still remain, such as the excessive rate of charge recombination favoured by the +interaction of the hydrophilic TiO2 surface with the aqueous reaction environment. They could be overcome +by designing composites with improved dye/semiconductor/water interfaces, as well as by introducing +semiconductors with tailored morphology to speed up charge transport and transfer to the HEC, thanks to the +help of more refined kinetic models.[72] +Requirements of efficiency enhancement and cost reduction are closely linked to the need for shifting from +model sacrificial electron donors, such as TEOA or EDTA, to more realistic species in terms of sustainability. +As discussed above, this could be achieved by employing simple alcohols (e. g. EtOH, iPrOH) or biomass- +derived reducing compounds (e. g. from glucose to more complex sugars, all the way to lignocellulose), either +as intermediate solutions towards the ultimate goal of water splitting, or as platforms for coupling H2 +generation with production of value-added, oxidized compounds. +In terms of stability, a crucial aspect will be once again the development of improved anchoring groups, +capable to ensure a robust attachment of the dye to the semiconductor surface with negligible hydrolysis, +without an excessive limitation of performances, also by exploration of multi-branched structures. At the same +time, it will also be necessary to design dyes devoid of labile functional groups, to avoid their oxidation or +decomposition during the photocatalytic reaction. +Regarding cost reduction, a crucial step in this direction would be the replacement of platinum +nanoparticles, usually employed as HEC, with cheaper and more readily available catalytic materials. Such +modification would also eliminate the risk of shortages of catalytic material in the hypothesis of a future large- +scale deployment of DSP technology. Although such work has already been done extensively in +photoreforming studies using fully inorganic systems,[119] it has not yet been explored in depth in the field of +DSP. Of particular interest is the work on supported molecular catalysts, as their structure can be tailored to +make them very specific, opening the way to the development of parallel processes able to produce more than +one compound at the same time: one such example is the dye-sensitized photocatalytic production of syngas +(H2+CO) recently published by Kang and co-workers.[120] +A summary of the most important recent advances in the fields and the possible directions of future +development, as discussed in the above paragraphs, is provided in Figure 15. + +27 + + +Figure 15. Recent advances and potential future developments of DSP research. +Finally, it is important that researchers working in the DSP field will try to adopt more consistent standards +for experimental procedures, laboratory setups and data reporting. Despite significant efforts by publishers to +promote “best practices” to perform measurements and data analysis, large discrepancies still remain in the +way materials and devices properties are reported, sometimes preventing a meaningful comparison of results. +It is mandatory to overcome these difficulties to ensure a correct future development of this research area. +As can be seen by the above discussion, despite the recent achievements documented in this article, many +unsolved problems and open questions still wait to be addressed in the field of DSP H2 production. With so +much work to do, we have little doubt that it will remain a very active field of research for many years to come. +12. Acknowledgements +Financial support from European Community (Projects H2020 − RIA-CE-NMBP-25 Program − Grant No. +862030 and H2020-LC-SC3-2019-NZE-RES-CC − Grant No. 884444), University of Trieste, CNR-ICCOM +('SOLARSYNT' Project) and INSTM Consortium is acknowledged. +13. References +[1] + Balzani V, Credi A and Venturi M 2008 Photochemical Conversion of Solar Energy ChemSusChem +1 26–58 +[2] + Dau H, Fujita E and Sun L 2017 Artificial Photosynthesis: Beyond Mimicking Nature +ChemSusChem 10 4228–35 +[3] + Armaroli N and Balzani V 2011 The Hydrogen Issue ChemSusChem 4 21–36 + +iRecentadvances: +Efficiency improvements by manipulation:of +lydrophobic/hydrophilic.properties; +Recentadvances: +IFutureprogress:! +lncreasedye.stabilityagainst.hydrolysis and +Future progress: +oxidation +Recentadvances: +:-Better.matching ofenergy levels + . . :.. +Betterinteraction.with.SED.to.improvedye +Useof.non-preciousmetal:NPs: +withthedye: +regeneration.ratesespecially.withalcohols. +Futureprogress. +iFull.water.splitting.in.photocatalyticconditions. +Improve:TONswithmolecularHECs +H.production.withother +reactions: +SED: +e +er +PSED? +Cat +TiO2 +Dye +I Recent advances: +Recentadvances: +Stableanchoringgroups in basicconditions: +Tio,materials with different morphologies.. +Future'progress: +Futureprogress:: +nvestigation:otpolvmorph:mixtures28 + +[4] + Armaroli N and Balzani V 2016 Solar Electricity and Solar Fuels: Status and Perspectives in the +Context of the Energy Transition Chem. – A Eur. J. 22 32–57 +[5] + Fujishima A and Honda K 1972 Electrochemical Photolysis of Water at a Semiconductor Electrode +Nature 238 37–8 +[6] + Wang Z, Li C and Domen K 2019 Recent developments in heterogeneous photocatalysts for solar- +driven overall water splitting Chem. Soc. Rev. 48 2109–25 +[7] + Carraro G, Maccato C, Gasparotto A, Montini T, Turner S, Lebedev O I, Gombac V, Adami G, Van +Tendeloo G, Barreca D and Fornasiero P 2014 Enhanced Hydrogen Production by Photoreforming of +Renewable Oxygenates Through Nanostructured Fe2O3 Polymorphs Adv. Funct. Mater. 24 372–8 +[8] + Uekert T, Kuehnel M F, Wakerley D W and Reisner E 2018 Plastic waste as a feedstock for solar- +driven H2 generation Energy Environ. Sci. 11 2853–7 +[9] + Chen X, Liu L, Yu P Y and Mao S S 2011 Increasing solar absorption for photocatalysis with black +hydrogenated titanium dioxide nanocrystals Science (80-. ). 331 746–50 +[10] + Maeda K 2013 Z ‑ Scheme Water Splitting Using Two Di ff erent Semiconductor Photocatalysts 2 +[11] + Zhou P, Yu J and Jaroniec M 2014 All-solid-state Z-scheme photocatalytic systems Adv. Mater. 26 +4920–35 +[12] + Zhang X, Peng T and Song S 2016 Recent advances in dye-sensitized semiconductor systems for +photocatalytic hydrogen production J. Mater. Chem. A 4 2365–402 +[13] + Hagfeldt A, Boschloo G, Sun L, Kloo L and Pettersson H 2010 Dye-Sensitized Solar Cells Chem. +Rev. 110 6595–663 +[14] + Li F, Yang H, Li W and Sun L 2018 Device Fabrication for Water Oxidation, Hydrogen Generation, +and CO2 Reduction via Molecular Engineering Joule 2 36–60 +[15] + Li J and Wu N 2015 Semiconductor-based photocatalysts and photoelectrochemical cells for solar +fuel generation: a review Catal. Sci. Technol. 5 1360–84 +[16] + Chen S, Takata T and Domen K 2017 Particulate photocatalysts for overall water splitting Nat. Rev. +Mater. 2 17050 +[17] + Pellegrin Y and Odobel F 2017 Les donneurs d’électron sacrificiels pour la production de +combustible solaire Comptes Rendus Chim. 20 283–95 +[18] + Watanabe M 2017 Dye-sensitized photocatalyst for effective water splitting catalyst Sci. Technol. +Adv. Mater. 18 705–23 +[19] + Abe R, Shinmei K, Koumura N, Hara K and Ohtani B 2013 Visible-light-induced water splitting +based on two-step photoexcitation between dye-sensitized layered niobate and tungsten oxide +photocatalysts in the presence of a triiodide/iodide shuttle redox mediator J. Am. Chem. Soc. 135 +16872–84 +[20] + Zhang X, Peng T, Yu L, Li R, Li Q and Li Z 2015 Visible/near-infrared-light-induced H2 production +over g-C3N4 co-sensitized by organic dye and zinc phthalocyanine derivative ACS Catal. 5 504–10 +[21] + Yu L, Zhang X, Zhuang C, Lin L, Li R and Peng T 2014 Syntheses of asymmetric zinc + +29 + +phthalocyanines as sensitizer of Pt-loaded graphitic carbon nitride for efficient visible/near-IR-light- +driven H 2 production Phys. Chem. Chem. Phys. 16 4106–14 +[22] + Ohtani B, Prieto-Mahaney O O, Li D and Abe R 2010 What is Degussa (Evonik) P25? Crystalline +composition analysis, reconstruction from isolated pure particles and photocatalytic activity test J. +Photochem. Photobiol. A Chem. 216 179–82 +[23] + Qureshi M and Takanabe K 2017 Insights on measuring and reporting heterogeneous photocatalysis: +Efficiency definitions and setup examples Chem. Mater. 29 158–67 +[24] + Kunz L Y, Diroll B T, Wrasman C J, Riscoe A R, Majumdar A and Cargnello M 2019 Artificial +inflation of apparent photocatalytic activity induced by catalyst-mass-normalization and a method to +fairly compare heterojunction systems Energy Environ. Sci. 12 1657–67 +[25] + Melchionna M and Fornasiero P 2020 Updates on the Roadmap for Photocatalysis ACS Catal. 10 +5493–501 +[26] + Melchionna M, Beltram A, Montini T, Monai M, Nasi L, Fornasiero P and Prato M 2016 Highly +efficient hydrogen production through ethanol photoreforming by a carbon nanocone/Pd@TiO2 +hybrid catalyst Chem. Commun. 52 764–7 +[27] + Kozuch S and Martin J M L 2012 “Turning Over” Definitions in Catalytic Cycles ACS Catal. 2 +2787–94 +[28] + Kisch H and Bahnemann D 2015 Best Practice in Photocatalysis: Comparing Rates or Apparent +Quantum Yields? J. Phys. Chem. Lett. 6 1907–10 +[29] + Hoy J, Morrison P J, Steinberg L K, Buhro W E and Loomis R A 2013 Excitation Energy +Dependence of the Photoluminescence Quantum Yields of Core and Core/Shell Quantum Dots J. +Phys. Chem. Lett. 4 2053–60 +[30] + Chatterjee D 2010 Effect of excited state redox properties of dye sensitizers on hydrogen production +through photo-splitting of water over TiO2 photocatalyst Catal. Commun. 11 336–9 +[31] + Suryani O, Higashino Y, Sato H and Kubo Y 2019 Visible-to-Near-Infrared Light-Driven +Photocatalytic Hydrogen Production Using Dibenzo-BODIPY and Phenothiazine Conjugate as +Organic Photosensitizer ACS Appl. Energy Mater. 2 448–58 +[32] + Cecconi B, Manfredi N, Montini T, Fornasiero P and Abbotto A 2016 Dye-Sensitized Solar +Hydrogen Production: The Emerging Role of Metal-Free Organic Sensitizers European J. Org. +Chem. 2016 5194–215 +[33] + Huang J-F, Lei Y, Luo T and Liu J-M 2020 Photocatalytic H2 Production from Water by Metal-free +Dye-sensitized TiO2 Semiconductors: The Role and Development Process of Organic Sensitizers +ChemSusChem 13 5863–95 +[34] + Lee C P, Lin R Y Y, Lin L Y, Li C T, Chu T C, Sun S S, Lin J T and Ho K C 2015 Recent progress +in organic sensitizers for dye-sensitized solar cells RSC Adv. 5 23810–25 +[35] + Wu Y, Zhu W H, Zakeeruddin S M and Grätzel M 2015 Insight into D-A-π-A structured sensitizers: +A promising route to highly efficient and stable dye-sensitized solar cells ACS Appl. Mater. Interfaces + +30 + +7 9307–18 +[36] + Watanabe M, Hagiwara H, Iribe A, Ogata Y, Shiomi K, Staykov A, Ida S, Tanaka K and Ishihara T +2014 Spacer effects in metal-free organic dyes for visible-light-driven dye-sensitized photocatalytic +hydrogen production J. Mater. Chem. A 2 12952–61 +[37] + Luo G G, Lu H, Wang Y H, Dong J, Zhao Y and Wu R B 2016 A D-π-A-π-A metal-free organic dye +with improved efficiency for the application of solar energy conversion Dye. Pigment. 134 498–505 +[38] + Ho P Y, Mark M F, Wang Y, Yiu S C, Yu W H, Ho C L, McCamant D W, Eisenberg R and Huang S +2018 Panchromatic Sensitization with ZnII Porphyrin-Based Photosensitizers for Light-Driven +Hydrogen Production ChemSusChem 11 2517–28 +[39] + Tiwari A, Krishna N V, Giribabu L and Pal U 2018 Hierarchical Porous TiO2 Embedded +Unsymmetrical Zinc-Phthalocyanine Sensitizer for Visible-Light-Induced Photocatalytic H2 +Production J. Phys. Chem. C 122 495–502 +[40] + Ho P-Y, Wang Y, Yiu S-C, Yu W-H, Ho C-L and Huang S 2017 Starburst Triarylamine Donor- +Based Metal-Free Photosensitizers for Photocatalytic Hydrogen Production from Water Org. Lett. 19 +1048–51 +[41] + Aslan E, Karaman M, Yanalak G, Can M, Ozel F and Patir I H 2019 The investigation of novel D-π- +A type dyes (MK-3 and MK-4) for visible light driven photochemical hydrogen evolution Dye. +Pigment. 171 107710 +[42] + Pastore M, Fantacci S and De Angelis F 2013 Modeling Excited States and Alignment of Energy +Levels in Dye-Sensitized Solar Cells: Successes, Failures, and Challenges J. Phys. Chem. C 117 +3685–700 +[43] + Zhang L and Cole J M 2015 Anchoring Groups for Dye-Sensitized Solar Cells ACS Appl. Mater. +Interfaces 7 3427–55 +[44] + Warnan J, Willkomm J, Farré Y, Pellegrin Y, Boujtita M, Odobel F and Reisner E 2019 Solar +electricity and fuel production with perylene monoimide dye-sensitised TiO 2 in water Chem. Sci. 10 +2758–66 +[45] + Narayanaswamy K, Tiwari A, Mondal I, Pal U, Niveditha S, Bhanuprakash K and Singh S P 2015 +Dithiafulvalene functionalized diketopyrrolopyrrole based sensitizers for efficient hydrogen +production Phys. Chem. Chem. Phys. 17 13710–8 +[46] + Manzhos S, Jono R, Yamashita K, Fujisawa J, Nagata M and Segawa H 2011 Study of Interfacial +Charge Transfer Bands and Electron Recombination in the Surface Complexes of TCNE, TCNQ, and +TCNAQ with TiO2 J. Phys. Chem. C 115 21487–93 +[47] + Ooyama Y and Harima Y 2012 Photophysical and Electrochemical Properties, and Molecular +Structures of Organic Dyes for Dye-Sensitized Solar Cells ChemPhysChem 13 4032–80 +[48] + Wang M, Grätzel C, Zakeeruddin S M and Grätzel M 2012 Recent developments in redox +electrolytes for dye-sensitized solar cells Energy Environ. Sci. 5 9394–405 +[49] + Robson K C D, Hu K, Meyer G J and Berlinguette C P 2013 Atomic Level Resolution of Dye + +31 + +Regeneration in the Dye-Sensitized Solar Cell J. Am. Chem. Soc. 135 1961–71 +[50] + Tiwari A, Duvva N, Rao V N, Venkatakrishnan S M, Giribabu L and Pal U 2019 Tetrathiafulvalene +Scaffold-Based Sensitizer on Hierarchical Porous TiO 2 : Efficient Light-Harvesting Material for +Hydrogen Production J. Phys. Chem. C 123 70–81 +[51] + Dessì A, Monai M, Bessi M, Montini T, Calamante M, Mordini A, Reginato G, Trono C, Fornasiero +P and Zani L 2018 Towards Sustainable H2Production: Rational Design of Hydrophobic +Triphenylamine-based Dyes for Sensitized Ethanol Photoreforming ChemSusChem 11 793–805 +[52] + Lee J, Kwak J, Ko K C, Park J H, Ko J H, Park N, Kim E, Ryu D H, Ahn T K, Lee J Y and Son S U +2012 Phenothiazine-based organic dyes with two anchoring groups on TiO 2 for highly efficient +visible light-induced water splitting Chem. Commun. 48 11431–3 +[53] + Manfredi N, Cecconi B, Calabrese V, Minotti A, Peri F, Ruffo R, Monai M, Romero-Ocaña I, +Montini T, Fornasiero P and Abbotto A 2016 Dye-sensitized photocatalytic hydrogen production: +Distinct activity in a glucose derivative of a phenothiazine dye Chem. Commun. 52 6977–80 +[54] + Manfredi N, Monai M, Montini T, Peri F, De Angelis F, Fornasiero P and Abbotto A 2018 Dye- +Sensitized Photocatalytic Hydrogen Generation: Efficiency Enhancement by Organic Photosensitizer- +Coadsorbent Intermolecular Interaction ACS Energy Lett. 3 85–91 +[55] + Martín C, Ziółek M and Douhal A 2016 Ultrafast and fast charge separation processes in real dye- +sensitized solar cells J. Photochem. Photobiol. C Photochem. Rev. 26 1–30 +[56] + Watanabe M, Hagiwara H, Ogata Y, Staykov A, Bishop S R, Perry N H, Chang Y J, Ida S, Tanaka K +and Ishihara T 2015 Impact of alkoxy chain length on carbazole-based, visible light-driven, dye +sensitized photocatalytic hydrogen production J. Mater. Chem. A 3 21713–21 +[57] + Tiwari A, Mondal I and Pal U 2015 Visible light induced hydrogen production over +thiophenothiazine-based dye sensitized TiO2 photocatalyst in neutral water RSC Adv. 5 31415–21 +[58] + Wang J, Chai Z, Liu S, Fang M, Chang K, Han M, Hong L, Han H, Li Q and Li Z 2018 Organic +Dyes based on Tetraaryl-1,4-dihydropyrrolo-[3,2-b]pyrroles for Photovoltaic and Photocatalysis +Applications with the Suppressed Electron Recombination Chem. - A Eur. J. 24 18032–42 +[59] + Huang J-F, Lei Y, Xiao L-M, Chen X-L, Zhong Y-H, Qin S and Liu J-M 2020 Photocatalysts for H2 +Generation from Starburst Triphenylamine/Carbazole Donor-Based Metal-Free Dyes and Porous +Anatase TiO2 Cube ChemSusChem 13 1037–43 +[60] + Bettucci O, Skaltsas T, Calamante M, Dessì A, Bartolini M, Sinicropi A, Filippi J, Reginato G, +Mordini A, Fornasiero P and Zani L 2019 Combining Dithienosilole-Based Organic Dyes with a +Brookite/Platinum Photocatalyst toward Enhanced Visible-Light-Driven Hydrogen Production ACS +Appl. Energy Mater. 2 5600–12 +[61] + Lee S H, Park Y, Wee K R, Son H J, Cho D W, Pac C, Choi W and Kang S O 2010 Significance of +hydrophilic characters of organic dyes in visible-light hydrogen generation based on TiO2 Org. Lett. +12 460–3 +[62] + Han W S, Wee K R, Kim H Y, Pac C, Nabetani Y, Yamamoto D, Shimada T, Inoue H, Choi H, Cho + +32 + +K and Kang S O 2012 Hydrophilicity control of visible-light hydrogen evolution and dynamics of the +charge-separated state in dye/TiO2/Pt hybrid systems Chem. - A Eur. J. 18 15368–81 +[63] + Bartolini M, Gombac V, Sinicropi A, Reginato G, Dessì A, Mordini A, Filippi J, Montini T, +Calamante M, Fornasiero P and Zani L 2020 Tuning the Properties of Benzothiadiazole Dyes for +Efficient Visible Light-Driven Photocatalytic H2 Production under Different Conditions ACS Appl. +Energy Mater. 0 +[64] + Tiwari A and Pal U 2015 Effect of donor-donor-π-acceptor architecture of triphenylamine-based +organic sensitizers over TiO2 photocatalysts for visible-light-driven hydrogen production Int. J. +Hydrogen Energy 40 9069–79 +[65] + Peter L M and Upul Wijayantha K G 2014 Photoelectrochemical Water Splitting at Semiconductor +Electrodes: Fundamental Problems and New Perspectives ChemPhysChem 15 1983–95 +[66] + Hisatomi T, Kubota J and Domen K 2014 Recent advances in semiconductors for photocatalytic and +photoelectrochemical water splitting Chem. Soc. Rev. 43 7520–35 +[67] + Moss B, Lim K K, Beltram A, Moniz S, Tang J, Fornasiero P, Barnes P, Durrant J and Kafizas A +2017 Comparing photoelectrochemical water oxidation, recombination kinetics and charge trapping +in the three polymorphs of TiO2 Sci. Rep. 7 2938 +[68] + Yamakata A, Vequizo J J M and Matsunaga H 2015 Distinctive Behavior of Photogenerated +Electrons and Holes in Anatase and Rutile TiO2 Powders J. Phys. Chem. C 119 24538–45 +[69] + Günnemann C, Haisch C, Fleisch M, Schneider J, Emeline A V and Bahnemann D W 2019 Insights +into Different Photocatalytic Oxidation Activities of Anatase, Brookite, and Rutile Single-Crystal +Facets ACS Catal. 9 1001–12 +[70] + Beltram A, Romero-Ocaña I, Josè Delgado Jaen J, Montini T and Fornasiero P 2016 Photocatalytic +valorization of ethanol and glycerol over TiO2 polymorphs for sustainable hydrogen production Appl. +Catal. A Gen. 518 167–75 +[71] + Vequizo J J M, Matsunaga H, Ishiku T, Kamimura S, Ohno T and Yamakata A 2017 Trapping- +Induced Enhancement of Photocatalytic Activity on Brookite TiO2 Powders: Comparison with +Anatase and Rutile TiO2 Powders ACS Catal. 7 2644–51 +[72] + Sieland F, Schneider J and Bahnemann D W 2017 Fractal Charge Carrier Kinetics in TiO 2 J. Phys. +Chem. C 121 24282–91 +[73] + Sieland F, Schneider J and Bahnemann D W 2018 Photocatalytic activity and charge carrier +dynamics of TiO2 powders with a binary particle size distribution Phys. Chem. Chem. Phys. 20 +8119–32 +[74] + Liu G, Yang H G, Pan J, Yang Y Q, Lu G Q (Max) and Cheng H-M 2014 Titanium Dioxide Crystals +with Tailored Facets Chem. Rev. 114 9559–612 +[75] + Monai M, Montini T and Fornasiero P 2017 Brookite: Nothing new under the sun? Catalysts 7 +[76] + Di Paola A, Bellardita M and Palmisano L 2013 Brookite, the least known TiO2 photocatalyst +Catalysts 3 36–73 + +33 + +[77] + Kusumawati Y, Hosni M, Martoprawiro M A, Cassaignon S and Pauporté T 2014 Charge Transport +and Recombination in TiO2 Brookite-Based Photoelectrodes J. Phys. Chem. C 118 23459–67 +[78] + Cargnello M, Montini T, Smolin S Y, Priebe J B, Jaén J J D, Doan-Nguyen V V T, McKay I S, +Schwalbe J A, Pohl M M, Gordon T R, Lu Y, Baxter J B, Brückner A, Fornasiero P and Murray C B +2016 Engineering titania nanostructure to tune and improve its photocatalytic activity Proc. Natl. +Acad. Sci. U. S. A. 113 3966–71 +[79] + Xie Y P, Yu Z B, Liu G, Ma X L and Cheng H-M 2014 CdS–mesoporous ZnS core–shell particles +for efficient and stable photocatalytic hydrogen evolution under visible light Energy Environ. Sci. 7 +1895–901 +[80] + Bae E, Choi W, Park J, Shin H S, Kim S Bin and Lee J S 2004 Effects of Surface Anchoring Groups +(Carboxylate vs Phosphonate) in Ruthenium-Complex-Sensitized TiO2 on Visible Light Reactivity in +Aqueous Suspensions J. Phys. Chem. B 108 14093–101 +[81] + Bae E and Choi W 2006 Effect of the Anchoring Group (Carboxylate vs Phosphonate) in Ru- +Complex-Sensitized TiO2 on Hydrogen Production under Visible Light J. Phys. Chem. B 110 14792– +9 +[82] + Warnan J, Willkomm J, Ng J N, Godin R, Prantl S, Durrant J R and Reisner E 2017 Solar H2 +evolution in water with modified diketopyrrolopyrrole dyes immobilised on molecular Co and Ni +catalyst-TiO2 hybrids Chem. Sci. 8 3070–9 +[83] + Abe R, Hara K, Sayama K, Domen K and Arakawa H 2000 Steady hydrogen evolution from water +on Eosin Y-fixed TiO2 photocatalyst using a silane-coupling reagent under visible light irradiation J. +Photochem. Photobiol. A Chem. 137 63–9 +[84] + Brennan B J, Llansola Portolés M J, Liddell P A, Moore T A, Moore A L and Gust D 2013 +Comparison of silatrane, phosphonic acid, and carboxylic acid functional groups for attachment of +porphyrin sensitizers to TiO2 in photoelectrochemical cells Phys. Chem. Chem. Phys. 15 16605–14 +[85] + Castellucci E, Monini M, Bessi M, Iagatti A, Bussotti L, Sinicropi A, Calamante M, Zani L, Basosi +R, Reginato G, Mordini A, Foggi P and Di Donato M 2017 Photoinduced excitation and charge +transfer processes of organic dyes with siloxane anchoring groups: A combined spectroscopic and +computational study Phys. Chem. Chem. Phys. 19 +[86] + Kakiage K, Aoyama Y, Yano T, Oya K, Fujisawa J and Hanaya M 2015 Highly-efficient dye- +sensitized solar cells with collaborative sensitization by silyl-anchor and carboxy-anchor dyes Chem. +Commun. 51 15894–7 +[87] + Sobuś J, Gierczyk B, Burdziński G, Jancelewicz M, Polanski E, Hagfeldt A and Ziółek M 2016 +Factors Affecting the Performance of Champion Silyl-Anchor Carbazole Dye Revealed in the +Femtosecond to Second Studies of Complete ADEKA-1 Sensitized Solar Cells Chem. – A Eur. J. 22 +15807–18 +[88] + Choi S K, Yang H S, Kim J H and Park H 2012 Organic dye-sensitized TiO 2 as a versatile +photocatalyst for solar hydrogen and environmental remediation Appl. Catal. B Environ. 121–122 + +34 + +206–13 +[89] + Watanabe M, Sun S, Ishihara T, Kamimura T, Nishimura M and Tani F 2018 Visible Light-Driven +Dye-Sensitized Photocatalytic Hydrogen Production by Porphyrin and its Cyclic Dimer and Trimer: +Effect of Multi-Pyridyl-Anchoring Groups on Photocatalytic Activity and Stability ACS Appl. Energy +Mater. 1 6072–81 +[90] + Ding H, Xu M, Zhang S, Yu F, Kong K, Shen Z and Hua J 2020 Organic blue-colored D-A-π-A dye- +sensitized TiO2 for efficient and stable photocatalytic hydrogen evolution under visible/near-infrared- +light irradiation Renew. Energy 155 1051–9 +[91] + Cecconi B, Manfredi N, Ruffo R, Montini T, Romero-Ocaña I, Fornasiero P and Abbotto A 2015 +Tuning Thiophene-Based Phenothiazines for Stable Photocatalytic Hydrogen Production +ChemSusChem 8 4216–28 +[92] + Li Q, Che Y, Ji H, Chen C, Zhu H, Ma W and Zhao J 2014 Ortho-Dihydroxyl-9,10-anthraquinone +dyes as visible-light sensitizers that exhibit a high turnover number for hydrogen evolution Phys. +Chem. Chem. Phys. 16 6550–4 +[93] + Lai H, Liu X, Zeng F, Peng G, Li J and Yi Z 2020 Multicarbazole-Based D−π–A Dyes Sensitized +Hydrogen Evolution under Visible Light Irradiation ACS Omega 5 2027–33 +[94] + Huang J-F, Liu J-M, Xiao L-M, Zhong Y-H, Liu L, Qin S, Guo J and Su C-Y 2019 Facile synthesis +of porous hybrid materials based on Calix-3 dye and TiO2 for high photocatalytic water splitting +performance with excellent stability J. Mater. Chem. A 7 2993–9 +[95] + Zhang X, Veikko U, Mao J, Cai P and Peng T 2012 Visible-Light-Induced Photocatalytic Hydrogen +Production over Binuclear RuII–Bipyridyl Dye-Sensitized TiO2 without Noble Metal Loading Chem. +– A Eur. J. 18 12103–11 +[96] + Kruth A, Hansen S, Beweries T, Brüser V and Weltmann K-D 2013 Plasma Synthesis of Polymer- +Capped Dye-Sensitised Anatase Nanopowders for Visible-Light-Driven Hydrogen Evolution +ChemSusChem 6 152–9 +[97] + Puga A V, Forneli A, García H and Corma A 2014 Production of H2 by Ethanol Photoreforming on +Au/TiO2 Adv. Funct. Mater. 24 241–8 +[98] + Imizcoz M and Puga A V 2019 Optimising hydrogen production via solar acetic acid photoreforming +on Cu/TiO2 Catal. Sci. Technol. 9 1098–102 +[99] + Imizcoz M and Puga A V 2019 Assessment of Photocatalytic Hydrogen Production from Biomass or +Wastewaters Depending on the Metal Co-Catalyst and Its Deposition Method on TiO2 Catalysts 9 +584 +[100] Jin Z, Zhang X, Li Y, Li S and Lu G 2007 5.1% Apparent quantum efficiency for stable hydrogen +generation over eosin-sensitized CuO/TiO2 photocatalyst under visible light irradiation Catal. +Commun. 8 1267–73 +[101] Le T T, Akhtar M S, Park D M, Lee J C and Yang O-B 2012 Water splitting on Rhodamine-B dye +sensitized Co-doped TiO2 catalyst under visible light Appl. Catal. B Environ. 111–112 397–401 + +35 + +[102] Yan Z, Yu X, Zhang Y, Jia H, Sun Z and Du P 2014 Enhanced visible light-driven hydrogen +production from water by a noble-metal-free system containing organic dye-sensitized titanium +dioxide loaded with nickel hydroxide as the cocatalyst Appl. Catal. B Environ. 160–161 173–8 +[103] Aslan E, Gonce M K, Yigit M Z, Sarilmaz A, Stathatos E, Ozel F, Can M and Patir I H 2017 +Photocatalytic H2 evolution with a Cu2WS4 catalyst on a metal free D-π-A organic dye-sensitized +TiO2 Appl. Catal. B Environ. 210 320–7 +[104] Patir I H, Aslan E, Yanalak G, Karaman M, Sarilmaz A, Can M, Can M and Ozel F 2019 Donor-Π- +acceptor dye-sensitized photoelectrochemical and photocatalytic hydrogen evolution by using Cu 2 +WS 4 co-catalyst Int. J. Hydrogen Energy 44 1441–50 +[105] Aslan E, Karaman M, Yanalak G, Bilgili H, Can M, Ozel F and Patir I H 2020 Synthesis of novel +tetrazine based D-π-A organic dyes for photoelectrochemical and photocatalytic hydrogen evolution +J. Photochem. Photobiol. A Chem. 390 112301 +[106] Lakadamyali F and Reisner E 2011 Photocatalytic H2 evolution from neutral water with a molecular +cobalt catalyst on a dye-sensitised TiO2 nanoparticle Chem. Commun. 47 1695–7 +[107] Lakadamyali F, Reynal A, Kato M, Durrant J R and Reisner E 2012 Electron Transfer in Dye- +Sensitised Semiconductors Modified with Molecular Cobalt Catalysts: Photoreduction of Aqueous +Protons Chem. – A Eur. J. 18 15464–75 +[108] Willkomm J, Muresan N M and Reisner E 2015 Enhancing H2 evolution performance of an +immobilised cobalt catalyst by rational ligand design Chem. Sci. 6 2727–36 +[109] Gross M A, Reynal A, Durrant J R and Reisner E 2014 Versatile Photocatalytic Systems for H2 +Generation in Water Based on an Efficient DuBois-Type Nickel Catalyst J. Am. Chem. Soc. 136 356– +66 +[110] Kudo A and Miseki Y 2009 Heterogeneous photocatalyst materials for water splitting Chem. Soc. +Rev. 38 253–78 +[111] Lhermitte C R and Sivula K 2019 Alternative Oxidation Reactions for Solar-Driven Fuel Production +ACS Catal. 9 2007–17 +[112] Chen X, Shen S, Guo L and Mao S S 2010 Semiconductor-based Photocatalytic Hydrogen +Generation Chem. Rev. 110 6503–70 +[113] Beltram A, Melchionna M, Montini T, Nasi L, Fornasiero P and Prato M 2017 Making H2 from light +and biomass-derived alcohols: the outstanding activity of newly designed hierarchical +MWCNT/Pd@TiO2 hybrid catalysts Green Chem. 19 2379–89 +[114] Li X, Cui S, Wang D, Zhou Y, Zhou H, Hu Y, Liu J G, Long Y, Wu W, Hua J and Tian H 2014 New +organic donor-acceptor-π-acceptor sensitizers for efficient dye-sensitized solar cells and +Photocatalytic hydrogen evolution under visible-light irradiation ChemSusChem 7 2879–88 +[115] Maitani M M, Zhan C, Mochizuki D, Suzuki E and Wada Y 2013 Influence of co-existing alcohol on +charge transfer of H2 evolution under visible light with dye-sensitized nanocrystalline TiO2 Appl. +Catal. B Environ. 140–141 406–11 + +36 + +[116] Cook A W and Waldie K M 2019 Molecular Electrocatalysts for Alcohol Oxidation: Insights and +Challenges for Catalyst Design ACS Appl. Energy Mater. +[117] Pho T V., Sheridan M V., Morseth Z A, Sherman B D, Meyer T J, Papanikolas J M, Schanze K S +and Reynolds J R 2016 Efficient Light-Driven Oxidation of Alcohols Using an Organic +Chromophore-Catalyst Assembly Anchored to TiO2 ACS Appl. Mater. Interfaces 8 9125–33 +[118] Kuehnel M F and Reisner E 2018 Solar Hydrogen Generation from Lignocellulose Angew. Chemie - +Int. Ed. 57 3290–6 +[119] Christoforidis K C and Fornasiero P 2017 Photocatalytic Hydrogen Production: A Rift into the +Future Energy Supply ChemCatChem 9 1523–44 +[120] Lee J S, Won D Il, Jung W J, Son H J, Pac C and Kang S O 2017 Widely Controllable Syngas +Production by a Dye-Sensitized TiO2Hybrid System with ReIand CoIIICatalysts under Visible-Light +Irradiation Angew. Chemie - Int. Ed. 56 976–80 + + diff --git a/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/load_file.txt b/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f78c97a2ebddb57c271441b473e2447afff8914c --- /dev/null +++ b/HNAzT4oBgHgl3EQfUvzA/content/tmp_files/load_file.txt @@ -0,0 +1,920 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf,len=919 +page_content='1 Design of dye-sensitized TiO2 materials for photocatalytic hydrogen production: light and shadow Lorenzo Zani,a Michele Melchionna,b Tiziano Montini,b Paolo Fornasiero b,* a Institute of Chemistry of Organometallic Compounds (CNR-ICCOM), Sesto Fiorentino 50019, Italy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' b Department of Chemical and Pharmaceutical Sciences, CNR-ICCOM Trieste Research Unit and INSTM Research Unit, University of Trieste, Trieste 34127, Italy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' email: pfornasiero@units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Table of Contents 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Introduction: visible light absorption and the relationship with DSSCs 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' How to properly compare data 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Charge transfer processes in DSP 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Design of dye scaffold for application in DSP 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hydrophobicity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' hydrophilicity of the photocatalyst surface 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Effect of dye loading on photocatalytic performances 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Impact of TiO2 crystal structure: which phase is the best?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Approaches to improve stability 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Nature of the hydrogen evolution catalyst 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sustainability of the sacrificial donor 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Perspectives 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' References Abstract: Visible light-driven production of fuels and value-added chemicals is currently one of the most intensely investigated research topics across various scientific disciplines, due to its potential to ease the World’s dependence on fossil fuels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this perspective, we recapitulate some of the main features of dye-sensitized photocatalytic systems aimed at solar H2 production, focusing in particular on TiO2-based three-component assemblies with organic sensitizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Relevant aspects include the structural and electronic properties of the sensitizers, the nature of the semiconductor and the hydrogen evolution catalysts, the role of the sacrificial donor and the effect of the reaction parameters on H2 production rate and stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Besides presenting the most significant recent developments of the field, we also analyse some of its common practices in terms of experimental design, laboratory procedures and data presentation, trying to highlight their weaknesses and suggesting possible improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' We then conclude with a short paragraph discussing the possible future development of this exciting research area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Introduction: visible light absorption and the relationship with DSSCs Due to the urgent need to replace fossil fuels as the World’s main energy source, the conversion of solar radiation into chemical energy in the form of so-called “solar fuels”, often referred to as “artificial photosynthesis”,[1] is currently of utmost scientific and technological relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [2] Among the different artificial photocatalytic processes, H2 production through water splitting (WS) has probably been the most intensely studied, since H2 is endowed with high volumetric energy density, no carbon footprint and can be either directly burned or used in fuel cells to produce electricity, thus constituting an almost ideal energy carrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [3,4] In 1972, the pioneering work of Honda and Fujishima demonstrated that WS into H2 and O2 could be achieved by irradiating a TiO2 photoanode connected to a platinum cathode in an electrochemical cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [5] The main drawback of such system was the use of a wide band-gap (≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 eV) semiconductor (SC) as the light- harvesting material, which hampered absorption and conversion of visible light (λ > 400 nm) and made it necessary to use UV radiation to drive the reaction forward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' To solve such an issue, several possible approaches to modify inorganic heterogeneous photocatalysts have been investigated,[6] including the use of narrow band-gap semiconductors[7,8] the chemical modification of large band-gap materials to impart them the ability to absorb visible light,[9] or the application of more complex photocatalytic assemblies such as Z-schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [10,11] Besides, another effective strategy has been the sensitization of semiconductors with molecular dyes, able to harvest light in the desired wavelength range and inject the resulting photogenerated electrons into the SC conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [12] This concept was first established in Dye-Sensitized Solar Cells (DSSC), in which, after excitation and charge injection, electrons are collected at a TiO2 photoanode while holes are transferred to the reduced form of a suitable redox mediator (typically I3−/I−), which is then regenerated at the cathode to close the cycle and produce an electric current (Figure 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [13] Due to the analogy with DSSCs, such photocatalytic systems are usually called Dye-Sensitized Photocatalysts (DSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' DSSC and DSP share the same dye/semiconductor interface but, in the latter, photogenerated electrons in the conduction band are transferred to an electrocatalyst (such as Pt) for solar fuel production, instead of being used for electricity generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Accordingly, in DSP the oxidized dye molecules must be reduced by a suitable hole scavenger to allow the process to continue (Figure 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In a proper WS procedure, electrons would be supplied by water itself, allowing coupling of H2 production with O2 evolution without formation of any other by-product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' However, water oxidation demands combining the sensitizers with appropriate catalysts, often a synthetically demanding operation,[14] and is usually affected by significant drawbacks, such as the need for a large overpotential,[15] the quick recombination of photogenerated charge carriers, and the rapid back reaction between H2 and O2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [16] Consequently, to achieve a high yield of H2 production, but also to better determine the photocatalyst intrinsic activity, dye regeneration is more commonly carried out by means of a sacrificial electron donor, usually abbreviated as SED (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [17] From the above discussion it is clear that, despite the similarities between the two systems, the materials used in DSSC or DSP, such as dyes and 3 semiconductors, must work under different conditions and thus will need to be developed independently to provide optimal performances in each application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Schematic representation of the working mechanisms of (a) a DSSC and (b) a DSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this perspective, the main features of selected DSP systems especially developed for H2 production will be critically presented, trying to highlight their strengths as well as the areas where there is still room for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although the concept of dye-sensitization has been applied to different kinds of materials,[18] inorganic[19] as well as organic,[20,21] we will focus on TiO2-based systems, since they are by far the most investigated in the literature and thus can be more easily compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the majority of such systems, TiO2 is used as the anatase crystalline form, or as the commercially available 80:20 anatase/rutile mixture known as P25,[22] but alternatives have also been described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Before starting the discussion, we will briefly introduce the topic of the correct presentation and comparison of photocatalytic data, as the adoption of a more homogeneous and shared standard will be of crucial importance for the future development of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' How to properly compare data The criticality of correctly evaluating the merits of a new proposed photocatalyst is one of the contemporary topics of discussions within the photocatalysis community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [23,24] In this respect, the importance of introducing more comprehensive and diligent practices when assessing and comparing photocatalysts performances has been recently highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [25] As an example, for heterogeneous photocatalysts it is very common to report the rate of evolved product per mass of photocatalyst, which gives also an idea of how stable it is, but does not take into account the contribution of its textural features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hence, adding a rate normalized by the material surface area provides a more thorough screening and is therefore recommended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [26] Turnover numbers (TON), or in alternative turnover frequency (TOF), are two other classic catalytic parameters, which in the specific case of DSP are calculated over the number of moles of dye covering the semiconductor nanoparticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hence, the catalytic sites are assumed to be equal to the number of molecules of Load (a) (b) e W @" Pt on Tco (reduction TCO hy hv catalyst) e 2H* Dye e CB SED* Ered Dye TiO2 H2 @ Sed Reduction catalyst M/M SeD = Sacrificial Electron Donor .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' dye M = redox mediator4 dyes, which may in principle lead to underestimated TON or TOF, if not all the dye molecules are in the right spatial configuration for electron transfer to the SC (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' formation of aggregates, intermolecular charge transfer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Moreover, apart from depending on several conditions such as temperature and pH, TOF is a kinetic- dependent parameter, so that it should be evaluated at low conversions (or at least the reactant or product concentrations should be provided), or ideally as an instantaneous value measured at specified product (or reactant) concentrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [27] Most studies on heterogeneous photocatalysts, however, compare them in terms of quantum yield (QY), quantum efficiency (QE), or photonic efficiencies, where instead of the number of catalytic sites (which for DSP is assumed to be the number of dye molecules), the number of incident photons is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [23] While the adoption of this parameter seems to remove the uncertainty on the effectiveness of the adsorbed dye to transfer electrons, it also introduces an element of ambiguity related to the heterogeneous nature of the photocatalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In fact, for heterogeneous systems, not all the incident photons are necessarily absorbed, with scattering phenomena taking place and decreasing the amount of utilized photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For heterogeneous photocatalysts, the term apparent quantum yield (AQY) is therefore more sensible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [28] As a result, the AQY is almost always an underestimation of the real QY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Moreover, as the AQY is a function of the excitation wavelength,[29] a fact that is at times ignored, the comparison between DSP with different absorption characteristics may be affected by inaccuracies, causing false esteems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A good practice will therefore be to plot the wavelength-dependent AQY profile by measuring it at successively increasing wavelengths, and then verify that the pattern follows that of the photocatalyst or sensitizer absorption spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Charge transfer processes in DSP As shown in Figure 1, the photocatalytic cycle in DSP is initiated by the two steps of light absorption and charge separation, which are of pivotal importance to determine the efficiency of H2 generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Two main mechanisms have been proposed for the charge separation process involving a photoexcited dye, the semiconductor (most commonly TiO2) and the SED, classified as reductive quenching and oxidative quenching, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [30] Following light absorption (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 1), the reductive quenching mechanism proceeds with an electron transfer from the SED to the excited dye, which is thus converted into a radical anion (D•−, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Subsequent electron injection into the semiconductor conduction band restores the dye in its ground state and completes charge separation (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the oxidative quenching mechanism, on the other hand, the first electron transfer step involves charge injection from the excited dye to the semiconductor, with concomitant formation of a dye radical cation (D•+, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The latter is then reduced by the SED, and the same charge separation state is reached (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finally, the electrons in the conduction band of the semiconductor will be used for H2 generation by proton reduction (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Besides these productive electron transfer events, however, it must be pointed out that detrimental, reverse charge transfer processes can also take place, such as charge recombination between injected electrons and the dye cation or the oxidized SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The ratio between the rates of forward and backward electron transfer processes is what ultimately dictates the efficiency of the photocatalytic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [12] 5 Photoexcitation: Pt/TiO2/D + hν → Pt/TiO2/D* (1) Reductive quenching: Pt/TiO2/D* + SED → Pt/TiO2/D•− + SED+ (2) Pt/TiO2/D•− → Pt/TiO2 (e−)/D (3) Oxidative quenching: Pt/TiO2/D → Pt/TiO2 (e−)/D + (4) Pt/TiO2 (e−)/D•+ + SED → Pt/TiO2 (e−)/D + SED+ (5) Proton reduction: Pt/TiO2 (e−)/D + H+ → Pt/TiO2/D + 1/2 H2 (6) In general,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' the oxidative quenching mechanism is considered to be predominant for almost all dye classes (see below),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' in analogy with what happens in DSSCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The reductive quenching mechanism is probably relevant only in the case of poorly reducing, cationic dyes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' thionine, methylene blue, nile blue A), and has been suggested to provide inferior results in terms of H2 production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [30] The efficiency of the charge transfer process between the dye and the semiconductor is usually assessed by means of photoluminescence decay studies: by comparing the excited state lifetime of the dye in solution to that of the dye/semiconductor assembly the rate constant for electron transfer can be calculated with good approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [31] 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Design of dye scaffold for application in DSP Dye design is certainly one of the most important factors affecting light harvesting and charge transfer efficiency in DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As mentioned in the introduction, the concept of dye-sensitization in DSP was originally derived from that of DSSCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Consequently, the main classes of dyes employed in photocatalysis resemble those already applied in solar cells, namely (i) metalorganic complexes, especially based on ruthenium with bi- o terpyridine ligands;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (ii) porphyrins and phthalocyanines bearing different central metals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (iii) metal-free organic dyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' This latter class of dyes has been the subject of the largest number of studies in recent years,[32,33] and can be further divided into sub-categories, such as emissive dyes traditionally used in chemical biology, or donor (D)-acceptor (A) structures, where electron-donating groups are connected to electron-accepting units via conjugated sections of various nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Such an arrangement allows extending and strengthening the absorption spectra of the resulting compounds, improving their light-harvesting ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In their simplest form, these compounds are usually denoted as D-π-A dyes, with the electron acceptor also fulfilling the role of anchoring group to the semiconductor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='[34] from them, more complex architectures such as D-A-π-A, D-D-π-A and others[35] have been derived by the insertion of additional donor or acceptor units in various parts of the structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A comprehensive review on the use of all the above classes of sensitizers in DSP is beyond the scope of this manuscript, and has already been presented elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [12] Here, we will focus our attention on the employment of organic dyes, since they have provided the best results in DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Moreover, the fact that they do not contain precious or toxic heavy metals makes them more sustainable than metalorganic complexes, which is particularly relevant in the field of renewable energy technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finally, they are usually accessible 6 through simple and modular synthetic processes, allowing to efficiently tune their stereoelectronic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Accordingly, they constitute an ideal platform to analyse how their structural and compositional changes can affect the overall performances of the DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite their similarities, organic dyes used in DSP have evolved independently from those employed in DSSCs, due to the different conditions in which they must operate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For example, they have to work efficiently in the aqueous environment used in DSP, while DSSC usually contain organic solvents and are moisture- sensitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In addition, they must be regenerated by SED molecules, which are different from the redox couples commonly used in DSSCs, thus requiring a different alignment of their energy levels (especially the HOMO level).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finally, the fact that DSSCs are self-contained devices in which the photo- and electroactive materials are supported onto electrodes while DSPs operate in heterogeneous suspension bears different requirements in terms of dyes molar absorptivity and loading onto the semiconductor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For the above reasons, although DSP and DSSC dyes usually have similar light harvesting properties, they can present significant differences in the way they are attached to the SC surface, in the balance of their hydrophobic and hydrophilic characteristics, and in their electrochemical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Some of these features will be discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' To work efficiently in a DSP system, any sensitizer has to fulfil two obvious requirements: (i) it should be able to absorb light efficiently in the visible region of the spectrum (where solar radiation is maximized);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (ii) it should transfer easily the photogenerated electrons to the conduction band of the semiconductor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Thanks to the extensive experience accumulated in the field of DSSC, it has been relatively straightforward to build a library of organic photosensitizers for DSP applications having both these properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [12,32] By changing the nature of the main chromophore and adjusting the length of the conjugated section, compounds have been reported with the main absorption band going from around 400 nm (as in the case of simple D-A structures, Figure 2, 1)[36,37] to almost 700 nm, close to the near-IR region (as in the case of porphyrin- or BODIPY- containing species, Figure 2, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [31,38,39] On the other hand, insertion in the structure of additional electron- donating or accepting fragments can serve to modulate the frontier orbitals energy levels and thus alter the rate of the intermolecular charge transfer processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [40,41] It should be noted that all such properties can be efficiently modelled by means of DFT calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [42] Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Structures of organic dyes having very different UV-Vis absorption maxima in solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Nevertheless, there are other characteristics the sensitizers must possess to boost the activity of a three- component photocatalytic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' First, to be able to transfer electrons quickly to the semiconductor, they should have a robust anchoring to its surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Due to the analogy with DSSC dyes, most compounds bind the 113 CN OH 2 O NC OH = 391 nm (THF) max7 semiconductor through a carboxylic acid group (either simple or as a part of a cyanoacrylic function).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [43] However, the aqueous conditions employed for H2 production and the different pH levels associated with different hole scavengers (see below) motivate the look for alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A systematic study was conducted by Reisner and co-workers, who compared the performances of perylene monoimide (PMI) dyes endowed with different anchoring groups (Figure 3a, Table 1) in acidic, neutral and basic conditions, using two hole scavengers (triethanolamine and ascorbic acid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [44] Their main finding was that while a dye bearing the carboxylic group was very active and sufficiently stable under acidic conditions, moving towards higher pH the use of a phosphonic acid anchor became clearly preferable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' interestingly, a dye with a hydroxyquinoline anchoring group (PMI-HQui) proved also very efficient under acidic conditions, but underwent fast deactivation as a result of detachment from TiO2 surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Structures of organic dyes with different anchoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' H2 generation efficiency of PMI dyes with different anchoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [44] Dye Dye loading [μmol/g] Conditions (SED, pH)a H2 produced [μmol] (24 h) TON (24 h) Retained activity after 24 hb AA, pH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='7 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='2 6461 ± 749 78% PMI CO2H 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 TEOA, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 471 ± 63 33% TEOA, pH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='1 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='4 490 ± 170 35% AA, pH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='2 2146 ± 203 80% PMI AcAc 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='2 TEOA, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='1 133 ± 13 51% TEOA, pH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='7 294 ± 67 52% AA, pH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 3546 ± 523 70% PMI PO3H2 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 TEOA, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='4 303 ± 30 46% TEOA, pH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 708 ± 107 48% AA, pH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='9 4928 ± 549 44% PMI HQui 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 TEOA, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 232 ± 26 38% TEOA, pH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='4 262 ± 36 41% (a) PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='COHRA COOH (b) BO PMI AcAc, R= Buo Heos!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' R PM POM,R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' POM A tB O PmhQu,R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ho C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='H DpP cA R CoOoH N DDP CN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='RACN tBu GOOH PMHDPA RE!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' COOH8 AA, pH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='4 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='9 3943 ± 394 54% PMI DPA 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='8 TEOA, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='2 366 ± 37 55% TEOA, pH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='7 444 ± 62 56% a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='25 mg Dye/TiO2/Pt in 3 mL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='1 M SED solution, UV-filltered simulated solar irradiation (AM 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 G, 100 mW cm−2, λ > 420 nm, 25 °C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' b Calculated by comparing TOF values after 1 h and after 24 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A peculiar result was reported by Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=', who compared the efficiency of two photocatalytic systems obtained with analogous dyes bearing a cyanoacrylic or a malononitrile anchoring group (Figure 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Surprisingly, it was the latter (DPP-CN) that produced the better result in terms of H2 production in typical conditions (dye loading 25 μmol/g, TEOA 10% vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' in H2O, pH 7, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 Sun irradiation, λ> 400 nm), with a TON of 9664 in 10 h (corresponding to 1208 μmol of evolved H2) compared to 6720 recorded for DPP-CA (840 μmol of evolved H2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [45] Although the authors did not provide details on the anchoring mode of malononitrile to TiO2, it is supposedly similar to that of dicyanomethylene compounds reported as sensitizers for DSSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [46,47] Nevertheless, the latter were used as Type-II sensitizers and have a much simpler molecular structure, and therefore the working mechanism is hardly comparable in the two cases: given the excellent results reported, it seems that a deeper investigation of dyes with malononitrile or related anchoring groups could be useful to shed light on their behavior and further improve their performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Another key point is that the sensitizer, after photoexcitation and charge injection, should be readily regenerated by the reductant present in solution (either water in WS processes or a SED).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Once again, this process has been thoroughly characterized in DSSC, and the main properties that a dye must possess to undergo efficient regeneration by a certain redox mediator are known in sufficient detail (driving force of the reaction i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' dye HOMO position,[48] presence of certain functional groups on the donor section[49]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the case of DSP systems, the situation is much less clear: an obvious requirement is for the sensitizer to have a more positive ground-state oxidation potential (ES+/S*) than the standard redox potential of the reducing agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' However, this condition is not met in every case: for example, TEOA redox potential is reported to be +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='82- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='07 V vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Normal Hydrogen Electrode (NHE),[17] but an efficient H2 production was found also when employing it as a SED in combination with dyes having oxidation potentials in the +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='64-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='74 range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [45,50] Conversely, despite an apparently appropriate driving force for regeneration, many organic dyes with triphenylamine donors were found inactive when used together with ethanol as a hole scavenger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [51] Such apparent contradiction is probably due to two main reasons: first, dyes ES+/S* values are usually measured on diluted organic solutions in CH2Cl2 or CH3CN, a very different environment compared to that in which they are actually used (adsorbed on TiO2 in aqueous environment);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' second, different hole scavengers may work according to different reaction mechanisms and their redox potentials usually vary with pH,[17] which affects dye regeneration rates and thus photocatalytic turnover frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In addition, the relative dye hydrophobicity/hydrophilicity could also influence its regeneration process (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' To better evaluate the ability of organic dyes to work in DSP systems, it would be therefore advisable to investigate their electrochemical properties in more detail and in conditions more relevant to their actual application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 9 Furthermore, the reference electrode against which potentials are measured and the formalism used to convert such values to orbital energies (vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' vacuum) should be clearly indicated, as incomplete information often hinders comparison of data reported in different studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As a final point of this paragraph, spatial organization of dye molecules on the semiconductor surface should also be precisely controlled, to maximize the photocatalyst light absorption ability and reduce losses due to energy dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Such a parameter has also often been associated with the relative hydrophobicity/hydrophilicity of the dyes, controlling their interactions with the solvent and the semiconductor surface (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ahn, Son and co-workers found that by decorating phenothiazine dyes with alkyl chains of different length (Figure 4, P1-P5) a macroscopic effect on H2 production efficiency could be observed, with the best result provided by dye P5 featuring the largest substituent (TON after 5 h increasing from 380 for P1 to 1026 for P5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' the authors claimed that “alkyl groups on nitrogen can induce a favorable orientation of dyes on TiO2, which may result in the efficient electron injection from excited dyes to TiO2”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [52] Such a concept was further developed by Abbotto, Fornasiero and co-workers, who modified the same class of dyes and placed different hydrophobic and hydrophilic chains on the nitrogen atom (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [53] They found that dye PTZ-ALK, featuring an n-octyl chain, showed a much higher H2 production efficiency compared to its hydrophilic counterparts (PTZ-TEG and PTZ-GLU) at low dye loading, but such a difference was largely reduced when the loading was increased up to 30 μmol g–1 (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' According to the authors, at high loadings the organization of PTZ-GLU is “similar to that of PTZ-ALK, with the PTZ units interacting with the Pt/TiO2 surface and the bulky lateral chains avoiding intermolecular quenching”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' when the loading is decreased, though, “the glucose unit could interact directly with the TiO2 surface through the remaining OH groups and it might change the orientation of the PTZ scaffold affecting the electron transfer to TiO2”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [53] Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) Structures of phenothiazine-based photosensitizers and GLUA additive;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) DFT computational analysis showing the H-bond interaction between dye PTZ-GLU and GLUA (in the red circle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reprinted with permission from reference [54] (© 2018, American Chemical Society).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The importance of having a correct disposition of sensitizers molecules on the semiconductor surface was later confirmed when the same group studied the effect of combining PTZ-GLU with different co-adsorbents, including in particular glucoronic acid (GLUA, Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [54] It was found that using the sensitizer and GLUA (a) (b) ONI ONT P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' rhch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' GN HooG COOHI Pizalk Ra coh?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hood PTZTEGLRS HO OH PTZGLU,RE oMe glucoronfic acid (GLUA) OH OHI10 in a 1:1 ratio clearly increased the TON of the photocatalyst;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' remarkably, this was not the case when a different and more hydrophobic co-adsorbent (chenodeoxycholic acid, CDCA) was used (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' By employing DFT computational analysis, the authors found that a “directional and selective” interaction was established between PTZ-GLU and GLUA, which helped stabilizing the dye-semiconductor assembly and was effective in hindering dye-dye intramolecular interactions, minimizing unproductive energy transfer phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' This was confirmed by the fact that, when PTZ-ALK was combined with either CDCA or GLUA in the same ratio, no improvement was observed, since no selective interaction could be established between the coadsorbents and the bare alkyl chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photocatalytic data for PTZ dyes in combination with different coadsorbents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [53,54]a In summary, although dye design principles for DSSC and DSP may be similar, sensitizers for the latter application should be developed in response to specific requirements to allow performance improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' While maintaining a wide and intense light absorption in the visible spectrum, charge injection rates into the SC should be improved, for example by investigating new anchoring groups exploiting unusual charge transfer mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Dye regeneration rates should also be enhanced by exact tuning of the sensitizers HOMO levels towards use with a specific electron donor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' this operation should be assisted by measuring the dyes electrochemical properties under more realistic conditions, and by performing time-resolved spectroscopic analysis of dye regeneration by different species, as already done in DSSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [55] Finally, dye organization on the SC surface should be optimized by exploiting the formation of ordered supramolecular structures, either using the dyes alone or by interaction with co-adsorbent species, not limited to those traditionally employed in DSSCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Dye Dye loading [μmol/g] Coadsorbent H2 produced [mmol/g] (20 h) TON (20 h) LFE20 [%]b AQY [%]c PTZ- GLU 1 - - 678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='008 - 30 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='88 59 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='024 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='071 30 GLUA (1:1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='37 91 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='037 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='139 30 CDCA (1:1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='73 48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='077 PTZ- ALK 1 - - 1232 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='017 - 30 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='96 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='026 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='081 30 GLUA (1:1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='66 44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='062 30 CDCA (1:1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='84 56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='023 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='073 PTZ- TEG 1 - - 396 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='005 - 30 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='421 29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='013 - a Conditions: TEOA 10% v/v solution in H2O, pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0, 20 h irradiation, visible light (λ > 420 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' b LFE20: light-to- fuel efficiency after 20 h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' for details on its calculation, see ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [32];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' c obtained with light irradiation at 450 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 11 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hydrophobicity vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' hydrophilicity of the photocatalyst surface Variation of the dyes relative hydrophobicity and hydrophilicity can have a significant impact on the photocatalyst performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' However, the simple question if it is better, in terms of H2 production efficiency, to use a more hydrophobic or hydrophilic sensitizer has not yet been definitively answered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Clearly, dye optimization should not only aim at improving the individual properties of the molecules (structural, spectroscopic, electrochemical), but should also take into account the specific conditions in which the photocatalytic reaction is conducted, including solvent, pH, presence and nature of a hole scavenger, type of illumination and so on;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' in this regard, it is then possible that the optimal sensitizer in one case will be outperformed by a different compound in another, if the reaction conditions are not the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As mentioned above, some early studies examined the effect of placing alkyl chains of different lengths on the donor section of the sensitizers, usually finding that photocatalysts based on dyes with long (up to C16) substituents provided the best results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [52,56,57] In a further refinement, the issue of where it is best to place such hydrophobic groups has also been recently investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although comparing reports on different classes of dyes is not always straightforward, it has emerged that putting alkyl chains on the middle part of the organic dye structures can also be advantageous,[58,59] and even lead to enhanced results, as shown in Figure 5a, where the TON values for dyes MB25 and AD418 are compared to that obtained for dye DF15 (TEOA as SED, pH 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [51] Such an effect was attributed to a more efficient shielding of TiO2 coupled with a higher dye regeneration rate, due to the lack of steric bulk on the donor group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Indeed, further increase of the dyes hydrophobicity by installation of alkyl chains both on their donor and intermediate sections can even be detrimental, as exemplified by the data collected for Pt@TiO2/OB1-3 photocatalysts (Figure 5b): after an initial improvement going from OB1 to OB2, performances with the OB3-based system were almost back to the initial level, probably as a consequence of an excessive steric bulk and non-optimal interaction with the hole scavenger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [60] HCo OH 300 DF15 MB25 AD418 250 DF15 GSH 200 HsCo 可 OHI 150 : er 100 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' MB25 50 TON=474 ToN=569 TON=872 T 5 10 15 20 5 101 15 20 5 10 15 20 tme(h) time(h) time (h) AD418 CsH (b) TON 510 + R NC TON= 251 SH OBTRECH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='ROH TON=210 OB2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='RE(CH2)/CH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='R =H12 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Structures of (a) dyes DF15, MB25, AD418 and (b) OB1-3, and the H2 production curves of the corresponding Pt/TiO2 dye-sensitized photocatalysts in the presence of TEOA as hole scavenger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Adapted with permission from references [51] (© 2018, Wiley-VCH) and [60] (© 2019, American Chemical Society).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Moving to the opposite direction in terms of dye polarity, Kang and co-workers investigated the impact of changing the hydrophilic and steric properties of a series of organic dyes in sensitized H2 generation using Pt/TiO2 photocatalysts (Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [61,62] When using EDTA as sacrificial donor at acidic pH, it was found that hydrophilic methoxymethyl substituents at the 4,4′-positions of the diphenylamino end group enhanced the photocatalytic activity compared to both the parent compound (without substituents) and a hydrophobic counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Differently from what seen above for hydrophobic chains, introduction of hydrophilic substituents also in the middle conjugated section of the molecules did not bring any further improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' By applying both transient spectroscopy techniques and DFT calculations, the authors concluded that the different performances of the photocatalysts were due to a different organization of solvent molecules around the hydrophilic or hydrophobic substituents, coupled with steric effects that determined the amount of dye adsorbed on the semiconductor surface, which collectively influenced the kinetics of charge transfer processes across the SED/dye/semiconductor interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For the best sensitizer, MOD, an AQY value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='03% was measured under monochromatic light irradiation at 436 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (top) Structures of the hydrophilic sensitizers designed by Kang and co-workers, and of the corresponding hydrophobic dye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (bottom) TON of the H2 production reaction of the corresponding Pt/TiO2 DSP in the presence of EDTA as a hole scavenger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [62] (© 2012, Wiley-VCH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite their obvious interest, the above results turned out to be quite specific, as shown by the previously mentioned work by Abbotto, Fornasiero and co-workers on phenothiazine dyes,[53] in which they reported OH R HD, R1 = R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='= H MOD,R=-CH,OCH3,R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='=H PD, R1 = -(CH2),CH3, R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' = H MO4D, R1 = R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' = -CH,OCH3 18 MOD 16 MO4D 14 HD PD 12 10- NOI 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 0 0 50 100 150 200 250 Time (min)13 that dyes with hydrophilic substituents on the donor section were actually less efficient than that featuring a simple alkyl chain;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' it should be noted that their experiments were conducted in water at neutral pH and using TEOA as SED, thus in very different conditions compared to those performed by Kang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The importance of correctly matching the sensitizers structure with the actual reaction conditions was further demonstrated in a recent study, in which a series of ten organic dyes based on the benzothiadiaziole (BTD) core and featuring a different number of hydrophobic and hydrophilic chains were used as sensitizers for Pt/TiO2 in H2 production experiments with three different hole scavengers (TEOA, ascorbic acid, EtOH), at different pH levels (Figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [63] The best performances with TEOA at pH 7 were obtained with highly hydrophobic dyes BB2a and BB2d (TON up to 295), whereas introduction of hydrophilic substituents on the donor section did not bring any improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Remarkably, when employing ascorbic acid as SED at pH 4, the situation was significantly changed, with the highest H2 amount produced by the photocatalysts based on hydrophilic dyes BB2e and BB3e (TON up to 2266).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although the exact reason for the reversal in relative performances is not known, the improved interaction of the hydrophilic dyes with the polar SED molecules, coupled with a better matching of their ground-state oxidation potentials (compared to TEOA) and the easier proton reduction at lower pH clearly contributed to the observed outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (top) Structures of the hydrophobic and hydrophilic sensitizers of the BB2 and BB3 series;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (bottom) TON values obtained in combination with different SEDs at different pH (dye@P25/Pt photocatalysts, dye loading 10 μmol/g, λ> 420 nm, irradiation time 15 h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In general, the results of all the above-mentioned studies suggest that no such thing as an “ideal dye” for DSP generation of H2 exists, and that optimization of sensitizers properties must always be assessed in relation to the specific reaction conditions applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In particular, choice of the sacrificial donor and of the pH level at which the reactions are conducted appear especially decisive in determining the H2 production efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this context, it will be imperative in future years to improve dye design by introducing on the donor section HiCs CHi HnCsCsHt R OH BB2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' RHi BB2e,R= BB3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='Ria Sensitizer TON Values BB2a BB2d BB2e IBB3e SED TEOa(pHz) 295 238 126 147 AA(pH4) 1231 780 2266 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='1714 functional groups able to interact efficiently with the selected SED molecule, which, together with appropriate tuning of the energy levels (see previous section), should help increase regeneration rate constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' To this end, we think that investigation of dyes with combined hydrophobic/hydrophilic sections should be continued, trying to favor structures able to provide a significant hydrophobic barrier against recombination near the SC surface, while at the same time bearing hydrophilic groups of carefully tuned steric bulk near the region where interaction with SED is thought to happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Effect of dye loading on photocatalytic performances The effect of dye loading on photocatalyst performances is usually evaluated in two different ways, either by saturation of the semiconductor surface with dye molecules or by adsorption of a precise amount of sensitizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the first approach, the semiconductor nanoparticles are suspended in a solution containing a large amount of dye, so that adsorption is maximized: as a consequence, different sensitizers will be adsorbed in different amounts, depending mostly on their size and on their geometrical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this way, it is possible to evaluate the relative H2 production abilities of the corresponding photocatalysts, but no precise information on the individual dye efficiency and on its optimal loading can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For example, this was the case in the above-cited work by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=',[59] where the maximum possible amount of “starbust” dyes DH1-4 was loaded on Pt/mc-TiO2 (an especially-developed anatase cubic “microcage” TiO2 material).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The TONs registered after 20 hours for dyes DH3-4 were higher than that obtained for dye DH2, but the latter had a much higher adsorption density on the semiconductor surface, and thus the corresponding photocatalyst produced a higher H2 amount (Figure 8 and Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Structures of dyes DH1-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [59] COOH spacer CN CN DH1 3 COOH DH4 spacer: DH1 Dh2 DH315 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photocatalytic data for DH1-4/Pt/mc-TiO2 three-component systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [59]a Dye Dye loading [μmol/g] H2 produced [mmol/g] (20 h)b TON (20 h)b DH1 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='18 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='42 984 DH2 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='11 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='75 1434 DH3 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='80 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='68 1583 DH4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='77 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='88 2285 a Conditions: 50 mg of dye/Pt/mc-TiO2 in 100 mL of a 10% TEOA solution in H2O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Irradiation with a 300W Xe lamp equipped with a cut-off filter (λ > 420 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' b Experiments were run in triplicate, only the best result is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the second approach, a solution containing a precise quantity of sensitizer is used to stain the semiconductor, so that after sensitization a colorless supernatant solution is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this way, a precise amount of dye can be loaded on the photocatalyst, allowing to determine the effect of different dye loadings and to assess the relative TON values of the dyes at the same level of superficial concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A common finding in this kind of experiments is that the overall amount of generated H2 initially increases with the increasing dye loading, but then reaches a maximum and starts decreasing again above a certain dye concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For example, such an effect was observed in several studies by Pal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' examining organic sensitizers with different structures and anchoring groups,[45,50,57,64] and was attributed to the fact that initially the fraction of incident light absorbed by the dye increases with increasing dye loading, but then the photocatalytic activity starts to decline due to dye aggregation (accompanied by unproductive intermolecular energy transfer) and shielding effects reducing the penetration depth of incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Clearly, since the maximization of dye loading on the semiconductor surface does not always lead to improved performances, this second approach appears preferable and a screening of the effect of dye concentration is recommended to obtain photocatalysts with optimized efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Impact of TiO2 crystal structure: which phase is the best?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the case of DSP, the semiconductor basically acts as an electron transporter from the sensitizer to the catalytically active site, so that, as mentioned above, one of the main requirements to be met by the sensitizer is that the injection of the excited electron into the semiconductor conduction band (CB) is allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Usually, such thermodynamic restriction is condensed into the need for “correct band alignment”, namely the potential energy of the LUMO level of the dye must be more negative than that of the semiconductor CB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The widespread prominence of TiO2 is often jeopardized by critical factors that compromise its performance, and decrease it to an unacceptable level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' From the point of view of the semiconductor, some of the setbacks, particularly pronounced for first row transition metal oxides, include a fast charge recombination, poor charge mobility, surface effects, size of the band-gap and others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [65,66] One additional aspect is the relationship between the metal oxide crystal structure and the performance, which can be usefully exploited for better 16 photocatalyst design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' TiO2, which is stable under ambient conditions in the three polymorphs rutile, anatase and brookite, is the best case study to fathom such a relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The three phases exhibit different photocatalysis-relevant properties such as charge recombination rate, band gap, density if states (DOS) and mode of charge carrier transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although such differences have been correlated to variations of photocatalytic efficiency,[67] establishing an univocal trend is a complex matter, because there is a strong dependence on the nature of the catalyst, being a single crystal, a thin film or a powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [68] For example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' while a recent study conducted on different anatase,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' brookite,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' and rutile single-crystal wafers with only one exposed surface showed that the anatase surfaces are generally more active than those of rutile and brookite for methanol photooxidation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='[69] investigation of composite materials for alcohol photoreforming revealed that the hydrogen production relative to the surface area increased with brookite content,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' suggesting that brookite facets were more active for proton reduction under those conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [70] Based on the catalyst nature, the presence, type and distribution of defects plays a very important role, whereby conduction band electrons can be trapped and stabilized to different extents, with the specific TiO2 crystal structure being a powerful determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [71] Furthermore, additional factors come into play as well, such as complex charge transport kinetics within TiO2[72] or varying particle size distribution,[73] making it difficult to shape a comprehensive and reliable paradigm related to predicted activity of each material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite such a complexity, the built knowledge on TiO2 crystal structure/photocatalytic dependence has resulted in very interesting new outputs, arising from the wise exploitation of advanced techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For instance, the once overlooked brookite, long considered an inactive phase, has recently gained attention due to its peculiar physico-chemical properties,[74,75] whose assessment was made possible by the emergence of new strategies for its synthesis in a pure form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [76] In the context of DSP, it was recently demonstrated that photocatalysts obtained by sensitization of nanocrystalline brookite/Pt with the above-mentioned sensitizer OB2 (Figure 5) provided better performances in H2 production experiments compared to their P25-based counterparts (Figure 9a), being also characterized by a remarkable stability (Figure 9b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [60] This result was attributed to a reduction in charge recombination rate due to the lower reactivity of conduction band electrons of brookite compared to anatase,[71] in agreement with previous studies conducted on DSSCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [77] In addition, the morphology of the TiO2 is to be taken into careful consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Several groups have reported the use of anatase-based semiconductors with tailor-made morphology for use in DSP systems, such as cubic “microcage” materials[59] or hierarchical porous structures,[31,39,50] showing enhanced performances compared to the commercial TiO2 sources, owing to improved electronic features or larger surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Cargnello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' demonstrated how the geometrical anisotropy of brookite nanorods was instrumental for improving charge separation, with the possibility to tune the photocatalytic activity for H2 evolution by controlling the nanorods length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [78] 17 Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) H2 production per photocatalyst surface area of OB2-sensitized P25/Pt (red circles) and brookite/Pt (black hollow circles) over 20 h visible light irradiation (λ > 420 nm, dye loading, 10 μmol·g–1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) H2 production relative to surface area of OB2@brookite/Pt photocatalyst over 170 h of visible light irradiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' All experiments were performed with TEOA as SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [60] (© 2019, American Chemical Society).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In view of the interesting results already obtained, investigations on the combination of dyes with different TiO2-based materials should be continued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In particular, studies should concentrate on the development of semiconductors with tailored morphology to speed up charge transport and transfer to the HEC, while minimizing charge recombination rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In addition, studies should be conducted on the sensitization of polymorph mixtures other than the common P25, such as for example brookite/anatase mixtures, to take advantage of both the higher reactivity towards hydrogen reduction and the enhanced degree of charge separation thanks to the presence of phase boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Approaches to improve stability Being as important as activity, the photocatalyst stability requires attention, and when optimizing a system for H2 production all possible phenomena contributing to its deactivation should be investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In the specific case of DSP, the typical deactivation mechanisms observed in non-sensitized SC photocatalysts, such as surface passivation or photocorrosion processes,[79] can be accompanied by additional sensitizer-related degradation pathways, which can be related both to the strength of their bond with the SC and their intrinsic chemical and photochemical stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' First, photocatalyst deactivation can occur due to partial or complete detachment of the dye from the semiconductor surface, which clearly depends on the kind of anchoring group placed on the sensitizer structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' We have already alluded to this aspect when discussing the work of Reisner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' on PMI dyes endowed with different anchoring groups (see above),[44] although there we mostly focused on photocatalytic performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In general, it has been reported that the carboxylate linkage may not be an optimal choice when employing dye-sensitized photocatalysts in aqueous environment, due to accelerated hydrolysis of the titanate ester linkage, especially at basic pH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' For this reason, the use of more robust anchors, such as phosphonate derivatives, has become increasingly popular, although it is still more common for Ru-based organometallic (a) (b) 80 0B2@brookite OB2@P25 400 0-0B2@Brookite 60 0 300 TON=549 40 TON=4201 200 TON=510 20 100 dye loading 10 μmol g-1 dyeloading7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5μmolg1 0 0 0 5 10 15 20 0 25 50 75 100 125 150175 Time (h) Time (h)18 dyes [80,81] than for metal-free organic structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [82] In this regard, an interesting alternative could be represented by the use of a silane coupling reagent to covalently anchor the sensitizer to TiO2: such approach was demonstrated in a seminal paper by Arakawa and co-workers, who reported that chemical fixation of Eosin Y through amide coupling with Pt/TiO2 functionalized with γ-aminopropyl-triethoxysilane yielded a stable and efficient photocatalytst for H2 production from TEOA (Figure 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [83] To the best of our knowledge, such strategy has not been applied further in DSP systems, although dyes with silane and silatrane anchors were later used to sensitize metal oxide electrodes for photoelectrochemical cells,[84,85] and were shown to give DSSCs with high power conversion efficiencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [86] Further studies could help establish how the siloxane anchoring group should be connected to the sensitizer structure to provide optimal charge transfer rates, a matter that has undergone in-depth scrutiny in the field of DSSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [87] Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) Eosin Y anchored to TiO2 through an aminosiloxane linker;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) stable H2 production along consecutive photocatalytic experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [83] (© 2000, Elsevier B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Furthermore, the anchoring stability of the dye can be improved by increasing the number of anchoring groups as studied in detail by Park and co-workers, who prepared three triphenylamine-based sensitizers, D1- 3 bearing one, two or three cyanoacrylic anchoring groups, respectively, and studied their possible binding modes on TiO2 (Figure 11a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [88] Although in situ IR studies suggested that simultaneous binding of all three carboxylic acids was hardly possible, dyes D2 was observed to give both mono- and bis-coordinated complexes on TiO2, while D3 was bound mostly in bis-coordinated fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Consequently, in photocatalytic experiments dyes D2-3 gave better efficiency and stability compared to D1 probably as an effect of their more robust anchoring on TiO2 (Figure 11a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Similar observations were made in the already-cited work by Son et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=', who observed that bidentate phenothiazine dyes yielded consistently better performances compared to their analogues with only one anchoring unit (Figure 11b),[52] as well as in a study by Watanabe, Tani and co- workers, investigating porphyrin derivatives with mono- or multi-pyridyl anchoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [89] (a) (b) ChangeTEOAaq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='solution (Centritugation) Br Br 2500 1st 2 nd 3rd HO 2000 Br Br (umol) 1500 TiO2 Si 1000 500 0 7 14 21 Time (h)19 Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) mono-, bis- and tris-cyanoacrylic dyes D1-3, and the performances of the corresponding photocatalysts in H2 evolution experiments with TEOA and EDTA as sacrificial donors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [88] (© Elsevier B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=', 2012);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) Photocatalytic data for mono- and bis-coordinating phenothiazine dyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [52] (© 2012, Royal Society of Chemistry).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Another key aspect to consider to enhance photocatalyst stability is preventing the intermolecular quenching that follows agglomeration of the dye molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A common approach to solve the issue, often an indispensable requirement, is to endow the dye molecule with an encumbered steric environment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' indeed, it has been repeatedly demonstrated that placing alkyl chains of sufficient length in the intermediate section of the sensitizers can provide the necessary steric bulk to avoid dye aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [51,59,60,64,90] A remarkable example was provided by Abbotto, Fornasiero and co-workers, in their work on H2 production by DSP featuring phenothiazine dyes (Figure 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [91] They found that, at the beginning of the photocatalytic experiment dye PTZ1 provided a better performance than all other analogues named PTZ2-6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' however, after a prolonged period of time, the overall amount of gas produced by dye PTZ5 was higher, as a result of a superior photocatalytic stability, as visible by its constant H2 evolution rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although the reasons for this result are not completely clear, the presence of n-butyl chains in the middle part of PTZ5 surely helped to reduce dye agglomeration and limit undesired energy transfer processes between dye molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As mentioned above, another strategy to optimize the dye geometry on the SC surface and hinder dye-dye interactions is to use co-adsorbents, especially by exploiting the formation of (a): R 20 136 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' CN 20 COOH : DL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='RIaREH 30 260 30 N tmmh) HOOD TEOA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' EDTA N D3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='R=Re (a) ECN NC COOH P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='51 2001 Hooc CN ON Hooo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C16H33 iP2 100 50 HOOC CN Q 21 3 Time (h) HooCr CNI20 directional hydrogen bonds with the sensitizer molecules,[54] but a definite effect on DSP stability for such systems has not been reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) Structures of sensitizers PTZ1 and PTZ5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) H2 production rates measured using the dye/Pt/TiO2 materials suspended in TEOA 10% v/v solution at pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 under irradiation with visible light (λ>420 nm);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (c) Degradation plots of the dye-sensitized Pt/TiO2 photocatalysts under visible irradiation in the same conditions of H2 production experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [91] (© 2015, Wiley-VCH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The instability of DSP can also derive from the degradation of the dye over time by reaction with chemical quenchers present in solution or reactive species formed during photocatalysis, such as H2 itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Indeed, it was observed early,[83] and confirmed subsequently,[92] that emissive dyes such as Eosin Y can undergo irreversible hydrogenation by H2 in the reaction conditions, giving species characterized by a lower degree of conjugation and as such less able to absorb visible light, thus hindering photocatalytic activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The different stability of the above-mentioned dyes MB25 and AD418 was interpreted in terms of their different resistance to degradation during photocatalysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' MB25 presented an electron-donating propilenedioxythiophene (ProDOT) ring next to a double bond, which activated a decomposition pathway starting with dye protonation and nucleophilic attack by water;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' AD418, in which the double bond was substituted by a thiophene ring, could not undergo the same side reaction and therefore gave rise to a much more stable photocatalytic system, resulting in a far higher TON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [51] Finally, in a recent paper Lai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' studied the degradation process of multicarbazole-based organic dyes to understand the issues related to stability of Pt/TiO2 photocatalysts for H2 evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Supported by combined UV–Vis, FT-IR, 1H and 13C NMR, and MS techniques, it was suggested that the decline of activity matched the progressive removal of the electron acceptor unit (consisting of cyanoacrylate moiety), via initial decarboxylation reaction followed by removal of the CN− group, a mechanism previously unreported for DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [93] (a) 1F HC4@ ON NG COOH GN NO Iza Hood PTZ3 COOH PTZ5 (6) (c) PTZ1 PTZ5 10 350 1:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 3300元 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='2 PTZ1 14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='0 2 4 6 18 20 si 20 Irradiation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='/h (rradiation time dh21 Thanks to the advances in dye design and in the investigation of photocatalyst deactivation pathways, several DSP systems, including some of those cited above, have been demonstrated to achieve prolonged stability in H2 production experiments, with the best examples being still noticeably active after more than 100 h under continuous illumination (Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Unfortunately, setup of such experiments is nontrivial, especially for those groups having access to only one photochemical reaction apparatus, and thus extended stability studies (at least > 48 h) are still lacking in some of the recently published works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Given the importance of the photocatalyst stability parameters, however, they appear indispensable for a complete and fair assessment of new DSP systems and should be always included whenever possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Stability data of some selected DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In view of the above discussion, improvement of DSP stability should be first pursued by making the dye/semiconductor assembly more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Accordingly, a more thorough exploration of structures with multiple binding sites to TiO2 should be carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' On the other hand, care shall also be placed in designing dyes not incorporating labile functional groups in their central section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In this regard, it will be preferable to prepare compounds with directly connected (hetero)aromatic rings, without the presence of multiple (double/triple) bonds, and without excessively electron-donating moieties, as they could be progressively oxidized during the H2 evolution reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Nature of the hydrogen evolution catalyst (HEC) Usually, in dye-sensitized photocatalytic systems for H2 production, proton reduction is carried out by metal nanoparticles adsorbed on the semiconductor surface, with platinum being by far the most common choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [12] Dye Reaction Time (h) Dye loading [μmol/g] H2 produced [mmol/g] TON SED (pH) Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Alizarin 80 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='91a 6326 TEOA (9) [92] Alizarin Red 92 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='93a 6342 TEOA (9) [92] PTZ5 90 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='6 -b -b TEOA (7) [91] S1 48 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='25 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='75 10200 AA (4) [40] Dimer 2 83 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='91 2860 AA (4) [89] OB2 170 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='75 4201 TEOA (7) [60] Calix-3 50 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3 630.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='97 16927 TEOA (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='8) [94] DH4 105 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='8 547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='22 16699 TEOA (n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='c) [59] BB3e 72 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='5 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='11 23285 AA (4) [63] a Calculated based on the TON and dye loading data presented in the original paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' b Exact values were not provided;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Figure S9 in the supporting information of the original publication shows a constant H2 production rate of approx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 250 μmol g−1 h−1 for the entire experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' c The authors report that the solution pH was adjusted by addition of perchloric acid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 22 Clearly, this is due to the excellent properties of platinum as a heterogeneous catalyst for H2 evolution, guaranteeing high activity and stability, but also to the fact that most of the studies focus on the investigation of other components of the system (such as the dye or the semiconductor) and therefore need to use the same catalyst to obtain results comparable with those already reported in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Nevertheless, several studies have focused on finding more readily available and cheaper catalysts than platinum, in the perspective of an industrial scale-up of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Indeed, it has even been shown that H2 production with dye-sensitized TiO2 can proceed also in the absence of adsorbed metals,[95] but usually gas evolution rates were not sufficient for practical purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In addition, the possibility to use dissolved homogenous metal catalysts, not anchored to TiO2, has also been explored: for example, Kruth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' reported the employment of commercially available PdCl2(CH3CN)2 and Pd(PPh3)2Cl2 as catalysts in combination with polymer-capped titania nanoparticles sensitized with ruthenium complex N3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [96] Although a moderate and stable H2 evolution was obtained, the authors mention that the results were inferior to those previously reported for other composite TiO2 photocatalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' More commonly, transition metal or metal salt nanoparticles adsorbed on the semiconductor surface have been reported as catalysts for DSP systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although this has been done more often for purely inorganic photocatalytic assemblies,[97–99] several examples exist also in the dye-sensitized field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Already in 2007, Lu and co-workers described the use of an Eosin Y-sensitized CuO/TiO2 nanocomposite, in which cuprous oxide played the double role of semiconductor and catalyst for water reduction, being able to collect electrons directly by injection from the sensitizer or through electron transfer from titania;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' its employment allowed to obtain a much higher H2 production rate compared to that observed in its absence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [100] More recently, the use of elemental Co was also reported in a similar system, in which Rhodamine B was used as the sensitizer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' remarkably, the authors reported the possibility to achieve a full water splitting process, avoiding the use of any sacrificial donor, thanks to the synergistic effect of the sensitizer and the neighbouring cobalt atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The fact that the reaction proceeded through the desired mechanism was supported by the production of nearly stoichiometric amounts of the two gases (H2:O2 ratio was approximately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [101] Du and co-workers examined several first-row transition metal-based oxide/hydroxide materials, such as cobalt oxide (CoOx), cobalt hydroxide (Co(OH)2), nickel oxide (NiOx), nickel hydroxide (Ni(OH)2), ferric hydroxide (Fe(OH)3) and copper hydroxide (Cu(OH)2), as catalysts in a three-component photocatalytic system with TiO2 as the semiconductor, Eosin Y as the sensitizer and TEOA as SED (Figure 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' They found that Ni(OH)2 exhibited the best performance, which was about 90 times higher than that of pure TiO2 under the same conditions and was kept stable for several hours through repeated illumination/evacuation cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [102] 23 Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (a) Mechanism of Eosin Y-sensitized H2 production with Ni(OH)2/TiO2 nanoparticles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' (b) comparison between different transition metal oxides/hydroxides used as HEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reproduced with permission from ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [102] (© 2014, Elsevier B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A series of studies was published by Patir and co-workers on the use of Cu2WS4 nanocubes as HEC in combination with TiO2 sensitized by a variety of different metal-free organic sensitizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [41,103–105] The new catalyst was synthesized by a hot injection method that produced nanocubic structures with 100-500 nm- long edges and characterized by a single crystalline phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photocatalytic studies revealed that use of Cu2WS4 caused an increase in the H2 production rate compared to the catalyst-free dye-sensitized semiconductor, but its performances were lower than those of Pt nanospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The system was also sufficiently stable under irradiation, although XPS measurements conducted both before and after the experiments indicated a partial hydrogenation of the Cu2WS4 structure during the photocatalytic reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finally, it should be mentioned that several examples of supported molecular catalysts have also been reported in DSP systems for H2 production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Many of these studies have been conducted by Reisner’s group, who focused especially on the development of Co- and Ni-based complexes (Figure 14), used in combination with both Ru-containing sensitizers and metal-free organic dyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Earlier work concerned the employment of cobaloxime complexes such as CoP1,[106,107] whose attachment to the semiconductor was allowed only by an axial pyridine ligand endowed with a phosphonate anchoring group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Later, the catalyst design was improved by preparing complex CoP3, featuring a single ligand incorporating both the diamine-dioxime equatorial unit and the axial pyridine:[108] accordingly, the authors reported that “CoP3 displays significant advantages over previously reported immobilized Co catalysts as it shows a higher catalytic proton reduction activity and provides a strong and more stable anchoring to metal oxides surfaces”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' At the same time, DuBois-type [Ni(P2R’N2R’’)2]2+ complexes were also investigated in combination with Ru tris(bipyridine) dyes, and it was shown that they could work in water reduction reactions both in homogenous phase or adsorbed on a semiconductor, albeit with different electron transfer mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [109] In general, the performances provided by these molecular catalysts were good, but inferior to those obtained with Pt nanoparticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=" [44,82] (a) (b) Ni(OH)2 40 Ni(OH) Visible Light Hydrogen evolution (μmol) H2 Cu(OH), 30 CB e' e H,O Co(OH), e 20 TiO2 00 10 Coo, EY Fe(OH), VB Blank Nio, 024 Figure 14." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Structures of molecular complexes used as HEC in dye-sensitized systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite that, we consider studies on alternative HECs of high relevance in the perspective of a potential future large-scale deployment of DSP technology, and recommend that they will be expanded in the future also by other research groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finding reliable catalytic species based on cheaper and more available metals than Pt could significantly reduce the projected cost of DSP systems, while at the same time eliminate (or largely reduce) the risk of shortages of critical materials in the long term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sustainability of the sacrificial donor As explained in the introduction, during photocatalysis on DSP (not differently from purely SC-based photocatalysts), charge separation following light irradiation generates two reactive sites, where the newly formed holes and electrons can promote oxidation and reduction reactions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' The development of new photocatalysts is heavily based on the detailed understanding of its intrinsic activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hence, it is convenient to simplify the investigation of the photocatalysts features by focusing on one half-reaction only, relying on the use of sacrificial electron donors or acceptors (SED or SEA respectively) that readily react with the photogenerated charge carriers, thus not placing kinetic restrictions that would affect the half-reaction of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [110] For example, such a practice is common in the photocatalytic water splitting field, where most studies focus on either the H2 evolution or on the water oxidation, using sacrificial agents for the other half- reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Focusing on the H2 evolution process, obviously the choice of the SED is subject to stringent thermodynamic requirements for the reaction to proceed efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Among them, the most important is that the HOMO of the dye must suitably match the redox potential of the SEDred/SEDox couple to ensure the rapid regeneration of the oxidized dye (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' the HOMO of dye must be more positive than the oxidation potential of the SED).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Typical SED include triethylamine (TEA), triethanolamine (TEOA), ethylenediaminetetraacetic acid (EDTA), ascorbic acid (AA), S2–, I- and others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [17] However, while alleviating the complexity demands of photocatalyst developments from fundamental perspective, this approach does not match sustainability concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' To address this aspect of photocatalysis, an increasing load of research has moved towards more useful SED, whose oxidation can be associated with other processes relevant for sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [111] For example, alcohols can act as efficient donors for many inorganic semiconductor photocatalysts including TiO2,[112] with potential oxidation to industrially relevant compounds, as recently demonstrated for ethanol and glycerol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [113] Despite that, the use of alcohols as hole H2O3 PO3H2 Ph PO3H2 Br Cop1 Cop3 H,O3P PO3H2 Du Bois type25 scavengers in DSP systems is still in its infancy, and has been reported only in a handful of studies, investigating the employment of MeOH,[114] EtOH[51,63] or glycerol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [50] Unfortunately, the performances obtained with such sacrificial donors are generally lower than those registered with TEOA or AA, and the structural and electronic requirements of the dyes to work efficiently with them have not yet been fully clarified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Probably, one key issue is that small alcohol molecules can adsorb on the SC surface, reducing the H+ reduction rate and enhancing charge recombination;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='[115] therefore, they should be used in combination with dyes able to efficiently shield the photocatalyst surface but at the same time small and hydrophilic enough to allow good interaction with the SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Achieving such a structural design is nontrivial and therefore studies on sensitizer optimization are still in progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In addition, alcohol oxidation could be promoted by combining the dyes with appropriate molecular catalysts,[116] also in an integrated dyad design, as already demonstrated in photoelectrochemical cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [117] Another promising research direction would be to explore the photoreforming (PR) of biomass-derived materials, such as lignin and lignocellulose, as hole scavengers, opening the way to the production of clean fuels from abundant and cheap raw materials, or even waste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [118] Despite their favourable thermodynamics, however, such raw materials are often characterized by limited solubility, brown-dark colour and slow oxidation kinetics, making it necessary to apply pre-digestion procedures and use appropriate catalysts for their efficient photoconversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Due to such issues, no DSP system for lignocellulose PR has been reported as of yet, but given its great potential such approach should definitely be pursued in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Perspectives In this article, we have highlighted some key aspects of the visible light-driven H2 production mediated by heterogeneous dye-sensitized photocatalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Compared to the other two main technologies currently employed for the production of solar H2, namely tandem photovoltaic-electrolysis systems and photoelectrochemical cells, the photocatalytic approach is still characterized by an inferior solar-to-hydrogen (STH) efficiency, but at the same time is comparatively simpler, less expensive and easier to scale-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [4] However, to be able to replace, at least partially, H2 generation methods based on more mature technologies (such as hydrocarbon reforming or water electrolysis), photocatalytic processes still need to overcome some serious obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In general, the major factors currently restricting large-scale application of DSP systems towards a possible industrialization can be traced back to their insufficient efficiency and stability and their excessive cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Focusing on the first aspect, it will be mandatory to improve the performances of DSP systems by further optimization of their active materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In terms of dyes, although a picture is starting to emerge regarding the need to precisely control their lipophilicity/hydrophilicity balance, as well as the precise position of their energy levels, more detailed design principles are required to develop structures able to work efficiently in the aqueous environment typical of DSP applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Crucial aspects to be considered are the development of improved anchoring groups,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' able to ensure a rapid charge injection rate into the conduction band of the sensitizer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' the use of panchromatic chromophores,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' to enhance light harvesting in the entirety of the visible 26 spectrum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' the attainment of a precise organization of dye molecules on the SC surface (also by the use of co- adsorbents),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' as well as the establishment of more efficient interactions with hole scavenger species present in solution,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' beyond the simple manipulation of orbital levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In parallel with the discovery of more efficient dye sensitizers, improvements are also required concerning the semiconductor structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Significant results have already been obtained by exploring different TiO2 polymorphs (either in pure form or as mixed phases) as well as precisely controlled titania nanostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite that, several problems still remain, such as the excessive rate of charge recombination favoured by the interaction of the hydrophilic TiO2 surface with the aqueous reaction environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' They could be overcome by designing composites with improved dye/semiconductor/water interfaces, as well as by introducing semiconductors with tailored morphology to speed up charge transport and transfer to the HEC, thanks to the help of more refined kinetic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [72] Requirements of efficiency enhancement and cost reduction are closely linked to the need for shifting from model sacrificial electron donors, such as TEOA or EDTA, to more realistic species in terms of sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As discussed above, this could be achieved by employing simple alcohols (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' EtOH, iPrOH) or biomass- derived reducing compounds (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' from glucose to more complex sugars, all the way to lignocellulose), either as intermediate solutions towards the ultimate goal of water splitting, or as platforms for coupling H2 generation with production of value-added, oxidized compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' In terms of stability, a crucial aspect will be once again the development of improved anchoring groups, capable to ensure a robust attachment of the dye to the semiconductor surface with negligible hydrolysis, without an excessive limitation of performances, also by exploration of multi-branched structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' At the same time, it will also be necessary to design dyes devoid of labile functional groups, to avoid their oxidation or decomposition during the photocatalytic reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Regarding cost reduction, a crucial step in this direction would be the replacement of platinum nanoparticles, usually employed as HEC, with cheaper and more readily available catalytic materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Such modification would also eliminate the risk of shortages of catalytic material in the hypothesis of a future large- scale deployment of DSP technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Although such work has already been done extensively in photoreforming studies using fully inorganic systems,[119] it has not yet been explored in depth in the field of DSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Of particular interest is the work on supported molecular catalysts, as their structure can be tailored to make them very specific, opening the way to the development of parallel processes able to produce more than one compound at the same time: one such example is the dye-sensitized photocatalytic production of syngas (H2+CO) recently published by Kang and co-workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [120] A summary of the most important recent advances in the fields and the possible directions of future development, as discussed in the above paragraphs, is provided in Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 27 Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Recent advances and potential future developments of DSP research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Finally, it is important that researchers working in the DSP field will try to adopt more consistent standards for experimental procedures, laboratory setups and data reporting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Despite significant efforts by publishers to promote “best practices” to perform measurements and data analysis, large discrepancies still remain in the way materials and devices properties are reported, sometimes preventing a meaningful comparison of results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' It is mandatory to overcome these difficulties to ensure a correct future development of this research area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' As can be seen by the above discussion, despite the recent achievements documented in this article, many unsolved problems and open questions still wait to be addressed in the field of DSP H2 production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' With so much work to do, we have little doubt that it will remain a very active field of research for many years to come.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Acknowledgements Financial support from European Community (Projects H2020 − RIA-CE-NMBP-25 Program − Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 862030 and H2020-LC-SC3-2019-NZE-RES-CC − Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=" 884444), University of Trieste, CNR-ICCOM ('SOLARSYNT' Project) and INSTM Consortium is acknowledged." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' References [1] Balzani V, Credi A and Venturi M 2008 Photochemical Conversion of Solar Energy ChemSusChem 1 26–58 [2] Dau H, Fujita E and Sun L 2017 Artificial Photosynthesis: Beyond Mimicking Nature ChemSusChem 10 4228–35 [3] Armaroli N and Balzani V 2011 The Hydrogen Issue ChemSusChem 4 21–36 iRecentadvances: Efficiency improvements by manipulation:of lydrophobic/hydrophilic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='properties;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Recentadvances: IFutureprogress:!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' lncreasedye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='stabilityagainst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='hydrolysis and Future progress: oxidation Recentadvances: : Better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='matching ofenergy levels .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' :.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='. Betterinteraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='improvedye Useof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='non preciousmetal:NPs: withthedye: regeneration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='ratesespecially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='withalcohols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Futureprogress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' iFull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='photocatalyticconditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Improve:TONswithmolecularHECs H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='withother reactions: SED: e er PSED?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Cat TiO2 Dye I Recent advances: Recentadvances: Stableanchoringgroups in basicconditions: Tio,materials with different morphologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=". Future'progress: Futureprogress:: nvestigation:otpolvmorph:mixtures28 [4] Armaroli N and Balzani V 2016 Solar Electricity and Solar Fuels: Status and Perspectives in the Context of the Energy Transition Chem." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' – A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 22 32–57 [5] Fujishima A and Honda K 1972 Electrochemical Photolysis of Water at a Semiconductor Electrode Nature 238 37–8 [6] Wang Z, Li C and Domen K 2019 Recent developments in heterogeneous photocatalysts for solar- driven overall water splitting Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 48 2109–25 [7] Carraro G, Maccato C, Gasparotto A, Montini T, Turner S, Lebedev O I, Gombac V, Adami G, Van Tendeloo G, Barreca D and Fornasiero P 2014 Enhanced Hydrogen Production by Photoreforming of Renewable Oxygenates Through Nanostructured Fe2O3 Polymorphs Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 24 372–8 [8] Uekert T, Kuehnel M F, Wakerley D W and Reisner E 2018 Plastic waste as a feedstock for solar- driven H2 generation Energy Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 11 2853–7 [9] Chen X, Liu L, Yu P Y and Mao S S 2011 Increasing solar absorption for photocatalysis with black hydrogenated titanium dioxide nanocrystals Science (80-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 331 746–50 [10] Maeda K 2013 Z ‑ Scheme Water Splitting Using Two Di ff erent Semiconductor Photocatalysts 2 [11] Zhou P, Yu J and Jaroniec M 2014 All-solid-state Z-scheme photocatalytic systems Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 26 4920–35 [12] Zhang X, Peng T and Song S 2016 Recent advances in dye-sensitized semiconductor systems for photocatalytic hydrogen production J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A 4 2365–402 [13] Hagfeldt A, Boschloo G, Sun L, Kloo L and Pettersson H 2010 Dye-Sensitized Solar Cells Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 110 6595–663 [14] Li F, Yang H, Li W and Sun L 2018 Device Fabrication for Water Oxidation, Hydrogen Generation, and CO2 Reduction via Molecular Engineering Joule 2 36–60 [15] Li J and Wu N 2015 Semiconductor-based photocatalysts and photoelectrochemical cells for solar fuel generation: a review Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5 1360–84 [16] Chen S, Takata T and Domen K 2017 Particulate photocatalysts for overall water splitting Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 17050 [17] Pellegrin Y and Odobel F 2017 Les donneurs d’électron sacrificiels pour la production de combustible solaire Comptes Rendus Chim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 20 283–95 [18] Watanabe M 2017 Dye-sensitized photocatalyst for effective water splitting catalyst Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 18 705–23 [19] Abe R, Shinmei K, Koumura N, Hara K and Ohtani B 2013 Visible-light-induced water splitting based on two-step photoexcitation between dye-sensitized layered niobate and tungsten oxide photocatalysts in the presence of a triiodide/iodide shuttle redox mediator J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 135 16872–84 [20] Zhang X, Peng T, Yu L, Li R, Li Q and Li Z 2015 Visible/near-infrared-light-induced H2 production over g-C3N4 co-sensitized by organic dye and zinc phthalocyanine derivative ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5 504–10 [21] Yu L, Zhang X, Zhuang C, Lin L, Li R and Peng T 2014 Syntheses of asymmetric zinc 29 phthalocyanines as sensitizer of Pt-loaded graphitic carbon nitride for efficient visible/near-IR-light- driven H 2 production Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 16 4106–14 [22] Ohtani B, Prieto-Mahaney O O, Li D and Abe R 2010 What is Degussa (Evonik) P25?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Crystalline composition analysis, reconstruction from isolated pure particles and photocatalytic activity test J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photobiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 216 179–82 [23] Qureshi M and Takanabe K 2017 Insights on measuring and reporting heterogeneous photocatalysis: Efficiency definitions and setup examples Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 29 158–67 [24] Kunz L Y, Diroll B T, Wrasman C J, Riscoe A R, Majumdar A and Cargnello M 2019 Artificial inflation of apparent photocatalytic activity induced by catalyst-mass-normalization and a method to fairly compare heterojunction systems Energy Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 12 1657–67 [25] Melchionna M and Fornasiero P 2020 Updates on the Roadmap for Photocatalysis ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 10 5493–501 [26] Melchionna M, Beltram A, Montini T, Monai M, Nasi L, Fornasiero P and Prato M 2016 Highly efficient hydrogen production through ethanol photoreforming by a carbon nanocone/Pd@TiO2 hybrid catalyst Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 52 764–7 [27] Kozuch S and Martin J M L 2012 “Turning Over” Definitions in Catalytic Cycles ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 2787–94 [28] Kisch H and Bahnemann D 2015 Best Practice in Photocatalysis: Comparing Rates or Apparent Quantum Yields?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 6 1907–10 [29] Hoy J, Morrison P J, Steinberg L K, Buhro W E and Loomis R A 2013 Excitation Energy Dependence of the Photoluminescence Quantum Yields of Core and Core/Shell Quantum Dots J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 4 2053–60 [30] Chatterjee D 2010 Effect of excited state redox properties of dye sensitizers on hydrogen production through photo-splitting of water over TiO2 photocatalyst Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 11 336–9 [31] Suryani O, Higashino Y, Sato H and Kubo Y 2019 Visible-to-Near-Infrared Light-Driven Photocatalytic Hydrogen Production Using Dibenzo-BODIPY and Phenothiazine Conjugate as Organic Photosensitizer ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 448–58 [32] Cecconi B, Manfredi N, Montini T, Fornasiero P and Abbotto A 2016 Dye-Sensitized Solar Hydrogen Production: The Emerging Role of Metal-Free Organic Sensitizers European J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2016 5194–215 [33] Huang J-F, Lei Y, Luo T and Liu J-M 2020 Photocatalytic H2 Production from Water by Metal-free Dye-sensitized TiO2 Semiconductors: The Role and Development Process of Organic Sensitizers ChemSusChem 13 5863–95 [34] Lee C P, Lin R Y Y, Lin L Y, Li C T, Chu T C, Sun S S, Lin J T and Ho K C 2015 Recent progress in organic sensitizers for dye-sensitized solar cells RSC Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5 23810–25 [35] Wu Y, Zhu W H, Zakeeruddin S M and Grätzel M 2015 Insight into D-A-π-A structured sensitizers: A promising route to highly efficient and stable dye-sensitized solar cells ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Interfaces 30 7 9307–18 [36] Watanabe M, Hagiwara H, Iribe A, Ogata Y, Shiomi K, Staykov A, Ida S, Tanaka K and Ishihara T 2014 Spacer effects in metal-free organic dyes for visible-light-driven dye-sensitized photocatalytic hydrogen production J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A 2 12952–61 [37] Luo G G, Lu H, Wang Y H, Dong J, Zhao Y and Wu R B 2016 A D-π-A-π-A metal-free organic dye with improved efficiency for the application of solar energy conversion Dye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Pigment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 134 498–505 [38] Ho P Y, Mark M F, Wang Y, Yiu S C, Yu W H, Ho C L, McCamant D W, Eisenberg R and Huang S 2018 Panchromatic Sensitization with ZnII Porphyrin-Based Photosensitizers for Light-Driven Hydrogen Production ChemSusChem 11 2517–28 [39] Tiwari A, Krishna N V, Giribabu L and Pal U 2018 Hierarchical Porous TiO2 Embedded Unsymmetrical Zinc-Phthalocyanine Sensitizer for Visible-Light-Induced Photocatalytic H2 Production J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 122 495–502 [40] Ho P-Y, Wang Y, Yiu S-C, Yu W-H, Ho C-L and Huang S 2017 Starburst Triarylamine Donor- Based Metal-Free Photosensitizers for Photocatalytic Hydrogen Production from Water Org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 19 1048–51 [41] Aslan E, Karaman M, Yanalak G, Can M, Ozel F and Patir I H 2019 The investigation of novel D-π- A type dyes (MK-3 and MK-4) for visible light driven photochemical hydrogen evolution Dye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Pigment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 171 107710 [42] Pastore M, Fantacci S and De Angelis F 2013 Modeling Excited States and Alignment of Energy Levels in Dye-Sensitized Solar Cells: Successes, Failures, and Challenges J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 117 3685–700 [43] Zhang L and Cole J M 2015 Anchoring Groups for Dye-Sensitized Solar Cells ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Interfaces 7 3427–55 [44] Warnan J, Willkomm J, Farré Y, Pellegrin Y, Boujtita M, Odobel F and Reisner E 2019 Solar electricity and fuel production with perylene monoimide dye-sensitised TiO 2 in water Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 10 2758–66 [45] Narayanaswamy K, Tiwari A, Mondal I, Pal U, Niveditha S, Bhanuprakash K and Singh S P 2015 Dithiafulvalene functionalized diketopyrrolopyrrole based sensitizers for efficient hydrogen production Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 17 13710–8 [46] Manzhos S, Jono R, Yamashita K, Fujisawa J, Nagata M and Segawa H 2011 Study of Interfacial Charge Transfer Bands and Electron Recombination in the Surface Complexes of TCNE, TCNQ, and TCNAQ with TiO2 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 115 21487–93 [47] Ooyama Y and Harima Y 2012 Photophysical and Electrochemical Properties, and Molecular Structures of Organic Dyes for Dye-Sensitized Solar Cells ChemPhysChem 13 4032–80 [48] Wang M, Grätzel C, Zakeeruddin S M and Grätzel M 2012 Recent developments in redox electrolytes for dye-sensitized solar cells Energy Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5 9394–405 [49] Robson K C D, Hu K, Meyer G J and Berlinguette C P 2013 Atomic Level Resolution of Dye 31 Regeneration in the Dye-Sensitized Solar Cell J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 135 1961–71 [50] Tiwari A, Duvva N, Rao V N, Venkatakrishnan S M, Giribabu L and Pal U 2019 Tetrathiafulvalene Scaffold-Based Sensitizer on Hierarchical Porous TiO 2 : Efficient Light-Harvesting Material for Hydrogen Production J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 123 70–81 [51] Dessì A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Monai M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Bessi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Montini T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Calamante M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mordini A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reginato G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Trono C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Fornasiero P and Zani L 2018 Towards Sustainable H2Production: Rational Design of Hydrophobic Triphenylamine-based Dyes for Sensitized Ethanol Photoreforming ChemSusChem 11 793–805 [52] Lee J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Kwak J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ko K C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Park J H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ko J H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Park N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Kim E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ryu D H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ahn T K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lee J Y and Son S U 2012 Phenothiazine-based organic dyes with two anchoring groups on TiO 2 for highly efficient visible light-induced water splitting Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 48 11431–3 [53] Manfredi N, Cecconi B, Calabrese V, Minotti A, Peri F, Ruffo R, Monai M, Romero-Ocaña I, Montini T, Fornasiero P and Abbotto A 2016 Dye-sensitized photocatalytic hydrogen production: Distinct activity in a glucose derivative of a phenothiazine dye Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 52 6977–80 [54] Manfredi N, Monai M, Montini T, Peri F, De Angelis F, Fornasiero P and Abbotto A 2018 Dye- Sensitized Photocatalytic Hydrogen Generation: Efficiency Enhancement by Organic Photosensitizer- Coadsorbent Intermolecular Interaction ACS Energy Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 3 85–91 [55] Martín C, Ziółek M and Douhal A 2016 Ultrafast and fast charge separation processes in real dye- sensitized solar cells J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photobiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 26 1–30 [56] Watanabe M, Hagiwara H, Ogata Y, Staykov A, Bishop S R, Perry N H, Chang Y J, Ida S, Tanaka K and Ishihara T 2015 Impact of alkoxy chain length on carbazole-based, visible light-driven, dye sensitized photocatalytic hydrogen production J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A 3 21713–21 [57] Tiwari A, Mondal I and Pal U 2015 Visible light induced hydrogen production over thiophenothiazine-based dye sensitized TiO2 photocatalyst in neutral water RSC Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 5 31415–21 [58] Wang J, Chai Z, Liu S, Fang M, Chang K, Han M, Hong L, Han H, Li Q and Li Z 2018 Organic Dyes based on Tetraaryl-1,4-dihydropyrrolo-[3,2-b]pyrroles for Photovoltaic and Photocatalysis Applications with the Suppressed Electron Recombination Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' - A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 24 18032–42 [59] Huang J-F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lei Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Xiao L-M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chen X-L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Zhong Y-H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Qin S and Liu J-M 2020 Photocatalysts for H2 Generation from Starburst Triphenylamine/Carbazole Donor-Based Metal-Free Dyes and Porous Anatase TiO2 Cube ChemSusChem 13 1037–43 [60] Bettucci O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Skaltsas T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Calamante M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Dessì A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Bartolini M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sinicropi A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Filippi J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Reginato G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mordini A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Fornasiero P and Zani L 2019 Combining Dithienosilole-Based Organic Dyes with a Brookite/Platinum Photocatalyst toward Enhanced Visible-Light-Driven Hydrogen Production ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 2 5600–12 [61] Lee S H, Park Y, Wee K R, Son H J, Cho D W, Pac C, Choi W and Kang S O 2010 Significance of hydrophilic characters of organic dyes in visible-light hydrogen generation based on TiO2 Org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 12 460–3 [62] Han W S, Wee K R, Kim H Y, Pac C, Nabetani Y, Yamamoto D, Shimada T, Inoue H, Choi H, Cho 32 K and Kang S O 2012 Hydrophilicity control of visible-light hydrogen evolution and dynamics of the charge-separated state in dye/TiO2/Pt hybrid systems Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' - A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 18 15368–81 [63] Bartolini M, Gombac V, Sinicropi A, Reginato G, Dessì A, Mordini A, Filippi J, Montini T, Calamante M, Fornasiero P and Zani L 2020 Tuning the Properties of Benzothiadiazole Dyes for Efficient Visible Light-Driven Photocatalytic H2 Production under Different Conditions ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 0 [64] Tiwari A and Pal U 2015 Effect of donor-donor-π-acceptor architecture of triphenylamine-based organic sensitizers over TiO2 photocatalysts for visible-light-driven hydrogen production Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hydrogen Energy 40 9069–79 [65] Peter L M and Upul Wijayantha K G 2014 Photoelectrochemical Water Splitting at Semiconductor Electrodes: Fundamental Problems and New Perspectives ChemPhysChem 15 1983–95 [66] Hisatomi T, Kubota J and Domen K 2014 Recent advances in semiconductors for photocatalytic and photoelectrochemical water splitting Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 43 7520–35 [67] Moss B, Lim K K, Beltram A, Moniz S, Tang J, Fornasiero P, Barnes P, Durrant J and Kafizas A 2017 Comparing photoelectrochemical water oxidation, recombination kinetics and charge trapping in the three polymorphs of TiO2 Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 7 2938 [68] Yamakata A, Vequizo J J M and Matsunaga H 2015 Distinctive Behavior of Photogenerated Electrons and Holes in Anatase and Rutile TiO2 Powders J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 119 24538–45 [69] Günnemann C, Haisch C, Fleisch M, Schneider J, Emeline A V and Bahnemann D W 2019 Insights into Different Photocatalytic Oxidation Activities of Anatase, Brookite, and Rutile Single-Crystal Facets ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 9 1001–12 [70] Beltram A, Romero-Ocaña I, Josè Delgado Jaen J, Montini T and Fornasiero P 2016 Photocatalytic valorization of ethanol and glycerol over TiO2 polymorphs for sustainable hydrogen production Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 518 167–75 [71] Vequizo J J M, Matsunaga H, Ishiku T, Kamimura S, Ohno T and Yamakata A 2017 Trapping- Induced Enhancement of Photocatalytic Activity on Brookite TiO2 Powders: Comparison with Anatase and Rutile TiO2 Powders ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 7 2644–51 [72] Sieland F, Schneider J and Bahnemann D W 2017 Fractal Charge Carrier Kinetics in TiO 2 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 121 24282–91 [73] Sieland F, Schneider J and Bahnemann D W 2018 Photocatalytic activity and charge carrier dynamics of TiO2 powders with a binary particle size distribution Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 20 8119–32 [74] Liu G, Yang H G, Pan J, Yang Y Q, Lu G Q (Max) and Cheng H-M 2014 Titanium Dioxide Crystals with Tailored Facets Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 114 9559–612 [75] Monai M, Montini T and Fornasiero P 2017 Brookite: Nothing new under the sun?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catalysts 7 [76] Di Paola A, Bellardita M and Palmisano L 2013 Brookite, the least known TiO2 photocatalyst Catalysts 3 36–73 33 [77] Kusumawati Y, Hosni M, Martoprawiro M A, Cassaignon S and Pauporté T 2014 Charge Transport and Recombination in TiO2 Brookite-Based Photoelectrodes J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' C 118 23459–67 [78] Cargnello M, Montini T, Smolin S Y, Priebe J B, Jaén J J D, Doan-Nguyen V V T, McKay I S, Schwalbe J A, Pohl M M, Gordon T R, Lu Y, Baxter J B, Brückner A, Fornasiero P and Murray C B 2016 Engineering titania nanostructure to tune and improve its photocatalytic activity Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 113 3966–71 [79] Xie Y P, Yu Z B, Liu G, Ma X L and Cheng H-M 2014 CdS–mesoporous ZnS core–shell particles for efficient and stable photocatalytic hydrogen evolution under visible light Energy Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 7 1895–901 [80] Bae E, Choi W, Park J, Shin H S, Kim S Bin and Lee J S 2004 Effects of Surface Anchoring Groups (Carboxylate vs Phosphonate) in Ruthenium-Complex-Sensitized TiO2 on Visible Light Reactivity in Aqueous Suspensions J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B 108 14093–101 [81] Bae E and Choi W 2006 Effect of the Anchoring Group (Carboxylate vs Phosphonate) in Ru- Complex-Sensitized TiO2 on Hydrogen Production under Visible Light J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B 110 14792– 9 [82] Warnan J, Willkomm J, Ng J N, Godin R, Prantl S, Durrant J R and Reisner E 2017 Solar H2 evolution in water with modified diketopyrrolopyrrole dyes immobilised on molecular Co and Ni catalyst-TiO2 hybrids Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 8 3070–9 [83] Abe R, Hara K, Sayama K, Domen K and Arakawa H 2000 Steady hydrogen evolution from water on Eosin Y-fixed TiO2 photocatalyst using a silane-coupling reagent under visible light irradiation J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photobiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 137 63–9 [84] Brennan B J, Llansola Portolés M J, Liddell P A, Moore T A, Moore A L and Gust D 2013 Comparison of silatrane, phosphonic acid, and carboxylic acid functional groups for attachment of porphyrin sensitizers to TiO2 in photoelectrochemical cells Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 15 16605–14 [85] Castellucci E, Monini M, Bessi M, Iagatti A, Bussotti L, Sinicropi A, Calamante M, Zani L, Basosi R, Reginato G, Mordini A, Foggi P and Di Donato M 2017 Photoinduced excitation and charge transfer processes of organic dyes with siloxane anchoring groups: A combined spectroscopic and computational study Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 19 [86] Kakiage K, Aoyama Y, Yano T, Oya K, Fujisawa J and Hanaya M 2015 Highly-efficient dye- sensitized solar cells with collaborative sensitization by silyl-anchor and carboxy-anchor dyes Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 51 15894–7 [87] Sobuś J, Gierczyk B, Burdziński G, Jancelewicz M, Polanski E, Hagfeldt A and Ziółek M 2016 Factors Affecting the Performance of Champion Silyl-Anchor Carbazole Dye Revealed in the Femtosecond to Second Studies of Complete ADEKA-1 Sensitized Solar Cells Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' – A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 22 15807–18 [88] Choi S K, Yang H S, Kim J H and Park H 2012 Organic dye-sensitized TiO 2 as a versatile photocatalyst for solar hydrogen and environmental remediation Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 121–122 34 206–13 [89] Watanabe M, Sun S, Ishihara T, Kamimura T, Nishimura M and Tani F 2018 Visible Light-Driven Dye-Sensitized Photocatalytic Hydrogen Production by Porphyrin and its Cyclic Dimer and Trimer: Effect of Multi-Pyridyl-Anchoring Groups on Photocatalytic Activity and Stability ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 1 6072–81 [90] Ding H, Xu M, Zhang S, Yu F, Kong K, Shen Z and Hua J 2020 Organic blue-colored D-A-π-A dye- sensitized TiO2 for efficient and stable photocatalytic hydrogen evolution under visible/near-infrared- light irradiation Renew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy 155 1051–9 [91] Cecconi B, Manfredi N, Ruffo R, Montini T, Romero-Ocaña I, Fornasiero P and Abbotto A 2015 Tuning Thiophene-Based Phenothiazines for Stable Photocatalytic Hydrogen Production ChemSusChem 8 4216–28 [92] Li Q, Che Y, Ji H, Chen C, Zhu H, Ma W and Zhao J 2014 Ortho-Dihydroxyl-9,10-anthraquinone dyes as visible-light sensitizers that exhibit a high turnover number for hydrogen evolution Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 16 6550–4 [93] Lai H, Liu X, Zeng F, Peng G, Li J and Yi Z 2020 Multicarbazole-Based D−π–A Dyes Sensitized Hydrogen Evolution under Visible Light Irradiation ACS Omega 5 2027–33 [94] Huang J-F, Liu J-M, Xiao L-M, Zhong Y-H, Liu L, Qin S, Guo J and Su C-Y 2019 Facile synthesis of porous hybrid materials based on Calix-3 dye and TiO2 for high photocatalytic water splitting performance with excellent stability J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A 7 2993–9 [95] Zhang X, Veikko U, Mao J, Cai P and Peng T 2012 Visible-Light-Induced Photocatalytic Hydrogen Production over Binuclear RuII–Bipyridyl Dye-Sensitized TiO2 without Noble Metal Loading Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' – A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 18 12103–11 [96] Kruth A, Hansen S, Beweries T, Brüser V and Weltmann K-D 2013 Plasma Synthesis of Polymer- Capped Dye-Sensitised Anatase Nanopowders for Visible-Light-Driven Hydrogen Evolution ChemSusChem 6 152–9 [97] Puga A V, Forneli A, García H and Corma A 2014 Production of H2 by Ethanol Photoreforming on Au/TiO2 Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 24 241–8 [98] Imizcoz M and Puga A V 2019 Optimising hydrogen production via solar acetic acid photoreforming on Cu/TiO2 Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 9 1098–102 [99] Imizcoz M and Puga A V 2019 Assessment of Photocatalytic Hydrogen Production from Biomass or Wastewaters Depending on the Metal Co-Catalyst and Its Deposition Method on TiO2 Catalysts 9 584 [100] Jin Z, Zhang X, Li Y, Li S and Lu G 2007 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content='1% Apparent quantum efficiency for stable hydrogen generation over eosin-sensitized CuO/TiO2 photocatalyst under visible light irradiation Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 8 1267–73 [101] Le T T, Akhtar M S, Park D M, Lee J C and Yang O-B 2012 Water splitting on Rhodamine-B dye sensitized Co-doped TiO2 catalyst under visible light Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 111–112 397–401 35 [102] Yan Z, Yu X, Zhang Y, Jia H, Sun Z and Du P 2014 Enhanced visible light-driven hydrogen production from water by a noble-metal-free system containing organic dye-sensitized titanium dioxide loaded with nickel hydroxide as the cocatalyst Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 160–161 173–8 [103] Aslan E, Gonce M K, Yigit M Z, Sarilmaz A, Stathatos E, Ozel F, Can M and Patir I H 2017 Photocatalytic H2 evolution with a Cu2WS4 catalyst on a metal free D-π-A organic dye-sensitized TiO2 Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 210 320–7 [104] Patir I H, Aslan E, Yanalak G, Karaman M, Sarilmaz A, Can M, Can M and Ozel F 2019 Donor-Π- acceptor dye-sensitized photoelectrochemical and photocatalytic hydrogen evolution by using Cu 2 WS 4 co-catalyst Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Hydrogen Energy 44 1441–50 [105] Aslan E, Karaman M, Yanalak G, Bilgili H, Can M, Ozel F and Patir I H 2020 Synthesis of novel tetrazine based D-π-A organic dyes for photoelectrochemical and photocatalytic hydrogen evolution J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Photobiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' A Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 390 112301 [106] Lakadamyali F and Reisner E 2011 Photocatalytic H2 evolution from neutral water with a molecular cobalt catalyst on a dye-sensitised TiO2 nanoparticle Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 47 1695–7 [107] Lakadamyali F, Reynal A, Kato M, Durrant J R and Reisner E 2012 Electron Transfer in Dye- Sensitised Semiconductors Modified with Molecular Cobalt Catalysts: Photoreduction of Aqueous Protons Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' – A Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 18 15464–75 [108] Willkomm J, Muresan N M and Reisner E 2015 Enhancing H2 evolution performance of an immobilised cobalt catalyst by rational ligand design Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 6 2727–36 [109] Gross M A, Reynal A, Durrant J R and Reisner E 2014 Versatile Photocatalytic Systems for H2 Generation in Water Based on an Efficient DuBois-Type Nickel Catalyst J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 136 356– 66 [110] Kudo A and Miseki Y 2009 Heterogeneous photocatalyst materials for water splitting Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 38 253–78 [111] Lhermitte C R and Sivula K 2019 Alternative Oxidation Reactions for Solar-Driven Fuel Production ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 9 2007–17 [112] Chen X, Shen S, Guo L and Mao S S 2010 Semiconductor-based Photocatalytic Hydrogen Generation Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 110 6503–70 [113] Beltram A, Melchionna M, Montini T, Nasi L, Fornasiero P and Prato M 2017 Making H2 from light and biomass-derived alcohols: the outstanding activity of newly designed hierarchical MWCNT/Pd@TiO2 hybrid catalysts Green Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 19 2379–89 [114] Li X, Cui S, Wang D, Zhou Y, Zhou H, Hu Y, Liu J G, Long Y, Wu W, Hua J and Tian H 2014 New organic donor-acceptor-π-acceptor sensitizers for efficient dye-sensitized solar cells and Photocatalytic hydrogen evolution under visible-light irradiation ChemSusChem 7 2879–88 [115] Maitani M M, Zhan C, Mochizuki D, Suzuki E and Wada Y 2013 Influence of co-existing alcohol on charge transfer of H2 evolution under visible light with dye-sensitized nanocrystalline TiO2 Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' B Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 140–141 406–11 36 [116] Cook A W and Waldie K M 2019 Molecular Electrocatalysts for Alcohol Oxidation: Insights and Challenges for Catalyst Design ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' [117] Pho T V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=', Sheridan M V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=', Morseth Z A, Sherman B D, Meyer T J, Papanikolas J M, Schanze K S and Reynolds J R 2016 Efficient Light-Driven Oxidation of Alcohols Using an Organic Chromophore-Catalyst Assembly Anchored to TiO2 ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Interfaces 8 9125–33 [118] Kuehnel M F and Reisner E 2018 Solar Hydrogen Generation from Lignocellulose Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chemie - Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 57 3290–6 [119] Christoforidis K C and Fornasiero P 2017 Photocatalytic Hydrogen Production: A Rift into the Future Energy Supply ChemCatChem 9 1523–44 [120] Lee J S, Won D Il, Jung W J, Son H J, Pac C and Kang S O 2017 Widely Controllable Syngas Production by a Dye-Sensitized TiO2Hybrid System with ReIand CoIIICatalysts under Visible-Light Irradiation Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Chemie - Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} +page_content=' 56 976–80' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HNAzT4oBgHgl3EQfUvzA/content/2301.01273v1.pdf'} diff --git a/HtAyT4oBgHgl3EQfS_fv/content/2301.00099v1.pdf b/HtAyT4oBgHgl3EQfS_fv/content/2301.00099v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1c7db13c1fec67b89b4c91a6cab82e725726502e --- /dev/null +++ b/HtAyT4oBgHgl3EQfS_fv/content/2301.00099v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:15bad84a0152e4b0839d7b31b7065665da235a97fa7cf7c8b3ed658fd187c418 +size 4855166 diff --git a/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/2301.03134v1.pdf.txt b/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/2301.03134v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..f7f2073b7d498b10b6dae07f735de0a349c8e486 --- /dev/null +++ b/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/2301.03134v1.pdf.txt @@ -0,0 +1,2035 @@ +1 + +A Semi-supervised Approach for Activity +Recognition from Indoor Trajectory Data + +Mashud Rana, Ashfaqur Rahman, and Daniel Smith + + Abstract—The increasingly wide usage of location aware +sensors has made it possible to collect large volume of trajectory +data in diverse application domains. Machine learning allows to +study the activities or behaviours of moving objects (e.g., people, +vehicles, +robot) +using +such +trajectory +data +with +rich +spatiotemporal information to facilitate informed strategic and +operational decision making. In this study, we consider the task +of classifying the activities of moving objects from their noisy +indoor trajectory data in a collaborative manufacturing +environment. Activity recognition can help manufacturing +companies to develop appropriate management policies, and +optimise safety, productivity, and efficiency. We present a semi- +supervised machine learning approach that first applies an +information theoretic criterion to partition a long trajectory into +a set of segments such that the object exhibits homogeneous +behaviour within each segment. The segments are then labelled +automatically based on a constrained hierarchical clustering +method. Finally, a deep learning classification model based on +convolutional neural networks is trained on trajectory segments +and the generated pseudo labels. The proposed approach has +been evaluated on a dataset containing indoor trajectories of +multiple workers collected from a tricycle assembly workshop. +The proposed approach is shown to achieve high classification +accuracy (F-score varies between 0.81 to 0.95 for different +trajectories) using only a small proportion of labelled trajectory +segments. + +Index Terms—Activity recognition, behaviour classification, +trajectory analytics, smart manufacturing, deep learning, semi- +supervised model. + +I. INTRODUCTION +ANUFACTURING systems form a vital part of the +society and economy, providing jobs to workers +and products to consumers. The manufacturing +industry is continuously developing new initiatives (such as +Industry 4.0, Industrial Internet) to transform traditional +manufacturing +paradigms. +Smart +manufacturing +is +a +technology-driven approach to improve various factors +affecting the performance of manufacturing systems through +the integration of sensor data, analytics and automation [1]. +The computational analysis of data streams collected from + +This research was supported by the Future Digital Manufacturing Fund +(FDMF) at Data61, Commonwealth Scientific and Industrial Research +Organisation (CSIRO), Australia. Thanks to Reena Kapoor, Peter +Baumgartner, and Elena Tartaglia for providing feedback on different sections +of the paper. +Mashud Rana, Ashfaqur Rahman, and Daniel Smith are with Data61, +CSIRO, +Australia. +Emails: +mdmashud.rana@data61.csiro.au, +ashfaqur.rahman@data61.csiro.au, daniel.v.smith@data61.csiro.au. + +Internet of Things (IoT) based sensors at various stages of +production enables evidence-based decision making, and +provides a systematic way to monitor and improve +manufacturing systems [2, 3]. +Numerous studies investigated the diverse machine learning +and data mining techniques for analysing heterogenous data +for a great variety of manufacturing applications. A few +prominent applications include fault detection and diagnostic +[4], predictive analytics [5], quality control and monitoring +[6], efficiency monitoring [7], process optimisation [8], +product life cycle management [9], workflow evaluation [10], +indoor space modelling [11], streamlining supply chains [12], +and safety [13]. Most of these studies primarily focused on +utilising the data collected from workstations or equipment via +accelerometers, gyroscopes, magnetometers etc. Moreover, +many of the key dynamics of a manufacturing process can be +observed from trajectory data that has been collected by using +tracking devices attached to entities or objects. Trajectory data +consists of the spatial coordinates of an object as a function of +time as well as the features describing the object that is being +tracked. In a manufacturing system, the movement of +materials, vehicles, products, logistics, tools, and workers can +be used to determine its current state. Translating these +observations into meaningful insights is the realm of +movement analytics [14], where machine learning and other +statistical methods are used to uncover object semantics based +on its movement patterns. +In this study, we are interested in a specific aspect of +movement analytics, viz., activity recognition. Activity +recognition is generally defined as the task of identifying the +actions of objects from a series of motion related +measurements captured by sensors [15, 16]. It can play a vital +role +to +identify +inefficiencies +or +bottlenecks +within +manufacturing processes. It also helps to identify the possible +reasons behind the deviation of the relevant entities from their +expected behaviours. The decision makers can use this +information to develop appropriate management policies, and +optimise the safety, productivity, and efficiency. For example, +a worker may move back and forth between workstations for +several reasons including delivery of items produced to co- +workers for subsequent processing, finding misplaced or +missing tools. Obviously, it is a problematic activity and +indicative of operational inefficiencies if the visits are related +to searching for misplaced tools or components. Hence, +identifying which tools or workstations are involved in these +activities could help to identify the problems within the +manufacturing process which is a prerequisite for improving +operational efficiency. +M + +2 + +Although activity recognition has widespread application +across different fields (e.g., retail ([17, 18]), health [19, 20]), +tourism [21], construction [22]), it has rarely been studied with +respect to manufacturing applications. Several studies (e.g., +[23-25]) provide insights on the current state of the literature +to detect, recognize, and monitor activities utilising diverse +datasets and methods. The two main approaches for activity +recognition are either vision-based or sensor-based [24]. +Vision-based approaches utilise cameras to passively capture +video of the entities of interest, while sensor-based approaches +commonly use time series from motion sensors (i.e., +accelerometers, gyroscopes) attached to the entities. In +contrast to most of these previous studies, we aim to develop a +model for human activity recognition using spatiotemporal +trajectories +acquired +with +sensor-based +localisation +technologies. Activity recognition especially from indoor +trajectory data is challenging due to spontaneous nature of +human movement within a limited indoor space [16]. In +contrast to outdoor trajectory data of the objects moving over +large geographical area (e.g., vehicle or tourist trajectories in +cities, vessels trajectories in oceans), indoor trajectory covers +a small area with overlaps. The frequent movement of human +within a small indoor area makes the indoor trajectory data +noisy and difficult to model. Moreover, majority of activity +recognition approaches use supervised machine learning +models, which rely upon large sets of labelled data (ground +truth) for the training of classification models [15]. Generating +labelled datasets is a labour intensive and costly process that +can be a major bottleneck for using supervised machine +learning. For activity recognition, it is often unwieldly to +manually label the large number of segments pertaining to the +different activities that may be present across time. Hence, in +this study we adopt semi-supervised learning, which only +requires fewer labelled segments as examples to train the +activity recognition model. +Specifically, our contributions in this paper can be +summarised as follows. We develop an approach for human +activity recognition from spatiotemporal trajectory data in an +indoor environment. The proposed approach consists of three +steps. Firstly, each complete trajectory is partitioned into a set +of segments by optimising an information coding metric, the +minimum description length. Partitioning allows to identify +and classify the different activities of a worker across different +time periods of their work shift. Secondly, the pseudo labels of +the trajectory segments were then generated based on a +constrained hierarchical clustering which requires a small set +of labelled segments. Finally, a Convolutional Neural Network +(CNN) based deep learning model is trained using the pseudo +labels of the trajectory segments. The model was then used to +classify the raw trajectories into a sequence of worker +activities. While the different components of the developed +approach (like trajectory partitioning, clustering, convolutional +neural networks) are all well-known, we emphasise that the +overall architecture combining these components is new for +semi-supervised activity recognition especially utilising indoor +trajectory data. We evaluate the proposed approach by using a +dataset of workers’ trajectories that were collected with a +motion capture positioning system during a tricycle assembly +process. We aim to identify a set of target activities specific to +the +manufacturing +working +environment: +standing +at +workstation, moving randomly, moving between workstations, +restocking. However, we note that our approach is generic and +can be applied to such other activities as well, thus preserving +the motivation for helping improve operational efficiency. +This study is the first of its kind to design and develop a semi- +supervised machine learning activity recognition model based +on indoor trajectory data for manufacturing application. +II. RELATED WORK +The technological innovations in tracking systems and IoT +based sensors have made it possible to collect data from +moving objects over space and time. In the era of cyber- +physical systems, machine learning has been an integral part +of smart manufacturing to develop analytics utilising such data +for intelligent decision making [5]. Numerous studies (e.g., [6, +7, 26-28]) in the literature investigated the application of +machine learning to support different applications. In this +section, we review previous research related to the application +of machine learning in manufacturing. Whilst reviewing the +literature, we limit the scope to movement analytics in the +manufacturing domain and activity recognition in general. +A. Movement Analytics in Manufacturing +Movement analytics (also known as trajectory data +analytics) refers to the process of extraction and utilisation of +knowledge from tracking data for providing meaningful +solutions to decision makers [14]. The spatiotemporal tracking +data can be utilised for optimising the production processes in +manufacturing and developing domain specific applications. +Szabo et al. [10] studied the feasibility of different Real Time +Locating Systems (RTLS) for capturing location data of +moving +objects +to +support +different +applications +in +manufacturing. They also presented a use case to identify the +bottlenecks in defined production zones and measure cycle +time deviation at the workstations in an automotive company. +To identify the bottlenecks (in terms of temporary storage or +unplanned workstations in the production process), they +grouped the position data by applying the k-means clustering +algorithm. The cycle time of workstations was measured based +on classified zone data that were visualized later to provide +real-time status of the production process. Arkan and Van +Landeghem [29] considered improving Work-in-Process +(WIP) visibility in the semi-automated shop floor of an +automotive manufacturing company. They utilised the +spatiotemporal data collected with RTLS from a multi-item +production line to compute a set of Key Performance +Indicators (KPIs) such as cycle time, cycle speed, production +time, defect reject ratio and workspace utilization. These KPIs +were then analysed to evaluate the existing workflow and +redesign the floor with a simulation tool. Similarly, Gyulai et +al. [30] developed analytics to compute KPIs (from simulated +trajectory data) to evaluate the performance of a production +system and facilitate the implementation of situation aware +production control. + +3 + +Moreover, different objects are likely to work together in a +collaborative manufacturing environment. Therefore, it is +important for the objects to efficiently and accurately identify +the task plans of others and respond in a safe manner. Chen et +al. [13] presented an analytics framework to predict human +trajectories and to infer the work plan to facilitate safe and +effective collaboration between objects (human and robots). A +Long Short-Term Memory (LSTM) recurrent networks was +used to model the temporal dynamics of sequential movement +data and Bayesian inference method was applied to infer the +potential plans of workers utilising LSTM based predictions. +Locklin et al. [31] also predicted future positions of human +trajectories by fitting a second degree polynomial function to +historical location data to enable collaboration amongst a large +number of workers in the indoor space. Zhang et al. [32] +proposed an LSTM based method to predict the future motion +trajectory of human operators for facilitating a robot’s action +planning and execution in a car engine assembly factory. +Wang et al. [33] proposed a similarity based model for +trajectory prediction within indoor spaces. Specifically, they +applied the k-Nearest Neighbours (kNN) algorithm to find a +trajectory from the database that was most similar to the given +trajectory. The next location of the given trajectory was then +predicted from the path of similar trajectory. The main novelty +of this model was the formulation of a distance metric that +considered both the spatial and semantic distance between +trajectories, which were computed based on the longest +common sub sequences and dynamic time warping, +respectively. +Furthermore, the optimal utilisation of available indoor +space (such as shop floor, production floor, etc.) is vital for +mass production. Movement data can be used to understand +the geospatial interaction patterns between objects, and hence, +helps to design more efficient factory layouts. Han et al. [11] +presented a method to study indoor space utilisation based on +the common movement patterns in the trajectory data of +multiple users. They first partitioned each trajectory into a set +of segments by optimising an information theoretic criterion +and then grouped the segments from all of the trajectories into +a set of clusters by applying the GDBSCAN algorithm [34]. +The clustering results were used to identify heavily utilised +regions and visualize the evolution of utilisation over time for +the better design of indoor spaces in the future. Additionally, +Cai et al. [35] proposed a spatiotemporal data model for +monitoring IoT enabled production systems. Their model +combined the principle of the Apriori algorithm [36] and depth +first search to find the frequent trajectory patterns of WIP. Bu +[37] also described a framework based on the Apriori +algorithm to mine frequent path patterns from the massive +amounts of tracking data. This enabled material flow paths to +be adjusted and helped to reschedule the route of automatic +guided vehicle robots in a production environment. +B. Activity Recognition +Recognising the activities of objects (people, vehicles, +robots) is a key factor in developing appropriate strategies for +industrial applications in many domains including but not +limited to retail ([17, 18]), health ([19, 20]), construction +([22]) and transport ([38]). Shum et al. [39] reviewed +utilisation of different types of tracking data collected in +variety of domains for human activity recognition. Arslan et +al. [22] developed a model for workers’ activity recognition at +hazardous construction sites for improving safety management +strategies. The raw GPS data was transformed into semantic +trajectories to label mobility related activities in terms of their +building environment. A Hidden Markov Model (HMM) was +then trained using the semantic trajectories to classify the +mobility patterns of workers. Polanti et al. [17] developed an +intelligent system to improve the shopping experience by +utilising the movement trajectories of customers in retail +environments. A HMM was trained with the shopping +trajectories of customers in order to predict the customer’s +future shopping preferences. The system then presented a +route map to direct customers to their preferred products in the +retail store. Alahi et al. [38] proposed social LSTM, a model +to predict human movement within crowds utilising their +spatial trajectories. Given the motion of individuals within a +crowded space are affected by the behaviour of others, the +social LSTM architecture modelled these spatial interactions. +The movement of individuals were represented by separate +LSTMs and a shared pooling layer was used to connect the +latent states of all the individuals (their LSTMs) within the +crowded space. The social LSTM was then used to predict the +future movement of individuals and groups of individuals. +Several studies investigated activity recognition from indoor +tracking data to detect early symptoms of abnormal +behaviours or health risks. Gochoo et al. [19] presented a non- +obtrusive activity recognition model for elderly people living +alone. The indoor tracking data of individuals was converted +into two-dimensional activity images that were then used to +train a Deep Convolutional Neural Network (DCNN) with a +predefined set of home activity classes. The application of +DCNN and other machine learning models including Random +Forest (RF) and Gradient Boosting (GBM) were also +investigated in [40] for the detection of dementia related +behaviours of elderly people using movement data. Similarly, +Fang et al. [41] identified abnormal behaviour patterns linked +with different health risks in order to prevent their occurrence. +A hybrid model based on an LSTM and Grey Model was +proposed using the past movement data of an individual to +predict their future location and activity class. In contrast to +the continuous valued position data considered in our study, +the trajectory data used in [19, 40, 41] consists of binary +on/off signals from a set of fixed indoor sensors. +Moreover, Yu et al. [42] presented a feature-oriented method +for identifying truck parking behaviours from the vehicle’s +trajectory data. The raw GPS trajectories were processed to +extract a set of exploratory features and then association rule +mining was applied to the extracted features to identify legal +and illegal parking patterns. Lei [43] described a framework to +identify the anomalous behaviour of vessels travelling in +maritime space from their trajectories. The framework mapped +the trajectories into spatial regions by applying a grid based +clustering algorithm and then extracted features reflecting the + +4 + +spatial, sequential, and behavioural characteristics. The +movement behaviours of the vessels were then classified using +a probabilistic suffix tree which utilised those features as +inputs. Likewise, Chatzikokolakis et al. [44] applied RF model +on vessels trajectories to identify search and rescue activities. +Kim et al. [45] developed a clustering based method to +discover travel patterns utilising vehicle trajectory data in a +traffic network. The vehicle trajectories were first grouped by +applying a density based clustering algorithm using the +Longest Common Subsequence (LCS) distance metric. The +overlapping LCS from all the clusters were then merged using +hierarchical +clustering +to +generate + +travel +patterns +representative of the dataset. New trajectories were then +classified by matching them against the clusters of +representative travel patterns. Song et al. [46] presented a +deep recurrent neural network architecture to simultaneously +solve multiple learning tasks using spatial trajectories across +large scale transportation networks. The future motion of an +individual and their transportation mode were simultaneously +predicted using a hierarchical network of LSTMs that +represent motion across different temporal scales. Two LSTM +based encoders were utilised to represent the inputs of each +task separately, two LSTMs were used to create a shared +feature representation and a pair of LSTM decoders that were +used to generate the outputs of each task. +C. Summary +Trajectory data can play a vital role in smart and adaptive +manufacturing. However, the above review indicates recent +activity recognition methods utilising tracking data have not +been well studied in the context of manufacturing. The +existing studies primarily utilised trajectory data for workflow +evaluation. There exists many applications that required +regular monitoring of activities or understanding the +behaviours of moving objects [47]. A few examples of such +applications include: i) monitoring suspicious activities in +large industrial workshops or chemical plants for security +purposes, ii) identifying when a worker interacted with other +workers to avoid spreading infectious diseases (e.g., COVID) +and loss of workforce, iii) understanding why and to what +extent a worker deviated from their intended workflow. On the +other hand, while numerous research investigated utilisation of +outdoor trajectory data (collected using GPS) for different +applications, activity recognition based on indoor tracking +data is not sufficiently studied especially for manufacturing +applications. Indoor tracking data covers small area with +overlaps. Contrast to outdoor trajectories that are relatively +smoothed, the segments of indoor trajectories are significantly +shorter and noisy that make the activity recognition task very +difficult. Given most of the existing methods for activity +recognition are supervised, they are not well suited to +manufacturing applications due to the difficulties in collecting +labelled activity data in such contexts. Hence, it is also +important to explore the feasibility of semi-supervised +methods on indoor tracking data. In this study, we aim to +address these deficits in the literature. +III. DATASET +The indoor tracking dataset used in study was collected from +a tricycle assembly workshop [48]. The workshop consists of +multiple workstations and provides a dynamic environment for +the workers during the assembly process with various +representative industrial scenarios. The dataset is publicly +available at [49]. + + +Fig. 1. Expected workflow of the people at the tricycle +assembly workshop which consists of several workstations. +Fig. 1 shows the arrangement of the workstations of the +tricycle assembly line and the expected movement scenarios +of the people across the workstations during the assembly +process. There are six workstations (also called rigs) in the +assembly line. The worker at each workstation is responsible +for building certain parts of a tricycle and concurrently works +in a collaborative manner with others during the assembly +process. The worker at rig 1 prepares the lower frame of +tricycles and delivers it to the worker at rig 2 who assembles +the axle with the lower frame. The worker at rig 3 builds the +saddle and pedal board, and then supplies these components to +the worker at rig 4. The worker at rig 4 builds the rear wheel +axle unit by assembling the units built by the workers at rigs 2 +and 3. The worker at rig 5 assemble the front wheel axle unit. +Finally, both the front wheel axle and rear wheel axle units are +assembled to finalise the tricycle construction by the worker at +rig 6. + + +记 +记 +记 +记5 + + +Fig. 2. The processed tracking data of the workers at the 10×9 square meters tricycle assembly workshop. The shaded area (■) +indicate the work zone where the workstations are placed, and the colors of the trajectory lines indicate data collection time. + +Six tricycles are expected to be built within three hours of +operation. The workstations can hold the components required +for the assembly of three tricycles. Hence, the workers need to +restock the required components from the storage area when +initial stocking is finished after the first round of work, or if +there are any missing components or tools. During the +assembly process each person is responsible for the pre- +assigned task, can go to help co-workers or take breaks as +necessary. For more details on the site setup and data +collection procedure, we refer to the previous study [48]. + + + +Fig. 3. Distribution (%) of the spatial points for six trajectories at the tricycle assembly workshop. + +Movement data of the workers in the workshop were +recorded using a Motion Captured (MoCap) system [50] for 3 +hours of operation. Mocap systems provides better indoor +positioning +accuracy +compared +to +other +available + +Tracjectory1 +Tracjectory2 +Tracjectory3 +8 +w +6 +4 +2 +0 +Tracjectory5 +Tracjectory +8 +w +6 +2 +0 +0 +2 +4 +6 +8 +0 +2 +4 +6 +8 +0 +2 +4 +6 +8 +x (m) +X (m) +X (m) +start +end +datacollectiontimeRig1 +Rig2 +Rig3 +30 +25 +15 +8 +20 +20 +(w) +6 +F 10 +15 +4 +10 +10 +2 +5 +0 +0 +0 +Rig4 +Rig5 +Rig6 +20 +OE +15 +15 +(w) +6 +20 +10 +4 +10 +> +10 +5 +2 +0 +0 +C +0 +8 +0 +8 +0 +4 +6 +8 +X (m) +X (m) +X (m)6 + +technologies. The interval between consecutive data samples +varies between 10 to 100 milliseconds. We down sample the +raw trajectory data for each worker to 1 sample per second to +synchronise the interval between successive samples and +reduce the number of missing samples. Fig. 2 shows the +processed trajectory data of each worker during the entire data +collection period. The tracking data shows that the workers +deviate from their planned movement protocol and visit +locations outside of the defined assembly zones as well. These +deviations could be associated with taking a break or other +unknown behaviours (e.g., activity of moving randomly). + + +Fig. 4. Factory layout based on distribution of spatial points +and site information. + +Moreover, we analyse the spatial distribution of worker +positions (Fig. 3) to identify the approximate location of the +workstations and map them into a factory layout. The factory +layout is required to manually label the different trajectory +segments. For each worker, the location of the workstation is +determined as the point of maximum density within the +distribution of the worker’s spatial positions over time, since +each worker should spend majority of his/her time at the +designated workstation to finish the assigned task. Fig. 4 +presents the approximate layout of the tricycle assembly line +based upon the spatial distribution of the workers’ trajectories. +As it shows, the six rigs are placed to make the interactions or +collaborations among the workers easy by following the +expected movement scenarios shown in Fig. 1. +IV. BACKGROUND +A. Definitions + Trajectory: a trajectory of an object or entity is an ordered +sequence of location points and is denoted as: 𝑇𝑅 = +{(𝑝1, 𝑡1), (𝑝2, 𝑡2), … , (𝑝𝑁, 𝑡𝑁) } ∶ 𝑡𝑖−1 < 𝑡𝑖, 𝑖 = 2, … , 𝑁, +where 𝑝𝑖 (1≤𝑖≤𝑁) ∈ 𝑅𝑑 is a multidimensional vector of spatial +location information of the object at timestamp 𝑡𝑖 and 𝑁 is the +total number of location points in 𝑇𝑅. In the simplest form, +𝑝𝑖 (1≤𝑖≤𝑁) ∈ 𝑅𝑑 represents the object’s location in a two +dimensional plane at timestamp 𝑡𝑖. However, the dimension of +the vector 𝑝𝑖 can be extended further by adding more features +(e.g., third spatial dimension, velocity, acceleration, etc.) +depending on the application. +Sub-trajectory: a sub-trajectory or trajectory segment of a +trajectory 𝑇𝑅 is a subset of time ordered spatial location points +in +𝑇𝑅 +and +is +denoted +as: +𝑆𝑈𝐵𝑇𝑅 = +{(𝑝𝑘, 𝑡𝑘), (𝑝𝑘+1, 𝑡𝑘+1), … , (𝑝𝑘+𝑛, 𝑡𝑘+𝑛) } ∶ 𝑡𝑘 < 𝑡𝑘+1, 1 ≤ 𝑘 < +𝑛 ≤ 𝑁 − 1. The straight line joining the two endpoints +(𝑝𝑘, 𝑝𝑘+𝑛) of 𝑆𝑈𝐵𝑇𝑅is called a trajectory partition of 𝑇𝑅. +B. Problem Statement +Given a set of trajectories 𝒯 = {𝑇𝑅1, 𝑇𝑅2, … , 𝑇𝑅𝑊}, where +each trajectory represents the movement patterns of an object +in an indoor manufacturing environment. For each trajectory +𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 +𝑊 , the goal is to partition the trajectory into +a set of non-overlapping segments and then classify each +segment as a category from a set of four predefined activities: +[𝑚𝑜𝑣𝑖𝑛𝑔 𝑟𝑎𝑛𝑑𝑜𝑚𝑙𝑦, 𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑡 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛, +𝑚𝑜𝑣𝑖𝑛𝑔 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑠, 𝑟𝑒𝑠𝑡𝑜𝑐𝑘𝑖𝑛𝑔]. +The activity of an object is labelled as ‘moving randomly’ +for the duration of a trajectory segment if the object moves +outside the work zone (i.e., outside of the tricycle assembly +area as shown in Fig. 4) for a different purpose such as taking +a break, meeting others, etc. ‘Standing at workstation’ +indicates that the object is busy at the designated workstation +to finish the assigned tasks. ‘Moving between workstations’ +represents the collaborative behaviour – a worker may visit +other workstations to deliver the products (or components) +built according to the workflow or help co-workers. Finally, +‘restocking’ refers to the activity of visiting storage area if the +stock required to complete the assigned task at a workstation +is finished, or when searching for tools or component if they +are not available at the workstation as expected. +In a typical manufacturing setting, many objects (e.g., +workers, AVG, robots, etc.) work collaboratively in a dynamic +environment. Each of these objects generate its own trajectory +over time. Segmenting each of the trajectories and labelling +them manually are not feasible since it requires time, +resources, and expertise. In this study, we aim to automatically +segment the trajectories by identifying a set of changepoints +(or characteristic points) and then develop a semi-supervised +model that required only few labelled segments (can be as low +as one labelled segment for each category of the activities or +behaviours). +C. Constrained Hierarchical Clustering +Clustering is the process of grouping the samples (or +observations) in a dataset such that the samples (e.g., +trajectory segments in our case) within the same group (called +a cluster) are similar to one another and dissimilar to the +samples in other groups. Agglomerative hierarchical clustering +initially assigns each data sample into a separate cluster and +then successively merges them using a bottom-up approach. In +each iteration, the two closest or most similar pair of clusters +are merged into a single cluster where the closeness or +similarity is measured based on a linkage criterion. Single link +refers to distance between the two nearest samples whereas + +10 +storage area +outerzone +work zone +8 +Rig1 +Rig6 +6 +Rig2 +(w), +Rig5 +4- +Rig3 +Rig4 +2 +outerzone +0 + +0 +1 +2 +m +4 +5 +6 +-7 +00 +X (m)7 + +complete link refers to the distance between the two farthest +samples as the similarity between two clusters, respectively. +Average link considers the average of the distances of each +pair of samples in two clusters. The merging process is +finished when all the data samples form a single cluster. This +method produces a set of nested clusters in hierarchical +structure that can be visualised using a dendrogram which is +tree like diagram to record the sequence of merges. The +expected number of clusters can be obtained by drawing lines +at different levels on the dendrogram depending on the +applications or specifying the number of clusters during the +merging process. +Moreover, it is possible to specify the structural constraint +into hierarchal clustering process in the form of must link and +cannot link. Must link constraint indicates which group of data +samples should be part of the same cluster whereas cannot link +constraint refers to the samples that should be in different +clusters. Fig. 5 shows an example of agglomerative +hierarchical clustering using structural constraints. The +distance matrix indicates that data samples (b, d) should be +part of same cluster (must link), whereas pairs of samples in +(a, e) and (g, f) cannot be in same cluster (cannot link). The +dendrogram for this example shows that there are two +different clusters are possible at the top due to the cannot link +constrained. + + + +Fig. 5. Constraint agglomerative hierarchical clustering using both must link and cannot link constraint: distance measure +between examples (left), ‘must link’ and ‘cannot link’ constraint (middle), and clusters merging process (right). In each iteration, +pair of clusters are merged considering distance measured based on single link criteria. + + + +Fig. 6. A typical architecture of a convolutional neural networks + + +a +b +p +e +f +g +h +a +x +6 +3 +8 +2 +4 +7 +20 +b +x +1 +2 +9 +3 +5 +7 +c +x +7 +30 +4 +8 +5 +p +x +9 +6 +4 +8 +e +X +4 +3 +9 +f +x +5 +7 +g +x +40 +h +xa +b +c +p +e +f +g +h +a +CL +b +ML +c +e +f +CL +g +hConv layerwithN filters +Conv layerwithMfilters +Nfeatmaps +Mfeatmaps +Poolinglayer +inputdata +[2D] +Poolinglayer8 + +D. Convolutional Neural Networks +CNNs [51] are prominent deep learning models that can +identify the spatial patterns and translation invariant features +from the input in a layered structure for classification or +prediction. As shown in Fig. 6, a typical CNN architecture +consists of a series of convolutional and pooling layers +followed by one or more fully connected layers (also known +as dense layers). The convolutional layers are the major +building blocks of CNNs that apply a set of learnable filters +(also known as kernels) to local regions of the input to extract +useful features and create an internal network representation. +The repeated application of the filters across different input +locations creates a set of feature maps. The stacking of +convolutional layers in a deep network allows the shallower +layers to learn low-level features and the deeper layers to learn +high-order or more abstract features. +The feature map outputs from the convolutional layers are +location sensitive, that is, the layer outputs are dependent upon +the feature’s position within the data. To make the feature +maps ‘local translation invariance’ (i.e., the output is not +changed by local shifts in the feature position) and reduce the +dimensionality of network representations, it is common for +pooling layers to be added after the convolutional layers. +Pooling is a down sampling operation that involves applying a +sliding window to approximate local regions of the features. +The approximation commonly involves computing the +maximum or mean value within the feature window. As such, +pooling has been considered as a technique to generalize +feature representations. Overall, this structure allows the +network to learn filters that represent patterns in the data that +can be used for prediction or classification [52]. Pooling also +makes the CNNs more noise tolerant and creates a hierarchy +of features to extract meaningful patterns at different +temporal scales [53]. +The last part of a CNN is analogous to traditional +feedforward NNs and consists of one or more dense layers. +Before feeding the extracted feature maps to the fully +connected layer, it is required that the feature maps are +flattened into a vector. The dense layers are the final network +layers that apply nonlinear combination of the extracted +features to compute output predictions. For more detail +information on CNNs, we refer to [51, 52, 54]. +V. PROPOSED APPROACH FOR ACTIVITY RECOGNITION + +Fig. 7 shows an illustrative diagram of our proposed +approach for activity recognition from indoor trajectory data. +The approach consists of three main steps: trajectory +partitioning, clustering, and model training. The first step +focuses upon partitioning each trajectory into a set of +segments representing various movement patterns. This is +achieved with a segmentation algorithm that identifies a set of +characteristics points where the statistics or distributions of the +trajectory changes rapidly. The second step generates pseudo +labels of the unlabelled segments by applying a clustering +method: this requires a small proportion of trajectory +segments to be labelled as input. The last step trains a +classification model for activity recognition utilising the +segments and their pseudo labels. + + + +Fig. 7. A simplified schematic diagram of the proposed +approach for activity recognition. +A. Trajectory Partitioning +We aim to partition the individual trajectories into non- +overlapping segments. The key idea is to identify a set of 𝑀 +characteristics +points +(or +change +points) +𝐶𝑃 = +{(𝑝𝑐1, 𝑡𝑐1), (𝑝𝑐2, 𝑡𝑐2), … , (𝑝𝑐𝑀, 𝑡𝑐𝑀)} ∶ 𝑡𝑐1 < 𝑡𝑐2 < ⋯ < 𝑡𝑐𝑀 +from each trajectory 𝑇𝑅𝑖 ∊ 𝒯 and use those to partition each +trajectory into 𝑀 − 1 segments. These segments represent the +different movement patterns in an individual trajectory. +To discover the characteristics points from individual +trajectories, we apply an information theoretic criterion, +Minimum Description Length (MDL) [55]. There are two +desirable properties of the trajectory partitioning [56]: +preciseness and conciseness. Preciseness represents the +accuracy in which a set of chosen trajectory segments +represent the original trajectory, whereas conciseness +represents the number of segments (i.e., model parameters) +used within its representation. These two properties are +contradictory. For example, the preciseness is maximised (and +conciseness is minimised) if we consider all the points within +a trajectory as characteristics points. Likewise, the conciseness +is maximised (and preciseness is minimised) if only the two +end points of the trajectory are considered as the characteristic +points. The MDL principle identifies the characteristics points +of the trajectories by finding the optimal trade-off between the + +Individualtrajectorypartitioning +Automatic labelling of segments +inSubasedonclustering +Training of a CNN based classification model9 + +preciseness and conciseness properties [11, 56]. +The function defining the MDL principle is given in (1) +where 𝐻 represents a hypothesis, 𝐷 is the data, 𝐿(𝐻) is the +description length of the hypothesis and 𝐿(𝐷|𝐻) is the +description length of the data encoded using the hypothesis, +both expressed in bits. The hypothesis 𝐻 with the minimum +𝑀𝐷𝐿 is the one that achieves the highest data compression, or +equivalently, the best explanation of the data. For our +segmentation task, the hypothesis 𝐻 corresponds to the set of +partitions of our trajectory data. Therefore, finding the optimal +partitioning of the trajectories can be translated into finding +the best hypothesis based on MDL. + +𝑀𝐷𝐿 = 𝐿(𝐻) + 𝐿(𝐷|𝐻) (1) + +The two terms of the MDL function can be formulated using +(2) and (3), respectively [56]. 𝐿(𝐻) in (2) represents the total +length of all trajectory partitions where 𝑙𝑒𝑛 (𝑝𝑐𝑗𝑝𝑐𝑗+1) is the +length of a line segment (𝑝𝑐𝑗𝑝𝑐𝑗+1) that is computed using the +Euclidean distance between two consecutive characteristics +points 𝑝𝑐𝑗 and 𝑝𝑐𝑗+1. On the other hand, the formulation of +𝐿(𝐷|𝐻) in (3) refers to the sum of the difference between a +trajectory and a set of its trajectory partitions. For each +partition, the difference between partition and the representing +line segment is computed by taking the sum of the +perpendicular distance 𝑑⊥ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1) and the angular +distance 𝑑Ѳ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1). + +𝐿(𝐻) = ∑ +𝑙𝑜𝑔2 (𝑙𝑒𝑛 (𝑝𝑐𝑗𝑝𝑐𝑗+1)) +𝑀−1 +𝑗=1 + (2) + +𝐿(𝐷|𝐻) = ∑ +∑ +{𝑙𝑜𝑔2 (𝑑⊥ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1)) + +𝑐𝑗+1−1 +𝑘=𝑐𝑗 +𝑀−1 +𝑗=1 +𝑙𝑜𝑔2 (𝑑Ѳ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1))} (3) + +The above formulation of 𝐿(𝐻) represents a measure of the +conciseness, where as 𝐿(𝐷|𝐻) indicates a measure of the +preciseness. For our segmentation task, 𝐿(𝐻) increases as the +number to partitions increases. On the other hand, larger +deviations between the set of trajectory partitions and original +trajectory causes 𝐿(𝐷|𝐻) to increase. We aim to find the +optimal partitioning that minimises the sum of 𝐿(𝐻) and +𝐿(𝐷|𝐻). +Moreover, the cost of finding the optimal partitioning for a +trajectory is exhaustive as it requires every subset of points in +the trajectory to be considered. Hence, an approximate +algorithm [56] with time complexity of 𝑂(𝑁) has been applied +which considers a set of local optima as the global optimum. +Let 𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) represents the MDL cost (i.e., 𝐿(𝐻) + +𝐿(𝐷|𝐻)) of a trajectory between two points 𝑝𝑖 and 𝑝𝑗 (𝑖 < 𝑗) +considering 𝑝𝑖 and 𝑝𝑗 are the only characteristic points, +whereas 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) is the MDL cost when persevering +the original trajectory – i.e., if there is no characteristic point +between 𝑝𝑖 and 𝑝𝑗. It is obvious that 𝐿(𝐷|𝐻) in +𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) is zero. Hence, a local optimum is the +longest trajectory partition 𝑝𝑖𝑝𝑗 which satisfies the condition +𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) ≤ 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) ∶ ∀𝑘 𝑖 < 𝑘 ≤ 𝑗. This +means if 𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) smaller than 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑘), the +selection of 𝑝𝑘 as a characteristic point will cause the MDL +cost smaller compared to the MDL cost if 𝑝𝑘 is not chosen. +The approximation process considers the first data point 𝑝1 +from the trajectory as the starting characteristic point and +repeatedly compute 𝑀𝐷𝐿𝑝𝑎𝑟 and 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟 for each +subsequent point. In each step, if the cost of partitioning is +equal or less than the cost of not partitioning, we increase the +length of trajectory partition and continue computing the two +costs for next point. Otherwise, we consider the previous point +as the characteristics point and repeat the same procedure to +search the next characteristic point until all data points are +checked. +B. Cluster and Label +In this section, we introduce the method for labelling the +trajectory segments generated by the partitioning process. The +main idea here is to generate a set of pseudo labels for the +trajectory segments by applying constrained agglomerative +hierarchical clustering with a small proportion of labelled +segments. +Let +𝑆𝐿 = {(𝑠𝑙1, 𝑦𝑙2), (𝑠𝑙2, 𝑦𝑙2), … , (𝑠𝑖, 𝑦𝑙𝑖) } +and +𝑆𝑈 = +{𝑠𝑢1, 𝑠𝑢2, … , 𝑠𝑢𝑗 } are the sets of labelled and unlabelled +segments, respectively. The members of segments in 𝑆𝐿 are +called seeds. Our task is to automatically label the trajectory +segments in 𝑆𝑈 so that we can train a classification model +using the data samples (e.g., segments in both 𝑆𝐿 and 𝑆𝑈). The +classification model will then be applied to predict the class +labels of the data samples in 𝑆𝑇𝑒𝑠𝑡 that represent the set of test +segments. +We adopt the hierarchical clustering method to generates +labels for trajectory segments in 𝑆𝑈. In contrast to traditional +clustering approach, we introduce constraints to the clustering +structure to define how the seeds should be grouped. +Specifically, we impose cannot-link constraints on the +elements of 𝑆𝐿 to ensure that no more than one seed should be +present in any cluster, even if the seeds have the same label. +Each of the clusters will be comprised of trajectory segments +that are most similar to its seed, and hence, its members (i.e., +segments from 𝑆𝑈) will be labelled according to the class of its +seed. +When +applying +constraint +agglomerative hierarchical +clustering, it is very important to choose an appropriate +distance metric for the linkage criteria used to compute the +similarity between clusters. The standard metrics based on +point-to-point distance are not suitable for spatial data +especially when the length of the time series are not same, as +in our case [57, 58]. Hence, we apply the Hausdorff distance +to compute the distance between pairs of trajectory segments. +Considering the segments as geometric curves, the Hausdorff +distance from a set of points 𝐴 to another set of points 𝐵 is the + +10 + +maximum distance of a set 𝐴 to the nearest point in the set 𝐵 +and is defined as in (5). + +𝐻𝐷𝐴→𝐵 = max +𝑎∈𝐴 {min +𝑏∈𝐵 𝑑(𝑎, 𝑏)} (5) + +where 𝑑(𝑎, 𝑏) is the distance between points 𝑎 and 𝑏 +computed using any chosen distance metric (e.g., Euclidean +distance). Generally, the Hausdorff distance is directed, which +means that distance 𝐻𝐷𝐴→𝐵 from 𝐴 to 𝐵 is not equal to the +distance 𝐻𝐷𝐵→𝐴 from 𝐵 to 𝐴. An undirected Hausdorff +distance can be computed by taking the average of the two +directed distances as in (6). + +𝐻𝐷𝐴→𝐵 = 𝐻𝐷𝐵→𝐴 = 𝑚𝑒𝑎𝑛(𝐻𝐷𝐴→𝐵, 𝐻𝐷𝐵→𝐴) (6) + +The presented clustering method can be explained from a +graph-theoretic perspective. Let 𝐹 = 𝑆𝐿 ∪ 𝑆𝑈 be the set of all +training observations. Consider 𝐺 = (𝑉, 𝐸) as an undirected +graph. The set of vertices 𝑉 in 𝐺 represents all the +observations in 𝐹 and a super-vertex (∗). On the other hand, 𝐸 +represents the edges among the vertices for all elements in 𝐹 +as well as the edges between the super-vertex and vertices +representing all the seeds. The weights of the first group of +edges corresponds to the distance of two observations (i.e., +segments) computed using the undirected Hausdorff distance. +On the other hand, for the edges between the super-vertex (∗) +and vertices representing the seeds, the weights are set to zero. +The labelling of the observations in 𝑆𝑈 then can be viewed as +a specific way of finding a minimum spanning tree of 𝐺 using +Kruskal’s algorithm considering that the forest which is +successively joined by Kruskal’s algorithm is a set of clusters +generated by the agglomerative hierarchical clustering +dendrogram [59]. Since the weights of the edges between the +super-vertex and vertices representing the seeds (i.e., the +labelled segments in 𝑆𝐿) is zero, Kruskal’s algorithm will add +all the seeds at the beginning to the minimum spanning tree in +the first 𝑅 iterations where 𝑅 is the cardinality of 𝑆𝐿. This will +leave 𝑅 branches in the tree – these branches are called the +main branches. The tree will then grow along the main +branches in the successive iterations without created any new +branches since all the edges from the super-vertex have +already been added by 𝑅 iterations. This is equivalent to +imposing cannot-link constraints in agglomerative hierarchical +clustering between each pair of seeds. Upon termination of the +algorithm, each of the branches in the tree corresponds to a +cluster in the agglomerative hierarchical clustering. + + + + +TABLE I. PARAMETERS OF THE CNNS USED FOR STEPWISE SEARCH +Parameters +Description +Values used for grid search +Filters +number of convolutional filters or kernels. +(𝐹1, 𝐹2, … 𝐹𝐿) indicates network consists of 𝐿 +convolutional layers and each layer 𝑙 consist of +𝐹𝑙 filters +[(16), (32), (64), (128), (32, 16), (32, +32), (64, 32), (64, 16), (128, 64), (64, +32, 16), (128, 64, 32, 16)] +Kernel size +length of the convolution filters +[3, 5] +Activation +activation functions for convolutional layers +['relu', 'sigmoid', 'tanh'] +Strides +distance +between +two +successive +kernel +positions is called a stride +[1,2,3] +Padding +how the centre of each kernel to overlap the +outermost element of the inputs +[‘valid, ‘same’] +Kernel initializer +how to set initials weights of the convolutional +filters +[‘glorot_uniform’, random_uniform’] +Pooling +pooling operation to perform on convolutional +feature map +[None, ‘max’, ‘avg’] +Dropout rate +fraction of neurons and their associated weights +to disregard at each training epoch +[0, 0.1, 0.2, 0.3] +Dense neurons +number of layers in fully connected layers. +(𝑁1, 𝑁2, … 𝑁𝐿) indicates 𝐿 fully connected +layers and each layer 𝑙 consist of 𝑁𝑙 neurons +[(4,), (10, 4), (20, 4)] +Dense activation +activation functions for neurons in fully +connected layers +[‘relu’, and/or ‘softmax’] +Batch size +number of training samples per gradient update +[64, 128] +Epochs +number of epochs to train the model +[250, 500] + + +11 + +C. Classification model +To develop the classification models, we apply CNNs. The +rationale of selecting CNNs are their ability to automatically +learn features that represent meaningful patterns from large +spatial or temporal datasets. +The CNNs used in this paper consist of multiple +convolutional and pooling layers. Hence, the hyper-parameters +of the networks have a significant influence on generalization +ability, robustness, and overall predictive performance of the +models. We find the optimal topology of CNNs and tune their +hyper-parameters based on a stepwise search method. +Specifically, we optimise one parameter at a time while +keeping the remaining parameters unchanged by training the +CNNs using training data and evaluating its performance on +the validation data. We apply a stepwise search instead of an +exhaustive grid search to reduce the training time. We +consider CNNs up to 4 convolutional layers with a different +number of filters in the range of 16 to 128, multiple filter sizes +in each convolutional layer in the range of 3 to 5, two different +types of pooling layers – max and average pooling, and +multiple combinations of fully connected layers with a +different number of nodes. +To optimise the parameters, we apply Adam optimization +algorithm [60] with a differing number of epochs, minimizing +the sparse categorical cross entropy, and applying dropout at +each layer. Dropout [61] is a regularization method that +randomly chooses specified fraction of nodes at each training +epoch and disables their connection, hence disregards them +during weight optimization. This technique has been found +very effective for deep learning models to reduce over-fitting. +TABLE I presents the entire search space considered to find +the optimal structure and tune hyper-parameters of CNNs. + + + +Fig. 8. Partitioning of trajectories. Lines indicate part (randomly selected) of trajectories and circles represent the identified +partitioning points. The raw noisy data points between partitioning points are not shown for better representation. + +The selected best architectures of the CNNs models for all +the trajectories have similar structures with number of +convolutional layers between 1 to 2. As an example, the best +architectures obtained based on stepwise searching for the +trajectory data for the operator at rig 6 includes 2 1D +convolutional layers with 32 and 16 filters respectively. Both +convolutional layers share the same kernel size, strides, +padding method, and activation function: 3, 1, ‘same’, and +‘tanh’, respectively. Moreover, each convolutional layer is +also followed by a max pooling layer, a dropout layer with +dropout fraction of 0.2. The fully connected component +consists of one dense layer with a softmax activation function +and provides a probability of the 4 classes of activities. The +weights of the CNNs were optimised with a maximum of 500 +epochs and batch size of 128. +For each trajectory in our dataset, we develop a separate +classification model using CNNs. Inputs to the CNNs models +include the trajectory segments along with duration of the +segments. Each of the models has been trained using the +observations +in +both +in +𝑆𝐿 +and +𝑆𝑈 = +{(𝑠𝑢1, 𝑦𝑝𝑙1), (𝑠𝑢2, 𝑦𝑝𝑙2), … , (𝑠𝑢𝑗, 𝑦𝑝𝑙𝑗) } where 𝑠𝑢𝑖 (1≤𝑖≤𝑗) is the +an element of 𝑆𝑈 and 𝑦𝑝𝑙𝑖the pseudo label for 𝑠𝑢𝑖. This means +the training data for each trajectory contains both the segments +in 𝑆𝐿 with their actual class labels, and the segments in 𝑆𝑈 +with the pseudo labels generated in clustering step. +Fig. 9. Distribution of activities of workers into 4 defined +categories. + +TR1 +TR2 +TR3 +TR4 +TR5 +TR612 + +Fig. 10. Distribution of activities of workers into 4 defined +categories. +VI. EXPERIMENTS AND RESULTS +The partitioning algorithm is applied to each trajectory 𝑇𝑅𝑖 +in 𝒯 = {𝑇𝑅𝑖}𝑖=1 +𝑊 separately. Fig. 8 shows the partitioning +results (the partition points and the segments joining those +points) for a small proportion of data points (2-3 minutes) +from each trajectory. The raw noisy trajectory data points are +not shown for better visualisation. As we can see, the MDL +based algorithm correctly identify the trajectory segments with +different characteristics – the portioning points are chosen +where the behaviour of the trajectories changes significantly. +The segments have different lengths and represent different +activities of the workers in the factory. TABLE II presents the +summary of trajectory partitioning results. The number of +partitioning points for the trajectories varies in the range of +223 for 𝑇𝑅1 to 388 for 𝑇𝑅6. The variation in the number of +partitioning points is expected since different workers show +different movement patterns. Fig. 9 presents the distribution +of activities of the workers into predefined categories: +standing at workstation, moving randomly, moving between +workstations, restocking. More than 50% of segments of all +trajectories are labelled as standing at workstation which +highlights that the workers are mostly busy completing their +assigned task for a majority of the time. The workers also +spend a significant proportion of time moving between +different workstations – the proportion of segments classified +as moving between workstations varies between 11.71% to +24.71%. This is due to the collaborative nature of the tricycle +assembly task and can be explained by the workflow in Fig. +1. As shown in Fig. 1, during the assembly process, the +components built at each workstation needs to be delivered to +another co-worker until the completion of work in progress. + +TABLE II. SUMMARY INFORMATION ON TRAJECTORY SEGMENTATION +Trajectory +Duration (sec) +Length +Partition points +Total segments +𝑇𝑅1 +3790 +7727 +223 +222 +𝑇𝑅2 +5214 +7840 +328 +327 +𝑇𝑅3 +3475 +7266 +252 +251 +𝑇𝑅4 +3107 +7712 +264 +263 +𝑇𝑅5 +7194 +7803 +341 +340 +𝑇𝑅6 +7356 +7847 +388 +387 +Moreover, moving randomly is the third most frequent +observed activity. The worker at rig 1 has the highest +percentage of segments labelled as moving randomly (22.97% +segments) followed by the worker at rig 3 (16.33%) and rig 2 +(15.90% segments). The percentage of segments labelled as +moving randomly is relatively low for the workers at the other +three rigs. The high percentage of moving randomly segments +for workers of the rig 1, 2, and 3 is due to the fact that they +start working earlier compared to the workers at rigs 4, 5, and +6. This is because workers at the later rigs require their +components to be built by the other rigs before they can +commence their tasks. This allows the workers at rig 1, 2, and +4 to complete their assign tasks earlier and visit outside +assembly area for taking break, meeting colleagues, etc. The +restocking is the least frequent activity shown by all workers, +1.53% to 6.73% segments are labelled as restocking. This is +expected since all the workstations hold the components they +require to assemble 3 tricycles. Workers are then required to +occasionally restock the parts until 6 tricycles are completed +within 3 hours. +For each trajectory 𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 +𝑊 we aim to develop a +separate semi-supervised classification model. To achieve this, +the spatial trajectory segments for each trajectory 𝑇𝑅𝑖 are +divided into 3 non-overlapping subsets: 𝑆𝐿, 𝑆𝑈, and 𝑆𝑇𝑒𝑠𝑡. 𝑆𝐿 +contains only very small proportion (20%) of trajectory +segments that are manually labelled. 𝑆𝑈 and 𝑆𝑇𝑒𝑠𝑡 respectively +contains 80% and 20% of the remaining segments. The +segments in 𝑆𝑈 are labelled using the constrained +agglomerative hierarchical clustering. The segments in both +𝑆𝐿and 𝑆𝑈 are used to train the classification model whereas the +segments in 𝑆𝑇𝑒𝑠𝑡 are used to evaluate the accuracy of the +classification model. +To evaluate the performance of the models we use two +different +metrics: +misclassification +rate +and +F-score. +Misclassification Rate (MCR) refers to the percentage of +observations +that +were +incorrectly +predicted +by +the +classification model. MCR has a range of 0 to 1: a lower value +of MCR indicates a higher accuracy. The F-score is a standard +measure for classification and is defined as in (7) for a binary +classification problem. For multi-class classification task as +ours, this is the average of the F-score of each class with +weighting determined by the number of observations in each +class. The F-score also has a range of 0 to 1, with 1 being the +most accurate classifier and 0 indicating the worst possible +0 +20 +40 +60 +80 +100 +TR1 +TR2 +TR3 +TR4 +TR5 +TR6 +Activity distribution (%) +moving between workstations +restocking +randomly moving +standing at workstation + +13 + +classifier. Although we present the numerical results using +both metrics, F-score will be considered as the primary metric +for analysis of prediction accuracy. + +𝐹𝑠𝑐𝑜𝑟𝑒 = 2 × +(𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ×𝑟𝑒𝑐𝑎𝑙𝑙) +(𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+𝑟𝑒𝑐𝑎𝑙𝑙) (7) +where precision is the fraction of observations that the +model classified as positive that were true positives and recall +refers to the fraction of true positive observations that the +model correctly classified as positive. + +TABLE III. ACCURACY OF THE SEMI-SUPERVISED APPROACH IN +TERMS OF THE F-SCORE AND MISCLASSIFICATION RATE +Trajectory +F-score +MCR +𝑇𝑅1 +0.81 +0.19 +𝑇𝑅2 +0.92 +0.08 +𝑇𝑅3 +0.85 +0.15 +𝑇𝑅4 +0.93 +0.07 +𝑇𝑅5 +0.95 +0.05 +𝑇𝑅6 +0.85 +0.15 + +TABLE III presents the classification accuracy evaluated on +the trajectory segments in 𝑆𝑇𝑒𝑠𝑡 for each trajectory 𝑇𝑅𝑖 in 𝒯 = +{𝑇𝑅𝑖}𝑖=1 +𝑊 . The classification accuracy (in terms of F-score) for +the trajectories generated by the workers at all rigs is 81% or +higher. The higher classification accuracy indicates the ability +of the proposed approach to classify the activities of the +workers with using only a small set of labelled segments. +Amongst the trajectories of all six workers, the trajectory for +the worker at rig 5 achieved the highest classification accuracy +followed by the trajectory for workers at rig 4 and 2, +respectively – their F-scores are above 90%. On the other +hand, the classification accuracy was lowest for the trajectory +of the worker at rig 1. The F-scores of the trajectories of two +other workers is 85% The main reason for relatively lower +accuracy for the trajectory of worker at rig 1 is the smaller +number of training samples used in 𝑆𝐿. There are 44 segments +in 𝑆𝐿 for trajectories of the worker at rig 1 compared 65 +segments in 𝑆𝐿 for trajectories of the worker at rig 2 for +example. The higher number of labelled segments in 𝑆𝐿 help +to generate pseudo labels with better accuracy confidence. For +example, the accuracy of the pseudo labels generated by the +hierarchical clustering is 80% and 90% for trajectories for +workers at rig 1 and 2, respectively. Using the more accurate +pseudo labels helps to train the final CNN models to better +learn the patterns which consequently reflected in the final +accuracy results. +Moreover, we reserve 20% of labelled segments into 𝑆𝐿 for +each trajectory as previously mentioned. These segments +(called seeds) are then used in the clustering phase to generate +pseudo labels for the segments in 𝑆𝑈. Hence, it is important to +check the influence this selection of labelled segments on the +performance of the semi-supervised classification model. We +repeated all the experiments with different proportions of +labelled data in 𝑆𝐿: 5% to 20% with 5% increments. Fig. 11 +presents the F-scores of the classification models with respect +to different proportions of segments in 𝑆𝐿 for each trajectory. +The classification accuracy of all trajectories monotonically +increases as the proportion of labelled segments in 𝑆𝐿 increase +from 5% to 20% The improvement in classification accuracy +is expected since a higher proportion of segments in 𝑆𝐿 +provides more information for the clustering algorithm to +exploit for pseudo label generation. In other words, more +manually labelled segments means availability of more +patterns of different activity types during clustering algorithm +which consequently helps to the clustering process to generate +more accurate the pseudo labels for segments in 𝑆𝑈. These +results provide more accurate training of the final prediction +models. + +Fig. 11. Classification accuracy (F-score) of the model with +different proportion of manually labelled segments in 𝑆𝐿 used +to generate pseudo labels for segment in 𝑆𝑈. + +The predicted labels of activities for the trajectory segments +can be used in diverse ways for decision making purposes. For +example, the distribution of activities of workers during their +shift (as shown in Fig. 9) can help to improve worker +productivity. As we can see, the worker at rig 1 spends second +highest proportion of time doing random movements. The +worker at rig 1 is the first person in the workflow and likely to +complete the assigned task before any of the other workers. +Moreover, from the data it is evident that worker at rig 1 +makes most of the random moves later part of shift. This time +can be better utilised doing productive work as decided by the +management. Similarly, the worker at rig 5 spends second +highest time on moving between workstations as per +distribution of activities in Fig. 9. If the movements are +happening to search for missing components or tools, those +can be made available at rig 5 to reduce the searching time. + +TABLE IV. CENTROIDS OF THE TEN CLUSTERS REPRESENTING +JOINT ACTIVITIES OF WORKERS. WE USE SHORT NAMES FOR +FOUR ACTIVITY CLASSES (STAND: STANDING AT WORKSTATION, +MOVE: MOVE BETWEEN WORKSTATIONS, RANDOM: RANDOMLY +MOVING, AND RESTOCK: RESTOCKING.) +Cluster +ID +Centroid [Concurrent activities of 6 workers] +1 +['stand', 'stand', 'stand', 'stand', 'stand', 'stand'] +2 +['stand', 'stand', 'stand', 'move', 'stand', 'stand'] +3 +['stand', 'stand', 'stand', 'stand', 'stand', 'move'] +4 +['stand', 'stand', 'move', 'stand', 'stand', 'stand'] +5 +['stand', 'stand', 'move', 'random', 'stand', 'stand'] +6 +['stand', 'random', 'random', 'stand', 'stand', 'stand'] +7 +[restock, 'stand', 'stand', 'stand', 'stand', 'stand'] +8 +['random', 'stand', 'stand', 'stand', 'stand', 'stand'] +9 +['move', 'stand', 'stand', 'stand', 'stand', 'stand'] +10 +['stand', 'stand', 'stand', 'stand', 'move', 'stand'] +0.00 +0.20 +0.40 +0.60 +0.80 +1.00 +TR1 +TR2 +TR3 +TR4 +TR5 +TR6 +F-score +5% +10% +15% +20% + +14 + + + +Fig. 12. Cluster (State) distribution of the joint activity data + +Another interesting inference that can be made from the +activity classification results is ‘factory floor state’. A state +can be defined in numerous ways. In this case, we refer to the +joint behaviour of workers as a state, i.e., what the workers are +doing concurrently. We clustered the joint activity class labels +of all six workers to obtain the factory floor state. TABLE IV +presents the centroids of the ten clusters obtained using K- +mode algorithm [62]. Fig. 12 shows the distribution of +clusters over joint activity data. Workers working at their +respective stations is the most common state (cluster 1) and it +constitutes 46.6% of the joint behaviour classes. The second +highest cluster observed is cluster 4 where most workers are at +their rigs except worker at rig 3 who is moving between +stations. We also observe a lot of movement of that worker +from rig 3 to rig 2 and this observation aligns well with the +workflow (see Fig. 1). The third most common state is when +most workers are at their rigs except the worker at rig 1 who is +moving randomly (cluster 8). As discussed previously, the +worker at rig 1 starts the assigned task at the beginning of the +workflow with no dependencies hence finishes work early and +moves randomly later while other workers are at their rigs. +Such state estimation through clustering can summarise +concisely what’s happening at the factory floor and can be +used for operational decision making. +VII. CONCLUSIONS +We presented an approach for human activity recognition +from noisy indoor trajectory data and studied its application in +manufacturing context. The proposed approach adopted the +concept of semi-supervised learning: generated pseudo labels +based on constraint hierarchical clustering and trained +convolutional neural networks as the classifiers that used the +trajectory segments as inputs and respective pseudo labels as +outputs. The approach is comprehensively evaluated using six +trajectories of human workers at a tricycle assembly +workshop. Results indicate that proposed approach can +accurately classify the activities of the workers at different +part of their trajectories – the classification accuracy in terms +of F-score varies between 0.81 to 0.95. Moreover, this +performance is achieved with small proportion of labelled +examples. The key advantage of this approach over existing +supervised activity recognition models is that it saves time and +resources required for manual labelling of input-output +examples by the domain experts. In addition, although the +approach is developed to identify four target activities +(standing at workstation, moving randomly, moving between +workstations, +restocking) +specific +to +manufacturing +environment, it is generic and can be applied to such other +activities as well. Future research will focus on applying the +approach on the trajectory datasets from other domains and +improving pseudo label generation process based on advanced +self-supervised methods. Another avenue of future work is +representing the segments using raster images overlayed on +factory layout and then classify them. + +REFERENCES +[1] +H. S. Kang et al., "Smart manufacturing: Past research, present +findings, and future directions," International Journal of Precision +Engineering and Manufacturing-Green Technology, vol. 3, pp. +111–128, 2016, doi: 10.1007/s40684-016-0015-5. +[2] +K. Nagorny, P. Lima-Monteiro, J. Barata, and A. W. Colombo, +"Big Data Analysis in Smart Manufacturing: A Review," +International Journal of Communications, Network and System +Sciences, +vol. +10, +no. +3, +pp. +31-58, +2017, +doi: +10.4236/ijcns.2017.103003. +[3] +J. A. Harding, M. Shahbaz, Srinivas, and A. Kusiak, "Data Mining +in Manufacturing: A Review," Journal of Manufacturing Science +and Engineering, vol. 128, no. 4, pp. 969-976, 2006, doi: +10.1115/1.2194554. +[4] +S.-K. S. Fan, C.-Y. Hsu, D.-M. Tsai, F. He, and C.-C. Cheng, +"Data-Driven Approach for Fault Detection and Diagnostic in +Semiconductor Manufacturing," IEEE Transactions on Automation +Science and Engineering, vol. 17, no. 4, pp. 1925 - 1936, 2020, +doi: 10.1109/TASE.2020.2983061. +[5] +A. Essien and C. Giannetti, "A Deep Learning Model for Smart +Manufacturing Using Convolutional LSTM Neural Network +Autoencoders," IEEE Transactions on Industrial Informatics, vol. +16, no. 9, pp. 6069 - 6078, 2020, doi: 10.1109/TII.2020.2967556. +[6] +L. Ren, Z. Meng, X. Wang, L. Zhang, and L. T. Yang, "A Data- +Driven Approach of Product Quality Prediction for Complex +Production +Systems," +IEEE +Transactions +on +Industrial +Informatics, vol. 19, no. 9, pp. 6457 - 6465, 2021, doi: +10.1109/TII.2020.3001054. +[7] +M. Syafrudin, G. Alfian, L. Fitriyani, and J. Rhee, "Performance +Analysis of IoT-Based Sensor, Big Data Processing, and Machine +Learning Model for Real-Time Monitoring System in Automotive +Manufacturing," Sensors, vol. 18, no. 9, p. 2946, 2018, doi: +10.3390/s18092946. +[8] +N. Sadati, R. B. Chinnam, and M. Z. Nezhad, "Observational data- +driven modeling and optimization of manufacturing processes," +Expert Systems with Applications, vol. 93, pp. 456-464, 2018, doi: +10.1016/j.eswa.2017.10.028. +[9] +Y. Zhang, S. Ren, Y. Liu, T. Sakao, and D. Huisingh, "A +framework for Big Data driven product lifecycle management," +Journal of Cleaner Production, vol. 159, pp. 229-240, 2017, doi: +10.1016/j.jclepro.2017.04.172. +[10] +A. Racz-Szabo, T. Ruppert, L. Bantay, A. Locklin, L. Jakab, and J. +Abonyi, "Real-Time Locating System in Production Management," +Sensors, vol. 20, pp. 1-21, 2020, doi: 10.3390/s20236766. +[11] +Y. Han, C. S. Tucker, T. W. Simpson, and E. Davidson, "A Data +Mining Trajectory Clustering Methodology for Modeling Indoor +Design Space Utilization " in International Design Engineering +Technical Conferences & Computers and Information in +Engineering +Conference +(IDETC/CIE), +USA, +2013, +doi: +10.1115/DETC2013-12690. +[12] +F. Tao, H. Zhang, A. Liu, and A. Y. C. Nee, "Digital Twin in +Industry: State-of-the-Art," IEEE Transactions on Industrial +Informatics, vol. 15, no. 4, pp. 2405 - 2415, 2019, doi: +10.1109/TII.2018.2873186. +[13] +Y. Cheng, L. Sun, C. Liu, and M. Tomizuka, "Towards Efficient +Human-Robot Collaboration With Robust Plan Recognition and +0 +10 +20 +30 +40 +50 +Cluster 1 +Cluster 2 +Cluster 3 +Cluster 4 +Cluster 5 +Cluster 6 +Cluster 7 +Cluster 8 +Cluster 9 +Cluster 10 +Proportion of joint activities +(%) + +15 + +Trajectory Prediction," IEEE Robotics and Automation Letters, +vol. +5, +no. +2, +pp. +2602 +- +2609, +2020, +doi: +10.1109/LRA.2020.2972874. +[14] +P. Baumgartner et al., "Movement Analytics: Current Status, +Application to Manufacturing, and Future Prospects from an AI +Perspective," +arXiv:2210.01344, +2022, +doi: +10.48550/arXiv.2210.01344. +[15] +J. Yin, Q. Yang, and J. J. Pan, "Sensor-Based Abnormal Human- +Activity Detection," IEEE Transactions on Knowledge and Data +Engineering, vol. 20, no. 8, pp. 1082 - 1090, 2008, doi: +10.1109/TKDE.2007.1042. +[16] +F. A. Machot, A. H. Mosa, M. Ali, and K. Kyamakya, "Activity +Recognition in Sensor Data Streams for Active and Assisted +Living Environments," IEEE Transactions on Circuits and Systems +for Video Technology, vol. 28, no. 10, pp. 2933 - 2945, 2018, doi: +10.1109/TCSVT.2017.2764868. +[17] +M. Paolanti, D. Liciotti, R. Pietrini, A. Mancini, and E. Frontoni, +"Modelling and Forecasting Customer Navigation in Intelligent +Retail Environments," Journal of Intelligent & Robotic Systems, +vol. 91, pp. 165–180, 2018, doi: 10.1007/s10846-017-0674-7. +[18] +T. Nakahara and K. Yada, "Analyzing consumers’ shopping +behavior using RFID data and pattern mining," vol. 6, pp. 355– +365, 2012, doi: 10.1007/s11634-012-0117-z. +[19] +M. Gochoo, T.-H. Tan, S.-H. Liu, F.-R. Jean, F. S. Alnajjar, and +S.-C. Huang, "Unobtrusive Activity Recognition of Elderly People +Living Alone Using Anonymous Binary Sensors and DCNN," +IEEE Journal of Biomedical and Health Informatics, vol. 23, no. 2, +pp. 693 - 702, 2019, doi: 10.1109/JBHI.2018.2833618. +[20] +M. Gochoo, T.-H. Tan, S.-C. Huang, S.-H. Liu, and F. S. Alnajjar, +"DCNN-based elderly activity recognition using binary sensors," +in International Conference on Electrical and Computing +Technologies and Applications (ICECTA), 2017: IEEE, doi: +10.1109/ICECTA.2017.8252040. +[21] +Y. Asakuraa and T. Iryo, "Analysis of tourist behaviour based on +the tracking data collected using a mobile communication +instrument," Transportation Research Part A: Policy and Practice, +vol. 41, no. 7, pp. 684-690, 2007, doi: 10.1016/j.tra.2006.07.003. +[22] +M. Arslan, C. Cruz, and D. Ginhac, "Understanding Worker +Mobility within the Stay Locations using HMMs on Semantic +Trajectories," +in +International +Conference +on +Emerging +Technologies +(ICET), +2018: +IEEE, +doi: +10.1109/ICET.2018.8603666. +[23] +M. H. Arshad, M. Bilal, and A. Gani, "Human Activity +Recognition: Review, Taxonomy and Open Challenges," Sensors, +vol. 22, no. 17, 2022, doi: 10.3390/s22176463. +[24] +J. Wang, Y. Chen, S. Hao, X. Peng, and L. Hu, "Deep learning for +sensor-based activity recognition: A survey," Pattern Recognition +Letters, +vol. +191, +no. +1, +pp. +3-11, +2019, +doi: +10.1016/j.patrec.2018.02.010. +[25] +C. Dhimana and D. K. Vishwakarm, "A review of state-of-the-art +techniques for abnormal human activity recognition," Engineering +Applications of Artificial Intelligence, vol. 77, pp. 21-45, 2019, +doi: 10.1016/j.engappai.2018.08.014. +[26] +Y. Cheng, K. Chen, H. Sun, Y. Zhang, and F. Tao, "Data and +knowledge mining with big data towards smart production," +Journal of Industrial Information Integration, vol. 1, pp. 1-13, +2018, doi: 10.1016/j.jii.2017.08.001. +[27] +W. Ji and L. Wang, "Big data analytics based fault prediction for +shop floor scheduling," Journal of Manufacturing Systems, vol. 43, +no. 1, pp. 187-194, 2017, doi: 10.1016/j.jmsy.2017.03.008. +[28] +F. Tao, Q. Qi, A. Liu, and A. Kusiak, "Data-driven smart +manufacturing," Journal of Manufacturing Systems, vol. 48, no. C, +pp. 157-169, 2018, doi: 10.1016/j.jmsy.2018.01.006. +[29] +I. Arkan and H. V. Landeghem, "Evaluating the performance of a +discrete manufacturing process using RFID: A case study," +Robotics and Computer-Integrated Manufacturing, vol. 19, no. 6, +pp. 502-512, 2013, doi: 10.1016/j.rcim.2013.06.003. +[30] +D. Gyulai, A. Pfeiffer, and J. Bergmann, "Analysis of asset +location data to support decisions in production management and +control," in CIRP Conference on Intelligent Computation in +Manufacturing +Engineering, +Italy, +2019, +doi: +10.1016/j.procir.2020.05.035. +[31] +A. Löcklin, T. Ruppert, L. Jakab, R. Libert, N. Jazdi, and M. +Weyrich, "Trajectory Prediction of Humans in Factories and +Warehouses with Real-Time Locating Systems," in IEEE +International Conference on Emerging Technologies and Factory +Automation +(ETFA), +Austria, +2020, +doi: +10.1109/ETFA46521.2020.9211913. +[32] +J. Zhang, H. Liu, Q. Chang, L. Wang, and R. X. Gao, "Recurrent +neural network for motion trajectory prediction in human-robot +collaborative assembly," CIRP Annals, vol. 69, no. 1, pp. 9-12, +2020, doi: 10.1016/j.cirp.2020.04.077. +[33] +P. Wang, J. Yang, and J. Zhang, "Location Prediction for Indoor +Spaces based on Trajectory Similarity," in ACM International +Conference on Data Science and Information Technology (DSIT), +China, 2021, pp. 402–407, doi: 10.1145/3478905.3478983. +[34] +J. Sander, M. Ester, H.-P. Kriegel, and X. Xu, "Density-Based +Clustering in Spatial Databases: The Algorithm GDBSCAN and Its +Applications," Data Mining and Knowledge Discovery, vol. 2, pp. +169–194, 1998, doi: 10.1023/A:1009745219419. +[35] +H. Cai, Y. Guo, W.-A. Yang, and K. Lu, "Mining frequent +trajectory patterns of WIP in Internet of Things-based spatial- +temporal database," International Journal of Computer Integrated +Manufacturing, vol. 30, no. 12, pp. 1253–1271, 2017, doi: +10.1080/0951192X.2017.1307522. +[36] +R. Agrawal, H. Mannila, R. Srikant, H. Toivonen, and A. I. +Verkamo, "Fast discovery of association rules," Advances in +knowledge discovery and data mining, vol. 12, no. 1, pp. 307-328., +1996. +[37] +F. Bu, "A Data Mining Framework for Massive RFID Data Based +on Apriori Algorithm," Journal of Physics: Conference Series, vol. +1087, no. 2, 2020, doi: 10.1088/1742-6596/1087/2/022020. +[38] +A. Alahi, K. Goel, V. Ramanathan, A. Robicquet, L. Fei-Fei, and +S. Savarese, "Social LSTM: Human Trajectory Prediction in +Crowded Spaces," in IEEE Conference on Computer Vision and +Pattern Recognition (CVPR), 2016. +[39] +L. C. Shum et al., "Indoor Location Data for Tracking Human +Behaviours: A Scoping Review," Sensors, vol. 22, no. 3, 2022, doi: +10.3390/s22031220. +[40] +M. Gochoo, S.-H. Liu, D. Bayanduuren, T.-H. Tan, V. Velusamy, +and T.-Y. Liu, "Deep convolutional neural network classifier for +travel patterns using binary sensors," in International Conference +on Awareness Science and Technology (iCAST), 2017: IEEE, doi: +10.1109/ICAwST.2017.8256432. +[41] +X. Fang, F. Lu, X. Chen, and X. Huang, "Accurate Indoor +Positioning Prediction Using the LSTM and Grey Model," in +International +Conference +on +Web +Information +Systems +Engineering, 2020, doi: 10.1007/978-3-030-62005-9_26. +[42] +J. G. Yu, B. Selby, N. Vlahos, V. Yadav, and J. Lemp, "A feature- +oriented vehicle trajectory data processing scheme for data mining: +A +case +study +for +Statewide +truck +parking +behaviors," +Transportation Research Interdisciplinary Perspectives, vol. 11, +2021, doi: 10.1016/j.trip.2021.100401. +[43] +P.-R. Lei, "A framework for anomaly detection in maritime +trajectory behavior," Knowledge and Information Systems, vol. 47, +pp. 189–214, 2016, doi: 10.1007/s10115-015-0845-4. +[44] +K. Chatzikokolakis, D. Zissis, G. Spiliopoulos, and K. Tserpes, +"Mining Vessel Trajectory Data for Patterns of Search and +Rescue," in EDBT/ICDT Workshops, 2018. +[45] +J. Kima and H. S. Mahmassani, "Spatial and Temporal +Characterization of Travel Patterns in a Traffic Network Using +Vehicle Trajectories," Transportation Research Procedia, vol. 9, +pp. 164-184, 2015, doi: 10.1016/j.trpro.2015.07.010. +[46] +X. Song, H. Kanasugi, and R. Shibasaki, "Deeptransport: +prediction and simulation of human mobility and transportation +mode at a citywide level," in International Joint Conference on +Artificial Intelligence (IJCAI), 2016. +[47] +Y. Liu, Y. Zhao, L. Chen, J. Pei, and J. Han, "Mining Frequent +Trajectory Patterns for Activity Monitoring Using Radio +Frequency Tag Arrays," IEEE Transactions on Parallel and +Distributed Systems, vol. 23, no. 11, pp. 2138-2149, 2012, doi: +10.1109/TPDS.2011.307. +[48] +M. Delamare, F. Duval, and R. Boutteau, "A New Dataset of +People Flow in an Industrial Site with UWB and Motion Capture +Systems," +Sensors, +vol. +20, +no. +16, +2020, +doi: +doi.org/10.3390/s20164511. +[49] +M. Delamare, F. Duva, and R. Boutteau. Dataset of person flows +during an assembly phase in an industrial site with an UWB +system in NLOS and a motion capture system. [Online]. Available: +https://github.com/vauchey/IndoorInsdustrialLocalisationDataset/ + +16 + +[50] +P. Merriaux, Y. Dupuis, R. Boutteau, P. Vasseur, and X. Savatier, +"A study of vicon system positioning performance," Sensors, vol. +17, no. 7, 2017, doi: 10.3390/s17071591. +[51] +A. Krizhevsky, I. Sutskever, and G. E. Hinton, "Imagenet +classification with deep convolutional neural networks," in +International Conference on Neural Information Processing +Systems (NIPS), 2012, doi: 10.1145/3065386. +[52] +A. Borovykh, S. Bohte, and C. W. Oosterlee, "Conditional Time +Series Forecasting with Convolutional Neural Networks," +arXiv:1703.04691v5, 2018, doi: 10.48550/arXiv.1703.04691. +[53] +G. Hinton et al., "Deep neural networks for acoustic modeling in +speech recognition: The shared views of four research groups," +IEEE Signal Processing Magazine, vol. 26, no. 6, pp. 82 - 97, +2012. +[54] +K. O'Shea and R. Nash, "An Introduction to Convolutional Neural +Networks," +arXiv:1511.08458, +2015, +doi: +10.48550/arXiv.1511.08458. +[55] +P. Grunwald, I. Myung, and M. Pitt, Advances in minimum +description length: Theory and applications. MIT press, 2005. +[56] +J.-G. Lee, J. Han, and K.-Y. Whang, "Trajectory clustering: a +partition-and-group framework," presented at the ACM SIGMOD +international conference on Management of data, China, 2007. +[57] +Y. Tao et al., "A comparative analysis of trajectory similarity +measures," GIScience & Remote Sensing vol. 58, no. 5, pp. 643– +669, 2021, doi: 10.1080/15481603.2021.1908927. +[58] +S. Wang, Z. Bao, J. S. Culpepper, and G. Cong, "A survey on +trajectory data management, analytics, and learning," ACM +Computing Surveys, vol. 54, no. 2, pp. 1–36, 2022, doi: +10.1145/3440207. +[59] +K. Marussy and K. Buza, "SUCCESS: A New Approach for Semi- +supervised Classification of Time-Series," in International +Conference on Artificial Intelligence and Soft Computing +(ICAISC), 2013, vol. 7894: Springer, in Lecture Notes in Computer +Science: Artificial Intelligence and Soft Computing, doi: +10.1007/978-3-642-38658-9_39. +[60] +D. P. Kingma and J. Ba, "Adam: A method for stochastic +optimization," arXiv preprint arXiv:1412.6980, 2014, doi: +10.48550/arXiv.1412.6980. +[61] +N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. +Salakhutdinov, "Dropout: A Simple Way to Prevent Neural +Networks from Overfitting," The journal of machine learning +research, vol. 15, no. 1, pp. 1929-1958, 2014. +[62] +W. W. Miguel A Carreira Perpinan, "The K-modes algorithm for +clustering," +arXiv:1304.6478, +2013, +doi: +10.48550/arXiv.1304.6478. + + + + diff --git a/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/load_file.txt b/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..bccfb7fdedce20834c72db936485cba25bdc98f2 --- /dev/null +++ b/I9E1T4oBgHgl3EQfYAS9/content/tmp_files/load_file.txt @@ -0,0 +1,1343 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf,len=1342 +page_content='1 A Semi-supervised Approach for Activity Recognition from Indoor Trajectory Data Mashud Rana, Ashfaqur Rahman, and Daniel Smith Abstract—The increasingly wide usage of location aware sensors has made it possible to collect large volume of trajectory data in diverse application domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Machine learning allows to study the activities or behaviours of moving objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', people, vehicles, robot) using such trajectory data with rich spatiotemporal information to facilitate informed strategic and operational decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this study, we consider the task of classifying the activities of moving objects from their noisy indoor trajectory data in a collaborative manufacturing environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Activity recognition can help manufacturing companies to develop appropriate management policies, and optimise safety, productivity, and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We present a semi- supervised machine learning approach that first applies an information theoretic criterion to partition a long trajectory into a set of segments such that the object exhibits homogeneous behaviour within each segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The segments are then labelled automatically based on a constrained hierarchical clustering method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Finally, a deep learning classification model based on convolutional neural networks is trained on trajectory segments and the generated pseudo labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The proposed approach has been evaluated on a dataset containing indoor trajectories of multiple workers collected from a tricycle assembly workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The proposed approach is shown to achieve high classification accuracy (F-score varies between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='81 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='95 for different trajectories) using only a small proportion of labelled trajectory segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Index Terms—Activity recognition, behaviour classification, trajectory analytics, smart manufacturing, deep learning, semi- supervised model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' INTRODUCTION ANUFACTURING systems form a vital part of the society and economy, providing jobs to workers and products to consumers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The manufacturing industry is continuously developing new initiatives (such as Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0, Industrial Internet) to transform traditional manufacturing paradigms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Smart manufacturing is a technology-driven approach to improve various factors affecting the performance of manufacturing systems through the integration of sensor data, analytics and automation [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The computational analysis of data streams collected from This research was supported by the Future Digital Manufacturing Fund (FDMF) at Data61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Thanks to Reena Kapoor, Peter Baumgartner, and Elena Tartaglia for providing feedback on different sections of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mashud Rana, Ashfaqur Rahman, and Daniel Smith are with Data61, CSIRO, Australia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Emails: mdmashud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='rana@data61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='csiro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='au, ashfaqur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='rahman@data61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='csiro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='au, daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='smith@data61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='csiro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Internet of Things (IoT) based sensors at various stages of production enables evidence-based decision making, and provides a systematic way to monitor and improve manufacturing systems [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Numerous studies investigated the diverse machine learning and data mining techniques for analysing heterogenous data for a great variety of manufacturing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A few prominent applications include fault detection and diagnostic [4], predictive analytics [5], quality control and monitoring [6], efficiency monitoring [7], process optimisation [8], product life cycle management [9], workflow evaluation [10], indoor space modelling [11], streamlining supply chains [12], and safety [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Most of these studies primarily focused on utilising the data collected from workstations or equipment via accelerometers, gyroscopes, magnetometers etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, many of the key dynamics of a manufacturing process can be observed from trajectory data that has been collected by using tracking devices attached to entities or objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Trajectory data consists of the spatial coordinates of an object as a function of time as well as the features describing the object that is being tracked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In a manufacturing system, the movement of materials, vehicles, products, logistics, tools, and workers can be used to determine its current state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Translating these observations into meaningful insights is the realm of movement analytics [14], where machine learning and other statistical methods are used to uncover object semantics based on its movement patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this study, we are interested in a specific aspect of movement analytics, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', activity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Activity recognition is generally defined as the task of identifying the actions of objects from a series of motion related measurements captured by sensors [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' It can play a vital role to identify inefficiencies or bottlenecks within manufacturing processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' It also helps to identify the possible reasons behind the deviation of the relevant entities from their expected behaviours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The decision makers can use this information to develop appropriate management policies, and optimise the safety, productivity, and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For example, a worker may move back and forth between workstations for several reasons including delivery of items produced to co- workers for subsequent processing, finding misplaced or missing tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Obviously, it is a problematic activity and indicative of operational inefficiencies if the visits are related to searching for misplaced tools or components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, identifying which tools or workstations are involved in these activities could help to identify the problems within the manufacturing process which is a prerequisite for improving operational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' M 2 Although activity recognition has widespread application across different fields (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', retail ([17, 18]), health [19, 20]), tourism [21], construction [22]), it has rarely been studied with respect to manufacturing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Several studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', [23-25]) provide insights on the current state of the literature to detect, recognize, and monitor activities utilising diverse datasets and methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The two main approaches for activity recognition are either vision-based or sensor-based [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Vision-based approaches utilise cameras to passively capture video of the entities of interest, while sensor-based approaches commonly use time series from motion sensors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', accelerometers, gyroscopes) attached to the entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In contrast to most of these previous studies, we aim to develop a model for human activity recognition using spatiotemporal trajectories acquired with sensor-based localisation technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Activity recognition especially from indoor trajectory data is challenging due to spontaneous nature of human movement within a limited indoor space [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In contrast to outdoor trajectory data of the objects moving over large geographical area (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', vehicle or tourist trajectories in cities, vessels trajectories in oceans), indoor trajectory covers a small area with overlaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The frequent movement of human within a small indoor area makes the indoor trajectory data noisy and difficult to model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, majority of activity recognition approaches use supervised machine learning models, which rely upon large sets of labelled data (ground truth) for the training of classification models [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Generating labelled datasets is a labour intensive and costly process that can be a major bottleneck for using supervised machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For activity recognition, it is often unwieldly to manually label the large number of segments pertaining to the different activities that may be present across time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, in this study we adopt semi-supervised learning, which only requires fewer labelled segments as examples to train the activity recognition model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Specifically, our contributions in this paper can be summarised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We develop an approach for human activity recognition from spatiotemporal trajectory data in an indoor environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The proposed approach consists of three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Firstly, each complete trajectory is partitioned into a set of segments by optimising an information coding metric, the minimum description length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Partitioning allows to identify and classify the different activities of a worker across different time periods of their work shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Secondly, the pseudo labels of the trajectory segments were then generated based on a constrained hierarchical clustering which requires a small set of labelled segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Finally, a Convolutional Neural Network (CNN) based deep learning model is trained using the pseudo labels of the trajectory segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The model was then used to classify the raw trajectories into a sequence of worker activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' While the different components of the developed approach (like trajectory partitioning, clustering, convolutional neural networks) are all well-known, we emphasise that the overall architecture combining these components is new for semi-supervised activity recognition especially utilising indoor trajectory data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We evaluate the proposed approach by using a dataset of workers’ trajectories that were collected with a motion capture positioning system during a tricycle assembly process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We aim to identify a set of target activities specific to the manufacturing working environment: standing at workstation, moving randomly, moving between workstations, restocking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' However, we note that our approach is generic and can be applied to such other activities as well, thus preserving the motivation for helping improve operational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This study is the first of its kind to design and develop a semi- supervised machine learning activity recognition model based on indoor trajectory data for manufacturing application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' RELATED WORK The technological innovations in tracking systems and IoT based sensors have made it possible to collect data from moving objects over space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In the era of cyber- physical systems, machine learning has been an integral part of smart manufacturing to develop analytics utilising such data for intelligent decision making [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Numerous studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', [6, 7, 26-28]) in the literature investigated the application of machine learning to support different applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this section, we review previous research related to the application of machine learning in manufacturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Whilst reviewing the literature, we limit the scope to movement analytics in the manufacturing domain and activity recognition in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Movement Analytics in Manufacturing Movement analytics (also known as trajectory data analytics) refers to the process of extraction and utilisation of knowledge from tracking data for providing meaningful solutions to decision makers [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The spatiotemporal tracking data can be utilised for optimising the production processes in manufacturing and developing domain specific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Szabo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [10] studied the feasibility of different Real Time Locating Systems (RTLS) for capturing location data of moving objects to support different applications in manufacturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' They also presented a use case to identify the bottlenecks in defined production zones and measure cycle time deviation at the workstations in an automotive company.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To identify the bottlenecks (in terms of temporary storage or unplanned workstations in the production process), they grouped the position data by applying the k-means clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The cycle time of workstations was measured based on classified zone data that were visualized later to provide real-time status of the production process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Arkan and Van Landeghem [29] considered improving Work-in-Process (WIP) visibility in the semi-automated shop floor of an automotive manufacturing company.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' They utilised the spatiotemporal data collected with RTLS from a multi-item production line to compute a set of Key Performance Indicators (KPIs) such as cycle time, cycle speed, production time, defect reject ratio and workspace utilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These KPIs were then analysed to evaluate the existing workflow and redesign the floor with a simulation tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Similarly, Gyulai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [30] developed analytics to compute KPIs (from simulated trajectory data) to evaluate the performance of a production system and facilitate the implementation of situation aware production control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3 Moreover, different objects are likely to work together in a collaborative manufacturing environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Therefore, it is important for the objects to efficiently and accurately identify the task plans of others and respond in a safe manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [13] presented an analytics framework to predict human trajectories and to infer the work plan to facilitate safe and effective collaboration between objects (human and robots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A Long Short-Term Memory (LSTM) recurrent networks was used to model the temporal dynamics of sequential movement data and Bayesian inference method was applied to infer the potential plans of workers utilising LSTM based predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Locklin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [31] also predicted future positions of human trajectories by fitting a second degree polynomial function to historical location data to enable collaboration amongst a large number of workers in the indoor space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [32] proposed an LSTM based method to predict the future motion trajectory of human operators for facilitating a robot’s action planning and execution in a car engine assembly factory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [33] proposed a similarity based model for trajectory prediction within indoor spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Specifically, they applied the k-Nearest Neighbours (kNN) algorithm to find a trajectory from the database that was most similar to the given trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The next location of the given trajectory was then predicted from the path of similar trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The main novelty of this model was the formulation of a distance metric that considered both the spatial and semantic distance between trajectories, which were computed based on the longest common sub sequences and dynamic time warping, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Furthermore, the optimal utilisation of available indoor space (such as shop floor, production floor, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=') is vital for mass production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Movement data can be used to understand the geospatial interaction patterns between objects, and hence, helps to design more efficient factory layouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [11] presented a method to study indoor space utilisation based on the common movement patterns in the trajectory data of multiple users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' They first partitioned each trajectory into a set of segments by optimising an information theoretic criterion and then grouped the segments from all of the trajectories into a set of clusters by applying the GDBSCAN algorithm [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The clustering results were used to identify heavily utilised regions and visualize the evolution of utilisation over time for the better design of indoor spaces in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Additionally, Cai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [35] proposed a spatiotemporal data model for monitoring IoT enabled production systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Their model combined the principle of the Apriori algorithm [36] and depth first search to find the frequent trajectory patterns of WIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bu [37] also described a framework based on the Apriori algorithm to mine frequent path patterns from the massive amounts of tracking data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This enabled material flow paths to be adjusted and helped to reschedule the route of automatic guided vehicle robots in a production environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Activity Recognition Recognising the activities of objects (people, vehicles, robots) is a key factor in developing appropriate strategies for industrial applications in many domains including but not limited to retail ([17, 18]), health ([19, 20]), construction ([22]) and transport ([38]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Shum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [39] reviewed utilisation of different types of tracking data collected in variety of domains for human activity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Arslan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [22] developed a model for workers’ activity recognition at hazardous construction sites for improving safety management strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The raw GPS data was transformed into semantic trajectories to label mobility related activities in terms of their building environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A Hidden Markov Model (HMM) was then trained using the semantic trajectories to classify the mobility patterns of workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Polanti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [17] developed an intelligent system to improve the shopping experience by utilising the movement trajectories of customers in retail environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A HMM was trained with the shopping trajectories of customers in order to predict the customer’s future shopping preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The system then presented a route map to direct customers to their preferred products in the retail store.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Alahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [38] proposed social LSTM, a model to predict human movement within crowds utilising their spatial trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Given the motion of individuals within a crowded space are affected by the behaviour of others, the social LSTM architecture modelled these spatial interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The movement of individuals were represented by separate LSTMs and a shared pooling layer was used to connect the latent states of all the individuals (their LSTMs) within the crowded space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The social LSTM was then used to predict the future movement of individuals and groups of individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Several studies investigated activity recognition from indoor tracking data to detect early symptoms of abnormal behaviours or health risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gochoo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [19] presented a non- obtrusive activity recognition model for elderly people living alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The indoor tracking data of individuals was converted into two-dimensional activity images that were then used to train a Deep Convolutional Neural Network (DCNN) with a predefined set of home activity classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The application of DCNN and other machine learning models including Random Forest (RF) and Gradient Boosting (GBM) were also investigated in [40] for the detection of dementia related behaviours of elderly people using movement data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Similarly, Fang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [41] identified abnormal behaviour patterns linked with different health risks in order to prevent their occurrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A hybrid model based on an LSTM and Grey Model was proposed using the past movement data of an individual to predict their future location and activity class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In contrast to the continuous valued position data considered in our study, the trajectory data used in [19, 40, 41] consists of binary on/off signals from a set of fixed indoor sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [42] presented a feature-oriented method for identifying truck parking behaviours from the vehicle’s trajectory data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The raw GPS trajectories were processed to extract a set of exploratory features and then association rule mining was applied to the extracted features to identify legal and illegal parking patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lei [43] described a framework to identify the anomalous behaviour of vessels travelling in maritime space from their trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The framework mapped the trajectories into spatial regions by applying a grid based clustering algorithm and then extracted features reflecting the 4 spatial, sequential, and behavioural characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The movement behaviours of the vessels were then classified using a probabilistic suffix tree which utilised those features as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Likewise, Chatzikokolakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [44] applied RF model on vessels trajectories to identify search and rescue activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [45] developed a clustering based method to discover travel patterns utilising vehicle trajectory data in a traffic network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The vehicle trajectories were first grouped by applying a density based clustering algorithm using the Longest Common Subsequence (LCS) distance metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The overlapping LCS from all the clusters were then merged using hierarchical clustering to generate travel patterns representative of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' New trajectories were then classified by matching them against the clusters of representative travel patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [46] presented a deep recurrent neural network architecture to simultaneously solve multiple learning tasks using spatial trajectories across large scale transportation networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The future motion of an individual and their transportation mode were simultaneously predicted using a hierarchical network of LSTMs that represent motion across different temporal scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Two LSTM based encoders were utilised to represent the inputs of each task separately, two LSTMs were used to create a shared feature representation and a pair of LSTM decoders that were used to generate the outputs of each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Summary Trajectory data can play a vital role in smart and adaptive manufacturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' However, the above review indicates recent activity recognition methods utilising tracking data have not been well studied in the context of manufacturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The existing studies primarily utilised trajectory data for workflow evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' There exists many applications that required regular monitoring of activities or understanding the behaviours of moving objects [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A few examples of such applications include: i) monitoring suspicious activities in large industrial workshops or chemical plants for security purposes, ii) identifying when a worker interacted with other workers to avoid spreading infectious diseases (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', COVID) and loss of workforce, iii) understanding why and to what extent a worker deviated from their intended workflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, while numerous research investigated utilisation of outdoor trajectory data (collected using GPS) for different applications, activity recognition based on indoor tracking data is not sufficiently studied especially for manufacturing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Indoor tracking data covers small area with overlaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Contrast to outdoor trajectories that are relatively smoothed, the segments of indoor trajectories are significantly shorter and noisy that make the activity recognition task very difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Given most of the existing methods for activity recognition are supervised, they are not well suited to manufacturing applications due to the difficulties in collecting labelled activity data in such contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, it is also important to explore the feasibility of semi-supervised methods on indoor tracking data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this study, we aim to address these deficits in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' DATASET The indoor tracking dataset used in study was collected from a tricycle assembly workshop [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The workshop consists of multiple workstations and provides a dynamic environment for the workers during the assembly process with various representative industrial scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The dataset is publicly available at [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Expected workflow of the people at the tricycle assembly workshop which consists of several workstations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1 shows the arrangement of the workstations of the tricycle assembly line and the expected movement scenarios of the people across the workstations during the assembly process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' There are six workstations (also called rigs) in the assembly line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at each workstation is responsible for building certain parts of a tricycle and concurrently works in a collaborative manner with others during the assembly process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 1 prepares the lower frame of tricycles and delivers it to the worker at rig 2 who assembles the axle with the lower frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 3 builds the saddle and pedal board, and then supplies these components to the worker at rig 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 4 builds the rear wheel axle unit by assembling the units built by the workers at rigs 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 5 assemble the front wheel axle unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Finally, both the front wheel axle and rear wheel axle units are assembled to finalise the tricycle construction by the worker at rig 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 记 记 记 记5 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The processed tracking data of the workers at the 10×9 square meters tricycle assembly workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The shaded area (■) indicate the work zone where the workstations are placed, and the colors of the trajectory lines indicate data collection time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Six tricycles are expected to be built within three hours of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The workstations can hold the components required for the assembly of three tricycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, the workers need to restock the required components from the storage area when initial stocking is finished after the first round of work, or if there are any missing components or tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' During the assembly process each person is responsible for the pre- assigned task, can go to help co-workers or take breaks as necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For more details on the site setup and data collection procedure, we refer to the previous study [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Distribution (%) of the spatial points for six trajectories at the tricycle assembly workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Movement data of the workers in the workshop were recorded using a Motion Captured (MoCap) system [50] for 3 hours of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mocap systems provides better indoor ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='positioning ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='accuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='compared ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='to ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='other ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='available ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Tracjectory1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Tracjectory2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Tracjectory3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Tracjectory5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Tracjectory ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='x (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='X (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='X (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='start ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='end ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='datacollectiontimeRig1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Rig2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Rig3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='(w) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='F 10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Rig4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Rig5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='Rig6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='OE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='(w) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='> ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='X (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='X (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='X (m)6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The interval between consecutive data samples varies between 10 to 100 milliseconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We down sample the raw trajectory data for each worker to 1 sample per second to synchronise the interval between successive samples and reduce the number of missing samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2 shows the processed trajectory data of each worker during the entire data collection period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The tracking data shows that the workers deviate from their planned movement protocol and visit locations outside of the defined assembly zones as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These deviations could be associated with taking a break or other unknown behaviours (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', activity of moving randomly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Factory layout based on distribution of spatial points and site information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, we analyse the spatial distribution of worker positions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3) to identify the approximate location of the workstations and map them into a factory layout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The factory layout is required to manually label the different trajectory segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For each worker, the location of the workstation is determined as the point of maximum density within the distribution of the worker’s spatial positions over time, since each worker should spend majority of his/her time at the designated workstation to finish the assigned task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4 presents the approximate layout of the tricycle assembly line based upon the spatial distribution of the workers’ trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As it shows, the six rigs are placed to make the interactions or collaborations among the workers easy by following the expected movement scenarios shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' BACKGROUND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Definitions Trajectory: a trajectory of an object or entity is an ordered sequence of location points and is denoted as: 𝑇𝑅 = {(𝑝1, 𝑡1), (𝑝2, 𝑡2), … , (𝑝𝑁, 𝑡𝑁) } ∶ 𝑡𝑖−1 < 𝑡𝑖, 𝑖 = 2, … , 𝑁, where 𝑝𝑖 (1≤𝑖≤𝑁) ∈ 𝑅𝑑 is a multidimensional vector of spatial location information of the object at timestamp 𝑡𝑖 and 𝑁 is the total number of location points in 𝑇𝑅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In the simplest form, 𝑝𝑖 (1≤𝑖≤𝑁) ∈ 𝑅𝑑 represents the object’s location in a two dimensional plane at timestamp 𝑡𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' However, the dimension of the vector 𝑝𝑖 can be extended further by adding more features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', third spatial dimension, velocity, acceleration, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=') depending on the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sub-trajectory: a sub-trajectory or trajectory segment of a trajectory 𝑇𝑅 is a subset of time ordered spatial location points in 𝑇𝑅 and is denoted as: 𝑆𝑈𝐵𝑇𝑅 = {(𝑝𝑘, 𝑡𝑘), (𝑝𝑘+1, 𝑡𝑘+1), … , (𝑝𝑘+𝑛, 𝑡𝑘+𝑛) } ∶ 𝑡𝑘 < 𝑡𝑘+1, 1 ≤ 𝑘 < 𝑛 ≤ 𝑁 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The straight line joining the two endpoints (𝑝𝑘, 𝑝𝑘+𝑛) of 𝑆𝑈𝐵𝑇𝑅is called a trajectory partition of 𝑇𝑅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Problem Statement Given a set of trajectories 𝒯 = {𝑇𝑅1, 𝑇𝑅2, … , 𝑇𝑅𝑊}, where each trajectory represents the movement patterns of an object in an indoor manufacturing environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For each trajectory 𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 𝑊 , the goal is to partition the trajectory into a set of non-overlapping segments and then classify each segment as a category from a set of four predefined activities: [𝑚𝑜𝑣𝑖𝑛𝑔 𝑟𝑎𝑛𝑑𝑜𝑚𝑙𝑦, 𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑡 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛, 𝑚𝑜𝑣𝑖𝑛𝑔 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑠, 𝑟𝑒𝑠𝑡𝑜𝑐𝑘𝑖𝑛𝑔].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The activity of an object is labelled as ‘moving randomly’ for the duration of a trajectory segment if the object moves outside the work zone (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', outside of the tricycle assembly area as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4) for a different purpose such as taking a break, meeting others, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ‘Standing at workstation’ indicates that the object is busy at the designated workstation to finish the assigned tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ‘Moving between workstations’ represents the collaborative behaviour – a worker may visit other workstations to deliver the products (or components) built according to the workflow or help co-workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Finally, ‘restocking’ refers to the activity of visiting storage area if the stock required to complete the assigned task at a workstation is finished, or when searching for tools or component if they are not available at the workstation as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In a typical manufacturing setting, many objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', workers, AVG, robots, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=') work collaboratively in a dynamic environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Each of these objects generate its own trajectory over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Segmenting each of the trajectories and labelling them manually are not feasible since it requires time, resources, and expertise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this study, we aim to automatically segment the trajectories by identifying a set of changepoints (or characteristic points) and then develop a semi-supervised model that required only few labelled segments (can be as low as one labelled segment for each category of the activities or behaviours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Constrained Hierarchical Clustering Clustering is the process of grouping the samples (or observations) in a dataset such that the samples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', trajectory segments in our case) within the same group (called a cluster) are similar to one another and dissimilar to the samples in other groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Agglomerative hierarchical clustering initially assigns each data sample into a separate cluster and then successively merges them using a bottom-up approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In each iteration, the two closest or most similar pair of clusters are merged into a single cluster where the closeness or similarity is measured based on a linkage criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Single link refers to distance between the two nearest samples whereas 10 storage area outerzone work zone 8 Rig1 Rig6 6 Rig2 (w), Rig5 4- Rig3 Rig4 2 outerzone 0 + 0 1 2 m 4 5 6 7 00 X (m)7 complete link refers to the distance between the two farthest samples as the similarity between two clusters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Average link considers the average of the distances of each pair of samples in two clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The merging process is finished when all the data samples form a single cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This method produces a set of nested clusters in hierarchical structure that can be visualised using a dendrogram which is tree like diagram to record the sequence of merges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The expected number of clusters can be obtained by drawing lines at different levels on the dendrogram depending on the applications or specifying the number of clusters during the merging process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, it is possible to specify the structural constraint into hierarchal clustering process in the form of must link and cannot link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Must link constraint indicates which group of data samples should be part of the same cluster whereas cannot link constraint refers to the samples that should be in different clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 5 shows an example of agglomerative hierarchical clustering using structural constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The distance matrix indicates that data samples (b, d) should be part of same cluster (must link), whereas pairs of samples in (a, e) and (g, f) cannot be in same cluster (cannot link).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The dendrogram for this example shows that there are two different clusters are possible at the top due to the cannot link constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Constraint agglomerative hierarchical clustering using both must link and cannot link constraint: distance measure between examples (left), ‘must link’ and ‘cannot link’ constraint (middle), and clusters merging process (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In each iteration, pair of clusters are merged considering distance measured based on single link criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A typical architecture of a convolutional neural networks a b p e f g h a x 6 3 8 2 4 7 20 b x 1 2 9 3 5 7 c x 7 30 4 8 5 p x 9 6 4 8 e X 4 3 9 f x 5 7 g x 40 h xa b c p e f g h a CL b ML c e f CL g hConv layerwithN filters Conv layerwithMfilters Nfeatmaps Mfeatmaps Poolinglayer inputdata [2D] Poolinglayer8 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Convolutional Neural Networks CNNs [51] are prominent deep learning models that can identify the spatial patterns and translation invariant features from the input in a layered structure for classification or prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6, a typical CNN architecture consists of a series of convolutional and pooling layers followed by one or more fully connected layers (also known as dense layers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The convolutional layers are the major building blocks of CNNs that apply a set of learnable filters (also known as kernels) to local regions of the input to extract useful features and create an internal network representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The repeated application of the filters across different input locations creates a set of feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The stacking of convolutional layers in a deep network allows the shallower layers to learn low-level features and the deeper layers to learn high-order or more abstract features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The feature map outputs from the convolutional layers are location sensitive, that is, the layer outputs are dependent upon the feature’s position within the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To make the feature maps ‘local translation invariance’ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', the output is not changed by local shifts in the feature position) and reduce the dimensionality of network representations, it is common for pooling layers to be added after the convolutional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pooling is a down sampling operation that involves applying a sliding window to approximate local regions of the features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The approximation commonly involves computing the maximum or mean value within the feature window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As such, pooling has been considered as a technique to generalize feature representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Overall, this structure allows the network to learn filters that represent patterns in the data that can be used for prediction or classification [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pooling also makes the CNNs more noise tolerant and creates a hierarchy of features to extract meaningful patterns at different temporal scales [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The last part of a CNN is analogous to traditional feedforward NNs and consists of one or more dense layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Before feeding the extracted feature maps to the fully connected layer, it is required that the feature maps are flattened into a vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The dense layers are the final network layers that apply nonlinear combination of the extracted features to compute output predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For more detail information on CNNs, we refer to [51, 52, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' PROPOSED APPROACH FOR ACTIVITY RECOGNITION Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 7 shows an illustrative diagram of our proposed approach for activity recognition from indoor trajectory data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The approach consists of three main steps: trajectory partitioning, clustering, and model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The first step focuses upon partitioning each trajectory into a set of segments representing various movement patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This is achieved with a segmentation algorithm that identifies a set of characteristics points where the statistics or distributions of the trajectory changes rapidly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The second step generates pseudo labels of the unlabelled segments by applying a clustering method: this requires a small proportion of trajectory segments to be labelled as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The last step trains a classification model for activity recognition utilising the segments and their pseudo labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A simplified schematic diagram of the proposed approach for activity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Trajectory Partitioning We aim to partition the individual trajectories into non- overlapping segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The key idea is to identify a set of 𝑀 characteristics points (or change points) 𝐶𝑃 = {(𝑝𝑐1, 𝑡𝑐1), (𝑝𝑐2, 𝑡𝑐2), … , (𝑝𝑐𝑀, 𝑡𝑐𝑀)} ∶ 𝑡𝑐1 < 𝑡𝑐2 < ⋯ < 𝑡𝑐𝑀 from each trajectory 𝑇𝑅𝑖 ∊ 𝒯 and use those to partition each trajectory into 𝑀 − 1 segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These segments represent the different movement patterns in an individual trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To discover the characteristics points from individual trajectories, we apply an information theoretic criterion, Minimum Description Length (MDL) [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' There are two desirable properties of the trajectory partitioning [56]: preciseness and conciseness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Preciseness represents the accuracy in which a set of chosen trajectory segments represent the original trajectory, whereas conciseness represents the number of segments (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', model parameters) used within its representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These two properties are contradictory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For example, the preciseness is maximised (and conciseness is minimised) if we consider all the points within a trajectory as characteristics points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Likewise, the conciseness is maximised (and preciseness is minimised) if only the two end points of the trajectory are considered as the characteristic points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The MDL principle identifies the characteristics points of the trajectories by finding the optimal trade-off between the Individualtrajectorypartitioning Automatic labelling of segments inSubasedonclustering Training of a CNN based classification model9 preciseness and conciseness properties [11, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The function defining the MDL principle is given in (1) where 𝐻 represents a hypothesis, 𝐷 is the data, 𝐿(𝐻) is the description length of the hypothesis and 𝐿(𝐷|𝐻) is the description length of the data encoded using the hypothesis, both expressed in bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The hypothesis 𝐻 with the minimum 𝑀𝐷𝐿 is the one that achieves the highest data compression, or equivalently, the best explanation of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For our segmentation task, the hypothesis 𝐻 corresponds to the set of partitions of our trajectory data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Therefore, finding the optimal partitioning of the trajectories can be translated into finding the best hypothesis based on MDL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝑀𝐷𝐿 = 𝐿(𝐻) + 𝐿(𝐷|𝐻) (1) The two terms of the MDL function can be formulated using (2) and (3), respectively [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐿(𝐻) in (2) represents the total length of all trajectory partitions where 𝑙𝑒𝑛 (𝑝𝑐𝑗𝑝𝑐𝑗+1) is the length of a line segment (𝑝𝑐𝑗𝑝𝑐𝑗+1) that is computed using the Euclidean distance between two consecutive characteristics points 𝑝𝑐𝑗 and 𝑝𝑐𝑗+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, the formulation of 𝐿(𝐷|𝐻) in (3) refers to the sum of the difference between a trajectory and a set of its trajectory partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For each partition, the difference between partition and the representing line segment is computed by taking the sum of the perpendicular distance 𝑑⊥ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1) and the angular distance 𝑑Ѳ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐿(𝐻) = ∑ 𝑙𝑜𝑔2 (𝑙𝑒𝑛 (𝑝𝑐𝑗𝑝𝑐𝑗+1)) 𝑀−1 𝑗=1 (2) 𝐿(𝐷|𝐻) = ∑ ∑ {𝑙𝑜𝑔2 (𝑑⊥ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1)) + 𝑐𝑗+1−1 𝑘=𝑐𝑗 𝑀−1 𝑗=1 𝑙𝑜𝑔2 (𝑑Ѳ (𝑝𝑐𝑗𝑝𝑐𝑗+1, 𝑝𝑘𝑝𝑘+1))} (3) The above formulation of 𝐿(𝐻) represents a measure of the conciseness, where as 𝐿(𝐷|𝐻) indicates a measure of the preciseness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For our segmentation task, 𝐿(𝐻) increases as the number to partitions increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, larger deviations between the set of trajectory partitions and original trajectory causes 𝐿(𝐷|𝐻) to increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We aim to find the optimal partitioning that minimises the sum of 𝐿(𝐻) and 𝐿(𝐷|𝐻).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, the cost of finding the optimal partitioning for a trajectory is exhaustive as it requires every subset of points in the trajectory to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, an approximate algorithm [56] with time complexity of 𝑂(𝑁) has been applied which considers a set of local optima as the global optimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Let 𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) represents the MDL cost (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', 𝐿(𝐻) + 𝐿(𝐷|𝐻)) of a trajectory between two points 𝑝𝑖 and 𝑝𝑗 (𝑖 < 𝑗) considering 𝑝𝑖 and 𝑝𝑗 are the only characteristic points, whereas 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) is the MDL cost when persevering the original trajectory – i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', if there is no characteristic point between 𝑝𝑖 and 𝑝𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' It is obvious that 𝐿(𝐷|𝐻) in 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑗) is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, a local optimum is the longest trajectory partition 𝑝𝑖𝑝𝑗 which satisfies the condition 𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) ≤ 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) ∶ ∀𝑘 𝑖 < 𝑘 ≤ 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This means if 𝑀𝐷𝐿𝑝𝑎𝑟(𝑝𝑖𝑝𝑘) smaller than 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟(𝑝𝑖𝑝𝑘), the selection of 𝑝𝑘 as a characteristic point will cause the MDL cost smaller compared to the MDL cost if 𝑝𝑘 is not chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The approximation process considers the first data point 𝑝1 from the trajectory as the starting characteristic point and repeatedly compute 𝑀𝐷𝐿𝑝𝑎𝑟 and 𝑀𝐷𝐿𝑛𝑜𝑛𝑝𝑎𝑟 for each subsequent point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In each step, if the cost of partitioning is equal or less than the cost of not partitioning, we increase the length of trajectory partition and continue computing the two costs for next point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Otherwise, we consider the previous point as the characteristics point and repeat the same procedure to search the next characteristic point until all data points are checked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cluster and Label In this section, we introduce the method for labelling the trajectory segments generated by the partitioning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The main idea here is to generate a set of pseudo labels for the trajectory segments by applying constrained agglomerative hierarchical clustering with a small proportion of labelled segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Let 𝑆𝐿 = {(𝑠𝑙1, 𝑦𝑙2), (𝑠𝑙2, 𝑦𝑙2), … , (𝑠𝑖, 𝑦𝑙𝑖) } and 𝑆𝑈 = {𝑠𝑢1, 𝑠𝑢2, … , 𝑠𝑢𝑗 } are the sets of labelled and unlabelled segments, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The members of segments in 𝑆𝐿 are called seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Our task is to automatically label the trajectory segments in 𝑆𝑈 so that we can train a classification model using the data samples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', segments in both 𝑆𝐿 and 𝑆𝑈).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The classification model will then be applied to predict the class labels of the data samples in 𝑆𝑇𝑒𝑠𝑡 that represent the set of test segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We adopt the hierarchical clustering method to generates labels for trajectory segments in 𝑆𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In contrast to traditional clustering approach, we introduce constraints to the clustering structure to define how the seeds should be grouped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Specifically, we impose cannot-link constraints on the elements of 𝑆𝐿 to ensure that no more than one seed should be present in any cluster, even if the seeds have the same label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Each of the clusters will be comprised of trajectory segments that are most similar to its seed, and hence, its members (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', segments from 𝑆𝑈) will be labelled according to the class of its seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' When applying constraint agglomerative hierarchical clustering, it is very important to choose an appropriate distance metric for the linkage criteria used to compute the similarity between clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The standard metrics based on point-to-point distance are not suitable for spatial data especially when the length of the time series are not same, as in our case [57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, we apply the Hausdorff distance to compute the distance between pairs of trajectory segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Considering the segments as geometric curves, the Hausdorff distance from a set of points 𝐴 to another set of points 𝐵 is the 10 maximum distance of a set 𝐴 to the nearest point in the set 𝐵 and is defined as in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐻𝐷𝐴→𝐵 = max 𝑎∈𝐴 {min 𝑏∈𝐵 𝑑(𝑎, 𝑏)} (5) where 𝑑(𝑎, 𝑏) is the distance between points 𝑎 and 𝑏 computed using any chosen distance metric (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', Euclidean distance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Generally, the Hausdorff distance is directed, which means that distance 𝐻𝐷𝐴→𝐵 from 𝐴 to 𝐵 is not equal to the distance 𝐻𝐷𝐵→𝐴 from 𝐵 to 𝐴.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' An undirected Hausdorff distance can be computed by taking the average of the two directed distances as in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐻𝐷𝐴→𝐵 = 𝐻𝐷𝐵→𝐴 = 𝑚𝑒𝑎𝑛(𝐻𝐷𝐴→𝐵, 𝐻𝐷𝐵→𝐴) (6) The presented clustering method can be explained from a graph-theoretic perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Let 𝐹 = 𝑆𝐿 ∪ 𝑆𝑈 be the set of all training observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Consider 𝐺 = (𝑉, 𝐸) as an undirected graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The set of vertices 𝑉 in 𝐺 represents all the observations in 𝐹 and a super-vertex (∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, 𝐸 represents the edges among the vertices for all elements in 𝐹 as well as the edges between the super-vertex and vertices representing all the seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The weights of the first group of edges corresponds to the distance of two observations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', segments) computed using the undirected Hausdorff distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, for the edges between the super-vertex (∗) and vertices representing the seeds, the weights are set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The labelling of the observations in 𝑆𝑈 then can be viewed as a specific way of finding a minimum spanning tree of 𝐺 using Kruskal’s algorithm considering that the forest which is successively joined by Kruskal’s algorithm is a set of clusters generated by the agglomerative hierarchical clustering dendrogram [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Since the weights of the edges between the super-vertex and vertices representing the seeds (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', the labelled segments in 𝑆𝐿) is zero, Kruskal’s algorithm will add all the seeds at the beginning to the minimum spanning tree in the first 𝑅 iterations where 𝑅 is the cardinality of 𝑆𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This will leave 𝑅 branches in the tree – these branches are called the main branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The tree will then grow along the main branches in the successive iterations without created any new branches since all the edges from the super-vertex have already been added by 𝑅 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This is equivalent to imposing cannot-link constraints in agglomerative hierarchical clustering between each pair of seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Upon termination of the algorithm, each of the branches in the tree corresponds to a cluster in the agglomerative hierarchical clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' PARAMETERS OF THE CNNS USED FOR STEPWISE SEARCH Parameters Description Values used for grid search Filters number of convolutional filters or kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (𝐹1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐹2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' … 𝐹𝐿) indicates network consists of 𝐿 convolutional layers and each layer 𝑙 consist of 𝐹𝑙 filters [(16),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (32),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (64),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (128),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 32),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 32),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 64),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16)] Kernel size length of the convolution filters [3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 5] Activation activation functions for convolutional layers ['relu'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'sigmoid'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'tanh'] Strides distance between two successive kernel positions is called a stride [1," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3] Padding how the centre of each kernel to overlap the outermost element of the inputs [‘valid,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ‘same’] Kernel initializer how to set initials weights of the convolutional filters [‘glorot_uniform’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' random_uniform’] Pooling pooling operation to perform on convolutional feature map [None,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ‘max’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ‘avg’] Dropout rate fraction of neurons and their associated weights to disregard at each training epoch [0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3] Dense neurons number of layers in fully connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' (𝑁1, 𝑁2, … 𝑁𝐿) indicates 𝐿 fully connected layers and each layer 𝑙 consist of 𝑁𝑙 neurons [(4,), (10, 4), (20, 4)] Dense activation activation functions for neurons in fully connected layers [‘relu’, and/or ‘softmax’] Batch size number of training samples per gradient update [64, 128] Epochs number of epochs to train the model [250, 500] 11 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Classification model To develop the classification models, we apply CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The rationale of selecting CNNs are their ability to automatically learn features that represent meaningful patterns from large spatial or temporal datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The CNNs used in this paper consist of multiple convolutional and pooling layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, the hyper-parameters of the networks have a significant influence on generalization ability, robustness, and overall predictive performance of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We find the optimal topology of CNNs and tune their hyper-parameters based on a stepwise search method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Specifically, we optimise one parameter at a time while keeping the remaining parameters unchanged by training the CNNs using training data and evaluating its performance on the validation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We apply a stepwise search instead of an exhaustive grid search to reduce the training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We consider CNNs up to 4 convolutional layers with a different number of filters in the range of 16 to 128, multiple filter sizes in each convolutional layer in the range of 3 to 5, two different types of pooling layers – max and average pooling, and multiple combinations of fully connected layers with a different number of nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To optimise the parameters, we apply Adam optimization algorithm [60] with a differing number of epochs, minimizing the sparse categorical cross entropy, and applying dropout at each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Dropout [61] is a regularization method that randomly chooses specified fraction of nodes at each training epoch and disables their connection, hence disregards them during weight optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This technique has been found very effective for deep learning models to reduce over-fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE I presents the entire search space considered to find the optimal structure and tune hyper-parameters of CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Partitioning of trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lines indicate part (randomly selected) of trajectories and circles represent the identified partitioning points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The raw noisy data points between partitioning points are not shown for better representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The selected best architectures of the CNNs models for all the trajectories have similar structures with number of convolutional layers between 1 to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As an example, the best architectures obtained based on stepwise searching for the trajectory data for the operator at rig 6 includes 2 1D convolutional layers with 32 and 16 filters respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Both convolutional layers share the same kernel size, strides, padding method, and activation function: 3, 1, ‘same’, and ‘tanh’, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, each convolutional layer is also followed by a max pooling layer, a dropout layer with dropout fraction of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The fully connected component consists of one dense layer with a softmax activation function and provides a probability of the 4 classes of activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The weights of the CNNs were optimised with a maximum of 500 epochs and batch size of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For each trajectory in our dataset, we develop a separate classification model using CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Inputs to the CNNs models include the trajectory segments along with duration of the segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Each of the models has been trained using the observations in both in 𝑆𝐿 and 𝑆𝑈 = {(𝑠𝑢1, 𝑦𝑝𝑙1), (𝑠𝑢2, 𝑦𝑝𝑙2), … , (𝑠𝑢𝑗, 𝑦𝑝𝑙𝑗) } where 𝑠𝑢𝑖 (1≤𝑖≤𝑗) is the an element of 𝑆𝑈 and 𝑦𝑝𝑙𝑖the pseudo label for 𝑠𝑢𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This means the training data for each trajectory contains both the segments in 𝑆𝐿 with their actual class labels, and the segments in 𝑆𝑈 with the pseudo labels generated in clustering step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Distribution of activities of workers into 4 defined categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TR1 TR2 TR3 TR4 TR5 TR612 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Distribution of activities of workers into 4 defined categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' EXPERIMENTS AND RESULTS The partitioning algorithm is applied to each trajectory 𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 𝑊 separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 8 shows the partitioning results (the partition points and the segments joining those points) for a small proportion of data points (2-3 minutes) from each trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The raw noisy trajectory data points are not shown for better visualisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As we can see, the MDL based algorithm correctly identify the trajectory segments with different characteristics – the portioning points are chosen where the behaviour of the trajectories changes significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The segments have different lengths and represent different activities of the workers in the factory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE II presents the summary of trajectory partitioning results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The number of partitioning points for the trajectories varies in the range of 223 for 𝑇𝑅1 to 388 for 𝑇𝑅6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The variation in the number of partitioning points is expected since different workers show different movement patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9 presents the distribution of activities of the workers into predefined categories: standing at workstation, moving randomly, moving between workstations, restocking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' More than 50% of segments of all trajectories are labelled as standing at workstation which highlights that the workers are mostly busy completing their assigned task for a majority of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The workers also spend a significant proportion of time moving between different workstations – the proportion of segments classified as moving between workstations varies between 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='71% to 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='71%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This is due to the collaborative nature of the tricycle assembly task and can be explained by the workflow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, during the assembly process, the components built at each workstation needs to be delivered to another co-worker until the completion of work in progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' SUMMARY INFORMATION ON TRAJECTORY SEGMENTATION Trajectory Duration (sec) Length Partition points Total segments 𝑇𝑅1 3790 7727 223 222 𝑇𝑅2 5214 7840 328 327 𝑇𝑅3 3475 7266 252 251 𝑇𝑅4 3107 7712 264 263 𝑇𝑅5 7194 7803 341 340 𝑇𝑅6 7356 7847 388 387 Moreover, moving randomly is the third most frequent observed activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 1 has the highest percentage of segments labelled as moving randomly (22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='97% segments) followed by the worker at rig 3 (16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='33%) and rig 2 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='90% segments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The percentage of segments labelled as moving randomly is relatively low for the workers at the other three rigs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The high percentage of moving randomly segments for workers of the rig 1, 2, and 3 is due to the fact that they start working earlier compared to the workers at rigs 4, 5, and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This is because workers at the later rigs require their components to be built by the other rigs before they can commence their tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This allows the workers at rig 1, 2, and 4 to complete their assign tasks earlier and visit outside assembly area for taking break, meeting colleagues, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The restocking is the least frequent activity shown by all workers, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='53% to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='73% segments are labelled as restocking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This is expected since all the workstations hold the components they require to assemble 3 tricycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Workers are then required to occasionally restock the parts until 6 tricycles are completed within 3 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For each trajectory 𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 𝑊 we aim to develop a separate semi-supervised classification model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To achieve this, the spatial trajectory segments for each trajectory 𝑇𝑅𝑖 are divided into 3 non-overlapping subsets: 𝑆𝐿, 𝑆𝑈, and 𝑆𝑇𝑒𝑠𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝑆𝐿 contains only very small proportion (20%) of trajectory segments that are manually labelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝑆𝑈 and 𝑆𝑇𝑒𝑠𝑡 respectively contains 80% and 20% of the remaining segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The segments in 𝑆𝑈 are labelled using the constrained agglomerative hierarchical clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The segments in both 𝑆𝐿and 𝑆𝑈 are used to train the classification model whereas the segments in 𝑆𝑇𝑒𝑠𝑡 are used to evaluate the accuracy of the classification model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' To evaluate the performance of the models we use two different metrics: misclassification rate and F-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Misclassification Rate (MCR) refers to the percentage of observations that were incorrectly predicted by the classification model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' MCR has a range of 0 to 1: a lower value of MCR indicates a higher accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The F-score is a standard measure for classification and is defined as in (7) for a binary classification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For multi-class classification task as ours, this is the average of the F-score of each class with weighting determined by the number of observations in each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The F-score also has a range of 0 to 1, with 1 being the most accurate classifier and 0 indicating the worst possible 0 20 40 60 80 100 TR1 TR2 TR3 TR4 TR5 TR6 Activity distribution (%) moving between workstations restocking randomly moving standing at workstation 13 classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Although we present the numerical results using both metrics, F-score will be considered as the primary metric for analysis of prediction accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 𝐹𝑠𝑐𝑜𝑟𝑒 = 2 × (𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ×𝑟𝑒𝑐𝑎𝑙𝑙) (𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+𝑟𝑒𝑐𝑎𝑙𝑙) (7) where precision is the fraction of observations that the model classified as positive that were true positives and recall refers to the fraction of true positive observations that the model correctly classified as positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' ACCURACY OF THE SEMI-SUPERVISED APPROACH IN TERMS OF THE F-SCORE AND MISCLASSIFICATION RATE Trajectory F-score MCR 𝑇𝑅1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='19 𝑇𝑅2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='08 𝑇𝑅3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 𝑇𝑅4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='93 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='07 𝑇𝑅5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='05 𝑇𝑅6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='15 TABLE III presents the classification accuracy evaluated on the trajectory segments in 𝑆𝑇𝑒𝑠𝑡 for each trajectory 𝑇𝑅𝑖 in 𝒯 = {𝑇𝑅𝑖}𝑖=1 𝑊 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The classification accuracy (in terms of F-score) for the trajectories generated by the workers at all rigs is 81% or higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The higher classification accuracy indicates the ability of the proposed approach to classify the activities of the workers with using only a small set of labelled segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Amongst the trajectories of all six workers, the trajectory for the worker at rig 5 achieved the highest classification accuracy followed by the trajectory for workers at rig 4 and 2, respectively – their F-scores are above 90%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' On the other hand, the classification accuracy was lowest for the trajectory of the worker at rig 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The F-scores of the trajectories of two other workers is 85% The main reason for relatively lower accuracy for the trajectory of worker at rig 1 is the smaller number of training samples used in 𝑆𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' There are 44 segments in 𝑆𝐿 for trajectories of the worker at rig 1 compared 65 segments in 𝑆𝐿 for trajectories of the worker at rig 2 for example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The higher number of labelled segments in 𝑆𝐿 help to generate pseudo labels with better accuracy confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For example, the accuracy of the pseudo labels generated by the hierarchical clustering is 80% and 90% for trajectories for workers at rig 1 and 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Using the more accurate pseudo labels helps to train the final CNN models to better learn the patterns which consequently reflected in the final accuracy results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, we reserve 20% of labelled segments into 𝑆𝐿 for each trajectory as previously mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These segments (called seeds) are then used in the clustering phase to generate pseudo labels for the segments in 𝑆𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hence, it is important to check the influence this selection of labelled segments on the performance of the semi-supervised classification model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We repeated all the experiments with different proportions of labelled data in 𝑆𝐿: 5% to 20% with 5% increments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 11 presents the F-scores of the classification models with respect to different proportions of segments in 𝑆𝐿 for each trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The classification accuracy of all trajectories monotonically increases as the proportion of labelled segments in 𝑆𝐿 increase from 5% to 20% The improvement in classification accuracy is expected since a higher proportion of segments in 𝑆𝐿 provides more information for the clustering algorithm to exploit for pseudo label generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In other words, more manually labelled segments means availability of more patterns of different activity types during clustering algorithm which consequently helps to the clustering process to generate more accurate the pseudo labels for segments in 𝑆𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' These results provide more accurate training of the final prediction models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Classification accuracy (F-score) of the model with different proportion of manually labelled segments in 𝑆𝐿 used to generate pseudo labels for segment in 𝑆𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The predicted labels of activities for the trajectory segments can be used in diverse ways for decision making purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' For example, the distribution of activities of workers during their shift (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9) can help to improve worker productivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As we can see, the worker at rig 1 spends second highest proportion of time doing random movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The worker at rig 1 is the first person in the workflow and likely to complete the assigned task before any of the other workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, from the data it is evident that worker at rig 1 makes most of the random moves later part of shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' This time can be better utilised doing productive work as decided by the management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Similarly, the worker at rig 5 spends second highest time on moving between workstations as per distribution of activities in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' If the movements are happening to search for missing components or tools, those can be made available at rig 5 to reduce the searching time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' CENTROIDS OF THE TEN CLUSTERS REPRESENTING JOINT ACTIVITIES OF WORKERS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' WE USE SHORT NAMES FOR FOUR ACTIVITY CLASSES (STAND: STANDING AT WORKSTATION, MOVE: MOVE BETWEEN WORKSTATIONS, RANDOM: RANDOMLY MOVING, AND RESTOCK: RESTOCKING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=") Cluster ID Centroid [Concurrent activities of 6 workers] 1 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 2 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'move'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 3 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'move'] 4 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'move'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 5 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'move'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'random'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 6 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'random'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'random'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 7 [restock," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 8 ['random'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 9 ['move'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 10 ['stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'move'," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" 'stand'] 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='80 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='00 TR1 TR2 TR3 TR4 TR5 TR6 F-score 5% 10% 15% 20% 14 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cluster (State) distribution of the joint activity data Another interesting inference that can be made from the activity classification results is ‘factory floor state’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A state can be defined in numerous ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In this case, we refer to the joint behaviour of workers as a state, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', what the workers are doing concurrently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We clustered the joint activity class labels of all six workers to obtain the factory floor state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' TABLE IV presents the centroids of the ten clusters obtained using K- mode algorithm [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 12 shows the distribution of clusters over joint activity data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Workers working at their respective stations is the most common state (cluster 1) and it constitutes 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6% of the joint behaviour classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The second highest cluster observed is cluster 4 where most workers are at their rigs except worker at rig 3 who is moving between stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' We also observe a lot of movement of that worker from rig 3 to rig 2 and this observation aligns well with the workflow (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The third most common state is when most workers are at their rigs except the worker at rig 1 who is moving randomly (cluster 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' As discussed previously, the worker at rig 1 starts the assigned task at the beginning of the workflow with no dependencies hence finishes work early and moves randomly later while other workers are at their rigs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Such state estimation through clustering can summarise concisely what’s happening at the factory floor and can be used for operational decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' CONCLUSIONS We presented an approach for human activity recognition from noisy indoor trajectory data and studied its application in manufacturing context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The proposed approach adopted the concept of semi-supervised learning: generated pseudo labels based on constraint hierarchical clustering and trained convolutional neural networks as the classifiers that used the trajectory segments as inputs and respective pseudo labels as outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The approach is comprehensively evaluated using six trajectories of human workers at a tricycle assembly workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Results indicate that proposed approach can accurately classify the activities of the workers at different part of their trajectories – the classification accuracy in terms of F-score varies between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='81 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Moreover, this performance is achieved with small proportion of labelled examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' The key advantage of this approach over existing supervised activity recognition models is that it saves time and resources required for manual labelling of input-output examples by the domain experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' In addition, although the approach is developed to identify four target activities (standing at workstation, moving randomly, moving between workstations, restocking) specific to manufacturing environment, it is generic and can be applied to such other activities as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Future research will focus on applying the approach on the trajectory datasets from other domains and improving pseudo label generation process based on advanced self-supervised methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Another avenue of future work is representing the segments using raster images overlayed on factory layout and then classify them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' REFERENCES [1] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', "Smart manufacturing: Past research, present findings, and future directions," International Journal of Precision Engineering and Manufacturing-Green Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 111–128, 2016, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/s40684-016-0015-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [2] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Nagorny, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lima-Monteiro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Barata, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Colombo, "Big Data Analysis in Smart Manufacturing: A Review," International Journal of Communications, Network and System Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 31-58, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='4236/ijcns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='103003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Harding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Shahbaz, Srinivas, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kusiak, "Data Mining in Manufacturing: A Review," Journal of Manufacturing Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 128, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 969-976, 2006, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1115/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2194554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hsu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tsai, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' He, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cheng, "Data-Driven Approach for Fault Detection and Diagnostic in Semiconductor Manufacturing," IEEE Transactions on Automation Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1925 - 1936, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TASE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2983061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Essien and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Giannetti, "A Deep Learning Model for Smart Manufacturing Using Convolutional LSTM Neural Network Autoencoders," IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6069 - 6078, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2967556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ren, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yang, "A Data- Driven Approach of Product Quality Prediction for Complex Production Systems," IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6457 - 6465, 2021, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3001054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Syafrudin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Alfian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fitriyani, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Rhee, "Performance Analysis of IoT-Based Sensor, Big Data Processing, and Machine Learning Model for Real-Time Monitoring System in Automotive Manufacturing," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2946, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s18092946.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sadati, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chinnam, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Nezhad, "Observational data- driven modeling and optimization of manufacturing processes," Expert Systems with Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 93, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 456-464, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='eswa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sakao, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Huisingh, "A framework for Big Data driven product lifecycle management," Journal of Cleaner Production, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 159, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 229-240, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='jclepro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Racz-Szabo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ruppert, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bantay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Locklin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Jakab, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Abonyi, "Real-Time Locating System in Production Management," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1-21, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s20236766.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Han, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tucker, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Simpson, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Davidson, "A Data Mining Trajectory Clustering Methodology for Modeling Indoor Design Space Utilization " in International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), USA, 2013, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1115/DETC2013-12690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Nee, "Digital Twin in Industry: State-of-the-Art," IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2405 - 2415, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2873186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cheng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tomizuka, "Towards Efficient Human-Robot Collaboration With Robust Plan Recognition and 0 10 20 30 40 50 Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10 Proportion of joint activities (%) 15 Trajectory Prediction," IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2602 2609, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/LRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2972874.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [14] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Baumgartner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', "Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspective," arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='01344, 2022, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='01344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pan, "Sensor-Based Abnormal Human- Activity Detection," IEEE Transactions on Knowledge and Data Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1082 - 1090, 2008, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TKDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Machot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ali, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kyamakya, "Activity Recognition in Sensor Data Streams for Active and Assisted Living Environments," IEEE Transactions on Circuits and Systems for Video Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2933 - 2945, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TCSVT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2764868.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Paolanti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liciotti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pietrini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mancini, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Frontoni, "Modelling and Forecasting Customer Navigation in Intelligent Retail Environments," Journal of Intelligent & Robotic Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 91, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 165–180, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/s10846-017-0674-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Nakahara and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yada, "Analyzing consumers’ shopping behavior using RFID data and pattern mining," vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 355– 365, 2012, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/s11634-012-0117-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gochoo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Jean, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Alnajjar, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Huang, "Unobtrusive Activity Recognition of Elderly People Living Alone Using Anonymous Binary Sensors and DCNN," IEEE Journal of Biomedical and Health Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 693 - 702, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/JBHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2833618.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gochoo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Alnajjar, "DCNN-based elderly activity recognition using binary sensors," in International Conference on Electrical and Computing Technologies and Applications (ICECTA), 2017: IEEE, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/ICECTA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8252040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Asakuraa and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Iryo, "Analysis of tourist behaviour based on the tracking data collected using a mobile communication instrument," Transportation Research Part A: Policy and Practice, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 41, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 684-690, 2007, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='tra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Arslan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cruz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ginhac, "Understanding Worker Mobility within the Stay Locations using HMMs on Semantic Trajectories," in International Conference on Emerging Technologies (ICET), 2018: IEEE, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/ICET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8603666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Arshad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bilal, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gani, "Human Activity Recognition: Review, Taxonomy and Open Challenges," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 17, 2022, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s22176463.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Peng, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hu, "Deep learning for sensor-based activity recognition: A survey," Pattern Recognition Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 191, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3-11, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='patrec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [25] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Dhimana and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Vishwakarm, "A review of state-of-the-art techniques for abnormal human activity recognition," Engineering Applications of Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 77, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 21-45, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='engappai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [26] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tao, "Data and knowledge mining with big data towards smart production," Journal of Industrial Information Integration, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1-13, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='jii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [27] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ji and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, "Big data analytics based fault prediction for shop floor scheduling," Journal of Manufacturing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 187-194, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='jmsy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [28] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Qi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kusiak, "Data-driven smart manufacturing," Journal of Manufacturing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 48, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' C, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 157-169, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='jmsy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [29] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Arkan and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Landeghem, "Evaluating the performance of a discrete manufacturing process using RFID: A case study," Robotics and Computer-Integrated Manufacturing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 502-512, 2013, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='rcim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gyulai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pfeiffer, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bergmann, "Analysis of asset location data to support decisions in production management and control," in CIRP Conference on Intelligent Computation in Manufacturing Engineering, Italy, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='procir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Löcklin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ruppert, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Jakab, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Libert, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Jazdi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Weyrich, "Trajectory Prediction of Humans in Factories and Warehouses with Real-Time Locating Systems," in IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), Austria, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/ETFA46521.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='9211913.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gao, "Recurrent neural network for motion trajectory prediction in human-robot collaborative assembly," CIRP Annals, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9-12, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='cirp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhang, "Location Prediction for Indoor Spaces based on Trajectory Similarity," in ACM International Conference on Data Science and Information Technology (DSIT), China, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 402–407, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1145/3478905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3478983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sander, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ester, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kriegel, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Xu, "Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications," Data Mining and Knowledge Discovery, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 169–194, 1998, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1023/A:1009745219419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [35] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Guo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yang, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lu, "Mining frequent trajectory patterns of WIP in Internet of Things-based spatial- temporal database," International Journal of Computer Integrated Manufacturing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 30, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1253–1271, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1080/0951192X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1307522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [36] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Agrawal, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mannila, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Srikant, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Toivonen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Verkamo, "Fast discovery of association rules," Advances in knowledge discovery and data mining, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 307-328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [37] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bu, "A Data Mining Framework for Massive RFID Data Based on Apriori Algorithm," Journal of Physics: Conference Series, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1087, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1088/1742-6596/1087/2/022020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Alahi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Goel, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ramanathan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Robicquet, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fei-Fei, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Savarese, "Social LSTM: Human Trajectory Prediction in Crowded Spaces," in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Shum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', "Indoor Location Data for Tracking Human Behaviours: A Scoping Review," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 3, 2022, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s22031220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Gochoo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bayanduuren, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Velusamy, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, "Deep convolutional neural network classifier for travel patterns using binary sensors," in International Conference on Awareness Science and Technology (iCAST), 2017: IEEE, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/ICAwST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='8256432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [41] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Fang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chen, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Huang, "Accurate Indoor Positioning Prediction Using the LSTM and Grey Model," in International Conference on Web Information Systems Engineering, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/978-3-030-62005-9_26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Selby, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Vlahos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Yadav, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lemp, "A feature- oriented vehicle trajectory data processing scheme for data mining: A case study for Statewide truck parking behaviors," Transportation Research Interdisciplinary Perspectives, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 11, 2021, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='trip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='100401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [43] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lei, "A framework for anomaly detection in maritime trajectory behavior," Knowledge and Information Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 47, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 189–214, 2016, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/s10115-015-0845-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [44] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chatzikokolakis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zissis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Spiliopoulos, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tserpes, "Mining Vessel Trajectory Data for Patterns of Search and Rescue," in EDBT/ICDT Workshops, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [45] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kima and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Mahmassani, "Spatial and Temporal Characterization of Travel Patterns in a Traffic Network Using Vehicle Trajectories," Transportation Research Procedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 164-184, 2015, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='trpro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [46] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Song, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kanasugi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Shibasaki, "Deeptransport: prediction and simulation of human mobility and transportation mode at a citywide level," in International Joint Conference on Artificial Intelligence (IJCAI), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [47] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pei, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Han, "Mining Frequent Trajectory Patterns for Activity Monitoring Using Radio Frequency Tag Arrays," IEEE Transactions on Parallel and Distributed Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2138-2149, 2012, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1109/TPDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [48] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Delamare, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Duval, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Boutteau, "A New Dataset of People Flow in an Industrial Site with UWB and Motion Capture Systems," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 16, 2020, doi: doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s20164511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [49] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Delamare, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Duva, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Boutteau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Dataset of person flows during an assembly phase in an industrial site with an UWB system in NLOS and a motion capture system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Available: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='com/vauchey/IndoorInsdustrialLocalisationDataset/ 16 [50] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Merriaux, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Dupuis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Boutteau, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Vasseur, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Savatier, "A study of vicon system positioning performance," Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 7, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='3390/s17071591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [51] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Krizhevsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sutskever, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hinton, "Imagenet classification with deep convolutional neural networks," in International Conference on Neural Information Processing Systems (NIPS), 2012, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1145/3065386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [52] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Borovykh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bohte, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Oosterlee, "Conditional Time Series Forecasting with Convolutional Neural Networks," arXiv:1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='04691v5, 2018, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='04691.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hinton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', "Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups," IEEE Signal Processing Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 82 - 97, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [54] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=" O'Shea and R." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Nash, "An Introduction to Convolutional Neural Networks," arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='08458, 2015, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='08458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [55] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Grunwald, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Myung, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Pitt, Advances in minimum description length: Theory and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' MIT press, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [56] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Han, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Whang, "Trajectory clustering: a partition-and-group framework," presented at the ACM SIGMOD international conference on Management of data, China, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [57] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Tao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=', "A comparative analysis of trajectory similarity measures," GIScience & Remote Sensing vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 58, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 643– 669, 2021, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1080/15481603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1908927.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [58] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Bao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Culpepper, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Cong, "A survey on trajectory data management, analytics, and learning," ACM Computing Surveys, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1–36, 2022, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1145/3440207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [59] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Marussy and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Buza, "SUCCESS: A New Approach for Semi- supervised Classification of Time-Series," in International Conference on Artificial Intelligence and Soft Computing (ICAISC), 2013, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 7894: Springer, in Lecture Notes in Computer Science: Artificial Intelligence and Soft Computing, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1007/978-3-642-38658-9_39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [60] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Kingma and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Ba, "Adam: A method for stochastic optimization," arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6980, 2014, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [61] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Srivastava, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Hinton, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Krizhevsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Sutskever, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Salakhutdinov, "Dropout: A Simple Way to Prevent Neural Networks from Overfitting," The journal of machine learning research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' 1929-1958, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' [62] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content=' Miguel A Carreira Perpinan, "The K-modes algorithm for clustering," arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6478, 2013, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} +page_content='6478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9E1T4oBgHgl3EQfYAS9/content/2301.03134v1.pdf'} diff --git a/INE3T4oBgHgl3EQfugsS/vector_store/index.pkl b/INE3T4oBgHgl3EQfugsS/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..8691076f23c6be5d862f9bb5a3a491ae2c4fd651 --- /dev/null +++ b/INE3T4oBgHgl3EQfugsS/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:838ba47f7c4129a04e2547ba108cfc5d80f430ce9d69df9399be06e133398e70 +size 91213 diff --git a/INFAT4oBgHgl3EQfuR6w/content/tmp_files/2301.08669v1.pdf.txt b/INFAT4oBgHgl3EQfuR6w/content/tmp_files/2301.08669v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..e1b3f175b09b02075c175938e5fc04eefc0c5c9c --- /dev/null +++ b/INFAT4oBgHgl3EQfuR6w/content/tmp_files/2301.08669v1.pdf.txt @@ -0,0 +1,1668 @@ +Preprint +HOLISTICALLY EXPLAINABLE VISION TRANSFORMERS +Moritz B¨ohle1, Mario Fritz2, Bernt Schiele1 +1Max Planck Institute for Informatics, Saarbr¨ucken +2CISPA Helmholtz Center for Information Security +ABSTRACT +Transformers increasingly dominate the machine learning landscape across many +tasks and domains, which increases the importance for understanding their out- +puts. While their attention modules provide partial insight into their inner work- +ings, the attention scores have been shown to be insufficient for explaining the +models as a whole. To address this, we propose B-cos transformers, which inher- +ently provide holistic explanations for their decisions. Specifically, we formulate +each model component—such as the multi-layer perceptrons, attention layers, and +the tokenisation module—to be dynamic linear, which allows us to faithfully sum- +marise the entire transformer via a single linear transform. We apply our proposed +design to Vision Transformers (ViTs) and show that the resulting models, dubbed +Bcos-ViTs, are highly interpretable and perform competitively to baseline ViTs +on ImageNet. Code will be made available soon. +1 +INTRODUCTION +Input +Ours +[W(x)]k +Ours +Eq. (7) +Rollout +FinAtt +rocking chair +blue bird +goldfish +magpie +cock +Ibizan hound +Fig. 1: Inherent explanations (cols. 2+3) of B-cos ViTs +vs. attention explanations (cols. 4+5) for the same model. +Note that W(x) faithfully reflects the whole model and +yields more detailed and class-specific explanations than +attention alone. For a detailed discussion, see supplement. +Convolutional neural networks (CNNs) have +dominated the last decade of computer vision. +However, recently they are often surpassed by +transformers (Vaswani et al., 2017), which— +if the current development is any indication— +will replace CNNs for ever more tasks and +domains. Transformers are thus bound to im- +pact many aspects of our lives: from health- +care, over judicial decisions, to autonomous +driving. Given the sensitive nature of such ar- +eas, it is of utmost importance to ensure that +we can explain the underlying models, which +still remains a challenge for transformers. +To explain transformers, prior work often fo- +cused on the models’ attention layers (Jain & +Wallace, 2019; Serrano & Smith, 2019; Ab- +nar & Zuidema, 2020; Barkan et al., 2021), as +they inherently compute their output in an in- +terpretable manner. However, as transformers +consist of many additional components, ex- +planations derived from attention alone have +been found insufficient to explain the full +models (Bastings & Filippova, 2020; Chefer +et al., 2021). +To address this, our goal is +to develop transformers that inherently pro- +vide holistic explanations for their decisions, +i.e. explanations that reflect all model com- +ponents. These model components are given by: a tokenisation module, a mechanism for providing +positional information to the model, multi-layer perceptrons (MLPs), as well as normalisation and +attention layers, see Fig. 2a. By addressing the interpretability of each component individually, we +obtain transformers that inherently explain their decisions, see, for example Fig. 1 and Fig. 2b. +In detail, our approach is based on the idea of designing each component to be dynamic linear, such +that it computes an input-dependent linear transform. This renders the entire model dynamic linear, +cf. B¨ohle et al. (2021; 2022), s.t. it can be summarised by a single linear transform for each input. +1 +arXiv:2301.08669v1 [cs.CV] 20 Jan 2023 + +Preprint +Dynamic Linear Transformation +Tokeniser: +B-cos CNN +B-cos +Attention +B-cos +MLP ++ +× L +B-cos +Classifier ++ +W +(x) +Tokens +W +(x) +Class +W +(x) +Att +l +W +(x) +MLP +l +W(x) +W +(x) +Tokens +W +(x) +Att +l +W +(x) +Class += +∏ +L +l=1 W +(x) +MLP +l +( +) +B-cos ViT +(a) +Input +Prediction +× += +× += +σ (Sum(ck(x))): +100.0% +Lesser Panda +[W(x)]k +ck(x) +Probability(Lesser Panda) = σ (Sum(ck(x))) = 100% +(b) +Fig. 2: (a) B-cos ViTs. We design each ViT component to be dynamic linear, allowing us to summarise the +entire model by a single linear transform W(x), as shown in the bottom. (b) Computation is Explanation. +The model output is exactly computed by the linear transform W(x). As a result, we can visualise this effective +linear transform either by the corresponding matrix row (center) or the contributions ck(x) (right), cf. Eq. (7). +In short, we make the following contributions. (I) We present a novel approach for designing in- +herently interpretable transformers. For this, (II) we carefully design each model component to be +dynamic linear and ensure that their combination remains dynamic linear and interpretable. Specifi- +cally, we address (IIa) the tokenisation module, (IIb) the attention layers, (IIc) the MLPs, and (IId) +the classification head. (III) Additionally, we introduce a novel mechanism for allowing the model +to learn attention priors, which breaks the permutation invariance of transformers and thus allows the +model to easily leverage positional information. In our experiments, we find that B-cos ViTs with +such a learnt ‘attention prior’ achieve significantly higher classification accuracies. (IV) Finally, we +evaluate a wide range of model configurations and show that the proposed B-cos ViTs are not only +highly interpretable, but also constitute powerful image classifiers. +2 +RELATED WORK +Attention as Explanation. As the name exemplifies, attention is often thought to give insight into +what a model ‘pays attention to’ for its prediction. As such, various methods for using attention to +understand the model output have been proposed, such as visualising the attention of single attention +heads, cf. Vaswani et al. (2017). However, especially in deeper layers the information becomes in- +creasingly distributed and it is thus unclear whether a given token still represents its original position +in the input (Serrano & Smith, 2019; Abnar & Zuidema, 2020), thus complicating the interpretation +of high attention values deep in the network (Serrano & Smith, 2019; Bastings & Filippova, 2020). +Therefore, Abnar & Zuidema (2020) proposed ‘attention rollout’, which summarises the various +attention maps throughout the layers. However, this summary still only includes the attention layers +and neglects all other network components (Bastings & Filippova, 2020). In response, various +improvements over attention rollout have been proposed, such as GradSAM (Barkan et al., 2021) or +an LRP-based explanation method (Chefer et al., 2021), that were designed to more accurately reflect +the computations of all model components. The significant gains in quantitative interpretability +metrics reported by Chefer et al. (2021) highlight the importance of such holistic explanations. +Similarly, we also aim to derive holistic explanations for transformers. However, instead of deriving +an explanation ‘post-hoc’ as in Chefer et al. (2021), we explicitly design our models to be holistically +explainable. For this, we formulate each component—and thus the full model—to be dynamic linear. +Dynamic Linearity. Plain linear models, i.e. y(x)=Wx, are usually considered interpretable, as +y(x) can be decomposed into individual contributions ci=wi xi from any dimension i: y= � +i ci +(Alvarez-Melis & Jaakkola, 2018). However, linear models have a limited capacity, which has lead +to various works aimed at extending their capacity without losing their interpretability, see Alvarez- +Melis & Jaakkola (2018); Brendel & Bethge (2019); B¨ohle et al. (2021; 2022). An appealing strategy +for this is formulating dynamic linear models (Alvarez-Melis & Jaakkola, 2018; B¨ohle et al., 2021; +2022), i.e. models that transform the input with a data-dependent matrix W(x): y(x)=W(x)x. +In this work, we rely on the B-cos framework (B¨ohle et al., 2022), but instead of focusing on CNNs +as in B¨ohle et al. (2022), we investigate the applicability of this framework to transformers. +Interpretability in DNNs. The question of interpretability extends, of course, beyond transformers +and many methods for explaining DNNs have been proposed. While other approaches exist, cf. Kim +2 + +Preprint +et al. (2018), these methods typically estimate the importance of individual input features, which can +be visualised as a heatmap, cf. Lundberg & Lee (2017); Petsiuk et al. (2018); Ribeiro et al. (2016); +Simonyan et al. (2014); Springenberg et al. (2015); Zhou et al. (2016); Bach et al. (2015); Selvaraju +et al. (2017); Shrikumar et al. (2017); Srinivas & Fleuret (2019); Sundararajan et al. (2017). +Similarly, our models yield explanations in form of contribution heatmaps. However, in contrast to +the above-referenced post-hoc explanation methods, the contribution maps of our B-cos ViTs are +model-inherent. Further, as the interpretability of the B-cos ViTs relies on aligning the weights with +the inputs, the weights can be visualised in colour as in B¨ohle et al. (2022), see Figs. 1 and 7. +3 +DESIGNING HOLISTICALLY EXPLAINABLE TRANSFORMERS +In the following, we present the overarching goal that we pursue and how we structure this section +around it. First, however, we introduce the necessary background and the notation used in our work. +Preliminaries. Vision Transformers (ViT) (Dosovitskiy et al., 2021) with L blocks are given by: +y(x) = Classifier ◦ �L +l=1 (MLPBlockl ◦ AttBlockl) ◦ Tokens(x) . +(1) +Here, the input x ∈ R(CHW ) denotes a vectorised image of H =W height and width and with C +color channels; the functions, concatenated by ◦, are defined in Eqs. (2) - (5) (left), with P, E ∈ +RD×N, N the number of tokens and D their dimensionality. Further, in Eqs. (2) - (5), CNN is a +convolutional neural network1, T ‘tokenises’ the CNN output (see Sec. 3.2), Linear is a learnable +linear transform p′(p)=Wp+b with parameters W and b that is applied to each token p (columns +of P) independently, MSA denotes Multi-head Self-Attention, and E is a learnable embedding. +Following Graham et al. (2021), Pool performs average pooling over the tokens, and the model +output is given by y(x) ∈ RM with M classes. Last, we omit indices for blocks and layers whenever +unambiguous and it may be assumed that each layer has its own set of learnable parameters. +Our goal in this work is to reformulate the ViTs such that they compute their output in a more +interpretable manner. Specifically, we aim to make them dynamic linear such that they compute +y(x) = W(x) x. Instead of using the ViTs to predict W(x), cf. Alvarez-Melis & Jaakkola (2018), +we achieve this by rendering each of the ViT components dynamic linear on their own as follows: +Tokens (x) = T (CNN(x)) + E −−→ B-cos Tokens +(x) = WTokens(x) x +(2) +AttBlock (P) = MSA(P) + P +−−→ B-cos AttBlock +(P) = WAtt +(P) P +(3) +MLPBlock (P) = MLP(P) + P +−−→ B-cos MLPBlock (P) = WMLP (P) P +(4) +Classifier (P) = Linear ◦ Pool(P) −−→ B-cos Classifier +(P) = WClass (P) P . +(5) +Crucially, we define each component such that it can be expressed as a dynamic linear function, see +the right-hand side of Eqs. (2) - (5). As a result, the entire model will become dynamic linear: +y(x) = WClass(x) �L +l=1 +� +WMLP +l +(x) WAtt +l (x) +� +WTokens(x) x = W(x) x . +(6) +Specifically, we develop the B-cos ViTs in accordance with the B-cos framework (B¨ohle et al., 2022) +to render W(x) interpretable by aligning it with relevant input patterns. +Outline. In the following, we shortly summarise the most relevant aspects of B-cos networks and +how to explain them (Sec. 3.1). Then, we discuss Eqs. (2) - (5) in detail and how we ensure that +the resulting linear transform W(x) will be interpretable. In particular, we discuss the tokenisation +(Sec. 3.2), attention (Sec. 3.3), and the multi-layer perceptrons (Sec. 3.4). Finally, in Sec. 3.5, we +discuss how we encode positional information in B-cos ViTs, introducing ‘position-aware’ attention. +3.1 +B-COS NETWORKS: INTERPRETABLE MODEL-INHERENT EXPLANATIONS +As shown in Eq. (6), a dynamic linear transformer is summarised exactly by a single matrix W(x) +for every x. These linear explanations lend themselves well for understanding the model decisions: +as in plain linear models, one can calculate linear contributions from individual features (e.g., pixels) +to each output unit. In detail, the effective linear contributions ck to the k-th class logit are given by +Dynamic Linear Contribution Maps: +ck(x) = [W(x)]T +k ⊙ x , +(7) +1To simplify later equations, we take advantage of the fact that conv. layers are equivalent to linear layers with +weight constraints (weight sharing and local connectivity) and assume the CNN to process vectorised images. +3 + +Preprint +with ⊙ denoting element-wise multiplication. Crucially, these contribution maps faithfully sum- +marise the entire model, as this linear summary is inherent to the model formulation, see also Fig. 2. +Thus, we use these contribution maps to explain the B-cos ViTs, see, e.g., Figs. 1, 2 and 7. +Note, however, that while the contribution maps in Eq. (7) accurately summarise any given dynamic +linear model, this summary need not be interpretable. E.g., for piece-wise linear models, which +are also dynamic linear, this amounts to ‘Input×Grad’, cf. Adebayo et al. (2018). For such models, +however, the contributions c are very noisy and not easily interpretable for humans. Hence, we de- +sign the transformers in accordance with the ‘B-cos’ framework (B¨ohle et al., 2022), which ensures +that W(x) aligns with relevant input features and thus becomes easily interpretable. In detail, the +B-cos transform induces weight alignment by suppressing outputs for badly aligned weights: +B-cos(a; W) = +� +cosB−1(a, W) ⊙ � +W +� +a = W(a)a . +(8) +here, cos is applied row-wise, � +W denotes that the matrix rows are of unit norm, and ⊙ represents +row-wise scaling. As can be seen on the RHS of Eq. (8), the B-cos transform is dynamic linear. +As a result, the matrix rows [W(x)]k align with relevant patterns of class k. By encoding the image +such that the color is uniquely determined by the angle of the pixel encodings, it is possible to +directly visualise those matrix rows in color, see Figs. 1 and 7. For details, see B¨ohle et al. (2022). +Requirements. To ensure that a B-cos network aligns W(x) with its inputs, each of its layers needs +to (a) be bounded, (b) yield its maximum output if and only if its weight vectors align with its input, +and (c) directly scale the overall model output by its own output norm, see B¨ohle et al. (2022). In the +following, we ensure that each of the model components (Eqs. (2)-(5)), fulfills these requirements. +3.2 +INTERPRETABLE TOKENISATION MODULES: B-COS CNNS +While the original Vision Transformer only applied a single-layered CNN, it has been shown that +deeper CNN backbones yield better results and exhibit more stable training behaviour (Xiao et al., +2021). Hence, to address the general case, and to take advantage of the increased training stability +and performance, we take the tokenisation module to be given by a general CNN backbone. Being +able to explain the full ViT models consequently requires using an explainable CNN for this. +Tokenisation. We use B-cos CNNs (B¨ohle et al., 2022) as feature extractors; thus, the requirements +(a-c), see Sec. 3.1, of B-cos networks are, of course, fulfilled. The input tokens are computed as +B-cos Token pi(x) = Ti ◦ B-cos CNN(x) = WTiWCNN(x) x = WTokens +i +(x) x . +(9) +Here, pi∈RD corresponds to the ith column in the token matrix P, Ti extracts the respective features +from the CNNs’ output with WTi denoting the corresponding linear matrix. WCNN is the dynamic +linear mapping computed by the B-cos CNN, and as color-indicated, WTokens +i +(x)=WTiWCNN(x). +Finally, note that we did not include the additive positional embedding E, cf. Eq. (2) (left). For a +detailed discussion on how to provide positional information to the B-cos ViTs, please see Sec. 3.5. +3.3 +B-COS ATTENTION +Interestingly, the attention operation itself is already dynamic linear and, as such, attention lends +itself well to be integrated into the linear model summary according to Eq. (6). To ensure that +the resulting linear transformation maintains the desired interpretability, we discuss the necessary +changes to make the attention layers compatible with the B-cos formulation as discussed in Sec. 3.1. +B-cos Attention. Note that conventional attention indeed computes a dynamic linear transform: +Attention(P; Q, K, V) = softmax +� +PT QT KP +� +� +�� +� +Attention matrix A(P) +VP +���� +Value(P) += A(P) V +� +�� +� +W(P) +P += W(P)P. +(10) +Here, Q, K and V denote the respective query, key, and value transformation matrices and P denotes +the input tokens to the attention layer; further, softmax is computed column-wise. +In multi-head self-attention (MSA), see Eq. (3) (left), H distinct attention heads are used in parallel +after normalising the input. Their concatenated outputs are then linearly projected by a matrix U: +MSA(�P) = U +� +W1(�P)�P, W2(�P)�P, ... , WH(�P)�P +� +with +�P = LayerNorm(P) +(11) +4 + +Preprint +While this can still2 be expressed as a dynamic linear transform of P, we observe the following +issues with respect to the requirements (a-c), see Sec. 3.1. First, (a) while the attention matrix A(P) +is bounded, the value computation VP and the projection by U are not. Therefore, as the output +can arbitrarily increased by scaling V and U, (b) a high weight alignment is not necessary to obtain +large outputs. Finally, by normalising the outputs of the previous layer, the scale of those outputs +does not affect the scale of the overall model output anymore, which violates requirement (c). +To address (a+b), we propose to formulate a B-cos Attention Block as follows. First, we replace the +value computation and the linear projection by U by corresponding B-cos transforms. As in B¨ohle +et al. (2022), we employ MaxOut and for a given input P the resulting projections are computed as +B-cos Linear(P; S) = MaxOut ◦ B-cos(P; S) = WS(P)P +with +S ∈ {U, V}. +(12) +To fulfill (c), whilst not foregoing the benefits of LayerNorm3, we propose to exclusively apply +LayerNorm before the computation of the attention matrix. i.e. we compute A(P), see Eq. (10) as +A(P; Q, K) = softmax +� +�PT QT K�P +� +with +�P = LayerNorm(P) . +(13) +In total, a ‘B-cos AttBlock’ thus computes the following linear transformation: +B-cos AttBlock(P) = +� +WU(P′) +� +Ah(P)WV +h (P) +�H +h=1 + I +� +P = WAtt(P) P , +(14) +Here, P′ = +� +Ah(P)WV +h (P) +�H +h=1, WU and WV as in Eq. (12), and Ah(P) as in Eq. (13); the +identity matrix I reflects the skip connection around the MSA computation, see Fig. 2 and Eq. (3). +For an ablation study regarding the proposed changes, we kindly refer the reader to the supplement. +3.4 +INTERPRETABLE MLPS AND CLASSIFIERS +To obtain dynamic linear and interpretable MLPs, we convert them to ‘B-cos’ MLPs, such that they +are compatible with the B-cos formulation (Sec. 3.1) and align their weights with relevant inputs. +B-cos MLPs. Typically, an MLP block in a ViT computes the following: +MLPBlock(P) = Linear2 ◦ GELU ◦ Linear1 ◦ LayerNorm(P) + P +(15) +Here, Linear is as in Eq. (5), the GELU activation function is as in Hendrycks & Gimpel (2016), and +LayerNorm as in Ba et al. (2016). +To obtain our ‘B-cos MLPBlock’, we follow B¨ohle et al. (2022) and replace the linear layers by B- +cos transforms, remove the non-linearities and the normalisation (cf. Sec. 3.3); further, each ‘neuron’ +is modelled by two units, to which we apply MaxOut (Goodfellow et al., 2013). As a result, each +MLP block becomes dynamic linear: +B-cos MLPBlock(P) = (M2(P) L2(P) M1(P) L1(P) + I)P = WMLP(P) P . +(16) +Here, Mi(P) and Li(P) correspond to the effective linear transforms performed by the MaxOut and +B-cos operation respectively, and I denotes the identity matrix stemming from the skip connection. +Classifier. Similar to the B-cos MLPs, we also replace the linear layer in the classifier, cf. Eq. (5) +(left), by a corresponding B-cos transform and the B-cos Classifier is thus defined as +B-cos Classifier(P) = B-cos ◦ Pool(P) = L(P′)WAvgPoolP = WClass(P) P , +(17) +with L(P′) the dynamic linear matrix corresponding to the B-cos transform and P′=Pool(P). +3.5 +POSITIONAL INFORMATION IN B-COS TRANSFORMERS +In contrast to CNNs, which possess a strong inductive bias w.r.t. spatial relations (local connectivity), +transformers (Vaswani et al., 2017) are invariant w.r.t. the token order and thus lack such a ‘locality +2To be exact, it can be represented as a dynamic affine transform, since LayerNorm adds a bias term. +3We noticed normalised inputs to be crucial for the computation of the attention matrix A(P) in Eq. (10): for +unconstrained inputs, softmax easily saturates and suffers from the vanishing gradient problem. +5 + +Preprint +bias’. To nevertheless leverage spatial information, it is common practice to break the symmetry +between tokens by adding a (learnt) embedding E to the input tokens P, see Eq. (2) (left). +However, within the B-cos framework, this strategy is not optimal: in particular, note that each B-cos +transformation needs to align its weights with its inputs to forward a large output to the next layer, +see Eq. (8) and B¨ohle et al. (2022). As a result, a B-cos ViT would need to associate contents (inputs) +with specific positions, which could negatively impact the model’s generalisation capabilities. +Therefore, we investigate two alternative strategies for providing positional information to the B- +cos ViTs: additive and multiplicative attention priors, see Eqs. (18) and (19) respectively. Specifi- +cally, we propose to add a learnable bias matrix Bl +h to each attention head h in every layer l in the +model. This pair-wise (between tokens) bias is then either added4 before the softmax operation or +multiplied to the output of the softmax operation in the following way (omitting sub/superscripts): +Aadd(P) = SM (R(P) + B) +(18) +and +Amul(P) = SM (R(P)) × SM (B) . +(19) +Here, R(P)=Q�P�PT KT and SM denotes softmax. The bias B thus allows the model to learn an +attention prior, and the attention operation is no longer invariant to the token order. As such, the +model can learn spatial relations between tokens and encode them explicitly in the bias matrix B. +In our experiments, this significantly improved the performance of the B-cos ViTs, see Sec. 5.1. +4 +EXPERIMENTAL SETTING +Dataset. In this work, we focus on Vision Transformers (ViTs, Dosovitskiy et al. (2021)) for image +classification. For this, we evaluate the B-cos and conventional ViTs and their explanations on the +ImageNet dataset (Deng et al., 2009). We use images of size 224×224. For B-cos models, we +encode the images as in B¨ohle et al. (2022). +Models. We follow prior work and evaluate ViTs of different sizes in common configurations: Tiny +(Ti), Small (S), and Base (B), cf. Steiner et al. (2021). We train these models on the frozen features +of publicly available (B¨ohle et al., 2022; Marcel & Rodriguez) (B-cos) DenseNet-121 models and +extract those features at different depths of the models: after 13, 38, or 87 layers. Model names are +thus as follows: (B-cos) ViT-{size}-{L} with size∈{Ti, S, B} and L∈{13, 38, 87}. We opted for +(B-cos) DenseNet-121 backbones, as the conventional and the B-cos version achieve the same top-1 +accuracy on the ImageNet validation set. In particular, we compare B-cos ViTs on B-cos backbones +to normal ViTs on normal backbones. +Training. We employ a simple training paradigm that is common across models for comparability. +All models are trained with RandAugment (Cubuk et al., 2020) for 100 epochs with a learning rate +of 2.5e−4, which is decreased by a factor of 10 after 60 epochs; for details, see supplement. +Evaluation Metrics. We evaluate all models with respect to their accuracy on the ImageNet valida- +tion set. Further, we employ two common metrics to assess the quality of the model explanations. +First, we evaluate the grid pointing game (B¨ohle et al., 2021). For this, we evaluate the explanations +(see below) on 250 synthetic image grids of size 448×448, containing 4 images of distinct classes, +see Fig. 4; the individual images are ordered by confidence and we measure the fraction of positive +attribution an explanation method assigns to the correct sub-image when explaining a given class. +Note that, in contrast to fully convolutional networks, transformers with positional embeddings ex- +pect a fixed-size input. To nevertheless evaluate the models on such synthetic image grids, we scale +down the image grid to the required input size of 224x224 to allow for applying the ViTs seamlessly. +Second, we evaluate two pixel perturbation metrics, cf. Chefer et al. (2021). For this, the pixels are +ranked according to the importance assigned by a given explanation method. Then, we increasingly +zero out up to 25% of the pixels in increasing (decreasing) order, whilst measuring the model confi- +dence in the ground truth class; a good explanation should obtain a high area under (over) the curve, +i.e. the model should be insensitive to unimportant pixels and sensitive to important ones. +We evaluate the perturbation metrics on the 250 most confidently and correctly classified images +to enable a fair comparison between models, as the confidence affects the metrics; more details in +supplement. Last, to succinctly summarise the two metrics, we evaluate the area between the curves. +4Note that an additive positional bias in attention layers has been proposed before (Graham et al., 2021). +6 + +Preprint +Tiny +Small +Base +Size of the B-cos ViT-size-87 +60 +70 +80 +Top-1 accuracy (%) +71.0 +71.5 +75.6 +74.3 +74.3 +76.6 +73.1 +73.9 +76.7 +Encoding of positional information +Position Embedding +Add. Att. Bias Eq. (18) +Mul. Att. Bias Eq. (19) +Fig. 3: ImageNet accuracy of differently sized B-cos ViTs (Tiny, +Small, Base) depending on the positional encoding. We find B- +cos ViTs with Amul, see Eq. (19), to perform significantly better. +Evidence for Fire Truck +Evidence for Lorikeet +Evidence for Tiger +Evidence for Taxi / Cab +Input +Localisation +Example +Fig. 4: In the localisation metric, we mea- +sure the fraction of pos. evidence assigned to +the correct grid cell for each occurring class. +Tiny +Small +Base +Transformer size +60 +70 +80 +Top-1 accuracy (%) +71.4 +72.1 +74.6 +Conventional +71.1 +74.3 +75.6 +B-cos +73.0 +74.5 +74.9 +Conventional +74.2 +75.7 +76.6 +B-cos +73.1 +74.3 +74.5 +Conventional +74.9 +76.6 +76.7 +B-cos +13 backbone layers +38 backbone layers +87 backbone layers +Fig. 5: ImageNet accuracies of B-cos ViTs with a multiplicative attention bias (Eq. (19)) compared to standard +ViTs and backbones, both for differently sized ViTs (Tiny, Small, Base) and backbones (13, 38, or 87 layers). +We find that the B-cos ViTs perform at least as well as the baseline ViTs over almost all tested configurations. +Explanation Methods. Apart from the model-inherent explanations (Eq. (7)), we evaluate two sets +of explanation methods. First, we follow Chefer et al. (2021) and evaluate common transformer- +specific explanations such as the attention in the final layer (FinAtt), attention rollout (Rollout) (Ab- +nar & Zuidema, 2020), a transformer-specific LRP implementation (CheferLRP) proposed by Chefer +et al. (2021), ‘partial LRP’(pLRP) (Voita et al., 2019), and ‘GradSAM’ (Barkan et al., 2021). +Further, we evaluate architecture-agnostic methods such as Integrated Gradients (IntGrad) (Sun- +dararajan et al., 2017), adapted GradCAM (Selvaraju et al., 2017) as in Chefer et al. (2021), and +‘Input×Gradient’ (IxG), cf. Adebayo et al. (2018). As no LRP rules are defined for B-cos ViTs we +only apply it to baseline models. For method details, we kindly refer the reader to the supplement. +We evaluate all of those methods (if applicable) to the proposed B-cos ViTs, as well as the baselines +consisting of conventional ViTs and backbones and compare them on the metrics described above. +5 +RESULTS +In the following, we present our experimental results. Specifically, in Sec. 5.1 we analyse the classi- +fication performance of the B-cos ViTs: we investigate how the encoding of positional information +affects model accuracy (see Sec. 3.5) and compare the classification performance of B-cos and con- +ventional ViTs. Further, in Sec. 5.2, we evaluate the model-inherent explanations of the B-cos ViTs +against common post-hoc explanation methods evaluated on the same models. To highlight the gain +in interpretability over conventional ViT models, we also compare the inherent explanations of the +B-cos ViTs to the best post-hoc explanations evaluated on conventional ViTs, see supplement. +7 + +Preprint +71 +72 +73 +74 +75 +76 +77 +Model accuracy +0.00 +0.25 +0.50 +0.75 +1.00 +Localisation score +×2.47 +Localisation Metric +71 +72 +73 +74 +75 +76 +77 +Model accuracy +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +Normalised ABC +×1.99 +Perturbation Metric +Ours +Rollout +GradSAM +IntGrad +IxG +FinAtt +GradCAM +Explanation Method +Fig. 6: Quantitative comparison of explanation methods according to two metrics: localisation (left) and per- +turbation (right); for a description of metrics and methods, see Sec. 4. We evaluated the methods for all B-cos +ViTs shown in Fig. 5 and plot the corresponding scores (markers). We also plot the mean score over all models +(dashed lines) per method and the average improvement of the model-inherent over the best post-hoc explana- +tion (localisation: ×2.47, perturbation: ×1.99). Note that for the perturbation metric, we normalised the area +between curves (ABC) by the scores of the model-inherent explanations for better cross-model comparison. +5.1 +CLASSIFICATION PERFORMANCE OF B-COS VITS +In Fig. 3, we compare the top-1 ImageNet accuracy of various B-cos ViTs trained on the feature +embeddings of the 87th layer of a frozen5 B-cos DenseNet-121 (B¨ohle et al., 2022). Specifically, we +compare ViTs of different sizes (Tiny, Small, Base) and with different ways of allowing the models +to use positional information, see Eqs. (2), (18) and (19). We find that the multiplicative attention +bias, see Eq. (19), consistently yields significant gains in performance. As discussed in Sec. 3.5, we +believe this could be due to the higher disentanglement between content and positional information. +However, in preliminary experiments with conventional ViTs, we did not observe significant benefits +from such a multiplicative prior and this seems to be particularly advantageous for B-cos ViTs. +Interestingly, once trained with such a multiplicative attention prior, we find the B-cos ViTs to +perform at least as good as their conventional counterparts over a wide range of configurations, see +Fig. 5; we find consistent results even without MaxOut in the Transformer layers (cf. Sec. 3), as we +show in Appendix B.3. However, these results have to be interpreted with caution: ViTs are known +to be highly sensitive to, e.g., the amount of data augmentation, the number of training iterations, +and model regularisation, see Steiner et al. (2021). Moreover, our goal in this work is to develop +interpretable ViTs and our focus thus lies on evaluating the quality of the explanations (Sec. 5.2). +5.2 +INTERPRETABILITY OF B-COS VITS +Here, we assess how well the inherent explanations (Eq. (7)) of B-cos ViTs explain their output and +compare to common post-hoc explanations; for comparisons to baseline ViTs, see supplement. +Localisation Metric. In Fig. 6 (left), we plot the mean localisation score per model configuration +(B-cos ViT-{size}-{L}) and explanation method, see Sec. 4. We find that across all configurations, +the model-inherent explanations according to Eq. (7) yield by far the best results under this metric +and outperform the best post-hoc explanation for the B-cos ViTs (Rollout) by a factor of 2.47. +Pixel Perturbation. As for the localisation, in Fig. 6 (right), we plot the normalised mean area +between the curves (ABC) per model configuration and explanation method of the B-cos ViTs. +Specifically, the mean ABC is computed as the mean area between the curves when first removing +the most / least important pixels from the images; we normalise the mean ABC for each explanation +by the mean ABC of the model-inherent explanation (Ours) per model configuration to facilitate +cross-model comparisons. Again, the model-inherent explanations perform best and, on average, +they outperform the second best post-hoc method (Rollout) on B-cos ViTs by a factor of 1.99. +Qualitative Examples. In Figs. 1 and 7, we qualitatively compare the inherent explanations (size: B, +38 backbone layers, see Fig. 5) to post-hoc explanations evaluated on the same model. As becomes +apparent, the model-inherent summaries not only perform well quantitatively (cf. Fig. 6), but are also +qualitatively convincing. Colour visualisations as in B¨ohle et al. (2022); more results in supplement. +5We chose to freeze the backbones to reduce the computational cost and compare the architectures across a wide +range of settings. We observed comparable results when training the full models for individual architectures. +8 + +Preprint +black swan +Input image +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IntGrad +forklift +digital clock +lion +Fig. 7: Comparison of the model-inherent explanations (Ours) of a B-cos ViT-B-38, and several post-hoc expla- +nations (GradSAM, GradCAM, Rollout, FinAtt, IntGrad) for class k (left). In particular, we show explanations +for the classes ‘black swan’, ‘forklift’, ‘digital clock’, and ‘lion’ on a synthetic image containing these classes, +as used in the localisation metric, see Fig. 4. As B-cos ViTs follow the B-cos formulation, we can visualise the +rows of W(x) in colour (B¨ohle et al., 2022). Additionally, we show contribution maps according to Eq. (7). +In contrast to attention explanations, which are not class-specific (Chefer et al., 2021), we find the +model-inherent explanations of B-cos ViTs to be highly detailed and class-specific. E.g., in Fig. 1, +we compare model-inherent explanations to attention-based explanations for single images from the +ImageNet dataset which are inherently ambiguous. In Fig. 7, we evaluate the model on images as +used in the localisation metric, see Sec. 4, i.e. synthetic images with multiple classes. In both cases +we find the model-inherent explanations to accurately highlight the respective features for the class +logit that we aim to explain, whereas other methods are much less sensitive to the class logit; in fact, +attention-based explanations are inherently agnostic to the choice of logit and thus the same for all +classes. For comparisons to explanations for conventional ViTs, see the supplement. +6 +CONCLUSION +We present a novel approach for designing ViTs that are holistically explainable. For this, we design +every component of the ViTs with the explicit goal of being able to summarise the entire model by +a single linear transform. By integrating recent advances in designing interpretable dynamic linear +models (B¨ohle et al., 2022), these summaries become interpretable, as they are implicitly optimised +to align with relevant input patterns. The resulting B-cos ViTs constitute competitive classifiers and +their inherent linear summaries outperform any post-hoc explanation method on common metrics. +Compared to attention-based explanations, our method can be understood to ‘fill the blanks’ in at- +tention rollout (Abnar & Zuidema, 2020). Specifically, attention rollout computes a linear summary +of the attention layers only. By integrating explanations for the remaining components (tokenisation, +attention, MLPs), we are able to obtain holistic explanations of high detail, see Figs. 1 and 7. +As transformers are highly modality-agnostic, we believe that our work has the potential to positively +impact model interpretability across a wide range of domains. Evaluating B-cos transformers on +different tasks and modalities is thus an exciting direction that we aim to explore in future work. +Limitations. While the B-cos ViTs allow us to extract model-faithful explanations for single images, +note that these explanations are always local in nature, i.e. for single data points. The explanations +thus help understanding an individual classification, but do not directly give insights into which +features the models most focus on over the entire dataset. It would thus be interesting to combine +B-cos ViTs with global explanation methods, such as in Bau et al. (2017); Kim et al. (2018). +Further, we focused primarily on the designing of interpretable transformers, and, to test across a +wide range of models, limited experiments to the ImageNet-1k dataset. As transformers are known +to significantly benefit from additional data and training (Dosovitskiy et al., 2021), it would be +interesting to test the limits of capacity of the B-cos ViTs and scale to more complex tasks. +9 + +Preprint +ETHICS STATEMENT +The growing adoption of deep neural network models in many different settings is accompanied by +an increasingly louder call for more transparency in the model predictions; especially in high-stake +situations, relying on an opaque decision process can have severe consequences (Rudin, 2019). With +this work, we make a step towards developing inherently more transparent neural network models +that explain their decisions without incurring losses in model performance. +However, we would like to emphasise that our contribution can only be seen as a step in this direc- +tion; while the explanations might seem meaningful on a per sample basis, they could lead to a false +sense of security in terms of ‘understanding’ model behaviour. Currently, we can give no formal +guarantees for model behaviour under unseen input data and more research on explainable machine +learning is necessary. Lastly, any research that holds the potential for accelerating the adoption of +machine learning systems could have unpredictable societal impacts. +REFERENCES +Samira Abnar and Willem Zuidema. Quantifying Attention Flow in Transformers. In Proceedings +of the Annual Meeting of the Association for Computational Linguistics (ACL), 2020. 1, 2, 7, 9, +14, 15, 23 +Julius Adebayo, Justin Gilmer, Michael Muelly, Ian J. Goodfellow, Moritz Hardt, and Been Kim. +Sanity Checks for Saliency Maps. +In Advances in Neural Information Processing Systems +(NeurIPS), 2018. 4, 7, 23 +David Alvarez-Melis and Tommi S. Jaakkola. Towards Robust Interpretability with Self-Explaining +Neural Networks. In Advances in Neural Information Processing (NeurIPS), 2018. 2, 3 +Lei Jimmy Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. +Layer Normalization. +CoRR, +abs/1607.06450, 2016. URL http://arxiv.org/abs/1607.06450. 5 +Sebastian Bach, Alexander Binder, Gr´egoire Montavon, Frederick Klauschen, Klaus-Robert M¨uller, +and Wojciech Samek. On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer- +Wise Relevance Propagation. PLoS ONE, 2015. 3 +Oren Barkan, Edan Hauon, Avi Caciularu, Ori Katz, Itzik Malkiel, Omri Armstrong, and Noam +Koenigstein. Grad-SAM: Explaining Transformers via Gradient Self-Attention Maps. In Pro- +ceedings of the International Conference on Information and Knowledge Management (CIKM), +pp. 2882–2887, 2021. 1, 2, 7, 23 +Jasmijn Bastings and Katja Filippova. The elephant in the interpretability room: Why use attention +as explanation when we have saliency methods? +In Proceedings of the Third BlackboxNLP +Workshop on Analyzing and Interpreting Neural Networks for NLP, 2020. 1, 2 +David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba. Network dissection: +Quantifying interpretability of deep visual representations. In Proceedings of the IEEE conference +on computer vision and pattern recognition, pp. 6541–6549, 2017. 9 +Wieland Brendel and Matthias Bethge. Approximating CNNs with Bag-of-local-Features models +works surprisingly well on ImageNet. In International Conference on Learning Representations +(ICLR), 2019. 2 +Moritz B¨ohle, Mario Fritz, and Bernt Schiele. Convolutional Dynamic Alignment Networks for +Interpretable Classifications. In Proceedings of the IEEE Conference on Computer Vision and +Pattern Recognition (CVPR), 2021. 1, 2, 6, 23, 24 +Moritz B¨ohle, Mario Fritz, and Bernt Schiele. B-cos Networks: Attention is All We Need for Inter- +pretability. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition +(CVPR), 2022. 1, 2, 3, 4, 5, 6, 8, 9, 14, 21, 22, 23 +Hila Chefer, Shir Gur, and Lior Wolf. Transformer interpretability beyond attention visualization. In +Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. +1, 2, 6, 7, 9, 22, 23 +10 + +Preprint +Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le. Randaugment: Practical automated +data augmentation with a reduced search space. In Proceedings of the Conference on Computer +Vision and Pattern Recognition (CVPR), Workshops, 2020. 6, 23 +Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. ImageNet: A large-scale +hierarchical image database. In Proceedings of the IEEE Conference on Computer Vision and +Pattern Recognition (CVPR), 2009. 6 +Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas +Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszko- +reit, and Neil Houlsby. An Image is Worth 16x16 Words: Transformers for Image Recogni- +tion at Scale. In International Conference on Learning Representations, 2021. URL https: +//openreview.net/forum?id=YicbFdNTTy. 3, 6, 9 +Ian Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio. Maxout +networks. In International Conference on Machine Learning (ICML), 2013. 5, 22 +Benjamin Graham, Alaaeldin El-Nouby, Hugo Touvron, Pierre Stock, Armand Joulin, Herv´e J´egou, +and Matthijs Douze. LeViT: a Vision Transformer in ConvNet’s Clothing for Faster Inference. In +Proceedings of the International Conference on Computer Vision (ICCV), 2021. 3, 6 +Dan Hendrycks and Kevin Gimpel. +Gaussian error linear units (gelus). +arXiv preprint +arXiv:1606.08415, 2016. 5, 22 +Sarthak Jain and Byron C Wallace. Attention is not Explanation. In Proceedings of the Conference of +the North American Chapter of the Association for Computational Linguistics: Human Language +Technologies (NAACL-HLT), pp. 3543–3556, 2019. 1 +Been Kim, Martin Wattenberg, Justin Gilmer, Carrie J. Cai, James Wexler, Fernanda B. Vi´egas, +and Rory Sayres. Interpretability Beyond Feature Attribution: Quantitative Testing with Concept +Activation Vectors (TCAV). In International Conference on Machine Learning (ICML), 2018. 2, +9 +Scott M. Lundberg and Su-In Lee. +A Unified Approach to Interpreting Model Predictions. +In +Advances in Neural Information Processing Systems (NeurIPS), 2017. 3 +S´ebastien Marcel and Yann Rodriguez. Torchvision library, pretrained models. pytorch.org/ +vision/stable/models.html. Accessed: 2021-11-11. 6 +Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor +Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward +Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, +Lu Fang, Junjie Bai, and Soumith Chintala. PyTorch: An Imperative Style, High-Performance +Deep Learning Library. In Advances in Neural Information Processing Systems (NeurIPS), 2019. +22, 23 +Vitali Petsiuk, Abir Das, and Kate Saenko. RISE: Randomized Input Sampling for Explanation +of Black-box Models. In British Machine Vision Conference (BMVC), 2018. URL http:// +bmvc2018.org/contents/papers/1064.pdf. 3 +Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. ”Why Should I Trust You?”: Explaining +the Predictions of Any Classifier. In International Conference on Knowledge Discovery and Data +Mining (SIGKDD), 2016. 3 +Cynthia Rudin. Stop explaining black box machine learning models for high stakes decisions and +use interpretable models instead. Nature Machine Intelligence, 1(5):206–215, 2019. 10 +Ramprasaath R. Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, +and Dhruv Batra. Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based +Localization. In International Conference on Computer Vision (ICCV), 2017. doi: 10.1109/ +ICCV.2017.74. URL https://doi.org/10.1109/ICCV.2017.74. 3, 7, 23 +Sofia Serrano and Noah A Smith. Is Attention Interpretable? In Proceedings of the Annual Meeting +of the Association for Computational Linguistics (ACL), 2019. 1, 2 +11 + +Preprint +Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. Learning Important Features Through +Propagating Activation Differences. In International Conference on Machine Learning (ICML), +2017. 3 +Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep Inside Convolutional Networks: +Visualising Image Classification Models and Saliency Maps. In International Conference on +Learning Representations (ICLR), Workshop, 2014. URL http://arxiv.org/abs/1312. +6034. 3 +Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin A. Riedmiller. Striving for +Simplicity: The All Convolutional Net. In International Conference on Learning Representations +(ICLR), Workshop, 2015. URL http://arxiv.org/abs/1412.6806. 3 +Suraj Srinivas and Franc¸ois Fleuret. Full-Gradient Representation for Neural Network Visualization. +In Advances in Neural Information Processing Systems (NeurIPS), 2019. 3 +Andreas Steiner, Alexander Kolesnikov, Xiaohua Zhai, Ross Wightman, Jakob Uszkoreit, and Lucas +Beyer. How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers. +arXiv e-prints, art. arXiv:2106.10270, June 2021. 6, 8 +Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic Attribution for Deep Networks. In +Doina Precup and Yee Whye Teh (eds.), International Conference on Machine Learning (ICML), +2017. 3, 7, 23 +Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, +Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in Neural Informa- +tion Processing Systems (NeurIPS), 2017. 1, 2, 5 +Elena Voita, David Talbot, Fedor Moiseev, Rico Sennrich, and Ivan Titov. Analyzing Multi-Head +Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned. In Proceedings +of the Annual Meeting of the Association for Computational Linguistics (ACL), 2019. 7, 23 +Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Doll´ar, and Ross Girshick. +Early +convolutions help transformers see better. In Advances in Neural Information Processing Systems +(NeurIPS), volume 34, pp. 30392–30400, 2021. 4 +Bolei Zhou, Aditya Khosla, `Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning Deep +Features for Discriminative Localization. In Proceedings of the IEEE Conference on Computer +Vision and Pattern Recognition (CVPR), 2016. 3 +12 + +Preprint +Supplementary Material +Table of Contents +In this supplement to our work on designing holistically explainable transformers, we provide: +(A) Additional Qualitative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 +In this section, we show additional qualitative results and discuss the quali- +tative differences between the various explanations methods in more detail. +For this, we include explanations for B-cos as well as for conventional ViTs. +(B) Additional Quantitative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 +In this section, we show additional quantitative results. In particular, we +compare the model-inherent explanations of the B-cos ViTs to explanations +for conventional ViTs, both for the localisation and the perturbation metrics. +Further, we present the results of an ablation study in which we investigate +the impact of the design choices within the attention layer in more detail. +(C) Implementation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 +In this section, we describe the model architectures, the training procedure, +the explanation methods, as well as the evaluation metrics in more detail. +13 + +Preprint +A +ADDITIONAL QUALITATIVE RESULTS +A.1 +COMPARISON TO ATTENTION EXPLANATIONS +Input +Ours +[W(x)]k +Ours +Eq. (7) +Rollout +FinAtt +rocking chair +blue bird +goldfish +magpie +cock +Ibizan hound +Fig. A1: Inherent explanations (cols. 2+3) of B-cos ViTs +vs. attention explanations (cols. 4+5) for the same model. +Note that W(x) faithfully reflects the whole model and +yields more detailed and class-specific explanations than +attention alone. For a detailed discussion, see Sec. A.1. +For the reader’s convenience, in Fig. A1 +we repeat the qualitative results presented in +Fig. 1, such as to facilitate the following dis- +cussion of the qualitative differences between +the holistic and the purely attention-based ex- +planations of B-cos ViTs. +In particular, we would like to point out sev- +eral key differences between our holistic ex- +planations as per Eq. (7) and the attention- +based explanations according to Attention +Rollout (Abnar & Zuidema, 2020) and the +last layer’s attention. +First, only the linear mapping W(x) used +for the contribution maps in Eq. (7) is able +to capture ‘negative evidence’ for the respec- +tive classes, see col. 2 in Fig. A1. Note that +this does not depend on the particular choice +of images shown here. +Instead, as the at- +tention matrices consist only of non-negative +values, the attention-based explanations can- +not distinguish between positively and neg- +atively contributing features. +Therefore, to +improve the attention visualisation and more +clearly highlight details in the attention maps, +we plot the attention-based explanations on +a colour scale from 0 to the maximal atten- +tion value. The model-inherent explanation, +in contrast, use a colour scale from [−p, p] with p the maximum absolute pixel contribution. +Importantly, as attention-based explanations do not distinguish between positively and negatively +contributing neurons / pixels, they are inherently not class-specific. For example, especially in +images in which various classes are present (rows 1, 2, 3, 5), attention focuses on all occurring +class instances: all birds in rows 2, 3, and 4, as well as both dogs in row 1. The model-inherent +explanations, on the other hand, clearly distinguish between positive and negative contributions and +are thus able to resolve class-specific details. +Secondly, the attention-based explanation are of much lower resolution than the model-inherent +ones. Again, this cannot be attributed to the choice of images, but reflects an intrinsic difference +between the explanations: whereas the linear mapping W(x) reflects the entire model including the +tokenisation module and thus attributes on the level of pixels, the attention explanations can only +yield attributions at the level of tokens, which highlights a key difference between the methods: +while the attention explanations only include a few layers in their attributions, the model-inherent +linear map W(x) constitutes an exact summary of the entire model. +Third, as shown in the first column, the rows of the linear mapping W(x) can directly be visualised +in colour space, as the B-cos ViTs are designed according to the B-cos framework proposed by +B¨ohle et al. (2022). Note that this is not a masked version of the original image, but instead a +direct reflection of the dynamically computed weight matrix W(x), for details see Sec. C.3. Such +visualisations are not possible with attention-based explanations. +Finally, we would like to highlight the relation between attention rollout and the model-inherent +linear mapping. Specifically, as shown in Eq. (6), note that the entire model can be summarised by +W(x) = WClass(x) �L +l=1 +� +WMLP +l +(x) WAtt +l (x) +� +WTokens(x) . +(A.1) +Interestingly, attention rollout in fact computes the overall attention attributions in a similar manner: +Arollout(x) = IClass �L +l=1 +� +IMLP +l +¯Al(x) +� +ITokens , +(A.2) +14 + +Preprint +with Ilayer replacing the actual linear transformation of a specific layer by an identity matrix and +¯Al denoting the average attention distribution of layer l, see Abnar & Zuidema (2020). Comparing +Eqs. (A.1) and (A.2) succinctly shows how solely attention-based explanations leave out a large part +of the model computations, which are seamlessly integrated in the complete linear mapping given +by W(x). +A.2 +NORMALISING THE VISUALISATIONS ACROSS MULTIPLE EXPLANATIONS +As we discuss in Appendix C.3, the individual explanations are normalised independently of each +other; i.e., all explanations shown on the blue-white-red colour map (Ours (Eq. (7)), GradSAM, +GradCAM, IxG, IntGrad, and pLRP) are plotted on a scale from −v to v with v the 99.9th percentile +of the absolute value of the given attribution map. As such, the resulting attribution maps are not +directly comparable across different explanations. To show the effect of normalising across multiple +explanations, in Fig. A2 we repeat Fig. 7 from the main paper, once normalised across contribution +maps, and once normalised independently. To normalise across contribution maps, v is computed +as the 99.9th percentile of the absolute value in all of the four class explanations per method in the +figure. +A.3 +ADDITIONAL EXPLANATIONS AND COMPARISONS +In Fig. A3, we compare the model-inherent explanations of a B-cos ViT-B-38 model to additional +explanation methods apart from purely attention-based ones. Moreover, we show explanations ex- +tracted for a conventional ViT-B-38 model in Fig. A4 for comparison. +We would like to highlight the following. First, we find that the model-inherent explanations of the +B-cos ViTs provide more detailed and convincing explanations than any of the post-hoc explanations +when evaluated on the same model. Crucially, these explanations do not only look convincing, but +in fact accurately reflect the model computations of the B-cos ViTs—i.e., they are model-faithful. +Further, the model-inherent explanations do not only compare favourably to other explanations eval- +uated on our newly proposed B-cos ViTs. Instead, they also provide much more detail and highlight +more class-specific features than any of the post-hoc explanation methods yield on conventional +ViTs, see Fig. A4. As such, we find that there is a clear gain in interpretability when using B-cos +ViTs instead of conventional ones. +B +ADDITIONAL QUANTITATIVE RESULTS +In this section, we quantitatively compare the interpretability of the B-cos ViTs to that of conven- +tional ViTs (Appendix B.1). Specifically, as in Sec. 5.2, we discuss the localisation and the pertur- +bation metrics. Additionally, in Appendix B.2, we present results of an ablation study in which we +investigate the design choices of the B-cos Attention module in more detail. +B.1 +INTERPRETABILITY COMPARISON: B-COS VS. CONVENTIONAL VIT MODELS +Localisation. In Fig. B1 (right) we present the localisation results of post-hoc explanation methods +evaluated on conventional ViTs; for comparison, we repeat the results of the B-cos ViTs (see Fig. 6) +on the left. As becomes apparent, no post-hoc explanation method evaluated on conventional ViTs +allows for localising the correct grid images (cf. Fig. 4) in the localisation metric to the same degree +as is possible with the model-inherent explanations. Specifically, we find that the model-inherent +explanations yield on average 2.32 times higher localisation scores across the various model config- +urations than the best post-hoc explanation method on conventional ViTs (IntGrad). +Perturbation. In Fig. B2 (right) we present the perturbation metric results of post-hoc explana- +tion methods evaluated on conventional ViTs; for comparison, we repeat the results of the B-cos +ViTs (see Fig. 6) on the left. Specifically, as discussed in the main paper, on the left we show the +normalised mean area between the curces (ABC) for each model configuration (differently sized +backbones and transformers), in which the ABC of each configuration is normalised by the ABC of +the model-inherent explanations (Ours). To enable a comparison between the conventional and the +B-cos ViTs, on the right we normalise by the best post-hoc method (FinAtt) and further multiply +the resulting score by the ratio between the mean scores across configurations of FinAtt on conven- +tional ViTs and the mean scores of Ours on B-cos ViTs (corresponding to the respective dashed lines +before normalisation). +As discussed in the main paper, we find that the model inherent explanations of B-cos ViTs con- +sistently yield the best pixel ranking for each of the configurations of the B-cos ViTs. Further, the +15 + +Preprint +black swan +Input image +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IntGrad +forklift +digital clock +lion +(a) Independently normalised attribution maps. +black swan +Input image +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IntGrad +forklift +digital clock +lion +(b) Jointly normalised attribution maps. +Fig. A2: (a) Repetition of Fig. 7 from the main paper, i.e., with each attribution map normalised independently. +(b) The same figure is shown again, but this time the normalisation is done column-wise, i.e., all explanations of +a given method are shown on the same scale (except for the coloured explanations in the second column, which +are unchanged). Note that the attention-based explanations are the same across all classes to begin with and +are thus not affected. The IntGrad explanations as well as the forklift explanation according to Ours (7) change +most notably—in the case of the model-inherent explanations, this directly reflects the fact that the model +has found the least evidence for forklift: the sum of positive contributions according to the model-inherent +contribution maps are 13.6 (black swan), 3.3 (forklift), 7.0 (digital clock), and 5.2 (lion). +ABC is on average much higher for the model-inherent explanations for B-cos ViTs than the ABC +resulting from the rankings of post-hoc explanations on conventional ViTs. Note, however, that this +could also reflect a difference in model stability and the comparisons across models have thus to be +interpreted with care. +B.2 +ABLATION STUDY: ANALYSING THE DESIGN CHOICES IN THE B-COS ATTENTION +MODULE +In this subsection, we analyse the impact of the proposed changes for the attention module in more +detail. Specifically, we investigate the effect of changing the position of the LayerNorm module +within the attention layer. Further, we discuss the effect of changing the model’s value computation +and projection layers to B-cos layers. +Position of the LayerNorm module. In Fig. B3, we present the classification performance results +of various B-cos ViT-S models trained on embeddings extracted at different depths of the back- +16 + +Preprint +ibex +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +limpkin +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +redshank +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +ambulance +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +harp +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +axolotl +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +traffic light +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +indigo bunting +Ours [W(x)]k +Ours Eq. (7) +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +Fig. A3: Comparison of inherent explanations (Ours) of a B-cos ViT-B-38, and several post-hoc explanations +for class k (left). For Ours, we show a colour visualisation (see Sec. C.3) of the corresponding row of the +weight matrix W(x) as well as the corresponding contribution maps as defined in Eq. (7). Note that of the +compared methods, the model-inherent explanations yield by far the most detail and class-specificity, as also +discussed in Sec. A.1 above. For a comparison to explanations generated for a conventional ViT-B-38 model +on the same set of images, see the following Fig. A4. +bone B-cos DenseNet-121 model. Specifically, we evaluate three different model configurations for +each backbone depth: ‘Standard Attention’, ‘Shifted LayerNorm (B=1)’, and ‘Shifted LayerNorm +(B=2)’. Here, ‘Standard Attention’ refers to the unchanged attention module as it is used in con- +ventional ViT models. On the other hand, the ‘Shifted LayerNorm’ models implement the change +described in eq. (13); i.e., for these models, the normalisation layer is moved inside the softmax +computation instead of being applied before the attention module as a whole. We observe that the +models with the shifted LayerNorm perform significantly better than those using standard attention, +especially for shallower backbone models. +We attribute this to the fact that using LayerNorm only within the softmax computation leaves the +norm of the value vectors unchanged, such that they are inherently on a similar scale as the token +embeddings they are added to in the skip connection—this allows the model to compute significant +and well-scaled updates of the token embeddings via the attention module. Moreover, the model can +learn bias and scale parameters that are specifically tailored to the softmax layer, instead of affecting +both the softmax computation as well as the value vectors at the same time. +In the standard attention module, on the other hand, the norm of the value vectors can differ signif- +icantly from the norm of the token embeddings in the residual connection, which can make it more +17 + +Preprint +ibex +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +limpkin +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +redshank +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +ambulance +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +harp +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +axolotl +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +traffic light +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +indigo bunting +CheferLRP +pLRP +GradSAM +GradCAM +Rollout +FinAtt +IxG +IntGrad +Fig. A4: Importance attributions given by common post-hoc explanation methods applied to a conventional +ViT-B-38 model (see Sec. 4 for the model specifications) on the same set of images as in Fig. A3. We find that +none of the common post-hoc explanations for conventional ViTs give similarly detailed results as the model- +inherent explanations do for B-cos ViTs, see Fig. A3. As such, we observe a clear gain in interpretability when +using B-cos ViTs instead of conventional ones. +difficult for the model to take advantage of the attention module. This hypothesis is corroborated +by an analysis of the norms of the embeddings. In particular, we find the embeddings coming from +the skip connections to be on average several orders of magnitude larger than those returned by the +attention layer in the models trained with standard attention: e.g., by a factor of 105 in the model +trained on a 13-layer backbone model. In contrast, in the Shifted LayerNorm model with B=2, this +factor is on the order of 100, i.e., both embeddings are in fact on a similar scale. While models with +standard attention could in principle learn large scale values in the LayerNorm modules, this would +effectively result in one-hot encodings in the softmax computation, which could hamper learning. +As the attention modules thus have very limited impact on the model output, we further observe that +the model does not seem to learn useful attention maps in the first place. E.g., in Fig. B4 we compare +the attention maps of the models with Standard Attention and the Shifted LayerNorm models on +various images and find those of the Standard Attention model to be much less structured; note that +for the Standard Attention model, the model output is no longer a dynamic linear transformation of +the input, due to the LayerNorm module. +B-cos transforms for value and projection layers. In the following, we discuss the impact of +replacing the linear layers typically used in the value computation and the projection layers by B- +cos layers (cf. eq. (14). In particular, we would first like to highlight that a B-cos transform with +18 + +Preprint +71 +72 +73 +74 +75 +76 +77 +Model accuracy +0.00 +0.25 +0.50 +0.75 +1.00 +Localisation score +×2.47 +B-Cos ViTs +71 +72 +73 +74 +75 +Model accuracy +×2.32 +Conventional ViTs +Localisation Metric +Ours +Rollout +FinAtt +IntGrad +IxG +GradSAM +GradCAM +pLRP +CheferLRP +Fig. B1: Left: Localisation metric results for the B-cos ViTs of various sizes, same as shown in the main paper +in Fig. 6 (left). Right: For comparison, we show the results of common post-hoc explanations evaluated on the +corresponding conventional ViTs. As can be seen, the model-inherent explanations of the B-cos ViTs not only +constitute the best localising explanation for any given B-cos ViT, but also achieve much higher localisation +scores than the best post-hoc explanations evaluated on conventional ViTs. +71 +72 +73 +74 +75 +76 +77 +Model accuracy +0.0 +0.5 +1.0 +Normalised ABC +×1.99 +B-Cos ViTs +71 +72 +73 +74 +75 +Model accuracy +×1.85 +Conventional ViTs +Perturbation Metric +Ours +Rollout +FinAtt +IntGrad +IxG +GradSAM +GradCAM +pLRP +CheferLRP +Fig. B2: Left: Perturbation metric results for the B-cos ViTs of various sizes, same as in the main paper in +Fig. 6 (left). Right: For comparison, we show the results of common post-hoc explanations evaluated on +the corresponding conventional ViTs. Note that, to allow for a comparison between the B-cos ViTs and the +conventional ViTs, we normalised the mean ABCs of the conventional ViTs by the mean ABC of the best post- +hoc method (FinAtt) and multiplied the results by the ratio between the mean ABCs FinAtt on conventional +ViTs and the mean ABCs of Ours on B-cos ViTs. For a detailed discussion, see Sec. B. +13 backbone layers +38 backbone layers +87 backbone layers +0.50 +0.55 +0.60 +0.65 +0.70 +0.75 +0.80 +Top-1 accuracy (%) +Standard Attention +Shifted LayerNorm (B=1) +Shifted LayerNorm (B=2) +Fig. B3: Ablation results for different version of the attention module. Specifically, we show the top-1 accuracy +on the ImageNet validation set for B-cos ViTs with the conventional attention module (‘Standard Attention’) +and the proposed B-cos Attention (‘Shifted LayerNorm’, see eq. (13)). Specifically, for the latter we show the +results of models trained with different values for B (B=1 and B=2) in the value computation and the projection +head, see eq. (14). Note that for B=1, the B-cos transform is equivalent to a linear transformation. As such, +‘Standard Attention’ and ‘Shifted LayerNorm (B=1)’ differ only in the positioning of the LayerNorm module. +19 + +Preprint +indigo bunting +Input +Rollout +FinAtt +redshank +limpkin +axolotl +Standard Attention +(a) +indigo bunting +Input +Ours [W(x)]k +Ours Eq. (7) +Rollout +FinAtt +redshank +limpkin +axolotl +Shifted LayerNorm (B=1) +(b) +indigo bunting +Input +Ours [W(x)]k +Ours Eq. (7) +Rollout +FinAtt +redshank +limpkin +axolotl +Shifted LayerNorm (B=2) +(c) +Fig. B4: Visualisation of attention-based explanations as well as the model-inherent explanations for models +trained with (a) the standard attention module, (b) Shifted LayerNorm (B=1), and (c) Shifted LayerNorm +(B=2); for details, see Sec. B.2. As we describe in that section, the models with standard attention seem unable +to take advantage of the attention module and thus do not learn structured attention maps (a). In contrast, once +the LayerNorm is shifted inside the softmax computation, the models are not only inherently explainable by a +single linear transformation, but also learn to use the attention layers in a much more structured manner (b+c). +20 + +Preprint +Tiny +Small +Base +Transformer size +60 +70 +80 +Top-1 accuracy (%) +66.9 +70.4 +73.7 +71.1 +74.3 +75.6 +72.7 +74.6 +76.1 +74.2 +75.7 +76.6 +75.3 +76.4 +76.8 +74.9 +76.6 +76.7 +B-cos ViT-{Ti/S/B}-13 ++ No MaxOut +B-cos ViT-{Ti/S/B}-38 ++ No MaxOut +B-cos ViT-{Ti/S/B}-87 ++ No MaxOut +(a) Comparison between B-cos ViTs with (solid) and without (striped) MaxOut in the Transformer layers. +Tiny +Small +Base +Transformer size +60 +70 +80 +Top-1 accuracy (%) +66.9 +70.4 +73.7 +71.4 +72.8 +74.6 +72.7 +74.6 +76.1 +73.0 +74.5 +74.9 +75.3 +76.4 +76.8 +73.1 +74.3 +74.5 +ViT-{Ti/S/B}-13 ++ B-cosify (No MaxOut) +ViT-{Ti/S/B}-38 ++ B-cosify (No MaxOut) +ViT-{Ti/S/B}-87 ++ B-cosify (No MaxOut) +(b) Comparison between B-cos ViTs (no MaxOut) (striped) in the Transformer layers and conventional ViTs. +Fig. B5: Understanding the impact of MaxOut on model performance. (a) For the Tiny transformers, we +find that MaxOut indeed significantly improves model performance. However, this performance gap between +models with and without MaxOut closes with increasing model size (Small and Base). (b) As such, when +comparing to conventional ViTs (same numbers as in Fig. 5), we find that B-cos ViTs without MaxOut can +achieve similar performance without adding additional parameters in the Transformer layers, as long as the +initial model size is sufficiently large. +B=1 is in fact equivalent to a linear layer and the Shifted LayerNorm (B=1) model thus only differs +from the conventional attention by the placement of the LayerNorm module. +When comparing the classification performance of the Shited LayerNorm models with different val- +ues for B, we find the models to perform very similarly, see Fig. B3. Given that the main difference +between those models is a slightly higher value of B in one of them, this is not surprising. Moreover, +given that both models still adhere to the B-cos formulation, both models are accurately summarised +by a global linear transformation and allow for a model-faithful decomposition into individual in- +put contributions, see Fig. B4; note that all other modules still use B=2 in both models and thus +already induce significant alignment, irrespective of the value and projection layers6. In contrast to +the model with Standard Attention, we find both models with Shifted LayerNorm to learn highly +structured attention maps, see Fig. B4. +B.3 +ABLATION STUDY: ANALYSING THE IMPACT OF MAXOUT ON PERFORMANCE +As discussed in Sec. 3, when converting the baseline ViTs to B-cos ViTs, we follow B¨ohle et al. +(2022) and add a MaxOut unit to every B-cos transformation. This, of course, doubles the number +of parameters, which can skew the comparison to the baseline models. In the following, we assess +how MaxOut impacts the model performance. +In particular, in Fig. B5 (a), we compare the performance of B-cos ViTs as presented in the main +paper to a version that does not use MaxOut when converting the baseline Transformer layers. We +6As was shown in B¨ohle et al. (2022), higher values of B can lead to a higher degree of alignment, but this +transition is smooth and a value of B=1 in the attention layers seems to be sufficient. +21 + +Preprint +observe that for smaller models (see, e.g., Tiny), MaxOut indeed significantly improves the perfor- +mance of the B-cos ViTs. However, with increasing model size (Small and Base), this performance +gap closes and the B-cos ViTs without MaxOut perform on par with those that have twice the number +of parameters in the Transformer layers. +As a result, we find that for sufficiently large Transformers (Small and Base), the B-cos ViTs without +MaxOut are able to achieve similar performance as the baseline models, without increasing the +parameter count, as we show in Fig. B5 (b). +C +IMPLEMENTATION DETAILS +In the following, we provide further implementation details regarding the models (C.1), the training +and evaluation procedure (C.2), the explanation methods (C.3), and the evaluation metrics (C.4). +C.1 +MODELS +For all models, we rely on the implementation by Chefer et al. (2021), which we use unchanged for +the conventional ViTs and modify as we describe below for the B-cos ViTs (C.1.1). The configu- +rations of the ViTs follow the conventional specifications for ViTs of size Ti, S, and B, cf. Chefer +et al. (2021). As described in Sec. 3, we use average pooling over the tokens and pass the result to +the classifier head for all models. The conventional ViTs use a DenseNet-121 backbone as available +in the torchvision library (Paszke et al., 2019). +C.1.1 +B-COS VITS +Tokenisation. For all B-cos ViTs, we use a pretrained7 B-cos DenseNet-121 as provided by B¨ohle +et al. (2022) as a tokenisation module, cf. Fig. 2a; specifically, we use the DenseNet-121 with the +training+ schedule, as this one achieves the same accuracy on the ImageNet validation set as the +conventional DenseNet-121 contained in the pytorch library (Paszke et al., 2019). As described in +the main paper, we freeze this backbone and extract features after either 13, 38, or 87 convolutional +layers. +We then apply a single B-cos convolutional layer with a kernel size k=1, 2, 4 and stride s=1, 2, 4 +with no padding on the feature maps after 87, 38, or 13 convolutional layers respectively, such that +the number of tokens is the same for all B-cos ViTs. We found it advantageous to scale the features +of the backbones by 103, as this improved signal propagation and lead to better results8. Depending +on the size of the transformer (Ti, S, B, see main paper), this B-cos convolution produced activations +with c=192, 384, 768 channels after MaxOut (Goodfellow et al., 2013) over every two output units. +The resulting activation map of size c×h×w is then reshaped to n×c with n the number of input +tokens. +Attention. As described in the main paper, we replace the value computation as well as the linear +projection of the attention heads by linear B-cos transformations. Further, we apply layer normalisa- +tion to the inputs before the query and key computations; the value computations use the raw input, +cf. Fig. 2a. Finally, when additionally learning ‘attention priors’, see Sec. 3.5, we add a learnable pa- +rameter B∈Rm×n×n to each attention layer, with m the number of attention heads. The parameter +B thus contains separate pair-wise priors between any two tokens for every attention head. +MLPs. As discussed in Sec. 3.4, we convert the MLPs to B-cos MLPs by replacing the linear +transformations by B-cos transformations with two units and MaxOut (Goodfellow et al., 2013). +Further, we remove the normalisation layer before the MLP block, and the GELU (Hendrycks & +Gimpel, 2016) non-linearities within the MLPs. +Classifier. We use a single B-cos transformation as a classification head, without MaxOut and +C=1000 output features, i.e., one output for each class. +General remarks. Similar to B¨ohle et al. (2022), we scale the output of every B-cos layer in the +network by a scaling factor γ=f/√c to improve signal propagation. In particular, as more channels +lead to a stronger decay, we used f =15, 20, 25 for ViTs of size Ti, S, B respectively; further, since +the multiplicative prior computes the product of two attention values ≤ 1, the activations in these +networks decay even more quickly and we scale each f by an additional factor of 10. Moreover, as +7The pretrained models were downloaded from github.com/moboehle/B-cos. +8Note that in contrast to standard ViTs, in which normalisation layers ensure that the input to each layer is +well-behaved, in B-cos Networks the activations can decay very quickly since no normalisation is used. +22 + +Preprint +in B¨ohle et al. (2022), we scale down the model output by 103 after which we add a logit bias b∈RC +to the model output which is set to log(0.01/0.99) for each of the C output logits. Lastly, for the +B-cos ViTs, we encode the input images as in B¨ohle et al. (2021), i.e., such that each pixel uses 6 +color channels [r, g, b, 1−r, 1−g, 1−b] with r, g, b∈[0, 1]. As we discuss in Sec. C, this allows for +visualising the matrices W(x) in color. +C.2 +TRAINING AND EVALUATION PROCEDURE +Training. We trained the B-cos ViTs with a batch size of 256. For the conventional ViTs, we found +larger batch sizes to yield better results and thus trained those with a batch size of 1024. Further, we +trained all our models with RandAugment (Cubuk et al., 2020) (n=2 and m=9) and used images +of size 224×224. While the conventional models were, as is common, trained with SoftMax and +a cross entropy loss, for the B-cos ViTs we followed B¨ohle et al. (2022) and trained with binary +cross entropy and sigmoid applied to the output logits. Note that, as discussed in B¨ohle et al. (2022), +binary cross entropy induces the necessary logit maximisation for every input, which in turn leads +to weight alignment with class-relevant patterns. +Evaluation. We evaluated all networks on the ImageNet validation set after resizing the images such +that the smaller dimension measured 256 pixels and then center-cropped images of size 224×224. +C.3 +ATTRIBUTION METHODS +In the following, we describe the explanation methods that we evaluate on the B-cos as well as the +conventional ViTs in more detail. +Model-inherent explanations. The model-inherent explanations that we quantitatively evaluated +are given by the contribution maps defined in Eq. (7). Specifically, for a given class logit, we +extract the effective linear contribution as performed by the model and multiply it with the input in +an element-wise manner and sum all values per pixel location, i.e., across the colour channels; note +that this is conceptually equivalent to ‘Input×Grad’ for piece-wise linear models. For a visualisation +of contribution maps, see Figs. 1 and 7; here, we use a blue-white-red colormap with blue colors +denoting negative, and red colors denoting positive contributions. This visualisation method is the +same for all methods except for those that use the jet colormap (CheferLRP, Rollout, and FinAtt). +Additionally, for better visibility, we clamp the contribution values to the interval [−v, v], with v +the 99.9th percentile of the absolute values of the given spatial attribution map (i.e., after summing +over the colour channels). Note that as a result, the explanations are normalised independently; for +a discussion of the effect of normalising across multiple explanations, see Appendix A.2. +Further, as also shown in those figures, the B-cos formulation allows to directly visualise the trans- +formation matrix W(x) in color. Specifically, note that the input to B-cos networks is encoded as +p = [r, g, b, 1−r, 1−g, 1−b] with r, g, b∈[0, 1] the color channels, cf. Sec. C.1.1 and B¨ohle et al. +(2022). As such, the color of each pixel is unambiguously encoded by the angle of the pixel vector p +and it is thus possible to reconstruct the image colors from the angles alone. Crucially, as discussed +in Sec. 3.1 W(x) is implicitly optimised to align with relevant patterns in the input, i.e., to have a +similar angle as the input, such that the weights for any given pixel can be mapped to a specific color +in RGB. We further follow B¨ohle et al. (2022) and use the norm of the pixel vectors to compute +the opacity α in an RGB-α encoding, for details see B¨ohle et al. (2022), and only show pixels that +positively contribute to the respective logit. +Transformer-specific explanations. As described in the main paper, we evaluate against common +transformer-specific explanations such as the average attention distribution in the final layer (FinAtt), +Attention Rollout as proposed by Abnar & Zuidema (2020), and GradSAM (Barkan et al., 2021). +On the conventional ViTs, we further evaluate LRP-based explanations: partial LRP (pLRP) Voita +et al. (2019) and the transformer-specific LRP adaptation by Chefer et al. (2021) (CheferLRP). For +all these transformer-specific explanations, we rely on the implementation provided by Chefer et al. +(2021). +Architecture-agnostic explanations. Further, as shown in Figs. 6 and 7, we also evaluate other +commonly used explanation methods. Specifically, we use IntGrad (Sundararajan et al., 2017) +with n=32 steps, ‘Input×Gradient’ (IxG), cf. Adebayo et al. (2018), as well as an adapted Grad- +CAM (Selvaraju et al., 2017) as in Chefer et al. (2021). For the last, we rely on the implementation +provided by Chefer et al. (2021). For the remaining methods, we use the implementations contained +in the captum library of pytorch (Paszke et al., 2019). +23 + +Preprint +C.4 +EVALUATION METRICS +C.4.1 +LOCALISATION METRIC +For the localisation metric, we evaluated all attribution methods on the grid pointing game (B¨ohle +et al., 2021). For this, we constructed 250 2×2 grid images, see, e.g., Fig. 4. As was done in B¨ohle +et al. (2021), we sorted the images according to the models’ classification confidence for each class +and then sampled a random set of classes for each multi-image. For each of the sampled classes, we +then included the most confidently classified image in the grid that had not already been used in a +previous grid image. +Further, transformers with positional information expect a fixed size input, see Sec. 4. To neverthe- +less evaluate the attribution methods on the localisation metric, which uses images of size 448×448, +we scale the synthetic images down by a factor of two such that they are of size 224×224 and thus +of a size that is compatible with the transformers. +C.4.2 +PERTURBATION METRIC +As for the pixel perturbation metrics, we proceed as follows. +First, we sort the images in the validation set by their classification confidence and evaluate on the +first 250 images for each model. We do this to reduce the computational cost of evaluating this metric +whilst nevertheless allowing for a fair comparison between models. Specifically, we observed the +model stability to correlate with the model confidence and by choosing the most confidently predict +images, each model is evaluated in a favourable setting, which ensures comparability. +Second, we remove up to 25% of the pixels from the images in increasing / decreasing order as +ranked by a given attribution method. Specifically, we sample the resulting confidence curves at 9 +equidistant points r in the interval [0, 25%] and ‘remove’ the pixels by zeroing out the respective +pixel encoding. +Finally, we record the mean model confidence at the sampled points, which we normalise by the +initial mean confidence; as such, each curve starts at (r, o)=(0, 1) with r the percentage of pixels +removed and o the normalised model confidence. To assess the quality of the ranking, we then +measure the area between the two confidence curves corresponding to the order in which we remove +the pixels, i.e., least / most important first, see, e.g., Fig. 6 (right). +24 + diff --git a/INFAT4oBgHgl3EQfuR6w/content/tmp_files/load_file.txt b/INFAT4oBgHgl3EQfuR6w/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e3a7a67f4f18c1c1d51bcbc1364044df793d9e72 --- /dev/null +++ b/INFAT4oBgHgl3EQfuR6w/content/tmp_files/load_file.txt @@ -0,0 +1,1435 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf,len=1434 +page_content='Preprint HOLISTICALLY EXPLAINABLE VISION TRANSFORMERS Moritz B¨ohle1, Mario Fritz2, Bernt Schiele1 1Max Planck Institute for Informatics, Saarbr¨ucken 2CISPA Helmholtz Center for Information Security ABSTRACT Transformers increasingly dominate the machine learning landscape across many tasks and domains, which increases the importance for understanding their out- puts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' While their attention modules provide partial insight into their inner work- ings, the attention scores have been shown to be insufficient for explaining the models as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To address this, we propose B-cos transformers, which inher- ently provide holistic explanations for their decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we formulate each model component—such as the multi-layer perceptrons, attention layers, and the tokenisation module—to be dynamic linear, which allows us to faithfully sum- marise the entire transformer via a single linear transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We apply our proposed design to Vision Transformers (ViTs) and show that the resulting models, dubbed Bcos-ViTs, are highly interpretable and perform competitively to baseline ViTs on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Code will be made available soon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 INTRODUCTION Input Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) Rollout FinAtt rocking chair blue bird goldfish magpie cock Ibizan hound Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1: Inherent explanations (cols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2+3) of B-cos ViTs vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' attention explanations (cols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4+5) for the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that W(x) faithfully reflects the whole model and yields more detailed and class-specific explanations than attention alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a detailed discussion, see supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Convolutional neural networks (CNNs) have dominated the last decade of computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, recently they are often surpassed by transformers (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017), which— if the current development is any indication— will replace CNNs for ever more tasks and domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Transformers are thus bound to im- pact many aspects of our lives: from health- care, over judicial decisions, to autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Given the sensitive nature of such ar- eas, it is of utmost importance to ensure that we can explain the underlying models, which still remains a challenge for transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To explain transformers, prior work often fo- cused on the models’ attention layers (Jain & Wallace, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Serrano & Smith, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Ab- nar & Zuidema, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Barkan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021), as they inherently compute their output in an in- terpretable manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, as transformers consist of many additional components, ex- planations derived from attention alone have been found insufficient to explain the full models (Bastings & Filippova, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To address this, our goal is to develop transformers that inherently pro- vide holistic explanations for their decisions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' explanations that reflect all model com- ponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' These model components are given by: a tokenisation module, a mechanism for providing positional information to the model, multi-layer perceptrons (MLPs), as well as normalisation and attention layers, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' By addressing the interpretability of each component individually, we obtain transformers that inherently explain their decisions, see, for example Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In detail, our approach is based on the idea of designing each component to be dynamic linear, such that it computes an input-dependent linear transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' This renders the entire model dynamic linear, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2022), s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' it can be summarised by a single linear transform for each input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='08669v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CV] 20 Jan 2023 Preprint Dynamic Linear Transformation Tokeniser: B-cos CNN B-cos Attention B-cos MLP + × L B-cos Classifier + W (x) Tokens W (x) Class W (x) Att l W (x) MLP l W(x) W (x) Tokens W (x) Att l W (x) Class = ∏ L l=1 W (x) MLP l ( ) B-cos ViT (a) Input Prediction × = × = σ (Sum(ck(x))): 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0% Lesser Panda [W(x)]k ck(x) Probability(Lesser Panda) = σ (Sum(ck(x))) = 100% (b) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2: (a) B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We design each ViT component to be dynamic linear, allowing us to summarise the entire model by a single linear transform W(x), as shown in the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (b) Computation is Explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The model output is exactly computed by the linear transform W(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, we can visualise this effective linear transform either by the corresponding matrix row (center) or the contributions ck(x) (right), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In short, we make the following contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (I) We present a novel approach for designing in- herently interpretable transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, (II) we carefully design each model component to be dynamic linear and ensure that their combination remains dynamic linear and interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifi- cally, we address (IIa) the tokenisation module, (IIb) the attention layers, (IIc) the MLPs, and (IId) the classification head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (III) Additionally, we introduce a novel mechanism for allowing the model to learn attention priors, which breaks the permutation invariance of transformers and thus allows the model to easily leverage positional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In our experiments, we find that B-cos ViTs with such a learnt ‘attention prior’ achieve significantly higher classification accuracies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (IV) Finally, we evaluate a wide range of model configurations and show that the proposed B-cos ViTs are not only highly interpretable, but also constitute powerful image classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2 RELATED WORK Attention as Explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As the name exemplifies, attention is often thought to give insight into what a model ‘pays attention to’ for its prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, various methods for using attention to understand the model output have been proposed, such as visualising the attention of single attention heads, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, especially in deeper layers the information becomes in- creasingly distributed and it is thus unclear whether a given token still represents its original position in the input (Serrano & Smith, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Abnar & Zuidema, 2020), thus complicating the interpretation of high attention values deep in the network (Serrano & Smith, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Bastings & Filippova, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Therefore, Abnar & Zuidema (2020) proposed ‘attention rollout’, which summarises the various attention maps throughout the layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, this summary still only includes the attention layers and neglects all other network components (Bastings & Filippova, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In response, various improvements over attention rollout have been proposed, such as GradSAM (Barkan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021) or an LRP-based explanation method (Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021), that were designed to more accurately reflect the computations of all model components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The significant gains in quantitative interpretability metrics reported by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021) highlight the importance of such holistic explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Similarly, we also aim to derive holistic explanations for transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, instead of deriving an explanation ‘post-hoc’ as in Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), we explicitly design our models to be holistically explainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we formulate each component—and thus the full model—to be dynamic linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Dynamic Linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Plain linear models, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' y(x)=Wx, are usually considered interpretable, as y(x) can be decomposed into individual contributions ci=wi xi from any dimension i: y= � i ci (Alvarez-Melis & Jaakkola, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, linear models have a limited capacity, which has lead to various works aimed at extending their capacity without losing their interpretability, see Alvarez- Melis & Jaakkola (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Brendel & Bethge (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' An appealing strategy for this is formulating dynamic linear models (Alvarez-Melis & Jaakkola, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2022), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' models that transform the input with a data-dependent matrix W(x): y(x)=W(x)x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In this work, we rely on the B-cos framework (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022), but instead of focusing on CNNs as in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), we investigate the applicability of this framework to transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Interpretability in DNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The question of interpretability extends, of course, beyond transformers and many methods for explaining DNNs have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' While other approaches exist, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Kim 2 Preprint et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018), these methods typically estimate the importance of individual input features, which can be visualised as a heatmap, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Lundberg & Lee (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Petsiuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Ribeiro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Simonyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Springenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Bach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Selvaraju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Shrikumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Srinivas & Fleuret (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Sundararajan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Similarly, our models yield explanations in form of contribution heatmaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, in contrast to the above-referenced post-hoc explanation methods, the contribution maps of our B-cos ViTs are model-inherent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, as the interpretability of the B-cos ViTs relies on aligning the weights with the inputs, the weights can be visualised in colour as in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 DESIGNING HOLISTICALLY EXPLAINABLE TRANSFORMERS In the following, we present the overarching goal that we pursue and how we structure this section around it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, however, we introduce the necessary background and the notation used in our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Preliminaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Vision Transformers (ViT) (Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021) with L blocks are given by: y(x) = Classifier ◦ �L l=1 (MLPBlockl ◦ AttBlockl) ◦ Tokens(x) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (1) Here, the input x ∈ R(CHW ) denotes a vectorised image of H =W height and width and with C color channels;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the functions, concatenated by ◦, are defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) - (5) (left), with P, E ∈ RD×N, N the number of tokens and D their dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) - (5), CNN is a convolutional neural network1, T ‘tokenises’ the CNN output (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2), Linear is a learnable linear transform p′(p)=Wp+b with parameters W and b that is applied to each token p (columns of P) independently, MSA denotes Multi-head Self-Attention, and E is a learnable embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Following Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), Pool performs average pooling over the tokens, and the model output is given by y(x) ∈ RM with M classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Last, we omit indices for blocks and layers whenever unambiguous and it may be assumed that each layer has its own set of learnable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Our goal in this work is to reformulate the ViTs such that they compute their output in a more interpretable manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we aim to make them dynamic linear such that they compute y(x) = W(x) x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Instead of using the ViTs to predict W(x), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Alvarez-Melis & Jaakkola (2018), we achieve this by rendering each of the ViT components dynamic linear on their own as follows: Tokens (x) = T (CNN(x)) + E −−→ B-cos Tokens (x) = WTokens(x) x (2) AttBlock (P) = MSA(P) + P −−→ B-cos AttBlock (P) = WAtt (P) P (3) MLPBlock (P) = MLP(P) + P −−→ B-cos MLPBlock (P) = WMLP (P) P (4) Classifier (P) = Linear ◦ Pool(P) −−→ B-cos Classifier (P) = WClass (P) P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (5) Crucially, we define each component such that it can be expressed as a dynamic linear function, see the right-hand side of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) - (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, the entire model will become dynamic linear: y(x) = WClass(x) �L l=1 � WMLP l (x) WAtt l (x) � WTokens(x) x = W(x) x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (6) Specifically, we develop the B-cos ViTs in accordance with the B-cos framework (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022) to render W(x) interpretable by aligning it with relevant input patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Outline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In the following, we shortly summarise the most relevant aspects of B-cos networks and how to explain them (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Then, we discuss Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) - (5) in detail and how we ensure that the resulting linear transform W(x) will be interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we discuss the tokenisation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2), attention (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3), and the multi-layer perceptrons (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5, we discuss how we encode positional information in B-cos ViTs, introducing ‘position-aware’ attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 B-COS NETWORKS: INTERPRETABLE MODEL-INHERENT EXPLANATIONS As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (6), a dynamic linear transformer is summarised exactly by a single matrix W(x) for every x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' These linear explanations lend themselves well for understanding the model decisions: as in plain linear models, one can calculate linear contributions from individual features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', pixels) to each output unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In detail, the effective linear contributions ck to the k-th class logit are given by Dynamic Linear Contribution Maps: ck(x) = [W(x)]T k ⊙ x , (7) 1To simplify later equations, we take advantage of the fact that conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' layers are equivalent to linear layers with weight constraints (weight sharing and local connectivity) and assume the CNN to process vectorised images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Preprint with ⊙ denoting element-wise multiplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Crucially, these contribution maps faithfully sum- marise the entire model, as this linear summary is inherent to the model formulation, see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Thus, we use these contribution maps to explain the B-cos ViTs, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note, however, that while the contribution maps in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) accurately summarise any given dynamic linear model, this summary need not be interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', for piece-wise linear models, which are also dynamic linear, this amounts to ‘Input×Grad’, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Adebayo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For such models, however, the contributions c are very noisy and not easily interpretable for humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Hence, we de- sign the transformers in accordance with the ‘B-cos’ framework (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022), which ensures that W(x) aligns with relevant input features and thus becomes easily interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In detail, the B-cos transform induces weight alignment by suppressing outputs for badly aligned weights: B-cos(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' W) = � cosB−1(a, W) ⊙ � W � a = W(a)a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (8) here, cos is applied row-wise, � W denotes that the matrix rows are of unit norm, and ⊙ represents row-wise scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As can be seen on the RHS of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (8), the B-cos transform is dynamic linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, the matrix rows [W(x)]k align with relevant patterns of class k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' By encoding the image such that the color is uniquely determined by the angle of the pixel encodings, it is possible to directly visualise those matrix rows in color, see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For details, see B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To ensure that a B-cos network aligns W(x) with its inputs, each of its layers needs to (a) be bounded, (b) yield its maximum output if and only if its weight vectors align with its input, and (c) directly scale the overall model output by its own output norm, see B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In the following, we ensure that each of the model components (Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2)-(5)), fulfills these requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 INTERPRETABLE TOKENISATION MODULES: B-COS CNNS While the original Vision Transformer only applied a single-layered CNN, it has been shown that deeper CNN backbones yield better results and exhibit more stable training behaviour (Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Hence, to address the general case, and to take advantage of the increased training stability and performance, we take the tokenisation module to be given by a general CNN backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Being able to explain the full ViT models consequently requires using an explainable CNN for this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Tokenisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We use B-cos CNNs (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022) as feature extractors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' thus, the requirements (a-c), see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1, of B-cos networks are, of course, fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The input tokens are computed as B-cos Token pi(x) = Ti ◦ B-cos CNN(x) = WTiWCNN(x) x = WTokens i (x) x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (9) Here, pi∈RD corresponds to the ith column in the token matrix P, Ti extracts the respective features from the CNNs’ output with WTi denoting the corresponding linear matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' WCNN is the dynamic linear mapping computed by the B-cos CNN, and as color-indicated, WTokens i (x)=WTiWCNN(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, note that we did not include the additive positional embedding E, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a detailed discussion on how to provide positional information to the B-cos ViTs, please see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 B-COS ATTENTION Interestingly, the attention operation itself is already dynamic linear and, as such, attention lends itself well to be integrated into the linear model summary according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To ensure that the resulting linear transformation maintains the desired interpretability, we discuss the necessary changes to make the attention layers compatible with the B-cos formulation as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B-cos Attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that conventional attention indeed computes a dynamic linear transform: Attention(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Q, K, V) = softmax � PT QT KP � � �� � Attention matrix A(P) VP ���� Value(P) = A(P) V � �� � W(P) P = W(P)P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (10) Here, Q, K and V denote the respective query, key, and value transformation matrices and P denotes the input tokens to the attention layer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' further, softmax is computed column-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In multi-head self-attention (MSA), see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (3) (left), H distinct attention heads are used in parallel after normalising the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Their concatenated outputs are then linearly projected by a matrix U: MSA(�P) = U � W1(�P)�P, W2(�P)�P, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' , WH(�P)�P � with �P = LayerNorm(P) (11) 4 Preprint While this can still2 be expressed as a dynamic linear transform of P, we observe the following issues with respect to the requirements (a-c), see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, (a) while the attention matrix A(P) is bounded, the value computation VP and the projection by U are not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Therefore, as the output can arbitrarily increased by scaling V and U, (b) a high weight alignment is not necessary to obtain large outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, by normalising the outputs of the previous layer, the scale of those outputs does not affect the scale of the overall model output anymore, which violates requirement (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To address (a+b), we propose to formulate a B-cos Attention Block as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, we replace the value computation and the linear projection by U by corresponding B-cos transforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), we employ MaxOut and for a given input P the resulting projections are computed as B-cos Linear(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' S) = MaxOut ◦ B-cos(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' S) = WS(P)P with S ∈ {U, V}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (12) To fulfill (c), whilst not foregoing the benefits of LayerNorm3, we propose to exclusively apply LayerNorm before the computation of the attention matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' we compute A(P), see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (10) as A(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Q, K) = softmax � �PT QT K�P � with �P = LayerNorm(P) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (13) In total, a ‘B-cos AttBlock’ thus computes the following linear transformation: B-cos AttBlock(P) = � WU(P′) � Ah(P)WV h (P) �H h=1 + I � P = WAtt(P) P , (14) Here, P′ = � Ah(P)WV h (P) �H h=1, WU and WV as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (12), and Ah(P) as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (13);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the identity matrix I reflects the skip connection around the MSA computation, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For an ablation study regarding the proposed changes, we kindly refer the reader to the supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 INTERPRETABLE MLPS AND CLASSIFIERS To obtain dynamic linear and interpretable MLPs, we convert them to ‘B-cos’ MLPs, such that they are compatible with the B-cos formulation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1) and align their weights with relevant inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B-cos MLPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Typically, an MLP block in a ViT computes the following: MLPBlock(P) = Linear2 ◦ GELU ◦ Linear1 ◦ LayerNorm(P) + P (15) Here, Linear is as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (5), the GELU activation function is as in Hendrycks & Gimpel (2016), and LayerNorm as in Ba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To obtain our ‘B-cos MLPBlock’, we follow B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022) and replace the linear layers by B- cos transforms, remove the non-linearities and the normalisation (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' further, each ‘neuron’ is modelled by two units, to which we apply MaxOut (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, each MLP block becomes dynamic linear: B-cos MLPBlock(P) = (M2(P) L2(P) M1(P) L1(P) + I)P = WMLP(P) P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (16) Here, Mi(P) and Li(P) correspond to the effective linear transforms performed by the MaxOut and B-cos operation respectively, and I denotes the identity matrix stemming from the skip connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Similar to the B-cos MLPs, we also replace the linear layer in the classifier, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (5) (left), by a corresponding B-cos transform and the B-cos Classifier is thus defined as B-cos Classifier(P) = B-cos ◦ Pool(P) = L(P′)WAvgPoolP = WClass(P) P , (17) with L(P′) the dynamic linear matrix corresponding to the B-cos transform and P′=Pool(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 POSITIONAL INFORMATION IN B-COS TRANSFORMERS In contrast to CNNs, which possess a strong inductive bias w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' spatial relations (local connectivity), transformers (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017) are invariant w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the token order and thus lack such a ‘locality 2To be exact, it can be represented as a dynamic affine transform, since LayerNorm adds a bias term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3We noticed normalised inputs to be crucial for the computation of the attention matrix A(P) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (10): for unconstrained inputs, softmax easily saturates and suffers from the vanishing gradient problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5 Preprint bias’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To nevertheless leverage spatial information, it is common practice to break the symmetry between tokens by adding a (learnt) embedding E to the input tokens P, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2) (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, within the B-cos framework, this strategy is not optimal: in particular, note that each B-cos transformation needs to align its weights with its inputs to forward a large output to the next layer, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (8) and B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, a B-cos ViT would need to associate contents (inputs) with specific positions, which could negatively impact the model’s generalisation capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Therefore, we investigate two alternative strategies for providing positional information to the B- cos ViTs: additive and multiplicative attention priors, see Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (18) and (19) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifi- cally, we propose to add a learnable bias matrix Bl h to each attention head h in every layer l in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' This pair-wise (between tokens) bias is then either added4 before the softmax operation or multiplied to the output of the softmax operation in the following way (omitting sub/superscripts): Aadd(P) = SM (R(P) + B) (18) and Amul(P) = SM (R(P)) × SM (B) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (19) Here, R(P)=Q�P�PT KT and SM denotes softmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The bias B thus allows the model to learn an attention prior, and the attention operation is no longer invariant to the token order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, the model can learn spatial relations between tokens and encode them explicitly in the bias matrix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In our experiments, this significantly improved the performance of the B-cos ViTs, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4 EXPERIMENTAL SETTING Dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In this work, we focus on Vision Transformers (ViTs, Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021)) for image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we evaluate the B-cos and conventional ViTs and their explanations on the ImageNet dataset (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We use images of size 224×224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For B-cos models, we encode the images as in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We follow prior work and evaluate ViTs of different sizes in common configurations: Tiny (Ti), Small (S), and Base (B), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Steiner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We train these models on the frozen features of publicly available (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Marcel & Rodriguez) (B-cos) DenseNet-121 models and extract those features at different depths of the models: after 13, 38, or 87 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Model names are thus as follows: (B-cos) ViT-{size}-{L} with size∈{Ti, S, B} and L∈{13, 38, 87}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We opted for (B-cos) DenseNet-121 backbones, as the conventional and the B-cos version achieve the same top-1 accuracy on the ImageNet validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we compare B-cos ViTs on B-cos backbones to normal ViTs on normal backbones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We employ a simple training paradigm that is common across models for comparability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' All models are trained with RandAugment (Cubuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2020) for 100 epochs with a learning rate of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5e−4, which is decreased by a factor of 10 after 60 epochs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for details, see supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Evaluation Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We evaluate all models with respect to their accuracy on the ImageNet valida- tion set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we employ two common metrics to assess the quality of the model explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, we evaluate the grid pointing game (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we evaluate the explanations (see below) on 250 synthetic image grids of size 448×448, containing 4 images of distinct classes, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the individual images are ordered by confidence and we measure the fraction of positive attribution an explanation method assigns to the correct sub-image when explaining a given class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that, in contrast to fully convolutional networks, transformers with positional embeddings ex- pect a fixed-size input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To nevertheless evaluate the models on such synthetic image grids, we scale down the image grid to the required input size of 224x224 to allow for applying the ViTs seamlessly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Second, we evaluate two pixel perturbation metrics, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, the pixels are ranked according to the importance assigned by a given explanation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Then, we increasingly zero out up to 25% of the pixels in increasing (decreasing) order, whilst measuring the model confi- dence in the ground truth class;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' a good explanation should obtain a high area under (over) the curve, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the model should be insensitive to unimportant pixels and sensitive to important ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We evaluate the perturbation metrics on the 250 most confidently and correctly classified images to enable a fair comparison between models, as the confidence affects the metrics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' more details in supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Last, to succinctly summarise the two metrics, we evaluate the area between the curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4Note that an additive positional bias in attention layers has been proposed before (Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 Preprint Tiny Small Base Size of the B-cos ViT-size-87 60 70 80 Top-1 accuracy (%) 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 Encoding of positional information Position Embedding Add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Att.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Bias Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (18) Mul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Att.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Bias Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (19) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3: ImageNet accuracy of differently sized B-cos ViTs (Tiny, Small, Base) depending on the positional encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We find B- cos ViTs with Amul, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (19), to perform significantly better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Evidence for Fire Truck Evidence for Lorikeet Evidence for Tiger Evidence for Taxi / Cab Input Localisation Example Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4: In the localisation metric, we mea- sure the fraction of pos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' evidence assigned to the correct grid cell for each occurring class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Tiny Small Base Transformer size 60 70 80 Top-1 accuracy (%) 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 Conventional 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 B-cos 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 Conventional 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 B-cos 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 Conventional 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 B-cos 13 backbone layers 38 backbone layers 87 backbone layers Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5: ImageNet accuracies of B-cos ViTs with a multiplicative attention bias (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (19)) compared to standard ViTs and backbones, both for differently sized ViTs (Tiny, Small, Base) and backbones (13, 38, or 87 layers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We find that the B-cos ViTs perform at least as well as the baseline ViTs over almost all tested configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Explanation Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Apart from the model-inherent explanations (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7)), we evaluate two sets of explanation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, we follow Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021) and evaluate common transformer- specific explanations such as the attention in the final layer (FinAtt), attention rollout (Rollout) (Ab- nar & Zuidema, 2020), a transformer-specific LRP implementation (CheferLRP) proposed by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), ‘partial LRP’(pLRP) (Voita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2019), and ‘GradSAM’ (Barkan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we evaluate architecture-agnostic methods such as Integrated Gradients (IntGrad) (Sun- dararajan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017), adapted GradCAM (Selvaraju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017) as in Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), and ‘Input×Gradient’ (IxG), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Adebayo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As no LRP rules are defined for B-cos ViTs we only apply it to baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For method details, we kindly refer the reader to the supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We evaluate all of those methods (if applicable) to the proposed B-cos ViTs, as well as the baselines consisting of conventional ViTs and backbones and compare them on the metrics described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5 RESULTS In the following, we present our experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 we analyse the classi- fication performance of the B-cos ViTs: we investigate how the encoding of positional information affects model accuracy (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5) and compare the classification performance of B-cos and con- ventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2, we evaluate the model-inherent explanations of the B-cos ViTs against common post-hoc explanation methods evaluated on the same models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To highlight the gain in interpretability over conventional ViT models, we also compare the inherent explanations of the B-cos ViTs to the best post-hoc explanations evaluated on conventional ViTs, see supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7 Preprint 71 72 73 74 75 76 77 Model accuracy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 Localisation score ×2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='47 Localisation Metric 71 72 73 74 75 76 77 Model accuracy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='25 Normalised ABC ×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='99 Perturbation Metric Ours Rollout GradSAM IntGrad IxG FinAtt GradCAM Explanation Method Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6: Quantitative comparison of explanation methods according to two metrics: localisation (left) and per- turbation (right);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for a description of metrics and methods, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We evaluated the methods for all B-cos ViTs shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5 and plot the corresponding scores (markers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We also plot the mean score over all models (dashed lines) per method and the average improvement of the model-inherent over the best post-hoc explana- tion (localisation: ×2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='47, perturbation: ×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='99).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that for the perturbation metric, we normalised the area between curves (ABC) by the scores of the model-inherent explanations for better cross-model comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 CLASSIFICATION PERFORMANCE OF B-COS VITS In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, we compare the top-1 ImageNet accuracy of various B-cos ViTs trained on the feature embeddings of the 87th layer of a frozen5 B-cos DenseNet-121 (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we compare ViTs of different sizes (Tiny, Small, Base) and with different ways of allowing the models to use positional information, see Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2), (18) and (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We find that the multiplicative attention bias, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (19), consistently yields significant gains in performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5, we believe this could be due to the higher disentanglement between content and positional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, in preliminary experiments with conventional ViTs, we did not observe significant benefits from such a multiplicative prior and this seems to be particularly advantageous for B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Interestingly, once trained with such a multiplicative attention prior, we find the B-cos ViTs to perform at least as good as their conventional counterparts over a wide range of configurations, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' we find consistent results even without MaxOut in the Transformer layers (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3), as we show in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, these results have to be interpreted with caution: ViTs are known to be highly sensitive to, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', the amount of data augmentation, the number of training iterations, and model regularisation, see Steiner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Moreover, our goal in this work is to develop interpretable ViTs and our focus thus lies on evaluating the quality of the explanations (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 INTERPRETABILITY OF B-COS VITS Here, we assess how well the inherent explanations (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7)) of B-cos ViTs explain their output and compare to common post-hoc explanations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for comparisons to baseline ViTs, see supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Localisation Metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 (left), we plot the mean localisation score per model configuration (B-cos ViT-{size}-{L}) and explanation method, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We find that across all configurations, the model-inherent explanations according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) yield by far the best results under this metric and outperform the best post-hoc explanation for the B-cos ViTs (Rollout) by a factor of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Pixel Perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As for the localisation, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 (right), we plot the normalised mean area between the curves (ABC) per model configuration and explanation method of the B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, the mean ABC is computed as the mean area between the curves when first removing the most / least important pixels from the images;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' we normalise the mean ABC for each explanation by the mean ABC of the model-inherent explanation (Ours) per model configuration to facilitate cross-model comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Again, the model-inherent explanations perform best and, on average, they outperform the second best post-hoc method (Rollout) on B-cos ViTs by a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Qualitative Examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and 7, we qualitatively compare the inherent explanations (size: B, 38 backbone layers, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5) to post-hoc explanations evaluated on the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As becomes apparent, the model-inherent summaries not only perform well quantitatively (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6), but are also qualitatively convincing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Colour visualisations as in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' more results in supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5We chose to freeze the backbones to reduce the computational cost and compare the architectures across a wide range of settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We observed comparable results when training the full models for individual architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 8 Preprint black swan Input image Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IntGrad forklift digital clock lion Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7: Comparison of the model-inherent explanations (Ours) of a B-cos ViT-B-38, and several post-hoc expla- nations (GradSAM, GradCAM, Rollout, FinAtt, IntGrad) for class k (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we show explanations for the classes ‘black swan’, ‘forklift’, ‘digital clock’, and ‘lion’ on a synthetic image containing these classes, as used in the localisation metric, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As B-cos ViTs follow the B-cos formulation, we can visualise the rows of W(x) in colour (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Additionally, we show contribution maps according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In contrast to attention explanations, which are not class-specific (Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021), we find the model-inherent explanations of B-cos ViTs to be highly detailed and class-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, we compare model-inherent explanations to attention-based explanations for single images from the ImageNet dataset which are inherently ambiguous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7, we evaluate the model on images as used in the localisation metric, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' synthetic images with multiple classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In both cases we find the model-inherent explanations to accurately highlight the respective features for the class logit that we aim to explain, whereas other methods are much less sensitive to the class logit;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' in fact, attention-based explanations are inherently agnostic to the choice of logit and thus the same for all classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For comparisons to explanations for conventional ViTs, see the supplement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 CONCLUSION We present a novel approach for designing ViTs that are holistically explainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we design every component of the ViTs with the explicit goal of being able to summarise the entire model by a single linear transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' By integrating recent advances in designing interpretable dynamic linear models (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2022), these summaries become interpretable, as they are implicitly optimised to align with relevant input patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The resulting B-cos ViTs constitute competitive classifiers and their inherent linear summaries outperform any post-hoc explanation method on common metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Compared to attention-based explanations, our method can be understood to ‘fill the blanks’ in at- tention rollout (Abnar & Zuidema, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, attention rollout computes a linear summary of the attention layers only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' By integrating explanations for the remaining components (tokenisation, attention, MLPs), we are able to obtain holistic explanations of high detail, see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As transformers are highly modality-agnostic, we believe that our work has the potential to positively impact model interpretability across a wide range of domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Evaluating B-cos transformers on different tasks and modalities is thus an exciting direction that we aim to explore in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' While the B-cos ViTs allow us to extract model-faithful explanations for single images, note that these explanations are always local in nature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for single data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The explanations thus help understanding an individual classification, but do not directly give insights into which features the models most focus on over the entire dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' It would thus be interesting to combine B-cos ViTs with global explanation methods, such as in Bau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we focused primarily on the designing of interpretable transformers, and, to test across a wide range of models, limited experiments to the ImageNet-1k dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As transformers are known to significantly benefit from additional data and training (Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021), it would be interesting to test the limits of capacity of the B-cos ViTs and scale to more complex tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 9 Preprint ETHICS STATEMENT The growing adoption of deep neural network models in many different settings is accompanied by an increasingly louder call for more transparency in the model predictions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' especially in high-stake situations, relying on an opaque decision process can have severe consequences (Rudin, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' With this work, we make a step towards developing inherently more transparent neural network models that explain their decisions without incurring losses in model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, we would like to emphasise that our contribution can only be seen as a step in this direc- tion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' while the explanations might seem meaningful on a per sample basis, they could lead to a false sense of security in terms of ‘understanding’ model behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Currently, we can give no formal guarantees for model behaviour under unseen input data and more research on explainable machine learning is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Lastly, any research that holds the potential for accelerating the adoption of machine learning systems could have unpredictable societal impacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' REFERENCES Samira Abnar and Willem Zuidema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Quantifying Attention Flow in Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 7, 9, 14, 15, 23 Julius Adebayo, Justin Gilmer, Michael Muelly, Ian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Goodfellow, Moritz Hardt, and Been Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Sanity Checks for Saliency Maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4, 7, 23 David Alvarez-Melis and Tommi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Jaakkola.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Towards Robust Interpretability with Self-Explaining Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing (NeurIPS), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2, 3 Lei Jimmy Ba, Jamie Ryan Kiros, and Geoffrey E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Layer Normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' CoRR, abs/1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='06450, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/abs/1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='06450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5 Sebastian Bach, Alexander Binder, Gr´egoire Montavon, Frederick Klauschen, Klaus-Robert M¨uller, and Wojciech Samek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer- Wise Relevance Propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' PLoS ONE, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Oren Barkan, Edan Hauon, Avi Caciularu, Ori Katz, Itzik Malkiel, Omri Armstrong, and Noam Koenigstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Grad-SAM: Explaining Transformers via Gradient Self-Attention Maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Pro- ceedings of the International Conference on Information and Knowledge Management (CIKM), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2882–2887, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 7, 23 Jasmijn Bastings and Katja Filippova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The elephant in the interpretability room: Why use attention as explanation when we have saliency methods?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Third BlackboxNLP Workshop on Analyzing and Interpreting Neural Networks for NLP, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2 David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Network dissection: Quantifying interpretability of deep visual representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6541–6549, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 9 Wieland Brendel and Matthias Bethge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2 Moritz B¨ohle, Mario Fritz, and Bernt Schiele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Convolutional Dynamic Alignment Networks for Interpretable Classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 6, 23, 24 Moritz B¨ohle, Mario Fritz, and Bernt Schiele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B-cos Networks: Attention is All We Need for Inter- pretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 3, 4, 5, 6, 8, 9, 14, 21, 22, 23 Hila Chefer, Shir Gur, and Lior Wolf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Transformer interpretability beyond attention visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 6, 7, 9, 22, 23 10 Preprint Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Randaugment: Practical automated data augmentation with a reduced search space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR), Workshops, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6, 23 Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' ImageNet: A large-scale hierarchical image database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszko- reit, and Neil Houlsby.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' An Image is Worth 16x16 Words: Transformers for Image Recogni- tion at Scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Learning Representations, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL https: //openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='net/forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='id=YicbFdNTTy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, 6, 9 Ian Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Maxout networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML), 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5, 22 Benjamin Graham, Alaaeldin El-Nouby, Hugo Touvron, Pierre Stock, Armand Joulin, Herv´e J´egou, and Matthijs Douze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' LeViT: a Vision Transformer in ConvNet’s Clothing for Faster Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the International Conference on Computer Vision (ICCV), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, 6 Dan Hendrycks and Kevin Gimpel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Gaussian error linear units (gelus).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' arXiv preprint arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='08415, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5, 22 Sarthak Jain and Byron C Wallace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Attention is not Explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3543–3556, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 Been Kim, Martin Wattenberg, Justin Gilmer, Carrie J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Cai, James Wexler, Fernanda B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Vi´egas, and Rory Sayres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2, 9 Scott M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Lundberg and Su-In Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A Unified Approach to Interpreting Model Predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 S´ebastien Marcel and Yann Rodriguez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Torchvision library, pretrained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/ vision/stable/models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Accessed: 2021-11-11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' PyTorch: An Imperative Style, High-Performance Deep Learning Library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 22, 23 Vitali Petsiuk, Abir Das, and Kate Saenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' RISE: Randomized Input Sampling for Explanation of Black-box Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In British Machine Vision Conference (BMVC), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL http:// bmvc2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/contents/papers/1064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' ”Why Should I Trust You?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=': Explaining the Predictions of Any Classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Knowledge Discovery and Data Mining (SIGKDD), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Cynthia Rudin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Nature Machine Intelligence, 1(5):206–215, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 10 Ramprasaath R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Computer Vision (ICCV), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1109/ ICCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1109/ICCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, 7, 23 Sofia Serrano and Noah A Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Is Attention Interpretable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2 11 Preprint Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Learning Important Features Through Propagating Activation Differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), Workshop, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/abs/1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Riedmiller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Striving for Simplicity: The All Convolutional Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), Workshop, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='org/abs/1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Suraj Srinivas and Franc¸ois Fleuret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Full-Gradient Representation for Neural Network Visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 Andreas Steiner, Alexander Kolesnikov, Xiaohua Zhai, Ross Wightman, Jakob Uszkoreit, and Lucas Beyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' How to train your ViT?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Data, Augmentation, and Regularization in Vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' arXiv e-prints, art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='10270, June 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6, 8 Mukund Sundararajan, Ankur Taly, and Qiqi Yan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Axiomatic Attribution for Deep Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Doina Precup and Yee Whye Teh (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' ), International Conference on Machine Learning (ICML), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, 7, 23 Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Advances in Neural Informa- tion Processing Systems (NeurIPS), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, 2, 5 Elena Voita, David Talbot, Fedor Moiseev, Rico Sennrich, and Ivan Titov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7, 23 Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Doll´ar, and Ross Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Early convolutions help transformers see better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), volume 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 30392–30400, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4 Bolei Zhou, Aditya Khosla, `Agata Lapedriza, Aude Oliva, and Antonio Torralba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Learning Deep Features for Discriminative Localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3 12 Preprint Supplementary Material Table of Contents In this supplement to our work on designing holistically explainable transformers, we provide: (A) Additional Qualitative Results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 14 In this section, we show additional qualitative results and discuss the quali- tative differences between the various explanations methods in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we include explanations for B-cos as well as for conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (B) Additional Quantitative Results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 15 In this section, we show additional quantitative results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we compare the model-inherent explanations of the B-cos ViTs to explanations for conventional ViTs, both for the localisation and the perturbation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we present the results of an ablation study in which we investigate the impact of the design choices within the attention layer in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (C) Implementation Details .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 22 In this section, we describe the model architectures, the training procedure, the explanation methods, as well as the evaluation metrics in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 13 Preprint A ADDITIONAL QUALITATIVE RESULTS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 COMPARISON TO ATTENTION EXPLANATIONS Input Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) Rollout FinAtt rocking chair blue bird goldfish magpie cock Ibizan hound Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A1: Inherent explanations (cols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2+3) of B-cos ViTs vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' attention explanations (cols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4+5) for the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that W(x) faithfully reflects the whole model and yields more detailed and class-specific explanations than attention alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a detailed discussion, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For the reader’s convenience, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A1 we repeat the qualitative results presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1, such as to facilitate the following dis- cussion of the qualitative differences between the holistic and the purely attention-based ex- planations of B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we would like to point out sev- eral key differences between our holistic ex- planations as per Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) and the attention- based explanations according to Attention Rollout (Abnar & Zuidema, 2020) and the last layer’s attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, only the linear mapping W(x) used for the contribution maps in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) is able to capture ‘negative evidence’ for the respec- tive classes, see col.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that this does not depend on the particular choice of images shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Instead, as the at- tention matrices consist only of non-negative values, the attention-based explanations can- not distinguish between positively and neg- atively contributing features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Therefore, to improve the attention visualisation and more clearly highlight details in the attention maps, we plot the attention-based explanations on a colour scale from 0 to the maximal atten- tion value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The model-inherent explanation, in contrast, use a colour scale from [−p, p] with p the maximum absolute pixel contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Importantly, as attention-based explanations do not distinguish between positively and negatively contributing neurons / pixels, they are inherently not class-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For example, especially in images in which various classes are present (rows 1, 2, 3, 5), attention focuses on all occurring class instances: all birds in rows 2, 3, and 4, as well as both dogs in row 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The model-inherent explanations, on the other hand, clearly distinguish between positive and negative contributions and are thus able to resolve class-specific details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Secondly, the attention-based explanation are of much lower resolution than the model-inherent ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Again,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' this cannot be attributed to the choice of images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' but reflects an intrinsic difference between the explanations: whereas the linear mapping W(x) reflects the entire model including the tokenisation module and thus attributes on the level of pixels,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the attention explanations can only yield attributions at the level of tokens,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' which highlights a key difference between the methods: while the attention explanations only include a few layers in their attributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the model-inherent linear map W(x) constitutes an exact summary of the entire model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Third, as shown in the first column, the rows of the linear mapping W(x) can directly be visualised in colour space, as the B-cos ViTs are designed according to the B-cos framework proposed by B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that this is not a masked version of the original image, but instead a direct reflection of the dynamically computed weight matrix W(x), for details see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Such visualisations are not possible with attention-based explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, we would like to highlight the relation between attention rollout and the model-inherent linear mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (6), note that the entire model can be summarised by W(x) = WClass(x) �L l=1 � WMLP l (x) WAtt l (x) � WTokens(x) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1) Interestingly, attention rollout in fact computes the overall attention attributions in a similar manner: Arollout(x) = IClass �L l=1 � IMLP l ¯Al(x) � ITokens , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2) 14 Preprint with Ilayer replacing the actual linear transformation of a specific layer by an identity matrix and ¯Al denoting the average attention distribution of layer l, see Abnar & Zuidema (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Comparing Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2) succinctly shows how solely attention-based explanations leave out a large part of the model computations, which are seamlessly integrated in the complete linear mapping given by W(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 NORMALISING THE VISUALISATIONS ACROSS MULTIPLE EXPLANATIONS As we discuss in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3, the individual explanations are normalised independently of each other;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', all explanations shown on the blue-white-red colour map (Ours (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7)), GradSAM, GradCAM, IxG, IntGrad, and pLRP) are plotted on a scale from −v to v with v the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9th percentile of the absolute value of the given attribution map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, the resulting attribution maps are not directly comparable across different explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To show the effect of normalising across multiple explanations, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A2 we repeat Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7 from the main paper, once normalised across contribution maps, and once normalised independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To normalise across contribution maps, v is computed as the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9th percentile of the absolute value in all of the four class explanations per method in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 ADDITIONAL EXPLANATIONS AND COMPARISONS In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A3, we compare the model-inherent explanations of a B-cos ViT-B-38 model to additional explanation methods apart from purely attention-based ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Moreover, we show explanations ex- tracted for a conventional ViT-B-38 model in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A4 for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We would like to highlight the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, we find that the model-inherent explanations of the B-cos ViTs provide more detailed and convincing explanations than any of the post-hoc explanations when evaluated on the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Crucially, these explanations do not only look convincing, but in fact accurately reflect the model computations of the B-cos ViTs—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', they are model-faithful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, the model-inherent explanations do not only compare favourably to other explanations eval- uated on our newly proposed B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Instead, they also provide much more detail and highlight more class-specific features than any of the post-hoc explanation methods yield on conventional ViTs, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, we find that there is a clear gain in interpretability when using B-cos ViTs instead of conventional ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B ADDITIONAL QUANTITATIVE RESULTS In this section, we quantitatively compare the interpretability of the B-cos ViTs to that of conven- tional ViTs (Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, as in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2, we discuss the localisation and the pertur- bation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Additionally, in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2, we present results of an ablation study in which we investigate the design choices of the B-cos Attention module in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 INTERPRETABILITY COMPARISON: B-COS VS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' CONVENTIONAL VIT MODELS Localisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B1 (right) we present the localisation results of post-hoc explanation methods evaluated on conventional ViTs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for comparison, we repeat the results of the B-cos ViTs (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6) on the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As becomes apparent, no post-hoc explanation method evaluated on conventional ViTs allows for localising the correct grid images (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4) in the localisation metric to the same degree as is possible with the model-inherent explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we find that the model-inherent explanations yield on average 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='32 times higher localisation scores across the various model config- urations than the best post-hoc explanation method on conventional ViTs (IntGrad).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B2 (right) we present the perturbation metric results of post-hoc explana- tion methods evaluated on conventional ViTs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for comparison, we repeat the results of the B-cos ViTs (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6) on the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, as discussed in the main paper, on the left we show the normalised mean area between the curces (ABC) for each model configuration (differently sized backbones and transformers), in which the ABC of each configuration is normalised by the ABC of the model-inherent explanations (Ours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To enable a comparison between the conventional and the B-cos ViTs, on the right we normalise by the best post-hoc method (FinAtt) and further multiply the resulting score by the ratio between the mean scores across configurations of FinAtt on conven- tional ViTs and the mean scores of Ours on B-cos ViTs (corresponding to the respective dashed lines before normalisation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As discussed in the main paper, we find that the model inherent explanations of B-cos ViTs con- sistently yield the best pixel ranking for each of the configurations of the B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, the 15 Preprint black swan Input image Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IntGrad forklift digital clock lion (a) Independently normalised attribution maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' black swan Input image Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IntGrad forklift digital clock lion (b) Jointly normalised attribution maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A2: (a) Repetition of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 7 from the main paper, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', with each attribution map normalised independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (b) The same figure is shown again, but this time the normalisation is done column-wise, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', all explanations of a given method are shown on the same scale (except for the coloured explanations in the second column, which are unchanged).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that the attention-based explanations are the same across all classes to begin with and are thus not affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The IntGrad explanations as well as the forklift explanation according to Ours (7) change most notably—in the case of the model-inherent explanations, this directly reflects the fact that the model has found the least evidence for forklift: the sum of positive contributions according to the model-inherent contribution maps are 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 (black swan), 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 (forklift), 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 (digital clock), and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 (lion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' ABC is on average much higher for the model-inherent explanations for B-cos ViTs than the ABC resulting from the rankings of post-hoc explanations on conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note, however, that this could also reflect a difference in model stability and the comparisons across models have thus to be interpreted with care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 ABLATION STUDY: ANALYSING THE DESIGN CHOICES IN THE B-COS ATTENTION MODULE In this subsection, we analyse the impact of the proposed changes for the attention module in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we investigate the effect of changing the position of the LayerNorm module within the attention layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we discuss the effect of changing the model’s value computation and projection layers to B-cos layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Position of the LayerNorm module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B3, we present the classification performance results of various B-cos ViT-S models trained on embeddings extracted at different depths of the back- 16 Preprint ibex Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad limpkin Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad redshank Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad ambulance Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad harp Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad axolotl Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad traffic light Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad indigo bunting Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) GradSAM GradCAM Rollout FinAtt IxG IntGrad Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A3: Comparison of inherent explanations (Ours) of a B-cos ViT-B-38, and several post-hoc explanations for class k (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For Ours, we show a colour visualisation (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3) of the corresponding row of the weight matrix W(x) as well as the corresponding contribution maps as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that of the compared methods, the model-inherent explanations yield by far the most detail and class-specificity, as also discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a comparison to explanations generated for a conventional ViT-B-38 model on the same set of images, see the following Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' bone B-cos DenseNet-121 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we evaluate three different model configurations for each backbone depth: ‘Standard Attention’, ‘Shifted LayerNorm (B=1)’, and ‘Shifted LayerNorm (B=2)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Here, ‘Standard Attention’ refers to the unchanged attention module as it is used in con- ventional ViT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' On the other hand, the ‘Shifted LayerNorm’ models implement the change described in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (13);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', for these models, the normalisation layer is moved inside the softmax computation instead of being applied before the attention module as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We observe that the models with the shifted LayerNorm perform significantly better than those using standard attention, especially for shallower backbone models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We attribute this to the fact that using LayerNorm only within the softmax computation leaves the norm of the value vectors unchanged, such that they are inherently on a similar scale as the token embeddings they are added to in the skip connection—this allows the model to compute significant and well-scaled updates of the token embeddings via the attention module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Moreover, the model can learn bias and scale parameters that are specifically tailored to the softmax layer, instead of affecting both the softmax computation as well as the value vectors at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In the standard attention module,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' on the other hand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the norm of the value vectors can differ signif- icantly from the norm of the token embeddings in the residual connection,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' which can make it more ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='17 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Preprint ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='ibex ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='limpkin ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='redshank ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='ambulance ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='harp ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='axolotl ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='traffic light ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='indigo bunting ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='CheferLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='pLRP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradSAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='GradCAM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Rollout ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='FinAtt ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IxG ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='IntGrad ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A4: Importance attributions given by common post-hoc explanation methods applied to a conventional ViT-B-38 model (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4 for the model specifications) on the same set of images as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We find that none of the common post-hoc explanations for conventional ViTs give similarly detailed results as the model- inherent explanations do for B-cos ViTs, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, we observe a clear gain in interpretability when using B-cos ViTs instead of conventional ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' difficult for the model to take advantage of the attention module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' This hypothesis is corroborated by an analysis of the norms of the embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we find the embeddings coming from the skip connections to be on average several orders of magnitude larger than those returned by the attention layer in the models trained with standard attention: e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', by a factor of 105 in the model trained on a 13-layer backbone model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In contrast, in the Shifted LayerNorm model with B=2, this factor is on the order of 100, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', both embeddings are in fact on a similar scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' While models with standard attention could in principle learn large scale values in the LayerNorm modules, this would effectively result in one-hot encodings in the softmax computation, which could hamper learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As the attention modules thus have very limited impact on the model output, we further observe that the model does not seem to learn useful attention maps in the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B4 we compare the attention maps of the models with Standard Attention and the Shifted LayerNorm models on various images and find those of the Standard Attention model to be much less structured;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' note that for the Standard Attention model, the model output is no longer a dynamic linear transformation of the input, due to the LayerNorm module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B-cos transforms for value and projection layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In the following, we discuss the impact of replacing the linear layers typically used in the value computation and the projection layers by B- cos layers (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, we would first like to highlight that a B-cos transform with 18 Preprint 71 72 73 74 75 76 77 Model accuracy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='00 Localisation score ×2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='47 B-Cos ViTs 71 72 73 74 75 Model accuracy ×2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='32 Conventional ViTs Localisation Metric Ours Rollout FinAtt IntGrad IxG GradSAM GradCAM pLRP CheferLRP Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B1: Left: Localisation metric results for the B-cos ViTs of various sizes, same as shown in the main paper in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Right: For comparison, we show the results of common post-hoc explanations evaluated on the corresponding conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As can be seen, the model-inherent explanations of the B-cos ViTs not only constitute the best localising explanation for any given B-cos ViT, but also achieve much higher localisation scores than the best post-hoc explanations evaluated on conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 71 72 73 74 75 76 77 Model accuracy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 Normalised ABC ×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='99 B-Cos ViTs 71 72 73 74 75 Model accuracy ×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='85 Conventional ViTs Perturbation Metric Ours Rollout FinAtt IntGrad IxG GradSAM GradCAM pLRP CheferLRP Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B2: Left: Perturbation metric results for the B-cos ViTs of various sizes, same as in the main paper in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Right: For comparison, we show the results of common post-hoc explanations evaluated on the corresponding conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that, to allow for a comparison between the B-cos ViTs and the conventional ViTs, we normalised the mean ABCs of the conventional ViTs by the mean ABC of the best post- hoc method (FinAtt) and multiplied the results by the ratio between the mean ABCs FinAtt on conventional ViTs and the mean ABCs of Ours on B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a detailed discussion, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 13 backbone layers 38 backbone layers 87 backbone layers 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='80 Top-1 accuracy (%) Standard Attention Shifted LayerNorm (B=1) Shifted LayerNorm (B=2) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B3: Ablation results for different version of the attention module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we show the top-1 accuracy on the ImageNet validation set for B-cos ViTs with the conventional attention module (‘Standard Attention’) and the proposed B-cos Attention (‘Shifted LayerNorm’, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (13)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, for the latter we show the results of models trained with different values for B (B=1 and B=2) in the value computation and the projection head, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that for B=1, the B-cos transform is equivalent to a linear transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, ‘Standard Attention’ and ‘Shifted LayerNorm (B=1)’ differ only in the positioning of the LayerNorm module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 19 Preprint indigo bunting Input Rollout FinAtt redshank limpkin axolotl Standard Attention (a) indigo bunting Input Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) Rollout FinAtt redshank limpkin axolotl Shifted LayerNorm (B=1) (b) indigo bunting Input Ours [W(x)]k Ours Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7) Rollout FinAtt redshank limpkin axolotl Shifted LayerNorm (B=2) (c) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B4: Visualisation of attention-based explanations as well as the model-inherent explanations for models trained with (a) the standard attention module, (b) Shifted LayerNorm (B=1), and (c) Shifted LayerNorm (B=2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for details, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As we describe in that section, the models with standard attention seem unable to take advantage of the attention module and thus do not learn structured attention maps (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In contrast, once the LayerNorm is shifted inside the softmax computation, the models are not only inherently explainable by a single linear transformation, but also learn to use the attention layers in a much more structured manner (b+c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 20 Preprint Tiny Small Base Transformer size 60 70 80 Top-1 accuracy (%) 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='8 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 B-cos ViT-{Ti/S/B}-13 + No MaxOut B-cos ViT-{Ti/S/B}-38 + No MaxOut B-cos ViT-{Ti/S/B}-87 + No MaxOut (a) Comparison between B-cos ViTs with (solid) and without (striped) MaxOut in the Transformer layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Tiny Small Base Transformer size 60 70 80 Top-1 accuracy (%) 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='8 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='7 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='6 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='0 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='8 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5 ViT-{Ti/S/B}-13 + B-cosify (No MaxOut) ViT-{Ti/S/B}-38 + B-cosify (No MaxOut) ViT-{Ti/S/B}-87 + B-cosify (No MaxOut) (b) Comparison between B-cos ViTs (no MaxOut) (striped) in the Transformer layers and conventional ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B5: Understanding the impact of MaxOut on model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (a) For the Tiny transformers, we find that MaxOut indeed significantly improves model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, this performance gap between models with and without MaxOut closes with increasing model size (Small and Base).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (b) As such, when comparing to conventional ViTs (same numbers as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 5), we find that B-cos ViTs without MaxOut can achieve similar performance without adding additional parameters in the Transformer layers, as long as the initial model size is sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B=1 is in fact equivalent to a linear layer and the Shifted LayerNorm (B=1) model thus only differs from the conventional attention by the placement of the LayerNorm module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' When comparing the classification performance of the Shited LayerNorm models with different val- ues for B, we find the models to perform very similarly, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Given that the main difference between those models is a slightly higher value of B in one of them, this is not surprising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Moreover, given that both models still adhere to the B-cos formulation, both models are accurately summarised by a global linear transformation and allow for a model-faithful decomposition into individual in- put contributions, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' note that all other modules still use B=2 in both models and thus already induce significant alignment, irrespective of the value and projection layers6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In contrast to the model with Standard Attention, we find both models with Shifted LayerNorm to learn highly structured attention maps, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 ABLATION STUDY: ANALYSING THE IMPACT OF MAXOUT ON PERFORMANCE As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, when converting the baseline ViTs to B-cos ViTs, we follow B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022) and add a MaxOut unit to every B-cos transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' This, of course, doubles the number of parameters, which can skew the comparison to the baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In the following, we assess how MaxOut impacts the model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B5 (a), we compare the performance of B-cos ViTs as presented in the main paper to a version that does not use MaxOut when converting the baseline Transformer layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We 6As was shown in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), higher values of B can lead to a higher degree of alignment, but this transition is smooth and a value of B=1 in the attention layers seems to be sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 21 Preprint observe that for smaller models (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', Tiny), MaxOut indeed significantly improves the perfor- mance of the B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' However, with increasing model size (Small and Base), this performance gap closes and the B-cos ViTs without MaxOut perform on par with those that have twice the number of parameters in the Transformer layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As a result, we find that for sufficiently large Transformers (Small and Base), the B-cos ViTs without MaxOut are able to achieve similar performance as the baseline models, without increasing the parameter count, as we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' B5 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C IMPLEMENTATION DETAILS In the following, we provide further implementation details regarding the models (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1), the training and evaluation procedure (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2), the explanation methods (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3), and the evaluation metrics (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 MODELS For all models, we rely on the implementation by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), which we use unchanged for the conventional ViTs and modify as we describe below for the B-cos ViTs (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The configu- rations of the ViTs follow the conventional specifications for ViTs of size Ti, S, and B, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3, we use average pooling over the tokens and pass the result to the classifier head for all models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The conventional ViTs use a DenseNet-121 backbone as available in the torchvision library (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 B-COS VITS Tokenisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For all B-cos ViTs, we use a pretrained7 B-cos DenseNet-121 as provided by B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022) as a tokenisation module, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' specifically, we use the DenseNet-121 with the training+ schedule, as this one achieves the same accuracy on the ImageNet validation set as the conventional DenseNet-121 contained in the pytorch library (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As described in the main paper, we freeze this backbone and extract features after either 13, 38, or 87 convolutional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We then apply a single B-cos convolutional layer with a kernel size k=1, 2, 4 and stride s=1, 2, 4 with no padding on the feature maps after 87, 38, or 13 convolutional layers respectively, such that the number of tokens is the same for all B-cos ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We found it advantageous to scale the features of the backbones by 103, as this improved signal propagation and lead to better results8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Depending on the size of the transformer (Ti, S, B, see main paper), this B-cos convolution produced activations with c=192, 384, 768 channels after MaxOut (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2013) over every two output units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The resulting activation map of size c×h×w is then reshaped to n×c with n the number of input tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As described in the main paper, we replace the value computation as well as the linear projection of the attention heads by linear B-cos transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we apply layer normalisa- tion to the inputs before the query and key computations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' the value computations use the raw input, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, when additionally learning ‘attention priors’, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='5, we add a learnable pa- rameter B∈Rm×n×n to each attention layer, with m the number of attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The parameter B thus contains separate pair-wise priors between any two tokens for every attention head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' MLPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4, we convert the MLPs to B-cos MLPs by replacing the linear transformations by B-cos transformations with two units and MaxOut (Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we remove the normalisation layer before the MLP block, and the GELU (Hendrycks & Gimpel, 2016) non-linearities within the MLPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We use a single B-cos transformation as a classification head, without MaxOut and C=1000 output features, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', one output for each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' General remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Similar to B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), we scale the output of every B-cos layer in the network by a scaling factor γ=f/√c to improve signal propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' In particular, as more channels lead to a stronger decay, we used f =15, 20, 25 for ViTs of size Ti, S, B respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' further, since the multiplicative prior computes the product of two attention values ≤ 1, the activations in these networks decay even more quickly and we scale each f by an additional factor of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Moreover, as 7The pretrained models were downloaded from github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='com/moboehle/B-cos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 8Note that in contrast to standard ViTs, in which normalisation layers ensure that the input to each layer is well-behaved, in B-cos Networks the activations can decay very quickly since no normalisation is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 22 Preprint in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), we scale down the model output by 103 after which we add a logit bias b∈RC to the model output which is set to log(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='01/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='99) for each of the C output logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Lastly, for the B-cos ViTs, we encode the input images as in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', such that each pixel uses 6 color channels [r, g, b, 1−r, 1−g, 1−b] with r, g, b∈[0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As we discuss in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C, this allows for visualising the matrices W(x) in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 TRAINING AND EVALUATION PROCEDURE Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We trained the B-cos ViTs with a batch size of 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For the conventional ViTs, we found larger batch sizes to yield better results and thus trained those with a batch size of 1024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, we trained all our models with RandAugment (Cubuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2020) (n=2 and m=9) and used images of size 224×224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' While the conventional models were, as is common, trained with SoftMax and a cross entropy loss, for the B-cos ViTs we followed B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022) and trained with binary cross entropy and sigmoid applied to the output logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that, as discussed in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), binary cross entropy induces the necessary logit maximisation for every input, which in turn leads to weight alignment with class-relevant patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We evaluated all networks on the ImageNet validation set after resizing the images such that the smaller dimension measured 256 pixels and then center-cropped images of size 224×224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='3 ATTRIBUTION METHODS In the following, we describe the explanation methods that we evaluate on the B-cos as well as the conventional ViTs in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Model-inherent explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' The model-inherent explanations that we quantitatively evaluated are given by the contribution maps defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, for a given class logit, we extract the effective linear contribution as performed by the model and multiply it with the input in an element-wise manner and sum all values per pixel location, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', across the colour channels;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' note that this is conceptually equivalent to ‘Input×Grad’ for piece-wise linear models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For a visualisation of contribution maps, see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 1 and 7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' here, we use a blue-white-red colormap with blue colors denoting negative, and red colors denoting positive contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' This visualisation method is the same for all methods except for those that use the jet colormap (CheferLRP, Rollout, and FinAtt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Additionally, for better visibility, we clamp the contribution values to the interval [−v, v], with v the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='9th percentile of the absolute values of the given spatial attribution map (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', after summing over the colour channels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Note that as a result, the explanations are normalised independently;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' for a discussion of the effect of normalising across multiple explanations, see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, as also shown in those figures, the B-cos formulation allows to directly visualise the trans- formation matrix W(x) in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, note that the input to B-cos networks is encoded as p = [r, g, b, 1−r, 1−g, 1−b] with r, g, b∈[0, 1] the color channels, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 and B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As such, the color of each pixel is unambiguously encoded by the angle of the pixel vector p and it is thus possible to reconstruct the image colors from the angles alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Crucially, as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 W(x) is implicitly optimised to align with relevant patterns in the input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', to have a similar angle as the input, such that the weights for any given pixel can be mapped to a specific color in RGB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We further follow B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022) and use the norm of the pixel vectors to compute the opacity α in an RGB-α encoding, for details see B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2022), and only show pixels that positively contribute to the respective logit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Transformer-specific explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As described in the main paper, we evaluate against common transformer-specific explanations such as the average attention distribution in the final layer (FinAtt), Attention Rollout as proposed by Abnar & Zuidema (2020), and GradSAM (Barkan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' On the conventional ViTs, we further evaluate LRP-based explanations: partial LRP (pLRP) Voita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2019) and the transformer-specific LRP adaptation by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021) (CheferLRP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For all these transformer-specific explanations, we rely on the implementation provided by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Architecture-agnostic explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 and 7, we also evaluate other commonly used explanation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we use IntGrad (Sundararajan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017) with n=32 steps, ‘Input×Gradient’ (IxG), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Adebayo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2018), as well as an adapted Grad- CAM (Selvaraju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2017) as in Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For the last, we rely on the implementation provided by Chefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For the remaining methods, we use the implementations contained in the captum library of pytorch (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 23 Preprint C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4 EVALUATION METRICS C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='1 LOCALISATION METRIC For the localisation metric, we evaluated all attribution methods on the grid pointing game (B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For this, we constructed 250 2×2 grid images, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' As was done in B¨ohle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' (2021), we sorted the images according to the models’ classification confidence for each class and then sampled a random set of classes for each multi-image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' For each of the sampled classes, we then included the most confidently classified image in the grid that had not already been used in a previous grid image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Further, transformers with positional information expect a fixed size input, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To neverthe- less evaluate the attribution methods on the localisation metric, which uses images of size 448×448, we scale the synthetic images down by a factor of two such that they are of size 224×224 and thus of a size that is compatible with the transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='2 PERTURBATION METRIC As for the pixel perturbation metrics, we proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' First, we sort the images in the validation set by their classification confidence and evaluate on the first 250 images for each model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' We do this to reduce the computational cost of evaluating this metric whilst nevertheless allowing for a fair comparison between models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we observed the model stability to correlate with the model confidence and by choosing the most confidently predict images, each model is evaluated in a favourable setting, which ensures comparability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Second, we remove up to 25% of the pixels from the images in increasing / decreasing order as ranked by a given attribution method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Specifically, we sample the resulting confidence curves at 9 equidistant points r in the interval [0, 25%] and ‘remove’ the pixels by zeroing out the respective pixel encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' Finally, we record the mean model confidence at the sampled points, which we normalise by the initial mean confidence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' as such, each curve starts at (r, o)=(0, 1) with r the percentage of pixels removed and o the normalised model confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' To assess the quality of the ranking, we then measure the area between the two confidence curves corresponding to the order in which we remove the pixels, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', least / most important first, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 6 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} +page_content=' 24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INFAT4oBgHgl3EQfuR6w/content/2301.08669v1.pdf'} diff --git a/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/2301.13471v1.pdf.txt b/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/2301.13471v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..43b5341d4faa1f13a50c7917812a0a4da86823d7 --- /dev/null +++ b/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/2301.13471v1.pdf.txt @@ -0,0 +1,508 @@ +arXiv:2301.13471v1 [astro-ph.EP] 31 Jan 2023 +What if planet 9 has satellites? +Man Ho Chan +Department of Science and Environmental Studies, The Education University of Hong +Kong, Hong Kong, China +chanmh@eduhk.hk +ABSTRACT +In the past decade, numerical simulations started to reveal the possible ex- +istence of planet 9 in our solar system. The planet 9 scenario can provide an +excellent explanation to the clustering in orbital elements for Kuiper Belt ob- +jects. However, no optical counterpart has been observed so far to verify the +planet 9 scenario. Therefore, some recent studies suggest that planet 9 could +be a dark object, such as a primordial black hole. In this article, we show that +the probability of capturing large trans-Neptunian objects (TNOs) by planet 9 +to form a satellite system in the scattered disk region (between the inner Oort +cloud and Kuiper Belt) is large. By adopting a benchmark model of planet 9, +we show that the tidal effect can heat up the satellites significantly, which can +give sufficient thermal radio flux for observations, even if planet 9 is a dark ob- +ject. This provides a new indirect way for examining the planet 9 hypothesis and +revealing the basic properties of planet 9. +Subject headings: Planet, Solar System +1. +Introduction +Currently, there are 8 planets officially identified in our solar system. +Most of the +newly discovered large astronomical objects outside Neptune are dwarf planets or large +asteroids called trans-Neptunian objects (TNOs). In view of the TNOs, the new discov- +ery of 2012 VP113 and some potential members of the inner Oort cloud has revealed a +strange clustering in orbital elements (Trujilio & Sheppard 2014). The perihelion distance +have arguments of perihelia ω clustered approximately round zero (Trujilio & Sheppard +2014; Batygin & Brown 2016a). Later analysis shows that the chance for this strange clus- +tering due to random is just 0.0007% (Batygin & Brown 2016a). +Therefore, a dynami- +cal mechanism involving a new planet located at more than 100 AU has been suggested + +– 2 – +(Batygin et al. 2019). Many studies have constrained the mass and the orbital properties +of the hypothesized planet 9 (P9) (Batygin & Brown +2016b; Sheppard & Trujillo +2016; +Gomes, Deienno & Morbidelli 2016; Becker et al. +2018; Sheppard et al. +2019). Current +benchmark models suggest that P9 has mass M9 ∼ 5 − 10M⊕, orbital semi-major axis +a9 ∼ 400 − 800 AU and eccentricity e9 ∼ 0.2 − 0.5 (Batygin et al. +2019). However, the +in-situ formation of P9 is strongly disfavored so that P9 might be a captured planet from +the free-floating objects nearby the solar system (Batygin et al. 2019; Kenyon & Bromley +2016). A more detailed assessment of the probability of capture can be found in Li & Adams +(2016). +Current benchmark models of P9 suggest that it has a temperature ∼ 40 K and a +radius ∼ 3 − 4R⊕ (Batygin et al. 2019). The possible location of P9 in the celestial sphere +is also constrained (Batygin et al. 2019; Fienga et al. 2016; Socas 2022). Based on these +properties, various observations, such as optical and microwave/infrared observations, have +been deployed to observe the hypothesized P9 (Meisner et al. +2017, 2018; Naess et al. +2021). However, no electromagnetic wave signal has been detected for P9 (Meisner et al. +2017, 2018; Linder & Mordasini +2016). +Careful examinations based on previous optical +surveys also do not reveal the existence of P9 (Linder & Mordasini 2016). Therefore, these +null results have made the P9 hypothesis more mysterious. +In view of these problems, some of the studies have suggested that P9 is a dark object +(dark P9), such as a compact object made by dark matter (Wang et al. 2022) or a primordial +black hole (PBH) (Scholtz & Unwin 2020). In particular, the proposal of the PBH P9 has +attracted many discussions because many studies beyond the standard models have already +proposed the existence of PBHs with mass ∼ M⊕. There are various mechanisms which can +generate PBHs in early universe (Carr et al. 2021). However, the direct signals emitted by +the PBH P9 (e.g. Hawking radiations) are too small to detect (Arbey & Auffinger 2020). +Even if we assume dark matter can distribute around the PBH P9, the resulting gamma- +ray signals might be smaller than the current observation limits (Scholtz & Unwin 2020). +Besides, a recent innovative proposal suggests that using a small laser-launched spacecraft +with a velocity of order 0.001c can reach the PBH P9 to detect its gravitational field, though +we need to wait for the measurement after roughly a decade (Witten 2020). +Nevertheless, there are a lot of TNOs orbiting about the sun inside the scattered disk +region (∼ 100 − 1000 AU), located between the inner Oort cloud and Kuiper Belt. These +TNOs are also known as detached objects. Most of them are either scattered from the central +solar system or Kuiper Belt region. In fact, we have already observed at least 47 large TNOs +with orbital semi-major axis larger than 100 AU and size larger than 100 km. Therefore, it +is possible that these large TNOs would be captured by P9 to become satellites of P9. Many + +– 3 – +dwarf planets such as Pluto and TNOs outside Neptune have satellite systems (Brown et al. +2006; Grundy et al. +2019). If these small objects can have satellites, it can be conceived +that the more massive P9 might also have a number of satellites. In this article, we discuss +some important observable features if P9 has captured satellites. For large satellites with +small orbital semi-major axis, the tidal heating effect due to P9 would be important. It can +be shown that these satellites would give an observable standard thermal radio spectrum. +If P9 is a dark object, observing the satellites would be another kind of investigation to +examine the P9 hypothesis in the near future. In the followings, we assume that P9 is a +dark object and we follow the benchmark model of P9 with mass M9 = 5M⊕, eccentricity +e9 = 0.2, orbital inclination i = 20◦, and semi-major axis a9 = 450 AU (Batygin et al. +2019). We simply take the semi-major axis a9 = 450 AU as the average distance to the dark +P9 from the Earth. +2. +Capturing probability +There are many large TNOs moving in the scattered disk region (∼ 100 − 1000 AU), +such as 2018 AG37, 2018 VG18 and 2020 BE102. It is quite likely that some of the large +TNOs (e.g. with size D ∼ 100 km) could be captured by the dark P9. In fact, many of the +Kulper Belt dwarf planets have at least one satellite. For example, the satellite of the dwarf +planet Eris has radius R ∼ 700 km and semi-major axis a ∼ 4 × 104 km (Brown & Butler +2018). +In general, when a TNO has a close encounter to a planet, energy will be lost in the cap- +turing process due to the inverse of the gravitational slingshot mechanism (Napier, Adams & Batygin +2021). The maximum capturing distance between the dark P9 and any TNOs can be char- +acterized by the impact parameter b (Napier, Adams & Batygin 2021): +b ∼ M9 +M⊙ +�GM⊙ +a9 +�3/2 +v−3a9, +(1) +where v is the incoming relative velocity between the dark P9 and any TNOs. Here, b can +be regarded as the closest distance between the dark P9 and the TNOs for the capturing +process. Therefore, the relative velocity between the dark P9 and the TNOs is given by +v ∼ +� +GM⊙ +a9 +− +� +GM⊙ +a9 ± b cos ∆i, +(2) +where ∆i is the orbital inclination difference between the dark P9 and the TNOs. As b ≪ a9, +the relative velocity is +v ∼ +� +GM⊙ +a9 +(1 − cos ∆i). +(3) + +– 4 – +Putting Eq. (3) into Eq. (1), we get +b ∼ a9(1 − cos ∆i)−3 +� M9 +M⊙ +� +. +(4) +The benchmark orbital inclination of the dark P9 is i = 20◦ (Batygin et al. +2019). Based +on the catalog compiled by the International Astronomical Union 1, the orbital inclinations +of the TNOs (with semi-major axis a > 100 AU) are quite close to i = 20◦, except three +with i > 100◦. The average difference between the orbital inclinations of P9 and the TNOs +is about ∆i = 18◦. Including the possible uncertainty of the benchmark orbital inclination +of the dark P9 δi = 5◦ (Batygin et al. +2019), we take a conservative choice of ∆i = 25◦, +which gives b ∼ 8.2 AU. +On the other hand, we can also apply the radius of influence Rin discussed in Bate +(1971) to characterize the value of the impact parameter (i.e. +b ≈ Rin). +The radius of +influence defines the region where the incoming TNO switches from a two-body problem +with central mass M⊙ to a two-body problem with central mass M9 in the matched conics +approximation (Napier, Adams & Batygin 2021). Based on this approximation, the impact +parameter is given by (Bate 1971) +b = Rin = a9 +� M9 +M⊙ +�2/5 +. +(5) +Using our benchmark parameters, the dark P9 can capture any TNOs moving within the +distance of b ∼ 5.3 AU. To get a more conservative estimation, in the followings, we adopt +the value of b = 5.3 AU as the impact parameter. In view of this, the dark P9 can create a +‘capturing volume’ when it is orbiting about the sun. All of the TNOs inside this capturing +volume would be likely captured by the dark P9. The capturing volume is given by +V = +� +2πa9 +� +1 − e2 +9 +2 +� +(πb2) = 2π2b2a9 +� +1 − e2 +9 +2 ≈ 2.5 × 105 AU3. +(6) +Generally speaking, very large TNOs (with size ≥ 500 km) would be easier for us to +identify. Based on the catalog compiled by the International Astronomical Union, there are +four TNOs with size ≥ 500 km (assuming a standard asteroid albedo p = 0.1) and orbital +semi-major axis a = 100−1000 AU. The number of very large TNOs can provide a standard +reference for estimating the amount of TNOs with different sizes inside the scattered disk +region. +1The +catalog +compiled +by +the +International +Astronomical +Union +can +be +found +in +https://minorplanetcenter.net/iau/lists/TNOs.html + +– 5 – +Consider the region of the scattered disk for a = 100 − 1000 AU. Based on the TNO +catalog, all of the reported TNOs with a ≤ 1000 AU are located within a scale disk thickness +of 72.5 AU above and below the P9 orbital plane. We therefore consider the volume of the +scattered disk Vd ∼ (2 × 72.5)π(10002 − 1002) ≈ 4.5 × 108 AU3. Assuming the distribution +of asteroid size is same as that in Kuiper Belt dN/dD ∝ D−q (Fraser et al. +2014). This +size distribution in Kuiper Belt is well represented by a broken power law in D for large and +small Kuiper Belt objects. For cold Kuiper Belt objects, the slope q for large objects (with +size D ≥ 140 km) is q = 8.2 ± 1.5 while q = 2.9 ± 0.3 for D < 140 km (Fraser et al. 2014). +Since there are four TNOs with size ≥ 500 km, taking q = 8.2, the average number density +of TNOs with size D ≥ 140 km inside Vd is 8.5 × 10−5 AU−3. +Since the capturing volume is 2.5 × 105 AU3, the average number of TNOs with size +D ≥ 140 km captured is about 20. Note that this number is close to the typical number of +satellites found in Jovian planets. In fact, the Jovian planets are somewhat close to each other +so that the gravitational perturbation effect is significant. This would reduce the capturing +volume and the number of satellites. However, there is almost no massive perturber for +P9. The closest massive object Sedna (semi-major axis a ∼ 500 AU) has a relatively small +mass ∼ 10−3M⊕ only, which cannot affect the capturing volume significantly. Therefore, we +expect that there is a considerable amount of captured TNOs to form a satellite system for +P9, like the satellite systems in Jovian planets. +3. +The tidal heating model +Consider a fiducial radius of the satellite R = D/2 = 100 km. For simplicity, let’s +assume that the satellite is spherical in shape. The tidal force on the satellite is large when +the satellite is close to P9. The Roche limit is ∼ 2 × 104 km if we assume the density of +the satellite to be ρ = 1 g/cm3. For Uranus and Neptune, which have mass similar to the +dark P9, the range of the orbital semi-major of the satellites is as ∼ 5 × 104 − 5 × 107 +km. +In the followings, we will mainly consider the range of the orbital semi-major axis +as = 105 − 106 km. Note that captured objects generally have large semi-major axis and +eccentricity initially (Goulinski & Ribak 2018; Napier, Adams & Batygin 2021). However, +orbital evolution through tidal effects would further decrease the values of semi-major axis +and eccentricity (see the discussion below). +The equilibrium temperature due to solar luminosity is approximately given by +T ≈ 54.8 +� +26 +a9 +K, +(7) +where we have neglected the albedo and the phase integral (Stansberry et al. +2008). For + +– 6 – +a9 = 450 AU, we get T = 13 K. However, if the satellite is very close to P9, the tidal heating +effect would be very significant. The tidal heating model has been discussed for more than +50 years (Goldreich & Soter 1966). In general, the tidal heating rate can be calculated by +(Segatz et al. 1988; Lainey et al. 2009; Renaud & Henning 2018) +˙E = 21C +2 +(Rn)5e2 +s +G +, +(8) +where n = +� +GM9/a3s is the mean orbital motion, and es is the eccentricity of the satellite +orbit (Segatz et al. 1988). Here, the constant C is related to the Love number k2 and the +quality factor Q which reflects the physical properties (e.g. elastic rigidity) of the satellite +(Segatz et al. 1988; Lainey et al. 2009; Hussmann et al. 2010). However, the value of C +for the satellite is uncertain. Theoretical prediction shows that the value of C should be +lower than 0.06 for high density satellite core (Kervazo et al. +2022). We adopt the value +revealed from the observational data of the Jupiter’s moon Io C ≈ 0.02 (Lainey et al. 2009). +In equilibrium, the tidal heating rate would be equal to the radiation cooling rate. Therefore, +we have +T = +� +˙E +4πσsǫνR2 +�1/4 +, +(9) +where σs is the Stefan-Boltzmann constant and ǫν is the gray-emissivity. For simplicity, we +assume ǫν = 1 here. +In Fig. 1 and Fig. 2, we plot the equilibrium temperature as a function of as, for different +values of R and es, respectively. We can see that the temperature can be quite high for some +values of as, R and es. Generally speaking, smaller value of as and larger values of R and es +can give a higher equilibrium temperature. For the fiducial values of as = 105 km, R = 100 +km and es = 0.5, we get ˙E = 1.4 × 1012 W. The equilibrium temperature of the satellite is +about 119 K, which can emit significant amount of radio radiation with frequency ν > 100 +GHz. Besides, we can estimate the time required for the satellite to heat up from 10 K to +100 K. Assuming a typical specific heat capacity for the satellite cs = 1000 J kg−1 K−1, the +time required is ∼ 104 yrs for the fiducial parameters used. +In the followings, we estimate the thermal radio flux emitted by the satellite with the +fiducial parameters. The thermal radio flux density is given by +Sν = +� +2hν3 +c2(ehν/kT − 1)dΩ ≈ +2πhν3 +c2(ehν/kT − 1) +� R +a9 +�2 +. +(10) +Therefore, we can get the expected thermal radio flux density as a function of ν for the fiducial +parameters (see Fig. 3). The radio flux density is ∼ 2 µJy for ν = 300 GHz. The observable +limit for the most sensitive sub-mm interferometer (e.g. Atacama Large Millimeter Array + +– 7 – +ALMA) is around 1 µJy at ν = 100 − 300 GHz. Hence, it is feasible to observe this small +flux using current observational technologies. For lower frequencies, the expected radio flux +density is Sν ≈ 10 nJy at ν = 20 GHz. This can be observable by the future SKA radio +interferometer. +Moreover, the thermal radio flux density Sν is proportional to the frequency ν2. This +can be differentiable from the normal background radio flux, which is usually modelled by +Sν ∝ ν−α with α > 0. +In other words, by obtaining the radio spectrum emitted from +the region of the dark P9, if we can detect a relatively strong thermal radio spectrum +(Sν ∝ ν2), this would be a solid evidence to verify the P9 hypothesis because there is no +other astrophysical mechanism which can increase the temperature of a distant object to +more than 50 K. For the conventional P9 model (not a dark object), the expected radio flux +emitted by P9 should be ∼ mJy at 200 GHz (Naess et al. 2021), which is 1000 times larger +than that of a satellite. In any case, either if we can detect mJy signal from P9 or µJy +signal from the satellite, the P9 hypothesis can be verified. Besides, if there is any potential +signal received from P9 or the satellites, we can track the source for a couple of years to see +whether the signal would follow a nearly Keplerian orbit over time or not. This can further +provide a smoking-gun evidence to verify the P9 hypothesis. +Previous studies have constrained the possible range of location for P9 (Batygin et al. +2019; Fienga et al. +2016; Socas 2022). A recent study has further constrained the exact +location of P9 to R.A. (48.2 ± 4)◦ and DEC (10.3 ± 1.8)◦ (Socas 2022). +Such a small +constrained region can make the observation much easier. The telescopes or interferometers +used can focus on the target region for a very long exposure time to gain enough sensitivity +to detect the potential thermal signals. +Note that the tidal heating rate gained by the satellite originates from the loss rate of the +gravitational potential energy of the P9-satellite system. The eccentricity would gradually +decrease so that the tidal heating rate would also decrease. The eccentricity fractional change +rate is given by +|˙es| +es += +�e2 +s − 1 +2e2s +� ˙E +E . +(11) +The time scale for the eccentricity shrinking is τ ∼ |es/˙es|, which is about 0.6 Myrs for +the fiducial parameters. This timescale is short compared to the age of the solar system. +In fact, there is a compromise between having the orbital parameters of the satellites such +that the radio emission is detectable (e.g. with small as) and sufficiently long-lived to make +the higher detection probability (e.g. with large as). Here, the range of as we considered +(as = 105 −106 km) is almost the optimal for examination. Nevertheless, the relatively short +eccentricity shrinking timescale would not be a big problem if the satellite capture event is + +– 8 – +a recent event. Also, as we have shown that the satellite capture is not a rare event, there +would be more than one satellite with size > 140 km at as ∼ 105 km. Therefore, we expect +that such a thermal radio signal of the satellite may still be observed. +4. +Discussion +In this article, we have demonstrated a theoretical framework to predict the possible +observable signal from the P9-satellite system. If the dark P9 has a satellite system, the +only current feasible observation is to detect the possible signals from the satellites. We +have shown that if a satellite with a typical size ∼ 100 km with average orbital radius +as ∼ 105 km from the dark P9, the temperature can be as large as ∼ 100 K due to tidal +heating effect. For such a high temperature, the satellite can emit strong enough thermal +radio flux (∼ 1 µJy at 100-300 GHz) that can be observed by ALMA. Moreover, the specific +thermal radio spectrum Sν ∝ ν2 could be easily differentiable from the background radio +flux so that it can provide a smoking-gun evidence for the P9 hypothesis. The only possible +reason for the existence of ∼ 100 K object at ∼ 450 AU from the sun is that it is a satellite +of a host planet. It is because a host dwarf planet or a minor planet does not have enough +mass to heat up the satellite to ∼ 100 K. +As we have shown above, there are a lot of TNOs with size > 140 km in the scattered +disk region. Therefore, the chance for these large TNOs (with R ∼ 100 km) captured by P9 is +not low. Besides, based on the example of Uranus (≈ 14M⊕), at least 13 satellites are located +within 105 km, which suggests that our fiducial value of as = 105 km is a reasonable choice +of consideration. For the eccentricity, simulations show that most of the captured objects +would be orbiting with a very high eccentricity ≈ 1 (Goulinski & Ribak 2018). Therefore, +our fiducial value es = 0.5 is a conservative choice of estimation. +Since no optical and radio signals have been detected so far for P9, the suggestion +of P9 being a PBH has become a hot topic recently. There are some suggestions to send +detectors to visit the alleged PBH P9 (Witten 2020; Hibberd, Lingam & Hein 2022). It +would be very exciting because this may be our only chance to visit a black hole within our +approachable distance. Nevertheless, we need to wait for at least 10 years for the detectors to +arrive the PBH P9. Some other studies have proposed to detect P9 by gravitational lensing +(Philippov & Chobanu 2016; Schneider 2017; Dom`enech & Pi 2022). However, the mass +of P9 is very small so that it requires a very sensitive measurement for the short-live lensing +event, which may not be very easy to get any good confirmation. +A recent study has +proposed a narrow possible locations of P9 (Socas 2022). If P9 is a dark object and it has a +satellite system, our proposal can directly observe the potential thermal signals emitted by + +– 9 – +the satellites now. Therefore, this would be a timely and effective method to confirm the P9 +hypothesis and verify whether P9 is a dark object or not. +5. +Acknowledgements +The work described in this paper was partially supported by a grant from the Re- +search Grants Council of the Hong Kong Special Administrative Region, China (Project No. +EdUHK 18300922). +REFERENCES +Arbey A. & Auffinger J., arXiv:2006.02944. +Bate R. R., Mueller D. D. & White J. E., 1971, Fundamentals of Astrodynamics (New York: +Dover). +Batygin K. & Brown M. E., 2016a, Astron. J. 151, 22. +Batygin K. & Brown M. E., 2016b, Astrophys. J. 833, L3. +Batygin K., Adams F. C., Brown M. E. & Becker J. C., 2019, Phys. Rep. 805, 1. +Becker J. C. et al., 2018, Astron. J. 156, 81. +Brown M. E. & Butler B. J., 2018, Astron. J. 156, 164. +Brown M. E. et al., 2006, Astrophys. J. 639, L43. +Carr B., Kohri K., Sendouda Y. & Yokoyama J., 2021, Rep. Prog. Phys. 84, 116902. +Dom`enech G. & Pi S., 2022, Sci. Chi. Phys. Mec. Astron. 65, 230411. +Fraser W. C., Brown M. E., Morbidelli A., Parker A. & Batygin K., 2014, Astrophys. J. 782, +100. +Fienga A., Laskar J., Manche H. & Gastineau M., 2016, Astron. Astrophys. 587, L8. +Goldreich P. & Soter S., 1966, Icarus 5, 375. +Gomes R., Deienno R. & Morbidelli A., 2016, Astron. J. 153, 27. +Goulinski N. & Ribak E. N., 2018, Mon. Not. R. Astron. Soc. 473, 1589. + +– 10 – +1e+005 +1e+006 +Semi-major axis (km) +0.01 +0.1 +1 +10 +100 +1000 +T (K) +es = 0.1 +es = 0.5 +es = 0.9 +Fig. 1.— The colored lines indicate the predicted temperature T of the satellite for different +values of orbital eccentricity (es = 0.1, es = 0.5 and es = 0.9). Here, we have neglected the +solar heating effect and we have assumed R = 100 km. + +– 11 – +1e+005 +1e+006 +Semi-major axis (km) +0.01 +0.1 +1 +10 +100 +1000 +T (K) +R = 50 km +R = 100 km +R = 200 km +Fig. 2.— The colored lines indicate the predicted temperature T of the satellite for different +values of satellite radii (R = 50 km, R = 100 km and R = 200 km). Here, we have neglected +the solar heating effect and we have assumed es = 0.5. + +– 12 – +100 +1000 +ν (GHz) +0.001 +0.01 +0.1 +1 +10 +100 +S(ν) (µJy) +R = 50 km, T = 70 K +R = 100 km, T = 119 K +R = 200 km, T = 199 K +Fig. 3.— The colored lines indicate the predicted thermal radio flux density S(ν) against ν +for different values of satellite radii (R = 50 km, R = 100 km and R = 200 km). Here, we +have assumed as = 105 km and es = 0.5. + +– 13 – +Grundy W. M. et al., 2019, Icarus 334, 62. +Hibberd A., Lingam M. & Hein A. M., arXiv:2208.10207. +Hussmann H., Choblet G., Lainey V., Matson D. L., Sotin C., Tobie G. & Van Hoolst T., +2010, Sp. Sci. Rev. 153, 317. +Kenyon S. J. & Bromley B. C., 2016, Astrophys. J. 825, 33. +Kervazo M., Tobie G., Choblet G., Dumoulin C. & Bˇehounkov´a M., 2022, Icarus 373, 114737. +Lainey V., Arlot J.-E., Karatekin ¨O & Van Hoolst T., 2009, Nature 459, 957. +Li G. & Adams F. C., 2016, Astrophys. J. 823, L3. +Linder E. F. & Mordasini C., 2016, Astron. Astrophys. 589, A134. +Meisner A. M., Bromley B. C., Nugent P. E., Schlegel D. J., Kenyon S. J., Schlafly E. F. & +Dawson K. S., 2017, Astron. J. 153, 65. +Meisner A. M., Bromley B. C., Kenyon S. J. & Anderson T. E., 2018, Astron. J. 155, 166. +Naess S. et al., 2021, Astrophys. J. 923, 224. +Napier K. J., Adams F. C. & Batygin K., 2021, Planetary Sci. J. 2, 53. +Philippov J. P. & Chobanu M. I., 2016, Publ. Astron. Soc. Aust. 33, 033. +Renaud J. P. & Henning W. G., 2018, Astrophys. J. 857, 98. +Segatz M., Spohn T., Ross M. N. & Schubert G., 1988, Icarus 75, 187. +Schneider J., 2017, Publ. Astron. Soc. Pac. 129, 104401. +Scholtz J. & Unwin J., 2020, Phys. Rev. Lett. 125, 051103. +Sheppard S. S. & Trujillo C., 2016, Astron. J. 152, 221. +Sheppard S. S., Trujillo C. A., Tholen D. J. & Kaib N., 2019, Astron. J. 157, 139. +Socas-Navarro H., arXiv:2205.07675. +Stansberry J., Grundy W., Brown M., Cruikshank D., Spencer J., Trilling D. & Margot +J.-L., 2008, The solar system beyond Neptune, M. A. Barucci, H. Boehnhardt, D. P. +Cruikshank & A. Morbidelli (eds.), Tucson: University of Arizona Press, 161-179. + +– 14 – +Trujillo C. A. & Sheppard S. S., 2014, Nature 507, 471. +Wang P., Tang Y.-C., Zu L., Chen Y.-Y. & Feng L., arXiv:2210.04147. +Witten E., arXiv:2004.14192. +This preprint was prepared with the AAS LATEX macros v5.2. + diff --git a/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/load_file.txt b/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..4fe9de611f76bd2b98b699957b52885be4b550e2 --- /dev/null +++ b/J9FRT4oBgHgl3EQfDDeX/content/tmp_files/load_file.txt @@ -0,0 +1,587 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf,len=586 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='13471v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='EP] 31 Jan 2023 What if planet 9 has satellites?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Man Ho Chan Department of Science and Environmental Studies, The Education University of Hong Kong, Hong Kong, China chanmh@eduhk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='hk ABSTRACT In the past decade, numerical simulations started to reveal the possible ex- istence of planet 9 in our solar system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The planet 9 scenario can provide an excellent explanation to the clustering in orbital elements for Kuiper Belt ob- jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, no optical counterpart has been observed so far to verify the planet 9 scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, some recent studies suggest that planet 9 could be a dark object, such as a primordial black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In this article, we show that the probability of capturing large trans-Neptunian objects (TNOs) by planet 9 to form a satellite system in the scattered disk region (between the inner Oort cloud and Kuiper Belt) is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' By adopting a benchmark model of planet 9, we show that the tidal effect can heat up the satellites significantly, which can give sufficient thermal radio flux for observations, even if planet 9 is a dark ob- ject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This provides a new indirect way for examining the planet 9 hypothesis and revealing the basic properties of planet 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Subject headings: Planet, Solar System 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Introduction Currently, there are 8 planets officially identified in our solar system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Most of the newly discovered large astronomical objects outside Neptune are dwarf planets or large asteroids called trans-Neptunian objects (TNOs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In view of the TNOs, the new discov- ery of 2012 VP113 and some potential members of the inner Oort cloud has revealed a strange clustering in orbital elements (Trujilio & Sheppard 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The perihelion distance have arguments of perihelia ω clustered approximately round zero (Trujilio & Sheppard 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Batygin & Brown 2016a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Later analysis shows that the chance for this strange clus- tering due to random is just 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='0007% (Batygin & Brown 2016a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, a dynami- cal mechanism involving a new planet located at more than 100 AU has been suggested – 2 – (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Many studies have constrained the mass and the orbital properties of the hypothesized planet 9 (P9) (Batygin & Brown 2016b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Sheppard & Trujillo 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Gomes, Deienno & Morbidelli 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Becker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Sheppard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Current benchmark models suggest that P9 has mass M9 ∼ 5 − 10M⊕, orbital semi-major axis a9 ∼ 400 − 800 AU and eccentricity e9 ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, the in-situ formation of P9 is strongly disfavored so that P9 might be a captured planet from the free-floating objects nearby the solar system (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Kenyon & Bromley 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A more detailed assessment of the probability of capture can be found in Li & Adams (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Current benchmark models of P9 suggest that it has a temperature ∼ 40 K and a radius ∼ 3 − 4R⊕ (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The possible location of P9 in the celestial sphere is also constrained (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Fienga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Socas 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Based on these properties, various observations, such as optical and microwave/infrared observations, have been deployed to observe the hypothesized P9 (Meisner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2017, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Naess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, no electromagnetic wave signal has been detected for P9 (Meisner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2017, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Linder & Mordasini 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Careful examinations based on previous optical surveys also do not reveal the existence of P9 (Linder & Mordasini 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, these null results have made the P9 hypothesis more mysterious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In view of these problems, some of the studies have suggested that P9 is a dark object (dark P9), such as a compact object made by dark matter (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2022) or a primordial black hole (PBH) (Scholtz & Unwin 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In particular, the proposal of the PBH P9 has attracted many discussions because many studies beyond the standard models have already proposed the existence of PBHs with mass ∼ M⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' There are various mechanisms which can generate PBHs in early universe (Carr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, the direct signals emitted by the PBH P9 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hawking radiations) are too small to detect (Arbey & Auffinger 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Even if we assume dark matter can distribute around the PBH P9, the resulting gamma- ray signals might be smaller than the current observation limits (Scholtz & Unwin 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Besides, a recent innovative proposal suggests that using a small laser-launched spacecraft with a velocity of order 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='001c can reach the PBH P9 to detect its gravitational field, though we need to wait for the measurement after roughly a decade (Witten 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Nevertheless, there are a lot of TNOs orbiting about the sun inside the scattered disk region (∼ 100 − 1000 AU), located between the inner Oort cloud and Kuiper Belt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' These TNOs are also known as detached objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Most of them are either scattered from the central solar system or Kuiper Belt region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In fact, we have already observed at least 47 large TNOs with orbital semi-major axis larger than 100 AU and size larger than 100 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, it is possible that these large TNOs would be captured by P9 to become satellites of P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Many – 3 – dwarf planets such as Pluto and TNOs outside Neptune have satellite systems (Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Grundy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' If these small objects can have satellites, it can be conceived that the more massive P9 might also have a number of satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In this article, we discuss some important observable features if P9 has captured satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For large satellites with small orbital semi-major axis, the tidal heating effect due to P9 would be important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' It can be shown that these satellites would give an observable standard thermal radio spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' If P9 is a dark object, observing the satellites would be another kind of investigation to examine the P9 hypothesis in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In the followings, we assume that P9 is a dark object and we follow the benchmark model of P9 with mass M9 = 5M⊕, eccentricity e9 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2, orbital inclination i = 20◦, and semi-major axis a9 = 450 AU (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' We simply take the semi-major axis a9 = 450 AU as the average distance to the dark P9 from the Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Capturing probability There are many large TNOs moving in the scattered disk region (∼ 100 − 1000 AU), such as 2018 AG37, 2018 VG18 and 2020 BE102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' It is quite likely that some of the large TNOs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' with size D ∼ 100 km) could be captured by the dark P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In fact, many of the Kulper Belt dwarf planets have at least one satellite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For example, the satellite of the dwarf planet Eris has radius R ∼ 700 km and semi-major axis a ∼ 4 × 104 km (Brown & Butler 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In general, when a TNO has a close encounter to a planet, energy will be lost in the cap- turing process due to the inverse of the gravitational slingshot mechanism (Napier, Adams & Batygin 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The maximum capturing distance between the dark P9 and any TNOs can be char- acterized by the impact parameter b (Napier, Adams & Batygin 2021): b ∼ M9 M⊙ �GM⊙ a9 �3/2 v−3a9, (1) where v is the incoming relative velocity between the dark P9 and any TNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, b can be regarded as the closest distance between the dark P9 and the TNOs for the capturing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, the relative velocity between the dark P9 and the TNOs is given by v ∼ � GM⊙ a9 − � GM⊙ a9 ± b cos ∆i, (2) where ∆i is the orbital inclination difference between the dark P9 and the TNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' As b ≪ a9, the relative velocity is v ∼ � GM⊙ a9 (1 − cos ∆i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (3) – 4 – Putting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (3) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (1), we get b ∼ a9(1 − cos ∆i)−3 � M9 M⊙ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (4) The benchmark orbital inclination of the dark P9 is i = 20◦ (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Based on the catalog compiled by the International Astronomical Union 1, the orbital inclinations of the TNOs (with semi-major axis a > 100 AU) are quite close to i = 20◦, except three with i > 100◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The average difference between the orbital inclinations of P9 and the TNOs is about ∆i = 18◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Including the possible uncertainty of the benchmark orbital inclination of the dark P9 δi = 5◦ (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019), we take a conservative choice of ∆i = 25◦, which gives b ∼ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' On the other hand, we can also apply the radius of influence Rin discussed in Bate (1971) to characterize the value of the impact parameter (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' b ≈ Rin).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The radius of influence defines the region where the incoming TNO switches from a two-body problem with central mass M⊙ to a two-body problem with central mass M9 in the matched conics approximation (Napier, Adams & Batygin 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Based on this approximation, the impact parameter is given by (Bate 1971) b = Rin = a9 � M9 M⊙ �2/5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (5) Using our benchmark parameters, the dark P9 can capture any TNOs moving within the distance of b ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='3 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' To get a more conservative estimation, in the followings, we adopt the value of b = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='3 AU as the impact parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In view of this, the dark P9 can create a ‘capturing volume’ when it is orbiting about the sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' All of the TNOs inside this capturing volume would be likely captured by the dark P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The capturing volume is given by V = � 2πa9 � 1 − e2 9 2 � (πb2) = 2π2b2a9 � 1 − e2 9 2 ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 × 105 AU3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (6) Generally speaking, very large TNOs (with size ≥ 500 km) would be easier for us to identify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Based on the catalog compiled by the International Astronomical Union, there are four TNOs with size ≥ 500 km (assuming a standard asteroid albedo p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1) and orbital semi-major axis a = 100−1000 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The number of very large TNOs can provide a standard reference for estimating the amount of TNOs with different sizes inside the scattered disk region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1The catalog compiled by the International Astronomical Union can be found in https://minorplanetcenter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='net/iau/lists/TNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='html – 5 – Consider the region of the scattered disk for a = 100 − 1000 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Based on the TNO catalog, all of the reported TNOs with a ≤ 1000 AU are located within a scale disk thickness of 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 AU above and below the P9 orbital plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' We therefore consider the volume of the scattered disk Vd ∼ (2 × 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5)π(10002 − 1002) ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 × 108 AU3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Assuming the distribution of asteroid size is same as that in Kuiper Belt dN/dD ∝ D−q (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This size distribution in Kuiper Belt is well represented by a broken power law in D for large and small Kuiper Belt objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For cold Kuiper Belt objects, the slope q for large objects (with size D ≥ 140 km) is q = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 while q = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='3 for D < 140 km (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Since there are four TNOs with size ≥ 500 km, taking q = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2, the average number density of TNOs with size D ≥ 140 km inside Vd is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 × 10−5 AU−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Since the capturing volume is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 × 105 AU3, the average number of TNOs with size D ≥ 140 km captured is about 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Note that this number is close to the typical number of satellites found in Jovian planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In fact, the Jovian planets are somewhat close to each other so that the gravitational perturbation effect is significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This would reduce the capturing volume and the number of satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, there is almost no massive perturber for P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The closest massive object Sedna (semi-major axis a ∼ 500 AU) has a relatively small mass ∼ 10−3M⊕ only, which cannot affect the capturing volume significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, we expect that there is a considerable amount of captured TNOs to form a satellite system for P9, like the satellite systems in Jovian planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The tidal heating model Consider a fiducial radius of the satellite R = D/2 = 100 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For simplicity, let’s assume that the satellite is spherical in shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The tidal force on the satellite is large when the satellite is close to P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The Roche limit is ∼ 2 × 104 km if we assume the density of the satellite to be ρ = 1 g/cm3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For Uranus and Neptune, which have mass similar to the dark P9, the range of the orbital semi-major of the satellites is as ∼ 5 × 104 − 5 × 107 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In the followings, we will mainly consider the range of the orbital semi-major axis as = 105 − 106 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Note that captured objects generally have large semi-major axis and eccentricity initially (Goulinski & Ribak 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Napier, Adams & Batygin 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, orbital evolution through tidal effects would further decrease the values of semi-major axis and eccentricity (see the discussion below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The equilibrium temperature due to solar luminosity is approximately given by T ≈ 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='8 � 26 a9 K, (7) where we have neglected the albedo and the phase integral (Stansberry et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For – 6 – a9 = 450 AU, we get T = 13 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, if the satellite is very close to P9, the tidal heating effect would be very significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The tidal heating model has been discussed for more than 50 years (Goldreich & Soter 1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In general, the tidal heating rate can be calculated by (Segatz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Lainey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Renaud & Henning 2018) ˙E = 21C 2 (Rn)5e2 s G , (8) where n = � GM9/a3s is the mean orbital motion, and es is the eccentricity of the satellite orbit (Segatz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, the constant C is related to the Love number k2 and the quality factor Q which reflects the physical properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' elastic rigidity) of the satellite (Segatz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Lainey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hussmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, the value of C for the satellite is uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Theoretical prediction shows that the value of C should be lower than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='06 for high density satellite core (Kervazo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' We adopt the value revealed from the observational data of the Jupiter’s moon Io C ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='02 (Lainey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In equilibrium, the tidal heating rate would be equal to the radiation cooling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, we have T = � ˙E 4πσsǫνR2 �1/4 , (9) where σs is the Stefan-Boltzmann constant and ǫν is the gray-emissivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For simplicity, we assume ǫν = 1 here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2, we plot the equilibrium temperature as a function of as, for different values of R and es, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' We can see that the temperature can be quite high for some values of as, R and es.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Generally speaking, smaller value of as and larger values of R and es can give a higher equilibrium temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For the fiducial values of as = 105 km, R = 100 km and es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5, we get ˙E = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='4 × 1012 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The equilibrium temperature of the satellite is about 119 K, which can emit significant amount of radio radiation with frequency ν > 100 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Besides, we can estimate the time required for the satellite to heat up from 10 K to 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Assuming a typical specific heat capacity for the satellite cs = 1000 J kg−1 K−1, the time required is ∼ 104 yrs for the fiducial parameters used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In the followings, we estimate the thermal radio flux emitted by the satellite with the fiducial parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The thermal radio flux density is given by Sν = � 2hν3 c2(ehν/kT − 1)dΩ ≈ 2πhν3 c2(ehν/kT − 1) � R a9 �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (10) Therefore, we can get the expected thermal radio flux density as a function of ν for the fiducial parameters (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The radio flux density is ∼ 2 µJy for ν = 300 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The observable limit for the most sensitive sub-mm interferometer (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Atacama Large Millimeter Array – 7 – ALMA) is around 1 µJy at ν = 100 − 300 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hence, it is feasible to observe this small flux using current observational technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For lower frequencies, the expected radio flux density is Sν ≈ 10 nJy at ν = 20 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This can be observable by the future SKA radio interferometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Moreover, the thermal radio flux density Sν is proportional to the frequency ν2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This can be differentiable from the normal background radio flux, which is usually modelled by Sν ∝ ν−α with α > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In other words, by obtaining the radio spectrum emitted from the region of the dark P9, if we can detect a relatively strong thermal radio spectrum (Sν ∝ ν2), this would be a solid evidence to verify the P9 hypothesis because there is no other astrophysical mechanism which can increase the temperature of a distant object to more than 50 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For the conventional P9 model (not a dark object), the expected radio flux emitted by P9 should be ∼ mJy at 200 GHz (Naess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2021), which is 1000 times larger than that of a satellite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In any case, either if we can detect mJy signal from P9 or µJy signal from the satellite, the P9 hypothesis can be verified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Besides, if there is any potential signal received from P9 or the satellites, we can track the source for a couple of years to see whether the signal would follow a nearly Keplerian orbit over time or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This can further provide a smoking-gun evidence to verify the P9 hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Previous studies have constrained the possible range of location for P9 (Batygin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Fienga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Socas 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A recent study has further constrained the exact location of P9 to R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2 ± 4)◦ and DEC (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='8)◦ (Socas 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Such a small constrained region can make the observation much easier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The telescopes or interferometers used can focus on the target region for a very long exposure time to gain enough sensitivity to detect the potential thermal signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Note that the tidal heating rate gained by the satellite originates from the loss rate of the gravitational potential energy of the P9-satellite system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The eccentricity would gradually decrease so that the tidal heating rate would also decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The eccentricity fractional change rate is given by |˙es| es = �e2 s − 1 2e2s � ˙E E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' (11) The time scale for the eccentricity shrinking is τ ∼ |es/˙es|, which is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='6 Myrs for the fiducial parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This timescale is short compared to the age of the solar system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' In fact, there is a compromise between having the orbital parameters of the satellites such that the radio emission is detectable (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' with small as) and sufficiently long-lived to make the higher detection probability (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' with large as).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, the range of as we considered (as = 105 −106 km) is almost the optimal for examination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Nevertheless, the relatively short eccentricity shrinking timescale would not be a big problem if the satellite capture event is – 8 – a recent event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Also, as we have shown that the satellite capture is not a rare event, there would be more than one satellite with size > 140 km at as ∼ 105 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, we expect that such a thermal radio signal of the satellite may still be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Discussion In this article, we have demonstrated a theoretical framework to predict the possible observable signal from the P9-satellite system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' If the dark P9 has a satellite system, the only current feasible observation is to detect the possible signals from the satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' We have shown that if a satellite with a typical size ∼ 100 km with average orbital radius as ∼ 105 km from the dark P9, the temperature can be as large as ∼ 100 K due to tidal heating effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For such a high temperature, the satellite can emit strong enough thermal radio flux (∼ 1 µJy at 100-300 GHz) that can be observed by ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Moreover, the specific thermal radio spectrum Sν ∝ ν2 could be easily differentiable from the background radio flux so that it can provide a smoking-gun evidence for the P9 hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' The only possible reason for the existence of ∼ 100 K object at ∼ 450 AU from the sun is that it is a satellite of a host planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' It is because a host dwarf planet or a minor planet does not have enough mass to heat up the satellite to ∼ 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' As we have shown above, there are a lot of TNOs with size > 140 km in the scattered disk region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, the chance for these large TNOs (with R ∼ 100 km) captured by P9 is not low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Besides, based on the example of Uranus (≈ 14M⊕), at least 13 satellites are located within 105 km, which suggests that our fiducial value of as = 105 km is a reasonable choice of consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' For the eccentricity, simulations show that most of the captured objects would be orbiting with a very high eccentricity ≈ 1 (Goulinski & Ribak 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, our fiducial value es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 is a conservative choice of estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Since no optical and radio signals have been detected so far for P9, the suggestion of P9 being a PBH has become a hot topic recently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' There are some suggestions to send detectors to visit the alleged PBH P9 (Witten 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hibberd, Lingam & Hein 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' It would be very exciting because this may be our only chance to visit a black hole within our approachable distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Nevertheless, we need to wait for at least 10 years for the detectors to arrive the PBH P9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Some other studies have proposed to detect P9 by gravitational lensing (Philippov & Chobanu 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Schneider 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Dom`enech & Pi 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' However, the mass of P9 is very small so that it requires a very sensitive measurement for the short-live lensing event, which may not be very easy to get any good confirmation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A recent study has proposed a narrow possible locations of P9 (Socas 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' If P9 is a dark object and it has a satellite system, our proposal can directly observe the potential thermal signals emitted by – 9 – the satellites now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Therefore, this would be a timely and effective method to confirm the P9 hypothesis and verify whether P9 is a dark object or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Acknowledgements The work described in this paper was partially supported by a grant from the Re- search Grants Council of the Hong Kong Special Administrative Region, China (Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' EdUHK 18300922).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' REFERENCES Arbey A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Auffinger J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='02944.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Bate R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Mueller D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & White J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 1971, Fundamentals of Astrodynamics (New York: Dover).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Batygin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016a, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 151, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Batygin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016b, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 833, L3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Batygin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Adams F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Becker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2019, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 805, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Becker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2018, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 156, 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Butler B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2018, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 156, 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2006, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 639, L43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Carr B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Kohri K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Sendouda Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Yokoyama J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2021, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 84, 116902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Dom`enech G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Pi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2022, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Chi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Mec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 65, 230411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Fraser W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Morbidelli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Parker A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Batygin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2014, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 782, 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Fienga A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Laskar J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Manche H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Gastineau M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 587, L8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Goldreich P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Soter S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 1966, Icarus 5, 375.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Gomes R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Deienno R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Morbidelli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 153, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Goulinski N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Ribak E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2018, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 473, 1589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' – 10 – 1e+005 1e+006 Semi-major axis (km) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1 1 10 100 1000 T (K) es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1 es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='9 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='— The colored lines indicate the predicted temperature T of the satellite for different values of orbital eccentricity (es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1, es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5 and es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, we have neglected the solar heating effect and we have assumed R = 100 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' – 11 – 1e+005 1e+006 Semi-major axis (km) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1 1 10 100 1000 T (K) R = 50 km R = 100 km R = 200 km Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='— The colored lines indicate the predicted temperature T of the satellite for different values of satellite radii (R = 50 km, R = 100 km and R = 200 km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, we have neglected the solar heating effect and we have assumed es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' – 12 – 100 1000 ν (GHz) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='1 1 10 100 S(ν) (µJy) R = 50 km, T = 70 K R = 100 km, T = 119 K R = 200 km, T = 199 K Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='— The colored lines indicate the predicted thermal radio flux density S(ν) against ν for different values of satellite radii (R = 50 km, R = 100 km and R = 200 km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Here, we have assumed as = 105 km and es = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' – 13 – Grundy W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2019, Icarus 334, 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hibberd A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Lingam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Hein A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='10207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Hussmann H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Choblet G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Lainey V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Matson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Sotin C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Tobie G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Van Hoolst T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2010, Sp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 153, 317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Kenyon S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Bromley B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 825, 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Kervazo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Tobie G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Choblet G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Dumoulin C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Bˇehounkov´a M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2022, Icarus 373, 114737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Lainey V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Arlot J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Karatekin ¨O & Van Hoolst T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2009, Nature 459, 957.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Li G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Adams F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 823, L3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Linder E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Mordasini C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 589, A134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Meisner A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Bromley B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Nugent P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Schlegel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Kenyon S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Schlafly E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Dawson K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2017, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 153, 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Meisner A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Bromley B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Kenyon S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Anderson T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2018, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 155, 166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Naess S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2021, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 923, 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Napier K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Adams F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Batygin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2021, Planetary Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 2, 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Philippov J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Chobanu M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Aust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 33, 033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Renaud J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Henning W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2018, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 857, 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Segatz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Spohn T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Ross M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Schubert G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 1988, Icarus 75, 187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Schneider J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2017, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Pac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 129, 104401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Scholtz J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Unwin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2020, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 125, 051103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Sheppard S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Trujillo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2016, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 152, 221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Sheppard S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Trujillo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Tholen D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Kaib N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2019, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' 157, 139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Socas-Navarro H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='07675.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Stansberry J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Grundy W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Brown M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Cruikshank D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Spencer J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Trilling D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Margot J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2008, The solar system beyond Neptune, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Barucci, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Boehnhardt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Cruikshank & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Morbidelli (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' ), Tucson: University of Arizona Press, 161-179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' – 14 – Trujillo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Sheppard S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', 2014, Nature 507, 471.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Wang P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Tang Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Zu L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', Chen Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' & Feng L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='04147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' Witten E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=', arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='14192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content=' This preprint was prepared with the AAS LATEX macros v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/J9FRT4oBgHgl3EQfDDeX/content/2301.13471v1.pdf'} diff --git a/JNAyT4oBgHgl3EQffviC/content/tmp_files/2301.00346v1.pdf.txt b/JNAyT4oBgHgl3EQffviC/content/tmp_files/2301.00346v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..564cf89a90739ebb6d1291811f35f2adeb9669b4 --- /dev/null +++ b/JNAyT4oBgHgl3EQffviC/content/tmp_files/2301.00346v1.pdf.txt @@ -0,0 +1,3379 @@ +An Adaptive Kernel Approach to Federated Learning +of Heterogeneous Causal Effects +Thanh Vinh Vo1 +Arnab Bhattacharyya1 +Young Lee2 +Tze-Yun Leong1 +1School of Computing, National University of Singapore +2Roche AG and Harvard University +{votv,arnabb,leongty}@nus.edu.sg +Abstract +We propose a new causal inference framework to learn causal effects from multiple, +decentralized data sources in a federated setting. We introduce an adaptive transfer +algorithm that learns the similarities among the data sources by utilizing Random +Fourier Features to disentangle the loss function into multiple components, each +of which is associated with a data source. The data sources may have different +distributions; the causal effects are independently and systematically incorporated. +The proposed method estimates the similarities among the sources through transfer +coefficients, and hence requiring no prior information about the similarity measures. +The heterogeneous causal effects can be estimated with no sharing of the raw +training data among the sources, thus minimizing the risk of privacy leak. We also +provide minimax lower bounds to assess the quality of the parameters learned from +the disparate sources. The proposed method is empirically shown to outperform +the baselines on decentralized data sources with dissimilar distributions. +1 +Introduction +Many important questions posed in the natural and social sciences are causal in nature: What are +the long-term effects of mild Covid-19 infection on lung and brain functions? How is mortality +rate influenced by the daily air pollution? How would a welfare policy affect employment rate of a +minority group? Causal inference has been applied in a wide range of domains, including economics +(Finkelstein and Hendren 2020), medicine (Henderson et al. 2016; Powers et al. 2018), and social +welfare (Gutman et al. 2017). The large amount of experimental and/or observation data needed +to accurately estimate the causal effects often resides across different sites. In most cases, the data +sources cannot be combined to support centralized processing due to some inherent organizational or +policy constraints. For example, in many countries, medical or health records of cancer patients are +kept strictly confidential at local hospitals; direct exchange or sharing of the records among hospitals, +especially for research purposes, are not allowed (Gostin et al. 2009). The main research question is: +How to securely access these diverse data sources to build an effective global causal effect estimator, +while balancing the risk of breaching data privacy and confidentiality? +Current causal inference approaches (e.g., Shalit et al. 2017; Yao et al. 2018) require the shared +data to be put in one place for processing. Current federated learning algorithms (e.g., Sattler et al. +2020; Wang et al. 2020) allow collaborative learning of joint models based on non-independent +and identically distributed (non iid) data; they cannot, however, directly support causal inference as +the different data sources might have disimilar distributions that would lead to biased causal effect +estimation. For example, the demographic profile and average age for cancer patients from two +different hospitals may be drastically different. If the two data sets are combined to support causal +inference, one distribution may dominate over the other, leading to biased causal effect estimation. +36th Conference on Neural Information Processing Systems (NeurIPS 2022). +arXiv:2301.00346v1 [cs.LG] 1 Jan 2023 + +We introduce a new approach to federated causal inference from multiple, decentralized, and disimi- +larly distributed data sources. Our contributions are summarized as follows: +• We propose a new federated causal inference algorithm, called CausalRFF 1, based on the structural +causal model (SCM) (Pearl 2009a), leveraging the Random Fourier Features (Rahimi and Recht +2007) for federated estimation of causal effects. The Random Fourier Features allow the objective +function to be divided into multiple components to support federated training of the model. +• We perform federated causal inference with CausalRFF from data sources with different distribu- +tions through the adaptive kernel functions; the inference is carried out without sharing raw data +among the sources, hence minimizing the risk of privacy leak. +• We provide the minimax lower bounds to explicate the limits of estimation and optimization +procedures in our federated causal inference framework. +Our work is an important step toward privacy-preserving causal inference. We explore the possibility +of combining CausalRFF with multiparty differential privacy at the end of the paper. +2 +Related Work +Little work has been done on combining causal inference with federated learning in a privacy +preserving manner. +On causal inference: The authors Hill (2011); Alaa and van der Schaar (2017, 2018); Shalit et al. +(2017); Yoon et al. (2018); Yao et al. (2018); Künzel et al. (2019); Nie and Wager (2020) proposed +learning causal effects directly from local data sources; these methods adopt the standard ignorability +assumption (Rosenbaum and Rubin 1983). Louizos et al. (2017); Madras et al. (2019) adapted the +structural causal model (SCM) of Pearl (1995) to estimate the causal effects with the existence of +latent confounding variables. +Our work is closely related to and extends the notion of transportability, where Pearl and Bareinboim +(2011); Bareinboim and Pearl (2016); Lee et al. (2020) and related work formulated and provided +theoretical analysis of intervention tools on one population to compute causal effects on another +population. Lee et al. (2020) generalized transportability to support identification of causal effects in +the target domain from the observational and interventional distributions on subsets of observable +variables, forming a foundation for drawing conclusions for observational and experimental data +(Tsamardinos et al. 2012; Bareinboim and Pearl 2016). Causal inference from multiple, decentralized, +dissimilarly distributed sources that cannot be combined or processed in a central site is not addressed. +Recently, Aglietti et al. (2020), conducted randomized experiments on the source to collect data and +then estimated a joint model of the interventional data from source population and the observational +data from target population. Our work is different in that we do not work with randomized data; +we estimate causal effects through transfers using only observational data. This corresponds to an +important setting in real-life, where only retrospective observational data are available, e.g., Covid-19 +related case and intervention records, bank and financial transaction records. +On federated learning: Federated learning enables collaboratively learning a shared prediction +model while keeping all the training data decentralized at source (McMahan et al. 2017). Some +federated learning approaches combine federated stochastic gradient descent (Shokri and Shmatikov +2015) and federated averaging (McMahan et al. 2017) to address regression problems Álvarez et al. +(2019); Zhe et al. (2019); de Wolff et al. (2020); Joukov and Kuli´c (2020) and Hard et al. (2018); +Zhao et al. (2018); Sattler et al. (2019); Mohri et al. (2019). Recent federated learning algorithms +allow collaborative learning of joint deep neural network models based on non-iid data (Sattler et al. +2020; Wang et al. 2020). All these algorithms, however, do not directly support causal inference +as the different data sources might have dissimilar distributions that would lead to biased causal +effect estimation. Little work has been focused on federated estimation of causal effects. Vo et al. +(2022) proposed a Bayesian approach that estimates posterior distributions of causal effects based +on Gaussian processes, which does not allow dissimilar distributions of the sources. Xiong et al. +(2021) estimated average treatment effect (ATE) and average treatment effect on the treated (ATT) +and assumed that the confounders are observed. Our work, on the other hand, estimate conditional +average treatment effect (CATE) (which is also known as individual treatment effect, ITE) and +average treatment effect (ATE) under the existence of latent confounders. We utilize Random Fourier +1Source code: https://github.com/vothanhvinh/CausalRFF +2 + +Features to build an integrative framework of causal inference in a federated setting that allows for +dissimilar data distributions. +3 +The Proposed Model +In this section, we first detail the problem formalization. We then present the causal effects of interest +and the scheme to estimate them. Lastly, we describe the assumptions and the structural equations. +3.1 +Problem Description +Problem setting & notations. +Suppose we have m sources of data, each denoted by Ds = +{(ws +i, ys +i, xs +i)}ns +i=1, where s ∈ S := {s1, s2, . . . , sm}, and the quantities ws +i, ys +i and xs +i are the treatment +assignments, observed outcome associated with the treatment, and covariates of individual i in source +s, respectively. These data sources Ds are located in different locations and their distributions might +be completely different. All the sources share the same causal graph as shown in Figure 1, but the data +distributions may be different, e.g., ps1(x, w, y) ̸= ps2(x, w, y), where ps1(·) and ps2(·) denote the +two distributions on two sources s1 and s2, respectively. Similarly, the marginal and the conditional +distributions with respect to these variables can also be different (or similar). The objective is to +develop a global causal inference model that satisfies both of the following two conditions: (i) the +causal inference model can be trained in a private setting where the data of each source are not shared +to an outsider, and (ii) the causal inference model can incorporate data from multiple sources to +improve causal effects estimation in each specific source. +Causal effects of interest. Given a causal model trained under the aforementioned setting, we are +interested in estimating the conditional average treatment effect (CATE)2 and average treatment +effect (ATE). Let Y , W, X be random variables denoting the outcome, treatment, and proxy variable, +respectively. Then, the CATE and ATE are defined as follows (Louizos et al. 2017; Madras et al. +2019) +τ(x) := E +� +Y |do(W=1), X=x +� +− E +� +Y |do(W=0), X=x +� +, +τ := E[τ(X)], +(1) +where do(W=w) represents that a treatment w ∈ {0, 1} is given to the individual. This definition is +followed from Louizos et al. (2017); Madras et al. (2019). Given a set of n new individuals whose +covariates/observed proxy variables are {xi}n +i=1, the CATE and ATE in this sub-population are +obtained by τ(xi) and τ = �n +i=1 τ(xi)/n. +Z +Y +W +X +Figure 1: The causal graph with latent +confounder Z, treatment W, outcome +Y , covariate/proxy variable X. +Source (1) +Source (2) +Source (3) +Server +Figure 2: An example of our proposed model with three +sources. The objective function J ≃ J(1) +J(2) +J(3) is +decomposed to 3 components, each associated with a source. +The central task to estimate CATE and ATE is to find E[Y | do(W = w), X = x]. Since the data +distribution of each source might be different from (or similar to) each other, we use the notation +E[Y |do(W = ws, X = xs] to denote the expectation of the outcome Y under an intervention on W +of an individual in source s. With the existence of the latent confounder Z, we can further expand +this quantity using do-calculus (Pearl 1995). In particular, from the backdoor adjustment formula, we +have +E +� +Y |do(W = ws), X = xs� += +� +E +� +Y |W = ws, Z = zs� +ps(zs|xs)dzs. +(2) +Eq. (2) shows that the causal effect is identifiable if we can find the conditional distributions +ps(ys|ws, zs) and ps(zs|xs) for each source s. The second distribution can be further expanded +by ps(zs|xs) = � +ws +� +ps(z|xs, ys +i, ws)ps(ys|xs, ws)ps(ws|xs)dys. Following the forward sampling +strategy, the remaining is to find the following distributions +ps(ws|xs), +ps(ys|xs, ws), +ps(zs|xs, ys, ws), +ps(ys|ws, zs), +(3) +2Also called individual treatment effect (ITE) +3 + +and then systematically draw samples from these estimated distributions to obtain the empirical +expectation of Y given do(W = ws) and X = xs. +Identification. The CATE and ATE are identifiable if we are able to learn the distributions in Eq. (3), +which involve latent confounder Z. Louizos et al. (2017) showed that this is possible if Z has a +relationship to the observed variables X, and there are many cases that it is identifiable such as: +Z is categorical and X is a Gaussian mixture model (Anandkumar et al. 2014), X includes three +independent views of Z (Goodman 1974; Allman et al. 2009; Anandkumar et al. 2012), Z is a +multivariate binary and X are noisy functions of Z (Jernite et al. 2013; Arora et al. 2017), to name a +few. Following the works by Louizos et al. (2017); Madras et al. (2019), we use variational inference +in the spirit of the variational auto-encoder (VAE) to recover the latent confounders, since it can learn +a rich class of latent-variable models, and thus recovering the causal effects. Identification of our +work follows closely from the literature, however our main contribution is in the federated setting of +the model. Please refer to Appendix for the proof of identifiability. +3.2 +The Causal Graph and Assumptions +Since our method adopts the SCM approach with the causal graph in Figure 1, there are some implicit +assumptions that follow from the axioms and properties of SCM: (A1) Consistency: W = w =⇒ +Y (w) = Y , this follows from the axioms of SCM. (A2) No interference: the treatment on one subject +does not affect the outcomes of another one. This is because the outcome has only a single treatment +node as its parent. (A3) Positivity: every subject has some positive probability to be assigned to every +treatment. These assumptions are standard in any causal inference algorithm. One can find further +discussion in Pearl (2009a,b); Morgan and Winship (2015). For our proposed federated setting, we +make two additional assumptions as follows: +(A4) The individuals in all sources have the same set of common covariates. +(A5) Any individual does not exist in more than one source. +Assumption (A4) has been implicitly shown in our setup since all the sources would share the same +causal graph. This is a reasonable assumption as we intend to build a unified model on all of the data +sources, e.g., decentralized data in Choudhury et al. (2019); Vaid et al. (2020); Flores et al. (2020) +satisfy this assumption for federated learning. Assumption (A5) is to ensure that no individuals would +dominate the other individuals when training the model. For example, if an individual appears in +all of the sources, the trained model would be biased by data of this individual (there is imbalance +caused by the use of more data from this particular individual than the others). Hence, this condition +would ensure that such bias does not exist. In practice, Assumption (A5) sometimes does not hold. +To address such a problem, we perform a pre-training step to exclude such duplicated individuals. +This step would use a one-way hash function to perform a secured matching procedure that identifies +duplicated individuals. Details of the pre-training step are presented in Appendix. +3.3 +The Structural Equations +This section presents how the causal relations are modeled. Since Z is the root node in the causal +graph, we model it as a multivariate normal distribution: Z ∼ N(µ, σ2 +zIdz) for the all sources. We +now detail the structural equations of Y , W and X. Let V be a univariate variable that represents a +node or a dimension of a node in the causal graph (Figure 1), i.e., V can be Y , W or a dimension of +X. Let pa(V ) be set of V ’s parent variables in the causal graph, i.e, the nodes with directed edges to +V . We model the structural equation of V in two cases as follows: +if V is continuous: +V = fv(pa(V )) + ϵv, +if V is binary: +V = 1[ϕ(fv(pa(V ))) > ϵv], (4) +where ϵv ∼ N(0, σ2 +v) for the former case and ϵv ∼ U[0, 1] for the latter case, ϕ(·) is the logistic +function and 1(·) is the indicator function. The latter case implies that V given pa(V ) follows +Bernoulli distribution with p(V = 1|pa(V )) = ϕ(fv(pa(V ))). Furthermore, if W ∈ pa(V ), then we +further model +fv(pa(V )) = (1 − W)fv0(pa(V ) \ {W}) + Wfv1(pa(V ) \ {W}). +(5) +Example. If Y ∈ R, W ∈ {0, 1} and Xk ∈ R (Xk is the k–th dimension of X), then the structural +equations are as follows: +Y = (1 − W)fy0(Z) + Wfy1(Z) + ϵy, +W = 1[ϕ(fw(Z)) > ϵw], +Xk = fxk(Z) + ϵXk. +In the subsequent sections, we present how to learn the functions fv (v ∈ {y0, y1, w, x}) in a +federated setting and then use them to estimate the causal effects of interest. +4 + +4 +CausalRFF: An Adaptive Federated Inference Algorithm +This section presents a new federated algorithm to learn the distributions in Eq. (3). The central task +is to decompose the objective function into multiple components, each associated with a source. +4.1 +Learning Distributions Involving Latent Confounder +To estimate causal effects, we need to estimate the four quantities detailed in Eq. (3). This section +presents how to learn ps(zs|xs, ys, ws) and ps(ys|ws, zs). Since the marginal likelihood has no +analytical form, we learn the above distributions using variational inference which maximizes the +evidence lower bound (ELBO) +L = +� +s∈S +ns +� +i=1 +� +Eq +� +log ps(ys +i|ws +i, zs +i) + log ps(ws +i|zs +i) + log ps(xs +i|zs +i) +� +− KL[q(zs +i)∥p(zs +i)] +� +, +(6) +where q(zs) = N(zs; fq(ys, ws, xs), σ2 +qI) is the variational posterior distribution. The function fq(·) +is modeled as follows: fq(ys, ws, xs) = (1 − ws)fq0(ys, xs) + wsfq1(ys, xs), where fq0 and fq1 +are two functions to be learned. The density functions ps(ys|ws, zs), ps(ws|zs) and ps(xs|zs) are +obtained from the structural equations as described in Section 3.3. Please refer to Appendix for +details on derivation of the ELBO. +Adaptive modeling. Since the observed data from each source might come from different (or similar) +distributions, we would model them separately and adaptively learn their similarities. In particular, we +propose a kernel-based approach to learn these distributions. To proceed, we first obtain the empirical +loss function �L from negative of the ELBO L by generating M samples of each latent confounder +Z using the reparameterization trick (Kingma and Welling 2013): zs +i[l] = fq(ys +i, ws +i, xs +i) + σqϵs +i[l], +where ϵs +i[l] is drawn from the standard normal distribution. We obtain a complete dataset +�Ds = +M +� +l=1 +� +(ws +i, ys +i, xs +i, zs +i[l]) +�ns +i=1, +∀s ∈ S. +(7) +Using this complete dataset, we minimize the following objective function +J = �L + +� +c∈A +R(fc) +(8) +with respect to fc, where A = {y0, y1, w, x, q0, q1}, and R(·) denotes a regularizer. The minimizer +of J would result in the following form of fc +fc(us) = +� +v∈S +nv×M +� +j=1 +κ(us, uv +j)αv +j, +(9) +where uv +j is obtained from the j–th tuple of the dataset ˜Dv. Details are presented in Appendix. Since +data from the sources might come from a completely different (or similar) distribution, we would use +an adaptive kernel to measure their similarity. In particular, let k(us, uv) be typical kernel function +such as squared exponential kernel, rational quadratic kernel, or Matérn kernel. The kernel used in +Eq. (9) is as follows: κ(us, uv) = λs,vk(us, uv), if s ̸= v; otherwise, κ(us, uv) = k(us, uv), where +λs,v ∈ [0, 1] is the adaptive factor and it is learned from the observed data. +Remark. Eq. (9) indicates that computing fc(us) requires collecting all data points from all sources, +and so the objective function in Eq. (8) cannot be optimized in a federated setting. Next, we present a +method known as Random Fourier Features to address the problem. +Random Fourier Features. We show how to adapt Random Fourier Features (Rahimi and Recht +2007) into our model. Let k(u, u′) be any translation-invariant kernel (e.g., squared exponential +kernel, rational quadratic kernel, or Matérn kernel). Then, by Bochner’s theorem (Wendland 2004, +Theorem 6.6), it can be written in the following form: +k(u, u′) = +� +eiω⊤(u−u′)s(ω)dω = +� +cos +� +ω⊤(u − u′) +� +s(ω)dω, +(10) +where s(ω) is a spectral density function associated with the kernel (please refer to Appendix for +spectral density of some popular kernels). The last equality follows from the fact that the kernel +function is real-valued and symmetric. This type of kernel can be approximated by +5 + +k(u, u′) ≃ B−1 +B +� +b=1 +cos(ω⊤ +b (u − u′)) = φ(u)⊤φ(u′), +{ωb}B +b=1 +i.i.d. +∼ s(ω), +(11) +where φ(u) = B− 1 +2 [cos(ω⊤ +1 u),..., cos(ω⊤ +Bu), sin(ω⊤ +1 u),..., sin(ω⊤ +Bu)]⊤. The last equality follows +from the trigonometric identity: cos(u − v) = cos u cos v + sin u sin v. Substituting the above +random Fourier Features into Eq. (9), we obtain +fc(us) ≃ +� +θs +c + +� +v∈S\{s} +λs,vθv +c +�⊤ +φ(us), +(12) +where θs +c = �ns +i=1 φ(us)αs +i and λs,v (s, v ∈ S). While optimizing the objective function J, instead of +learning αs +i, we can directly consider θs as parameter to be optimized. This has been used in several +works such as Rahimi and Recht (2007); Chaudhuri et al. (2011); Rajkumar and Agarwal (2012). +This approximation allows us to rewrite the objective function J as a summation of local objective +functions in each source: +J ≃ +� +s∈S +J(s), +where J(s) = �L(s) + m−1 � +v∈S +ζ∥θv∥2 +2, +(13) +where ζ ∈ R+ is a regularizer factor. Each component J(s) is associated with the source s and it +can be computed with the local data in this source. Hence, it enables federated optimization for the +objective function J. Figure 2 illustrates our proposed federated causal learning algorithm with three +sources, where θ denotes the set of all parameters to be learned including θs and λs,v from all the +sources. The federated learning algorithm can be summarized as follows: First, each source computes +the local gradient, ∇θJ(s), using its own data and sends to the server. The server, then, collects these +gradients from all sources and subsequently updates the model. Next, the server broadcasts the new +model to all the sources. +Minimax lower bound. We now compute the minimax lower bound of the proposed model, which +gives the rate at which our estimator can converge to the population quantity of interest as the sample +size increases. We first state the following result that concerns the last two terms in Eq. (3): +Lemma 1 (With presence of latent variables). Let θ = {θs +c : c ∈ {y0, y1, x, w}, s ∈ S} and ˆθ be its +estimate. Let ys +i ∈ R and xs +i ∈ Rdx. Let S\s = S \ {s}. Then, +inf +ˆθ +sup +P ∈P +EP +� +∥ˆθ − θ(P)∥2 +� +≥ +� +m(dx + 3) log(2√m) +64 +√ +B � +s∈S ns +� +1 + � +v∈S\sλs,v�2 . +(14) +The LHS of Eq. (14) can be seen as the worst case of the best estimator, whereas the RHS depicts +the behavior of the convergence. The bounds do not only depend on the number of samples (ns, +training size) of each source but also the adaptive factors λs,v. When the adaptive factors are small, +the lower bounds are large since data from a source s are only used to learn its own parameter θs. +When the adaptive factors are large, the lower bounds are smaller, which suggests that data from a +source would help infer parameters associated with the other sources. This bound gives a guarantee +on how data from all the sources impact the learned parameters that modulate the two distributions +ps(zs|xs, ys, ws) and ps(ys|ws, zs). The proof of Lemma 1 can be found in Appendix. +4.2 +Learning Auxiliary Distributions +The previous section has shown how to learn ps(zs|xs, ys, ws) and ps(ys|ws, zs). To compute treat- +ment effects, we need to learn two more conditional distributions, namely ps(ws|xs) and ps(ys|xs, ws). +Since all the variables in these two distributions are observed, we estimate them using maximum +likelihood estimation. In the following, we present a federated setting to learn ps(ws|xs). Similar +to the previous section, the objective function here can also be decomposed into m components +as follows: Jw ≃ � +s∈S J(s) +w , where J(s) +w += �ns +i=1 ℓ(ws +i, ϕ(g(xs +i))) + m−1 � +v∈S ζw∥ψv∥2 +2 and +g(xs +i) = � +v∈S φ(xs +i)⊤(ψs + γs,vψv), γs,v ∈ [0, 1] is the adaptive factor, ψs is the parameter associ- +ated with source s, and ℓ(·) denotes the cross-entropy loss function since ws +i is a binary value. The +first component of J(s) +w is obtained from the negative log-likelihood. Learning of ps(ys|xs, ws) is +6 + +similar. For convenience, in the subsequent analyses, we denote the parameters and adaptive factors +of this distribution as βs and ηs,v, where s, v ∈ S and s ̸= v. The next lemma shows the minimax +lower bound for the first two sets of parameters ψ and β in Eq. (3), but this time without involving +the latent variables: +Lemma 2 (Without the presence of latent variables). Let ψ = {ψs}m +s=1, β = {βs}m +s=1 and ˆψ, ˆβ be +their estimates, respectively. Let ys +i ∈ R. Then, +(i) inf +ˆψ +sup +P ∈P +EP +� +∥ ˆψ − ψ(P)∥2 +� +≥ +m log(2√m) +256 � +s∈S ns +� +1 + � +v∈S\s γs,v�, +(15) +(ii) inf +ˆβ +sup +P ∈P +EP +� +∥ˆβ − β(P)∥2 +� +≥ σ +2 +9 +2 +� +m log(2√m) +B � +s∈S ns +� +1 + � +v∈S\s ηs,v�2 +�1/2 +. +(16) +The proof of Lemma 2 can be found in Appendix. The bounds presented in Lemma 1 and 2 give +helpful information about the number of samples to be observed and the cooperation of multiple +sources of data through the transfer factors. Since we used variational inference and maximum +likelihood to learn the parameters in our model, these methods give consistent estimation as shown in +Kiefer and Wolfowitz (1956); Van der Vaart (2000); Wang and Blei (2019); Yang et al. (2020). +4.3 +Computing Causal Effects +The key to estimate causal effects in our model is to compute the outcome in Eq. (2). We pro- +ceed by drawing samples from the distributions in Eq. (3). Generating samples from the con- +ditional distributions ps(ws|xs), ps(ys|xs, ws), and ps(ys|ws, zs) is straightforward since they are +readily available as shown in either Section 4.1 or 4.2. There are two options to draw samples +from the posterior distribution of confounder ps(zs|xs, ys, ws). The first one is to draw from its +approximation, q(zs), since maximizing the ELBO in Section 4.1 is equivalent to minimizing +KL(q(zs)∥ps(zs|xs, ys, ws)). As a second option, we note that the exact posterior of confounder can +be rewritten as ps(zs|xs, ys, ws) ∝ ps(ys|zs, ws)ps(ws|zs)ps(xs|zs)p(zs), whose components on the +right hand side are also available in Section 4.1. Thus, we can draw from this distribution using the +Metropolis-Hastings (MH) algorithm. Since Z is a multidimensional random variable, the traditional +MH algorithm would require a long chain to converge. We overcome this problem by using the +MH with independent sampler (Liu 1996) where the proposal distribution is the variational posterior +distribution q(zs) learned in Section 4.1. The second approach would give more accurate samples +since we select the samples based on exact acceptance probability of the posterior ps(zs|xs, ys, ws). +This would help estimate the CATE given xs +i. The local ATE is the average of CATE of individuals +in a source s. These quantities can be estimated in a local source machine. To compute a global ATE, +the server would collect all the local ATE in each source and then compute their weighted average. +Further details are in Appendix. +5 +Experiments +The baselines. In this section, we first carry out the experiments to examine the performance of +CausalRFF against standard baselines such as BART (Hill 2011), TARNet (Shalit et al. 2017), CFR- +wass (CFRNet with Wasserstein distance) (Shalit et al. 2017), CFR-mmd (CFRNet with maximum +mean discrepancy distance) (Shalit et al. 2017), CEVAE (Louizos et al. 2017), OrthoRF (Oprescu et al. +2019), X-learner (Künzel et al. 2019), R-learner (Nie and Wager 2020), and FedCI (Vo et al. 2022). +In contrast to CausalRFF, these methods (except FedCI) do not consider causal inference within a +federated setting. We compare our method to these baselines trained in two ways: (a) training a +global model with the combined data from all the sources, (b) using bootstrap aggregating of Breiman +(1996) where m models are trained separately on each source data and then averaging the predicted +treatment effects based on each trained model. Note that case (a) violates federated data setting and +is only used for comparison purposes. In general, we expect that the performance of CausalRFF to +be close to that of the performance of the baselines in case (a) when the data distribution of all the +sources are the same. In addition, we also show that the performance of CausalRFF is better than that +of the baselines in case (a) when the data distribution of all the source are different. +Implementation of the baselines. The implementation of CEVAE is from Louizos et al. (2017). +Implementation of TARNet, CFR-wass, and CFR-mmd are from Shalit et al. (2017). For these +7 + +1 +2 +3 +4 +5 +Number of sources, m +1.0 +1.2 +1.4 +1.6 +1.8 +√ϵPEHE +The error of CATE +1 +2 +3 +4 +5 +Number of sources, m +0.0 +0.3 +0.6 +0.9 +1.2 +ϵATE +The error of ATE +CausalRFF +Combined data +Figure 3: Experimental results on DATAsame. +1 +2 +3 +4 +5 +Number of sources, m +0.0 +0.7 +1.4 +2.1 +2.8 +3.5 +4.2 +√ϵPEHE +Error of CATE +1 +2 +3 +4 +5 +Number of sources, m +0.0 +0.7 +1.4 +2.1 +2.8 +3.5 +4.2 +ϵATE +Error of ATE +CausalRFF +Combined data (stack) +Combined data (1-hot) +Figure 4: Experimental results on DATAdiff. +Table 1: +Out-of-sample errors on DATAsame +where top-3 performances are highlighted in bold +(lower is better). The dashes (-) in ‘ag’ (boot- +strap aggregating) indicate that the numbers are +the same as that of ‘cb’ (combined data). +Method +The error of CATE, √ϵPEHE +The error of ATE, ϵATE +1 source 3 sources 5 sources 1 source 3 sources 5 sources +BARTag +- +3.8±.10 3.8±.09 +- +2.3±.15 2.3±.14 +X-Learnerag +- +3.2±.07 3.1±.06 +- +0.6±.11 0.5±.13 +R-Learnerag +- +3.5±.17 3.9±.46 +- +1.5±.35 2.0±.70 +OthoRFag +- +5.4±.21 4.5±.12 +- +0.5±.10 0.7±.16 +TARNetag +- +3.9±.04 3.4±.03 +- +2.2±.07 2.0±.02 +CFR-wassag +- +3.0±.05 3.6±.02 +- +2.1±.03 1.8±.02 +CFR-mmdag +- +4.0±.03 3.9±.02 +- +2.3±.03 2.0±.01 +CEVAEag +- +2.9±.04 2.5±.04 +- +0.7±.08 0.5±.10 +BARTcb +3.7±.12 3.2±.07 3.1±.03 2.1±.20 1.0±.18 0.6±.13 +X-Learnercb 3.3±.06 3.4±.06 3.3±.04 0.5±.11 0.4±.06 0.5±.12 +R-Learnercb 4.2±.46 3.4±.07 3.4±.04 2.2±.72 0.6±.15 0.9±.15 +OthoRFcb +7.6±.29 4.3±.10 3.7±.07 1.4±.30 0.4±.12 0.5±.10 +TARNetcb +4.2±.07 3.8±.03 3.5±.02 2.2±.13 2.1±.06 2.1±.03 +CFR-wasscb 4.0±.11 3.8±.02 3.7±.02 2.1±.06 2.0±.03 1.9±.02 +CFR-mmdcb 3.8±.05 3.8±.02 3.7±.02 2.1±.04 2.1±.03 2.0±.02 +CEVAEcb +2.5±.03 2.4±.03 2.4±.03 0.5±.08 0.3±.06 0.3±.06 +FedCI +2.5±.03 2.4±.03 2.5±.03 0.4±.06 0.3±.11 0.3±.10 +CausalRFF 1.6±.09 1.5±.07 1.5±.05 0.8±.19 0.5±.12 0.4±.10 +methods, we use Exponential Linear Unit (ELU) activation function and fine-tune the number of +nodes in each hidden later from 10 to 200 with step size of addition by 10. For BART, we use package +BartPy, which is readily available. For X-learner and R-learner, we use the package causalml +(Chen et al. 2020). For OrthoRF, we use the package econml (Microsoft Research 2019). For FedCI, +we use the code from Vo et al. (2022). For all methods, the learning rate is fine-tuned from 10−4 to +10−1 with step size of multiplication by 10. Similarly, the regularizer factors are also fine-tuned from +10−4 to 100 with step size of multiplication by 10. We report two error metrics: ϵPEHE (precision in +estimation of heterogeneous effects) and ϵATE (absolute error) to compare the methods. We report +the mean and standard error over 10 replicates of the data. Further details are presented in Appendix. +5.1 +Synthetic Data +Data description. Obtaining ground truth for evaluating causal inference algorithm is a challenging +task. Thus, most of the state-of-the-art methods are evaluated using synthetic or semi-synthetic +datasets. In this experiment, the synthetic data is simulated with the following distributions: +zs +i ∼ Cat(ρ), +xs +ij ∼ Bern(ϕ(aj0 + (zs +i)⊤aj1)), +ws +i ∼ Bern(ϕ(b0 + (zs +i)⊤(b1 + ∆))), +ys +i(0) ∼ N(sp(c0 + (zs +i)⊤(c1 + ∆)), σ2 +0), +ys +i(1) ∼ N(sp(d0 + (zs +i)⊤(d1 + ∆)), σ2 +1), +where Cat(·), N(·), and Bern(·) denote the categorical distribution, normal distribution, and Bernoulli +distribution, respectively. ϕ(·) denotes the sigmoid function, sp(·) denotes the softplus function, +and xi = [xi1,..., xidx]⊤ ∈ Rdx with dx = 30. Herein, we convert zs +i to a one-hot vector. To +simulate data, we randomly set the ground truth parameters as follows: ρ = [.11, .17, .34, .26, .12]⊤, +(c0, d0) = (0.9, 7.9), (c1, d1, d1) are drawn i.i.d from N(0, 2I5), aj0 and elements of aj1 are drawn +i.i.d from N(0, 2). For each source, we simulate 10 replications with ns = 1000 records. We only +keep {(ys +i, ws +i, xs +i)}ns +i=1 as the observed data, where ys +i = ys +i(0) if ws +i = 0 and ys +i = ys +i(1) if ws +i = 1. +In each source, we use 50 data points for training, 450 for testing and 400 for validating. We report +the evaluation metrics and their standard errors over the 10 replications. +Result and discussion (I). In the first experiment, we study the performance of CausalRFF on +multiple sources whose data distributions are the same. To do that, we simulate m = 5 sources +from the same distribution, i.e., we set the ground truth ∆ = 0.0 for all the sources. We refer to this +dataset as DATAsame. In this experiment, we expect that the result of CausalRFF, which is trained in +federated setting, is as good as training on combined data. The results in Figure 3 show that the error +in two cases seem to move together in a correlated fashion, which verifies our hypothesis. +In addition, to study the performance of CausalRFF on the sources whose data distributions are +different, we also simulate m = 5 sources. However, the first source is with ∆ = 0.0 and the other +8 + +0 +1 +2 +3 +4 +5 +6 +7 +8 +Discrepancy of two sources, ∆ +1.0 +1.3 +1.6 +1.9 +2.2 +2.5 +√ϵPEHE +Error of CATE +0 +1 +2 +3 +4 +5 +6 +7 +8 +Discrepancy of two sources, ∆ +0.0 +0.4 +0.8 +1.2 +1.6 +2.0 +ϵATE +Error of ATE +CausalRFF +Combined data (stack) +Combined data (1-hot) +Figure 5: Experimental results on different levels +of discrepancy, ∆. +Table 2: Out-of-sample errors on DATAdiff. +Method +The error of CATE, √ϵATE +The error of ATE, ϵATE +1 source 3 sources 5 sources 1 source 3 sources 5 sources +BARTag +- +3.0±.01 3.0±.02 +- +1.3±.05 1.4±.10 +X-Learnerag +- +3.3±.03 3.3±.04 +- +1.2±.09 1.3±.09 +R-Learnerag +- +3.2±.03 3.1±.02 +- +1.0±.07 1.2±.09 +OthoRFag +- +3.6±.05 3.6±.05 +- +1.3±.09 1.6±.10 +TARNetag +- +6.1±.19 5.7±.05 +- +2.5±.06 3.0±.05 +CFR-wassag +- +5.6±.09 5.7±.07 +- +2.7±.05 2.8±.04 +CFR-mmdag +- +5.9±.08 5.6±.05 +- +2.5±.03 2.8±.02 +CEVAEag +- +4.2±.07 3.9±.05 +- +2.1±.09 1.8±.10 +BARTcb +3.1±.05 4.1±.10 4.2±.10 0.8±.17 2.8±.15 2.9±.14 +X-Learnercb 3.3±.03 5.0±.08 4.6±.10 0.5±.12 3.3±.11 3.1±.13 +R-Learnercb 3.3±.05 3.5±.05 3.3±.05 0.7±.18 1.1±.10 1.3±.10 +OthoRFcb +3.9±.06 5.2±.10 4.6±.09 0.5±.11 3.3±.14 3.0±.12 +TARNetcb +4.2±.07 5.9±.09 5.8±.06 2.2±.13 2.3±.04 2.9±.02 +CFR-wasscb 4.0±.11 5.7±.08 5.5±.08 1.9±.06 2.4±.03 2.9±.04 +CFR-mmdcb 3.8±.05 5.7±.08 5.5±.04 2.1±.04 2.4±.03 2.9±.04 +CEVAEcb +2.4±.03 5.0±.06 4.4±.07 0.3±.08 2.6±.10 2.0±.07 +FedCI +2.5±.03 2.6±.04 2.8±.04 0.2±.06 1.2±.12 1.5±.13 +CausalRFF 1.4±.07 1.7±.12 1.9±.17 0.5±.11 1.1±.19 1.4±.27 +four sources are with ∆ = 4.0. We refer to this dataset as DATAdiff. We test the error of CATE and +ATE on the first source. In this case, we expect that the errors of CausalRFF to be lower than that of +training on combined data since CausalRFF learns the adaptive factors which prevent negative impact +of the other four sources to the first source. The results in Figure 4 show that CausalRFF achieves +lower errors compared to training on combined data (there are two cases of combining: stacking data, +and adding one-hot vectors to indicate the source of each data point), which is as expected. +In the third experiment, we study the effect of ∆ on the performance of CausalRFF. We simulate +m = 2 sources with different values of ∆. In particular, the first source is with ∆ = 0.0 and the +second source is with ∆ varying from 0.0 to 8.0. We compare our CausalRFF method with that of +training on combined data. Again, Figure 5 shows that CausalRFF achieves lower errors as expected. +Result and discussion (II). This section aims to compare CausalRFF with the baselines on both +datasets: DATAsame and DATAdiff. Except FedCI (which is a Bayesian federated method), the other +baselines are trained on two cases: combined data (cb) and bootstrap aggregating (ag) as mentioned +earlier. On DATAsame, we expect that the performance of the proposed method is as good as the +baselines trained on combined data. The results in Table 1 show that the performance of CausalRFF +is as expected. For DATAdiff, we report the results on Table 2. The figures reveal that the performance +of CausalRFF is as good as the baselines in predicting ATE. In terms of predicting CATE, the +performance of the baselines significantly reduces as we add more data sources whose distribution +are different from the first source. Meanwhile, the performance of CausalRFF in predicting CATE is +slightly reduced, but it is still much better than those of the baselines. The reason of this is because +we used adaptive factors to learn for the similarity of data distributions among the sources. +5.2 +Large-scale Synthetic Data +Data description. In this section, we conduct experiments on a large number of sources. The set +up in this section is similar to that of Section 5.1. We simulate two cases: (1) DATA-LARGEsame: a +dataset of 100 sources, where we set ∆ = 0 for all sources so that their distributions are the same. +(2) DATA-LARGEdiff: a dataset of 100 sources, where we draw uniformly the discrepancy factor +∆ ∼ U[0, 8] for each source so that their distributions are different. In both cases, we use test set +from the first 20 sources for evaluation. +Result and discussion. Table 3 shows that CausalRFF achieves competitive results in estimating ATE +and CATE when the sources have the same distribution. Table 4 shows that CausalRFF outperforms +the baselines when the sources have different distributions. These results are consistent with our +discussions in Section 5.1. +5.3 +A Real World Dataset +Data description. The Infant Health and Development Program (IHDP) (Hill 2011) is a randomized +study on the impact of specialist visits (the treatment) on the cognitive development of children (the +9 + +Table 3: Errors on DATA-LARGEsame dataset. +Method +The error of CATE, √ϵATE +The error of ATE, ϵATE +20 +sources +50 +sources +100 +sources +20 +sources +50 +sources +100 +sources +BARTcb +3.4±.03 3.4±.01 3.3±.01 1.4±.06 1.3±.02 1.3±.01 +X-Learnercb 3.0±.01 2.9±.01 2.9±.01 .16±.02 .12±.02 .13±.02 +R-Learnercb 3.0±.01 2.9±.01 2.9±.01 .07±.01 .10±.02 .10±.02 +OthoRFcb +3.4±.03 3.3±.01 3.2±.01 1.2±.06 1.1±.02 1.0±.02 +TARNetcb +3.8±.03 3.7±.01 3.3±.01 1.1±.02 1.0±.01 .93±.01 +CFR-wasscb 3.7±.02 3.6±.01 3.2±.01 1.1±.02 .99±.01 .87±.01 +CFR-mmdcb 3.7±.02 3.6±.01 3.2±.01 1.1±.02 .98±.01 .87±.01 +CEVAEcb +2.3±.01 2.2±.01 2.0±.01 .19±.03 .17±.01 .17±.01 +FedCI +2.2±.02 2.2±.01 1.9±.01 .23±.04 .21±.01 .19±.01 +CausalRFF +1.6±.05 1.6±.01 1.5±.01 0.3±.04 0.2±.02 .16±.02 +Table 4: Errors on DATA-LARGEdiff dataset. +Method +The error of CATE, √ϵPEHE +The error of ATE, ϵATE +20 +sources +50 +sources +100 +sources +20 +sources +50 +sources +100 +sources +BARTcb +3.4±.03 3.5±.01 3.5±.01 1.4±.06 1.5±.02 1.5±.01 +X-Learnercb 3.3±.04 3.2±.01 3.2±.01 1.1±.08 1.2±.02 1.2±.02 +R-Learnercb 3.2±.03 3.1±.01 3.1±.01 .88±.07 .88±.02 .86±.01 +OthoRFcb +3.4±.03 3.4±.01 3.4±.01 1.2±.07 1.2±.02 1.3±.01 +TARNetcb +5.6±.04 5.6±.02 5.7±.02 2.7±.06 2.8±.02 2.8±.02 +CFR-wasscb 5.4±.05 5.5±.02 5.5±.02 2.7±.05 2.7±.02 2.7±.02 +CFR-mmdcb 5.4±.05 5.4±.02 5.5±.02 2.7±.05 2.7±.02 2.7±.02 +CEVAEcb +3.4±.04 3.4±.02 3.3±.01 1.2±.06 1.2±.02 1.2±.01 +FedCI +3.2±.03 3.2±.02 3.0±.01 1.2±.07 1.2±.01 1.2±.01 +CausalRFF +1.8±.03 1.7±.03 1.6±.01 .24±.04 .19±.14 .15±.01 +outcome). The dataset consists of 747 records with 25 covariates describing properties of the children +and their mothers. The treatment group includes children who received specialist visits and control +group includes children who did not receive. This dataset was ‘de-randomized’ by removing from +the treated set children with non-white mothers. For each child, a treated and a control outcome are +then simulated, thus allowing us to know the ‘true’ individual causal effects of the treatment. Further +details are presented in Appendix. +Table 5: Out-of-sample errors on IHDP dataset. +Method +The error of CATE, √ϵPEHE +The error of ATE, ϵATE +1 source 2 sources 3 sources 1 source 2 sources 3 sources +BARTag +- +2.3±.26 2.4±.22 +- +1.2±.23 1.3±.18 +X-Learnerag +- +1.8±.20 1.8±.22 +- +0.6±.15 0.4±.11 +R-Learnerag +- +2.4±.31 2.3±.21 +- +1.3±.34 1.2±.24 +OthoRFag +- +2.3±.21 2.1±.16 +- +0.6±.22 0.7±.13 +TARNetag +- +2.9±.13 2.7±.15 +- +0.7±.12 0.7±.16 +CFR-wassag +- +2.3±.31 2.2±.20 +- +0.7±.12 0.7±.11 +CFR-mmdag +- +2.6±.21 2.4±.15 +- +0.8±.19 0.7±.18 +CEVAEag +- +1.9±.14 1.6±.17 +- +1.2±.11 0.8±.10 +BARTcb +2.2±.22 2.1±.26 2.1±.25 1.0±.16 0.8±.20 0.7±.17 +X-Learnercb 1.9±.21 1.9±.21 1.8±.18 0.5±.21 0.5±.18 0.4±.11 +R-Learnercb 2.8±.31 2.6±.23 2.6±.17 1.6±.25 1.6±.26 1.6±.19 +OthoRFcb +2.8±.16 2.1±.14 1.9±.14 0.8±.15 0.6±.10 0.6±.10 +TARNetcb +3.5±.59 2.7±.12 2.5±.15 1.6±.61 0.7±.12 0.6±.17 +CFR-wasscb 2.2±.15 2.1±.22 2.1±.23 0.7±.23 0.6±.18 0.6±.16 +CFR-mmdcb 2.7±.19 2.3±.26 2.2±.10 0.9±.30 0.7±.17 0.5±.17 +CEVAEcb +1.8±.22 2.0±.11 1.7±.12 0.5±.14 1.4±.07 0.9±.07 +FedCI +1.6±.10 1.6±.12 1.7±.09 0.5±.10 0.5±.24 0.5±.09 +CausalRFF 1.7±.34 1.4±.33 1.2±.18 0.7±.14 0.7±.17 0.5±.16 +Result and discussion. Table 5 reports the ex- +perimental results on IHDP dataset. Again, we +see that the proposed method gives competitive +results compared to the baselines. In particu- +lar, the error of CausalRFF in predicting ATE is +as low as that of the baselines, which is as we +expected. In addition, the errors of CausalRFF +in predicting CATE are lower than those of the +baselines, which verifies the efficacy of the pro- +posed method. Most importantly, CausalRFF is +trained in a federated setting which minimizes +the risk of privacy breach for the individuals +stored in the local dataset. +6 +Conclusion +We have proposed a new method to learn causal effects from federated, observational data sources +with dissimilar distributions. Our method utilizes Random Fourier Features that naturally induce +the decomposition of the loss function to individual components. Our method allows for each +component data group to inherit different distributions, and requires no prior knowledge on data +discrepancy among the sources. We have also proved statistical guarantees which show how multiple +data sources are effectively incorporated in our causal model. Our work is an important step toward +privacy-preserving causal inference. Future work may include combining the proposed method with +a multiparty differential privacy technique (e.g., Pathak et al. 2010; Rajkumar and Agarwal 2012; +Pettai and Laud 2015; Hamm et al. 2016), which might lead to a stronger privacy guarantee model. +Another direction is to extend the proposed method with some recent ideas (e.g., Khemakhem et al. +2020; Sun et al. 2021) to study the identifiability of the model. +Acknowledgments and Disclosure of Funding +This research/project is supported by the National Research Foundation Singapore and DSO National +Laboratories under the AI Singapore Programme (AISG Award No: AISG2-RP-2020-016). +AB was supported by an NRF Fellowship for AI grant (NRFFAI1-2019-0002) and an Amazon +Research Award. +This work was conducted while YL was at Harvard University and the views expressed here do not +necessarily reflect the position of Roche AG. +10 + +References +Aglietti, V., Damoulas, T., Álvarez, M., and González, J. (2020). Multi-task causal learning with +Gaussian processes. In Advances in Neural Information Processing Systems, pages 6293–6304. +Alaa, A. and van der Schaar, M. (2018). Limits of estimating heterogeneous treatment effects: +Guidelines for practical algorithm design. In Proceedings of the 35th International Conference on +Machine Learning, pages 129–138. PMLR. +Alaa, A. M. and van der Schaar, M. (2017). Bayesian inference of individualized treatment effects +using multi-task Gaussian processes. In Advances in Neural Information Processing Systems, +pages 3424–3432. +Allman, E. S., Matias, C., and Rhodes, J. A. (2009). Identifiability of parameters in latent structure +models with many observed variables. The Annals of Statistics, 37(6A):3099–3132. +Álvarez, M. A., Ward, W., and Guarnizo, C. (2019). Non-linear process convolutions for multi-output +Gaussian processes. In The 22nd International Conference on Artificial Intelligence and Statistics, +pages 1969–1977. PMLR. +Anandkumar, A., Ge, R., Hsu, D., Kakade, S. M., and Telgarsky, M. (2014). Tensor decompositions +for learning latent variable models. Journal of Machine Learning Research, 15:2773–2832. +Anandkumar, A., Hsu, D., and Kakade, S. M. (2012). A method of moments for mixture models and +hidden markov models. In Proceedings of the 25th Annual Conference on Learning Theory, pages +33–1. PMLR. +Arora, S., Ge, R., Ma, T., and Risteski, A. (2017). Provable learning of noisy-OR networks. In +Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 1057– +1066. +Bareinboim, E. and Pearl, J. (2016). Causal inference and the data-fusion problem. Proceedings of +the National Academy of Sciences, 113(27):7345–7352. +Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2):123–140. +Chaudhuri, K., Monteleoni, C., and Sarwate, A. D. (2011). Differentially private empirical risk +minimization. Journal of Machine Learning Research, 12(3). +Chen, H., Harinen, T., Lee, J.-Y., Yung, M., and Zhao, Z. (2020). CausalML: Python package for +causal machine learning. +Choudhury, O., Park, Y., Salonidis, T., Gkoulalas-Divanis, A., Sylla, I., et al. (2019). Predicting +adverse drug reactions on distributed health data using federated learning. In AMIA Annual +Symposium Proceedings, volume 2019, page 313. American Medical Informatics Association. +de Wolff, T., Cuevas, A., and Tobar, F. (2020). Mogptk: The multi-output Gaussian process toolkit. +arXiv preprint arXiv:2002.03471. +Dorie, V. (2016). Npci: Non-parametrics for causal inference. URL: https://github. com/vdorie/npci. +Finkelstein, A. and Hendren, N. (2020). Welfare analysis meets causal inference. Journal of Economic +Perspectives, 34(4):146–67. +Flores, M., Dayan, I., Roth, H., Zhong, A., Harouni, A., Gentili, A., Abidin, A., Liu, A., Costa, A., +Wood, B., et al. (2020). Federated learning used for predicting outcomes in SARS-COV-2 patients. +Preprint. medRxiv. 2020;2020.08.11.20172809. +Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable +models. Biometrika, 61(2):215–231. +Gostin, L. O., Levit, L. A., Nass, S. J., et al. (2009). Beyond the HIPAA Privacy Rule: Enhancing +Privacy, Improving Health Through Research. National Academies Press. +11 + +Gutman, R., Intrator, O., and Lancaster, T. (2017). A Bayesian procedure for estimating the causal +effects of nursing home bed-hold policy. Biostatistics, 19(4):444–460. +Hamm, J., Cao, Y., and Belkin, M. (2016). Learning privately from multiparty data. In Proceedings +of the 33rd International Conference on Machine Learning, pages 555–563. PMLR. +Hard, A., Rao, K., Mathews, R., Ramaswamy, S., Beaufays, F., Augenstein, S., Eichner, H., Kiddon, +C., and Ramage, D. (2018). Federated learning for mobile keyboard prediction. arXiv preprint +arXiv:1811.03604. +Henderson, N. C., Louis, T. A., Wang, C., and Varadhan, R. (2016). Bayesian analysis of heteroge- +neous treatment effects for patient-centered outcomes research. Health Services and Outcomes +Research Methodology, 16(4):213–233. +Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference. Journal of Computational +and Graphical Statistics, 20(1):217–240. +Jernite, Y., Halpern, Y., and Sontag, D. (2013). Discovering hidden variables in noisy-OR networks +using quartet tests. Advances in Neural Information Processing Systems, 26:2355–2363. +Joukov, V. and Kuli´c, D. (2020). Fast approximate multi-output Gaussian processes. arXiv preprint +arXiv:2008.09848. +Khemakhem, I., Kingma, D., Monti, R., and Hyvarinen, A. (2020). Variational autoencoders and +nonlinear ICA: A unifying framework. In Proceedings of the 23rd International Conference on +Artificial Intelligence and Statistics, pages 2207–2217. PMLR. +Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence +of infinitely many incidental parameters. The Annals of Mathematical Statistics, pages 887–906. +Kingma, D. P. and Welling, M. (2013). Auto-encoding variational bayes. In Proceedings of the 2nd +International Conference on Learning Representations. +Künzel, S. R., Sekhon, J. S., Bickel, P. J., and Yu, B. (2019). Metalearners for estimating heteroge- +neous treatment effects using machine learning. Proceedings of the National Academy of Sciences, +116(10):4156–4165. +Lee, S., Correa, J., and Bareinboim, E. (2020). Generalized transportability: Synthesis of experiments +from heterogeneous domains. In Proceedings of the 34th AAAI Conference on Artificial Intelligence, +New York, NY. AAAI Press. +Liu, J. S. (1996). Metropolized independent sampling with comparisons to rejection sampling and +importance sampling. Statistics and Computing, 6(2):113–119. +Louizos, C., Shalit, U., Mooij, J. M., Sontag, D., Zemel, R., and Welling, M. (2017). Causal effect +inference with deep latent-variable models. In Advances in Neural Information Processing Systems, +pages 6446–6456. +Madras, D., Creager, E., Pitassi, T., and Zemel, R. (2019). Fairness through causal awareness: +Learning causal latent-variable models for biased data. In Proceedings of the Conference on +Fairness, Accountability, and Transparency, pages 349–358. ACM. +McMahan, B., Moore, E., Ramage, D., Hampson, S., and y Arcas, B. A. (2017). Communication- +efficient learning of deep networks from decentralized data. In Proceedings of the 20th International +Conference on Artificial Intelligence and Statistics, pages 1273–1282. PMLR. +Microsoft Research (2019). EconML: A python package for ML-based heterogeneous treatment +effects estimation. https://github.com/microsoft/EconML. Version 0.x. +Milton, P., Coupland, H., Giorgi, E., and Bhatt, S. (2019). Spatial analysis made easy with linear +regression and kernels. Epidemics, 29:100362. +Mohri, M., Sivek, G., and Suresh, A. T. (2019). Agnostic federated learning. In Proceedings of the +36th International Conference on Machine Learning, pages 4615–4625. PMLR. +12 + +Morgan, S. L. and Winship, C. (2015). Counterfactuals and Causal Inference. Cambridge University +Press. +Nie, X. and Wager, S. (2020). Quasi-oracle estimation of heterogeneous treatment effects. Biometrika. +Oprescu, M., Syrgkanis, V., and Wu, Z. S. (2019). Orthogonal random forest for causal inference. In +Proceedings of the 36th International Conference on Machine Learning, pages 4932–4941. PMLR. +Pathak, M., Rane, S., and Raj, B. (2010). Multiparty differential privacy via aggregation of locally +trained classifiers. Advances in Neural Information Processing Systems, 23. +Pearl, J. (1995). Causal diagrams for empirical research. Biometrika, 82(4):669–688. +Pearl, J. (2009a). Causal inference in statistics: An overview. Statistics Surveys, 3:96–146. +Pearl, J. (2009b). Causality: Models, Reasoning, and Inference. Cambridge University Press. +Pearl, J. and Bareinboim, E. (2011). Transportability of causal and statistical relations: A formal +approach. In Proceedings of the 25th AAAI Conference on Artificial Intelligence. +Pettai, M. and Laud, P. (2015). Combining differential privacy and secure multiparty computation. In +Proceedings of the 31st Annual Computer Security Applications Conference, pages 421–430. +Powers, S., Qian, J., Jung, K., Schuler, A., Shah, N. H., Hastie, T., and Tibshirani, R. (2018). Some +methods for heterogeneous treatment effect estimation in high dimensions. Statistics in Medicine, +37(11):1767–1787. +Rahimi, A. and Recht, B. (2007). Random features for large-scale kernel machines. Advances in +Neural Information Processing Systems, 20. +Rajkumar, A. and Agarwal, S. (2012). A differentially private stochastic gradient descent algorithm +for multiparty classification. In Proceedings of the 15th International Conference on Artificial +Intelligence and Statistics, pages 933–941. PMLR. +Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational +studies for causal effects. Biometrika, 70(1):41–55. +Sattler, F., Wiedemann, S., Müller, K.-R., and Samek, W. (2019). Robust and communication-efficient +federated learning from non-iid data. IEEE Transactions on Neural Networks and Learning Systems, +31(9):3400–3413. +Sattler, F., Wiedemann, S., Müller, K.-R., and Samek, W. (2020). Robust and communication-efficient +federated learning from non-i.i.d. data. IEEE Transactions on Neural Networks and Learning +Systems, 31(9):3400–3413. +Shalit, U., Johansson, F. D., and Sontag, D. (2017). Estimating individual treatment effect: general- +ization bounds and algorithms. In Proceedings of the 34th International Conference on Machine +Learning, pages 3076–3085. JMLR.org. +Shokri, R. and Shmatikov, V. (2015). Privacy-preserving deep learning. In ACM SIGSAC Conference +on Computer and Communications Security, pages 1310–1321. +Sun, X., Wu, B., Zheng, X., Liu, C., Chen, W., Qin, T., and Liu, T.-Y. (2021). Recovering latent +causal factor for generalization to distributional shifts. Advances in Neural Information Processing +Systems, 34:16846–16859. +Tsamardinos, I., Triantafillou, S., and Lagani, V. (2012). Towards integrative causal analysis of +heterogeneous data sets and studies. Journal of Machine Learning Research, 13:1097–1157. +Vaid, A., Jaladanki, S. K., Xu, J., Teng, S., Kumar, A., and Lee, S. (2020). Federated learning of +electronic health records improves mortality prediction in patients. Ethnicity, 52(77.6):0–001. +Van der Vaart, A. W. (2000). Asymptotic Statistics, volume 3. Cambridge University Press. +13 + +Vo, T. V., Lee, Y., Hoang, T. N., and Leong, T.-Y. (2022). Bayesian federated estimation of causal +effects from observational data. In Proceedings of the 38th Conference on Uncertainty in Artificial +Intelligence. +Wang, H., Kaplan, Z., Niu, D., and Li, B. (2020). +Optimizing federated learning on non-iid +data with reinforcement learning. In IEEE INFOCOM 2020 - IEEE Conference on Computer +Communications, pages 1698–1707. +Wang, Y. and Blei, D. M. (2019). Frequentist consistency of variational bayes. Journal of the +American Statistical Association, 114(527):1147–1161. +Wendland, H. (2004). Scattered Data Approximation, volume 17. Cambridge University Press. +Xiong, R., Koenecke, A., Powell, M., Shen, Z., Vogelstein, J. T., and Athey, S. (2021). Federated +causal inference in heterogeneous observational data. arXiv preprint arXiv:2107.11732. +Yang, Y., Pati, D., and Bhattacharya, A. (2020). α-variational inference with statistical guarantees. +The Annals of Statistics, 48(2):886–905. +Yao, L., Li, S., Li, Y., Huai, M., Gao, J., and Zhang, A. (2018). Representation learning for treatment +effect estimation from observational data. In Advances in Neural Information Processing Systems, +pages 2633–2643. +Yoon, J., Jordon, J., and van der Schaar, M. (2018). GANITE: Estimation of individualized treatment +effects using generative adversarial nets. In Proceedings of the 6th International Conference on +Learning Representations. +Zhao, Y., Li, M., Lai, L., Suda, N., Civin, D., and Chandra, V. (2018). Federated learning with non-iid +data. arXiv preprint arXiv:1806.00582. +Zhe, S., Xing, W., and Kirby, R. M. (2019). Scalable high-order gaussian process regression. In The +22nd International Conference on Artificial Intelligence and Statistics, pages 2611–2620. PMLR. +14 + +Appendix: +An Adaptive Kernel Approach to Federated Learning +of Heterogeneous Causal Effects +A +Pre-training step to remove duplicated individuals +As mentioned in the main text, we make five assumptions as follows: +(A1) Consistency: W = w =⇒ Y (w) = Y , this follows from the axioms of structural causal model. +(A2) No interference: treatment on one subject does not affect the outcomes of another one. This is +because the outcome only has a single node for treatment as a parent. +(A3) Positivity (also known as Overlap): every subject has some positive probability to be assigned +to every treatment. +(A4) The individuals in each source must have the same set of common covariates. +(A5) There is no individual whose data exists in more than one source. +Assumptions (A1), (A2) and (A3) are standard in any causal inference algorithm. +Assumption (A4) has been implicitly shown in our setup since all the sources would share the same +causal graph. This is a reasonable assumption as we intend to build a unified model on all of the data +sources. For example, decentralized data in Choudhury et al. (2019); Vaid et al. (2020); Flores et al. +(2020) (to name a few) satisfy this assumption for federated learning. +Assumption (A5) is to ensure that no individuals would dominate the other individuals when training +the model. For example, if an individual appears in all of the sources, the trained model would +be biased by data of this individual (there is imbalance caused by the use of more data from this +particular individual than the others). Hence, this condition would ensure that such bias does not +exist. +In practice, Assumption (A5) sometimes does not hold. To address such a problem, we propose a +pre-training step to exclude such duplicated individuals. The pre-training step are summarized as +follows: +(1) Suppose that an individual can be uniquely identified via a set of features. For example, a +pair of (national identity, nationality) can be used to uniquely identify a person. +(2) To identify duplicated individuals, we first encode the above features with a hash function +such as MD5, SHA256. +(3) We then send the encoded sequences to a central server. +(4) The server would collect all encoded sequences from all sources and find among them if an +encoded sequence is repeated. +(5) All of the repeated sequences are associated with duplicated individuals. Thus, we announce +the sources to exclude these individual from the training process. +We summarize the pre-training step in Figure 6 with three sources of data. +B +Identification +The causal effects are unidentifiable if the confounders are unobserved. However, Louizos et al. +(2017) showed that if the joint distribution ps(xs, ys, ws, zs) can be recovered, then the causal effects +are identifiable. In the following, we show how they are identifiable. +15 + +L1 = List of hashed sequences for +each individual in Source #1 +L3 = List of hashed sequences for +each individual in Source #3 +L2 = List of hashed sequences for +each individual in Source #2 +Source #1 +Source #2 +Source #3 +Search for duplicated individuals +among the lists: L1, L2, L3 +Figure 6: An illustration on how the pre-training step. This step is intended to identify duplicated +individuals among the sources. Furthermore, this step preserves privacy since each source sends only +their hashed sequences of the individuals. +Proof. The proof is adapted from Louizos et al. (Theorem 1, 2017). We need to show that the +distribution ps(ys|do(W = ws), xs) is identifiable from observational data. We have +ps(ys|do(W = ws), xs) = +� +ps(ys|do(W = ws), xs, zs)ps(zs|do(W = ws), xs)dzs += +� +ps(ys|ws, xs, zs)ps(zs|xs)dzs. +where the last equality is obtained by applying the do-calculus. +The last expression, +� +ps(ys|ws, xs, zs)ps(zs|xs)dzs, can be identified by the joint distribution ps(xs, ys, ws, zs). In +our work, ps(xs, ys, ws, zs) is recovered by its factorization with the distributions ps(ws|xs), +ps(ys|xs, ws), ps(zs|xs, ys, ws), ps(ys|ws, zs), and p(zs). Adaptively learning these distributions +in a federated setting is the main task of our work. This completes the proof. +C +Computing CATE, local ATE, and global ATE +This section gives details on how to compute CATE, local ATE and global ATE after training the +model. +C.1 +Computing the CATE and local ATE +After training the model, each source can compute the CATE and the local ATE on for its own source +and use it for itself. +E[ys +i|do(ws +i =w), xs +i] = +� +E[ys +i|ws +i =w, zs +i]p(zs +i|xs +i)dzs +i ≃ 1 +N +N +� +l=1 +fy(ws +i =w, zs +i[l]) +where fy(ws +i =w, zs +i[l]) is the mean function of ps(ys +i|ws +i, zs +i) and {zs +i[l]}N +l=1 +i.i.d. +∼ ps(zs +i|xs +i). +The problem is to draw {zs +i[l]}N +l=1 from ps(zs +i|xs +i). We observe that +ps(zs +i|xs +i) = +� +ws +i∈{0,1} +� +ps(zs +i|xs +i, ys +i, ws +i)ps(ys +i|xs +i, ws +i)ps(ws +i|xs +i) dys +i. +Hence, to draw samples, we proceed in the following steps: +16 + +(1) Draw a sample of ws +i from ps(ws +i|xs +i). +(2) Substitute the above sample of ws +i to ps(ys +i|xs +i, ws +i). +(3) Draw a sample of ys +i from ps(ys +i|xs +i, ws +i). +(4) Substitute the above sample of ys +i to ps(zs +i|xs +i, ys +i, ws +i). +(5) Draw a sample of zs +i from ps(zs +i|xs +i, ys +i, ws +i). +The density function of ps(ys +i|xs +i, ws +i) and ps(ws +i|xs +i) are available after training the model. As +described in the main text, there are two options to draw from ps(zs +i|xs +i, ys +i, ws +i). The first option is +to draw from q(xs +i) sine it approximates ps(zs +i|xs +i, ys +i, ws +i). The second option is to use Metropolis- +Hastings algorithm with independent sampler (Liu 1996). For the second option, we have that +ps(zs +i|xs +i, ys +i, ws +i) ∝ ps(ys +i|zs +i, ws +i)ps(ws +i|zs +i)ps(xs +i|zs +i)p(zs +i). +Hence, it can be used to compute the acceptance probability of interest. Note that the second option +would give more exact samples since it further filters the samples based on the exact acceptance +probability. +The above would help estimate the CATE given xs +i. The local ATE is the average of CATE of +individuals in a source s. These quantities can be estimated in a local source’s machine. We show +how to compute the global ATE in the next section. +C.2 +Computing the global ATE from local ATE of each Source +To compute a global ATE, the server would collect all the local ATE in each source and then compute +their weighted average. For example, suppose that we have three sources whose local ATE values are +7.0, 8.5, and 6.8. These local ATEs are averaged over 10, 5, and 12 individuals, in that order. Then, +the global ATE is given as follows: +global ATE = 10 × 7.0 + 8 × 8.5 + 12 × 6.8 +10 + 8 + 12 += 7.32. +Since each source only shares their local ATE and the number of individuals, it does not leak any +sensitive information about the individuals. +D +Comparison metrics +We report two error metrics in our experiments: +• Precision in estimation of heterogeneous effects (PEHE): +ϵPEHE = +n +� +i=1 +(τ(xi) − ˆτ(xi))2/n, +(17) +• Absolute error: +ϵATE = |τ − ˆτ|, +(18) +where τ(xi), τ are the ground truth of ITE and ATE, and ˆτ(xi), ˆτ are their estimates. We report the +mean and standard error over 10 replicates of the data with different random initializations of the +training algorithm. +E +Derivation of the loss functions +In this section, we present the loss functions and the form of functions that modulate the desired +distributions. +17 + +E.1 +Learning distributions involving latent confounder +The ELBO of the log marginal likelihood has the following expression +logp(x, y, w) = log +� +p(x, y, w, z)dz +≥ +� +q(z) log p(x, y, w, z) +q(z) +dz += +� +s∈S +ns +� +i=1 +� +Eq +� +log ps(ys +i|ws +i, zs +i) + log ps(ws +i|zs +i) + log ps(xs +i|zs +i) +� +− KL[q(zs +i)∥p(zs +i)] +� +=: L. +Using the complete dataset ˜Ds = �M +l=1 +� +(ws +i, ys +i, xs +i, zs +i[l]) +�ns +i=1, ∀s ∈ S, we minimize the following +loss function J: +J = �L + +� +c∈A +R(fc), +A = {y0, y1, q0, qq, x, w}, +where �L is the empirical loss function obtained from the negative of L. In the following, we find the +form of fc based on the representer theorem. +We further define fx = [fx,1,..., fx,dx], where fx,d is a function taking zs +i as input and mapping it to +a real value in R. Similarly, fq0 = [fq0,1,..., fq0,dz] and fq1 = [fq1,1,..., fq1,dz]. +Let Hc (c ∈ A) be a reproducing Kernel Hilbert space (RKHS) and κc(·, ·) be kernel function +associated with Hc. We define Bc as follows: +By0 = span +� +κy0(·, zs +i[l]), where s ∈ S; i = 1,..., ns; l = 1,..., M +� +, +By1 = span +� +κy1(·, zs +i[l]), where s ∈ S; i = 1,..., ns; l = 1,..., M +� +, +Bx = span {κx(·, zs +i[l]), where s ∈ S; i = 1,..., ns; l = 1,..., M} , +Bw = span {κw(·, zs +i[l]), where s ∈ S; i = 1,..., ns; l = 1,..., M} , +Bq0 = span {κq0(·, [xs +i, ys +i]), where s ∈ S; i = 1,..., ns} , +Bq1 = span {κq1(·, [xs +i, ys +i]), where s ∈ S; i = 1,..., ns} . +We posit the following regularizers: +R(fy0) = reg_factory0 × ∥fy0∥2 +Hy0, +R(fx) = +dx +� +d=1 +reg_factorx,d × ∥fx,d∥2 +Hx +(d = 1,..., dx). +The regularizers R(fy1) and R(fw) are similar to that of R(fy0), and R(fq0), R(fq1) are similar to +that of R(fx). +We see that Bc is a subspace of Hc. We project fy0, fy1, fw, fx,d (d = 1,..., dx), fq0,d (d = 1,..., dz) +and fq1,d (d = 1,..., dz) onto the subspaces By0, By1, Bw, Bx, Bq0 and Bq1, respectively, and obtain +f ′ +y0, f ′ +y1, f ′ +w, f ′ +x,d, f ′ +q0,d and f ′ +q1,d. Next, we also project them onto the perpendicular spaces of B(·) +to obtain f ⊥ +y0, f ⊥ +y1, f ⊥ +w , f ⊥ +x,d, f ⊥ +q0,d and f ⊥ +q1,d. +Note that f(·) = f ′ +(·) +f ⊥ +(·). Hence, ∥f(·)∥2 +H(·) = ∥f ′ +(·)∥2 +H(·) +∥f ⊥ +(·)∥2 +H(·) ≥ ∥f ′ +(·)∥2 +H(·), which implies +that reg_factor(·) × ∥f(·)∥2 +H(·) is minimized if f(·) is in its subspace B(·). +(I) +In addition, due to the reproducing property, we have +fy0(zs +i[l]) = +� +fy0, κy0(·, zs +i[l]) +� +Hy = +� +f ′ +y0, κy0(·, zs +i[l]) +� +Hy + +� +f ⊥ +y0, κy0(·, zs +i[l]) +� +Hy = f ′ +y0(zs +i[l]). +Similarly, we also have fy1(zd +i [l]) = f ′ +y1(zd +i [l]), fw(zd +i [l]) = f ′ +w(zd +i [l]), fx,d(zl +i) = f ′ +x,d(zd +i [l]), +fq0,d(yd +i , xd +i ) = f ′ +q0,d(yd +i , xd +i ) and fq1,d(yd +i , xd +i ) = f ′ +q1,d(yd +i , xd +i ). Hence, +�L(fy0, fy1, fq0, fq1, fx, fw) = �L(f ′ +y0, f ′ +y1, f ′ +q0, f ′ +q1, f ′ +x, f ′ +w). +(II) +(I) and (II) imply that fy0, fy1, fq0,d, fq1,d, fx,d, fw are the weighted sum of elements in their +18 + +corresponding subspace. Hence, +fc(us) = +� +v∈S +nv×M +� +j=1 +κ(us, uv +j)αv +j. +Using this form with the adaptive kernel and Random Fourier Feature described in the main text +(Section 4.1), we obtain the desired model. +E.2 +Learning auxiliary distributions +The derivation of Jw, Jy and the form of functions modulated the auxiliary distributions are similar to +those of J as detailed in Section E.1. The difference is that the empirical loss functions are obtained +from the negative log-likelihood instead of the ELBO. +F +Spectral distribution of some popular kernels +Table 6 (adopted from Milton et al. (2019)) presents some popular kernels and their associated +spectral density s(ω). Those density functions are needed to draw samples of ω for Random Fourier +Features presented in Section 4 of the main text. In our experiments, we used Gaussian kernel. +Table 6: Some popular kernels and their associated spectral density. Note that Kν(·) denotes the +modified Bessel function of the second kind, Γ(·) is the gamma function. +Kernel +Kernel function, k(x1 − x2) +Spectral density, s(ω) +Gaussian +exp +� +− ∥x1 − x2∥2 +2 +2ℓ2 +� +� 2π +ℓ2 +� −d +2 +exp +� +− ℓ2∥ω∥2 +2 +2 +� +Laplacian +exp +� +− ℓ∥x1 − x2∥1 +� +� 2 +π +� d +2 +d +� +i=1 +ℓ +ℓ2 + ω2 +i +Matérn +21−ν +Γ(ν) +� +√ +2ν ∥x1 − x2∥2 +ℓ +�ν +Kν +� +√ +2ν ∥x1 − x2∥2 +ℓ +� +2dπ +d +2 Γ(ν + d +2 )(2ν)ν +Γ(ν)ℓ2ν +� 2ν +ℓ2 + 4π2∥ω∥2 +2 +�− +� +ν+ d +2 +� +G +Proof of Lemma 1 +Let S\s := S \ {s}. The model is summarized as follows: +p(zs +i) = N(0, σ2 +zIdz), +p(ws +i|zs +i) = Bern +� +ϕ +�� +θs +w + +� +v∈S\s +λs,vθv +w +�⊤ +φ(zs +i) +�� +, +p(ys +i|ws +i, zs +i) = N +�� +ws +i +� +θs +y1 + +� +v∈S\s +λs,vθv +y1 +� ++ (1 − ws +i) +� +θs +y0 + +� +v∈S\s +λs,vθv +y0 +��⊤ +φ(zs +i), σ2 +y +� +, +p(xs +i|zs +i) = N +�� +θs +x + +� +v∈S\s +λs,vθv +x +�⊤ +φ(zs +i), σ2 +xIdx +� +, +where z(·) +i +∈ Rdz, y(·) +i +∈ R, w(·) +i +∈ {0, 1}, x(·) +i +∈ Rdx, λ > 0. +Let θ = {θs +w, θs +y0, θs +y1, θs +x}s∈S. Let Vw, Vy0, Vy1, Vx be 1/(2√m)-packing of the unit ∥ · ∥2- +balls with cardinality at least (2√m)2B, (2√m)2B, (2√m)2B, (2√m)2Bdx, respectively. Let +Vs = δ(Vw × Vy0 × Vy1 × Vx) and V = Vs1 × Vs2 ×... × Vsm. We see that +|V| ≥ (2√m)2mB(dx+3). +In the following, we derive the minimax bound: +19 + +Proof. We have that +∥θ1 − θ2∥2 = +�� +s∈S +� +c∈A +∥(θsc)1 − (θsc)2∥2 +2 ≥ +� +� +� +�� +s∈S +4 +� +δ +2√m +�2 += δ. +The marginal distribution +pθ(w, y, x) = +� +pθ(w, y, x, z)dz = +� +pθ(y|w, z)pθ(w|z)pθ(x|z)p(z)dz. +Moreover, we have that +DKL(pn +θ1 ∥ pn +θ2) = +� +s∈S +DKL(pns +θ1 ∥ pns +θ2). +We divide the proof into three parts (I), (II), and (III): +(I) The upper bound of DKL(pns +θ1 ∥ pns +θ2) +Since the data is independent, we have that +DKL(pns +θ1 ∥ pns +θ2) = nsDKL(p1 +θ1 ∥ p1 +θ2) +≤ns +� +DKL +� +pθ1(y|w, z)pθ1(w|z)pθ1(x|z) +���pθ2(y|w, z′)pθ2(w|z′)pθ2(x|z′) +� +p(z)p(z′)dzdz′ += ns +� � +pθ1(w = 0|z)DKL +� +pθ1(y|w = 0, z) +��pθ2(y|w = 0, z′) +� ++ pθ1(w = 1|z)DKL +� +pθ1(y|w = 1, z) +��pθ2(y|w = 1, z′) +� ++ DKL +� +pθ1(w|z) +��pθ2(w|z′) +� ++ DKL +� +pθ1(x|z) +��pθ2(x|z′) +�� +p(z)p(z′)dzdz′. +In the following, we find the upper bound of each component. +⋄ Upper bound of the first and second component +pθ1(w = 0|z)DKL +� +pθ1(y|w = 0, z) +��pθ2(y|w = 0, z′) +� +≤ +1 +2σ2y +�� +(θs +y0)1 + +� +v∈S\s +λs,v(θv +y0)1 +�⊤ +φ(z) − +� +(θs +y0)2 + +� +v∈S\s +λs,v(θv +y0)2 +�⊤ +φ(z′) +�2 +≤ +8B2δ2(1 + � +v∈S\s λs,v)2 +σ2y +. +Similarly, we also have +pθ1(w = 1|z)DKL +� +pθ1(y|w = 1, z) +��pθ2(y|w = 1, z′) +� +≤ +8B2δ2(1 + � +v∈S\s λs,v)2 +σ2y +. +⋄ Upper bound of the third component +DKL +� +pθ1(w|z) +��pθ2(w|z′) +� += ϕ +�� +(θs +w)1 + +� +v∈S\s +λs,v(θv +w)1 +�⊤ +φ(z) +� +log +ϕ +�� +(θs +w)1 + � +v∈S\s λs,v(θv +w)1 +�⊤ +φ(z) +� +ϕ +�� +(θsw)2 + � +v∈S\s λs,v(θvw)2 +�⊤ +φ(z′) +� ++ ϕ +� +− +� +(θs +w)1 + +� +v∈S\s +λs,v(θv +w)1 +�⊤ +φ(z) +� +log +ϕ +� +− +� +(θs +w)1 + � +v∈S\s λs,v(θv +w)1 +�⊤ +φ(z) +� +ϕ +� +− +� +(θsw)2 + � +v∈S\s λs,v(θvw)2 +�⊤ +φ(z′) +�. +For the first component, +ϕ +�� +(θs +w)1 + +� +v∈S\s +λs,v(θv +w)1 +�⊤ +φ(z) +� +log +ϕ +�� +(θs +w)1 + � +v∈S\s λs,v(θv +w)1 +�⊤ +φ(z) +� +ϕ +�� +(θsw)2 + � +v∈S\s λs,v(θvw)2 +�⊤ +φ(z′) +� +20 + +≤ +��� log +� +1 + e +− +� +(θs +w)2+� +v∈S\s λs,v(θv +w)2 +�⊤ +φ(z)� +− log +� +1 + e +− +� +(θs +w)1+� +v∈S\s λs,v(θv +w)1 +�⊤ +φ(z′)���� +≤ +���(θs +w)1 + +� +v∈S\s +λs,v(θv +w)1 +��� +2∥φ(z)∥2 + +���(θs +w)2 + +� +v∈S\s +λs,v(θv +w)2 +��� +2∥φ(z′)∥2 +≤ +� +δ + +� +v∈S\s +λs,vδ +� +∥φ(z)∥2 + +� +δ + +� +v∈S\s +λs,vδ +� +∥φ(z′)∥2 +≤ 4Bδ +� +1 + +� +v∈S\s +λs,v� +. +Similarly, we also have +ϕ +� +− +� +(θs +w)1 + +� +v∈S\s +λs,v(θv +w)1 +�⊤ +φ(z) +� +log +ϕ +� +− +� +(θs +w)1 + � +v∈S\s λs,v(θv +w)1 +�⊤ +φ(z) +� +ϕ +� +− +� +(θsw)2 + � +v∈S\s λs,v(θvw)2 +�⊤ +φ(z′) +� +≤ 4Bδ +� +1 + +� +v∈S\s +λs,v� +. +Thus, +DKL +� +pθ1(w|z) +��pθ2(w|z′) +� +≤ 8Bδ +� +1 + +� +v∈S\s +λs,v� +. +⋄ Upper bound of the fourth component +DKL +� +pθ1(x|z) +��pθ2(x|z′) +� += +1 +2σ2x +��� +� +(θs +x)1 + +� +v∈S\s +λs,v(θv +x)1 +�⊤ +φ(z) − +� +(θs +x)2 + +� +v∈S\s +λs,v(θv +x)2 +�⊤ +φ(z′) +��� +2 +2 +≤ +1 +2σ2x +���� +� +(θs +x)1 + +� +v∈S\s +λs,v(θv +x)1 +�⊤ +φ(z) +��� +2 + +��� +� +(θs +x)2 + +� +v∈S\s +λs,v(θv +x)2 +�⊤ +φ(z′) +��� +2 +�2 +≤ +8B2δ2� +1 + � +v∈S\s λs,v�2 +σ2x +. +(II) Combining the results +From the above upper bound of each of the components, we obtain +DKL(pns +θ1 ∥ pns +θ2) ≤ ns +� �16B2δ2(1 + � +v∈S\s λs,v)2 +σ2y ++ 8Bδ +� +1 + +� +v∈S\s +λs,v� ++ +8B2δ2(1 + � +v∈S\s λs,v)2 +σ2x +� +p(z)p(z′)dzdz′ += ns +�� 1 +σ2y ++ +1 +2σ2x +� +16B2δ2� +1 + +� +v∈S\s +λs,v�2 ++ 8Bδ +� +1 + +� +v∈S\s +λs,v�� +. +(III) The minimax lower bound +We have that +DKL(pn +θ1 ∥ pn +θ2) = +� +s∈S +DKL(pns +θ1 ∥ pns +θ2) +≤ +� +s∈S +ns +�� 1 +σ2y ++ +1 +2σ2x +� +16B2δ2� +1 + +� +v∈S\s +λs,v�2 ++ 8Bδ +� +1 + +� +v∈S\s +λs,v�� +. +21 + +Consequently, +inf +ˆθn +sup +P ∈P +EP +� +∥ˆθn−θ(P)∥2 +� +≥δ +2 +� +� +� +�1− +� +s∈S ns +�� +1 +σ2y + +1 +2σ2x +� +16B2δ2� +1+� +v∈S\s λs,v�2 ++8Bδ +� +1+� +v∈S\s λs,v�� ++log 2 +log |V| +� +� +� +� +≥δ +2 +� +� +� +�1− +� +s∈S ns +�� +1 +σ2y + +1 +2σ2x +� +16B2δ2� +1+� +v∈S\s λs,v�2 ++8Bδ +� +1+� +v∈S\s λs,v�� ++log 2 +2mB(dx + 3) log(2√m) +� +� +� +�. +We choose δ = +√ +mB(dx+3) log(2√m) +4B � +s∈S ns +� +1+� +v∈S\s λs,v�2 , then +1 − +� +s∈S ns +�� +1 +σ2y + +1 +2σ2x +� +16B2δ2� +1 + � +v∈S\s λs,v�2 ++ 8Bδ +� +1 + � +v∈S\s λs,v�� ++ log 2 +2mB(dx + 3) log(2√m) +≥ 1 − +� 1 +σ2y ++ +1 +2σ2x +� +log(2√m) +2 � +s∈S ns +� +1 + � +v∈S\s λs,v +�2 − +1 +� +mB(dx + 3) +− +1 +2mB(dx + 3) +≥ 1 − +� 1 +σ2y ++ +1 +2σ2x +� +log(2√m) +2 � +s∈S ns +� +1 + � +v∈S\s λs,v +�2 − 1 +2 − 1 +8. +If � +s∈S ns +� +1 + � +v∈S\s λs,v�2 +≥ 2 +� +1 +σ2y + +1 +2σ2x +� +log(2√m), then +inf +ˆθn +sup +P ∈P +EP +� +∥ˆθn−θ(P)∥2 +� +≥ 1 +2 × +� +mB(dx + 3) log(2√m) +4B � +s∈S ns +� +1 + � +v∈S\s λs,v�2 × +� +1 − 1 +4 − 1 +2 − 1 +8 +� += +� +m(dx + 3) log(2√m) +64 +√ +B � +s∈S ns +� +1 + � +v∈S\s λs,v�2 . +This completes the proof. +H +Proof of Lemma 2 +The proof of Lemma 2 is divided into two parts (i) and (ii). We compute them separately: +H.1 +Proof of Part (i) +We summarize the model as follows +ws ∼ Bern +� +ϕ +�� +ψs + +� +v∈S\s +γs,vψv�⊤ +φ(xs) +�� +. +Let ψ = {ψs}s∈S. Let Vs be 1/(2√m)-packing of the unit ∥ · ∥2-balls with cardinality at least +(2√m)2B. We now choose a set V = δ(Vs1 × Vs2 ×... × Vsm). We see that +|V| ≥ (2√m)2mB. +Proof. We have that +∥ψ1 − ψ2∥2 = +�� +s∈S +∥ψs +1 − ψs +2∥2 +2 ≥ δ/2. +22 + +Moreover, +DKL(pn +ψ1 ∥ pn +ψ2) = +� +s∈S +DKL(pns +ψ1 ∥ pns +ψ2). +We first find upper bound of DKL(pns +ψ1 ∥ pns +ψ2). Since the data is independent, we have that +DKL(pns +ψ1 ∥ pns +ψ2) = nsDKL(p1 +ψ1 ∥ p1 +ψ2) += ns +� +ϕ +�� +ψs +1 + +� +v∈S\s +γs,vψv +1 +�⊤ +φ(xs) +� +log +ϕ +�� +ψs +1 + � +v∈S\s γs,vψv +1 +�⊤ +φ(xs) +� +ϕ +�� +ψs +2 + � +v∈S\s γs,vψv +2 +�⊤ +φ(xs) +� ++ ϕ +� +− +� +ψs +1 + +� +v∈S\s +γs,vψv +1 +�⊤ +φ(xs) +� +log +ϕ +� +− +� +ψs +1 + � +v∈S\s γs,vψv +1 +�⊤ +φ(xs) +� +ϕ +� +− +� +ψs +2 + � +v∈S\s γs,vψv +2 +�⊤ +φ(xs) +� +� +. +The first component: +ϕ +�� +ψs +1+ +� +v∈S\s +γs,vψv +1 +�⊤ +φ(xs) +� +log +ϕ +�� +ψs +1 + � +v∈S\s γs,vψv +1 +�⊤ +φ(xs) +� +ϕ +�� +ψs +2 + � +v∈S\s γs,vψv +2 +�⊤ +φ(xs) +� +≤ +�����log +� +1 + e +− +� +ψs +2+� +v∈S\s γs,vψv +2 +�⊤ +φ(xs)� +− log +� +1 + e +− +� +ψs +1+� +v∈S\s γs,vψv +1 +�⊤ +φ(xs)������ +(⋆) +≤ +��� +� +ψs +2 + +� +v∈S\s +γs,vψv +2 +�⊤ +φ(xs) − +� +ψs +1 + +� +v∈S\s +γs,vψv +1 +�⊤ +φ(xs) +��� +≤ 4Bδ +� +1 + +� +v∈S\s +γs,v� +, +where (⋆) follows from the fact that the SoftPlus function log(1 + ex) is 1-Lipschitz. In particular, +�� log(1 + ex1) − log(1 + ex2) +�� = +���� +� x2 +x1 +ex +1 + ex dx +���� ≤ +���� +� x2 +x1 +1dx +���� = +��x1 − x2 +��. +Similarly, for the second component, we also have +ϕ +� +− +� +ψs +1 + +� +v∈S\s +γs,vψv +1 +�⊤ +φ(xs) +� +log +ϕ +� +− +� +ψs +1 + � +v∈S\s γs,vψv +1 +�⊤ +φ(xs) +� +ϕ +� +− +� +ψs +2 + � +v∈S\s γs,vψv +2 +�⊤ +φ(xs) +� +≤ 4Bδ +� +1 + +� +v∈S\s +γs,v� +. +Thus, +DKL(pns +ψ1 ∥ pns +ψ2) ≤ 8Bδ +� +1 + +� +v∈S\s +γs,v� +ns. +Consequently, +DKL(pn +ψ1 ∥ pn +ψ2) ≤ 8Bδ +� +s∈S +ns +� +1 + +� +v∈S\s +γs,v� +. +So, we have that +inf +ˆψn +sup +P ∈P +EP +� +∥ ˆψn − ψ(P)∥2 +� +≥ δ +4 +� +�1 − +8Bδ � +s∈S ns +� +1 + � +v∈S\s γs,v� ++ log 2 +log |V| +� +� +23 + +≥ δ +4 +� +�1 − +8Bδ � +s∈S ns +� +1 + � +v∈S\s γs,v� ++ log 2 +2mB log(2√m) +� +� . +We choose δ = +m log(2√m) +16 � +s∈S ns +� +1+� +v∈S\s γs,v�, then +1 − +8Bδ � +s∈S ns +� +1 + � +v∈S\s γs,v� ++ log 2 +2mB log(2√m) +≥ 1 +4. +Thus, +inf +ˆψn +sup +P ∈P +EP +� +∥ ˆψn − ψ(P)∥2 +� +≥ 1 +4 × +mB log(2√m) +16B � +s∈S ns +� +1 + � +v∈S\s γs,v� × 1 +4 += +m log(2√m) +256 � +s∈S ns +� +1 + � +v∈S\s γs,v�. +This completes the proof of part (i). +H.2 +Proof of Part (ii) +Proof. We summarize the model as follows +ys = +� +(1 − ws) +� +βs +0 + +� +v∈S\s +ηs,vβv +0 +� ++ ws� +βs +1 + +� +v∈S\s +ηs,vβv +1 +��⊤ +φ(xs) + ϵs, +ϵs ∼ N(0, σ2). +Let β = {βs +0, βs +1}s∈S. Let V0s and V1s be 1/(2√m)-packing of the unit ∥ · ∥2-balls with cardinality +at least (2√m)2B. Let Vs = V0s × V1s. We now choose a set V = δ(Vs1 × Vs2 ×... × Vsm). We see +that +|V| ≥ (2√m)4mB. +We have that +∥β1 − β2∥2 = +�� +s∈S +� +∥(βs +0)1 − (βs +0)2∥2 +2 + ∥(βs +1)1 − (βs +1)2∥2 +2 +� +≥ δ/ +√ +2. +Moreover, +DKL(pn +β1 ∥ pn +β2) = +� +s∈S +DKL(pns +β1 ∥ pns +β2) = +� +s∈S +nsDKL(p1 +β1 ∥ p1 +β2). +In addition, +DKL(p1 +β1 ∥ p1 +β2) += +1 +2σ2 +�� +(1 − ws) +� +(βs +0)1 + +� +v∈S\s +ηs,v(βv +0)1 +� ++ ws� +(βs +1)1 + +� +v∈S\s +ηs,v(βv +1)1 +��⊤ +φ(xs) +− +� +(1 − ws) +� +(βs +0)2 + +� +v∈S\s +ηs,v(βv +0)2 +� ++ ws� +(βs +1)2 + +� +v∈S\s +ηs,v(βv +1)2 +��⊤ +φ(xs) +�2 +≤ +1 +2σ2 +�� +(1 − ws) +� +2δ + +� +v∈S\s +ηs,v2δ +� ++ ws� +2δ + +� +v∈S\s +ηs,v2δ +�� +∥φ(xs)∥2 +�2 +≤ 8B2δ2 +σ2 +� +1 + +� +v∈S\s +ηs,v�2 +, +24 + +Thus, +DKL(pn +β1 ∥ pn +β2) ≤ 8B2δ2 +σ2 +� +s∈S +ns +� +1 + +� +v∈S\s +ηs,v�2 +. +Consequently, +inf +ˆβn +sup +P ∈P +EP +� +∥ˆβn − β(P)∥2 +� +≥ +δ +2 +√ +2 +� +� +�1 − +8B2δ2 +σ2 +� +s∈S ns +� +1 + � +v∈S\s ηs,v�2 ++ log 2 +log |V| +� +� +� +≥ +δ +2 +√ +2 +� +� +�1 − +8B2δ2 +σ2 +� +s∈S ns +� +1 + � +v∈S\s ηs,v�2 ++ log 2 +4mB log(2√m) +� +� +� . +We choose δ2 = +mB log(2√m) +4 B2 +σ2 +� +s∈S ns +� +1+� +v∈S\s ηs,v +�2 , then +1 − +8B2δ2 +σ2 +� +s∈S ns +� +1 + � +v∈S\s ηs,v�2 ++ log 2 +4mB log(2√m) += 1 − 2mB log(2√m) + log 2 +4mB log(2√m) +≥ 1 +4. +Thus, +inf +ˆβn +sup +P ∈P +EP +� +∥ˆβn − β(P)∥2 +� +≥ +1 +2 +√ +2 +� +� +� +� +4mB log(2√m) +2 8B2 +σ2 +� +s∈S ns +� +1 + � +v∈S\s ηs,v +�2 × 1 +4 += +σ +16 +√ +2 +� +� +� +� +m log(2√m) +B � +s∈S ns +� +1 + � +v∈S\s ηs,v +�2 . +This completes the proof of part (ii). +I +Further cases of the minimax lower bounds +In Lemma 1 and 2, we have presented the minimax lower bounds when ys +i ∈ R and xs +i ∈ Rdx. Here, +we briefly describe the other cases. +I.1 +Further cases of Lemma 1 +In this section, we further detail the lower bound for binary outcomes and binary proxy variables. In +this case, we need to re-derive the upper bound of +pθ1(w = j|z)DKL +� +pθ1(y|w = j, z) +��pθ2(y|w = j, z′) +� +and +DKL +� +pθ1(x|z) +��pθ2(x|z′) +� +, +where j = 1, 2. Using similar derivations as before for the quantity DKL +� +pθ1(w|z) +��pθ2(w|z′) +� +, we +have that +pθ1(w = j|z)DKL +� +pθ1(y|w = j, z) +��pθ2(y|w = j, z′) +� +≤ 8Bδ +� +1 + +� +v∈S\s +λs,v� +, +and +DKL +� +pθ1(x|z) +��pθ2(x|z′) +� +≤ dx8Bδ +� +1 + +� +v∈S\s +λs,v� +. +Combining the results, we have +DKL(pn +θ1 ∥ pn +θ2) = +� +s∈S +DKL(pns +θ1 ∥ pns +θ2) ≤ +� +s∈S +ns8(dx + 3)Bδ +� +1 + +� +v∈S\s +λs,v� +. +25 + +Consequently, we have that +inf +ˆθn +sup +P ∈P +EP +� +∥ˆθn−θ(P)∥2 +� +≥ δ +2 +� +�1− +� +s∈S ns8(dx + 3)Bδ +� +1 + � +v∈S\s λs,v� ++log 2 +2mB(dx + 3) log(2√m) +� +�. +We choose δ = +m log(2√m) +8 � +s∈S ns +� +1+� +v∈S\s λs,v +�, then +1 − +� +s∈S ns8(dx + 3)Bδ +� +1 + � +v∈S\s λs,v� ++log 2 +2mB(dx + 3) log(2√m) +≥ 3 +8. +Thus, +inf +ˆθn +sup +P ∈P +EP +� +∥ˆθn−θ(P)∥2 +� +≥ +3mB log(2√m) +128 � +s∈S nsB +� +1 + � +v∈S\s λs,v +�. +Remark 1. Note that the derivation in this Section and in Section H.1 give us enough tools to +compute the minimax lower bounds for any further case, i.e., any combination of the outcomes and +proxy variables (binary or continuous). The key is to initially find the upper bound of DKL(pn +θ1 ∥ pn +θ2) +based on the constructed packing. Then, using Fano’s method to obtain the minimax lower bounds. +I.2 +Further cases of Lemma 2 +Note that the lower bound of Lemma 2, part (i) has only one case since we only focus on binary +treatment, and it is presented in the main text. For part (ii), consider ys +i ∈ {0, 1}, then the model of +the outcomes would follow a Bernoulli distribution. Reusing the scheme in Section H.2, we need to +find the new upper bound of DKL(pn +β1 ∥ pn +β2). In particular, +DKL(pn +β1 ∥ pn +β2) = +� +s∈S +ns +� +ϕ(v1) log ϕ(v1) +ϕ(v2) + ϕ(−v1) log ϕ(−v1 +ϕ(−v2) +� +, +where vj = +� +(1 − ws) +� +(βs +0)j + � +v∈S\s ηs,v(βv +0)j +� ++ ws� +(βs +1)j + � +v∈S\s ηs,v(βv +1)j +��⊤ +φ(xs). We +have that +ϕ(v1) log ϕ(v1) +ϕ(v2) ≤ +����(1 − ws) +� +(βs +0)1 − (βs +0)2 + +� +v∈S\s +ηs,v[(βv +0)1 − (βv +0)2] +� ++ ws� +(βs +1)1 − (βs +1)2 + +� +v∈S\s +ηs,v[(βv +1)1 − (βv +1)2] +����� +2 +∥φ(xs)∥2 +≤ 4Bδ +� +1 + +� +v∈S\s +γs,v� +, +Similarly, ϕ(−v1) log ϕ(−v1 +ϕ(−v2) ≤ 4Bδ +� +1 + � +v∈S\s γs,v� +. Hence, +DKL(pn +β1 ∥ pn +β2) ≤ 8Bδ +� +s∈S +ns +� +1 + +� +v∈S\s +ηs,v� +. +Using similar technique in Section H.2, we obtain +inf +ˆβn +sup +P ∈P +EP +� +∥ˆβn − β(P)∥2 +� +≥ +m log(2√m) +32 +√ +2 � +s∈S ns +� +1 + � +v∈S\s ηs,v +�. +We observe that the lower bound is similar to that of Lemma 2, part (i) since they are both lower +bounds of a binary response variable. The constant in this bound is larger (1/(32 +√ +2)) than that +of Lemma 2, part (i) (1/256). This is expected since there are more parameters in this model, i.e., +{βs +0, βs +1}s∈S, as compared to the model in Lemma 2, part (i) ({ψs}s∈S). +26 + +J +Description of IHDP data +This section describe details of the IHDP data, which was skipped in the main text due to limited +space. +The Infant Health and Development Program (IHDP) is a randomized study on the impact of specialist +visits (the treatment) on the cognitive development of children (the outcome). The dataset consists of +747 records with 25 covariates describing properties of the children and their mothers. The treatment +group includes children who received specialist visits and control group includes children who did not +receive. Further details are presented in Appendix. For each child, a treated and a control outcome are +simulated using the numerical schemes provided in the NPCI package (Dorie 2016), thus allowing us +to know the true individual treatment effect. We use 10 replicates of the dataset in this experiment. +For each replicate, we divide into three sources, each consists of 249 data points. For each source, we +use the first 50 data points for training, the next 100 for testing and the rest 99 for validating. We +report the mean and standard error of the evaluation metrics over 10 replicates of the data. +—– END —– +27 + diff --git a/JNAyT4oBgHgl3EQffviC/content/tmp_files/load_file.txt b/JNAyT4oBgHgl3EQffviC/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..34a2381fa0ad92489dbe78e21538e32d02a48c1d --- /dev/null +++ b/JNAyT4oBgHgl3EQffviC/content/tmp_files/load_file.txt @@ -0,0 +1,2128 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf,len=2127 +page_content='An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects Thanh Vinh Vo1 Arnab Bhattacharyya1 Young Lee2 Tze-Yun Leong1 1School of Computing, National University of Singapore 2Roche AG and Harvard University {votv,arnabb,leongty}@nus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='sg Abstract We propose a new causal inference framework to learn causal effects from multiple, decentralized data sources in a federated setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We introduce an adaptive transfer algorithm that learns the similarities among the data sources by utilizing Random Fourier Features to disentangle the loss function into multiple components, each of which is associated with a data source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The data sources may have different distributions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' the causal effects are independently and systematically incorporated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The proposed method estimates the similarities among the sources through transfer coefficients, and hence requiring no prior information about the similarity measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The heterogeneous causal effects can be estimated with no sharing of the raw training data among the sources, thus minimizing the risk of privacy leak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We also provide minimax lower bounds to assess the quality of the parameters learned from the disparate sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The proposed method is empirically shown to outperform the baselines on decentralized data sources with dissimilar distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 1 Introduction Many important questions posed in the natural and social sciences are causal in nature: What are the long-term effects of mild Covid-19 infection on lung and brain functions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' How is mortality rate influenced by the daily air pollution?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' How would a welfare policy affect employment rate of a minority group?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal inference has been applied in a wide range of domains, including economics (Finkelstein and Hendren 2020), medicine (Henderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Powers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2018), and social welfare (Gutman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The large amount of experimental and/or observation data needed to accurately estimate the causal effects often resides across different sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In most cases, the data sources cannot be combined to support centralized processing due to some inherent organizational or policy constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, in many countries, medical or health records of cancer patients are kept strictly confidential at local hospitals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' direct exchange or sharing of the records among hospitals, especially for research purposes, are not allowed (Gostin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The main research question is: How to securely access these diverse data sources to build an effective global causal effect estimator, while balancing the risk of breaching data privacy and confidentiality?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Current causal inference approaches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2018) require the shared data to be put in one place for processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Current federated learning algorithms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Sattler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020) allow collaborative learning of joint models based on non-independent and identically distributed (non iid) data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' they cannot, however, directly support causal inference as the different data sources might have disimilar distributions that would lead to biased causal effect estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, the demographic profile and average age for cancer patients from two different hospitals may be drastically different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' If the two data sets are combined to support causal inference, one distribution may dominate over the other, leading to biased causal effect estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 36th Conference on Neural Information Processing Systems (NeurIPS 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='00346v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='LG] 1 Jan 2023 We introduce a new approach to federated causal inference from multiple, decentralized, and disimi- larly distributed data sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our contributions are summarized as follows: We propose a new federated causal inference algorithm, called CausalRFF 1, based on the structural causal model (SCM) (Pearl 2009a), leveraging the Random Fourier Features (Rahimi and Recht 2007) for federated estimation of causal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Random Fourier Features allow the objective function to be divided into multiple components to support federated training of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We perform federated causal inference with CausalRFF from data sources with different distribu- tions through the adaptive kernel functions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' the inference is carried out without sharing raw data among the sources, hence minimizing the risk of privacy leak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We provide the minimax lower bounds to explicate the limits of estimation and optimization procedures in our federated causal inference framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our work is an important step toward privacy-preserving causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We explore the possibility of combining CausalRFF with multiparty differential privacy at the end of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2 Related Work Little work has been done on combining causal inference with federated learning in a privacy preserving manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' On causal inference: The authors Hill (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Alaa and van der Schaar (2017, 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Künzel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Nie and Wager (2020) proposed learning causal effects directly from local data sources;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' these methods adopt the standard ignorability assumption (Rosenbaum and Rubin 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Madras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019) adapted the structural causal model (SCM) of Pearl (1995) to estimate the causal effects with the existence of latent confounding variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our work is closely related to and extends the notion of transportability, where Pearl and Bareinboim (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bareinboim and Pearl (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020) and related work formulated and provided theoretical analysis of intervention tools on one population to compute causal effects on another population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020) generalized transportability to support identification of causal effects in the target domain from the observational and interventional distributions on subsets of observable variables, forming a foundation for drawing conclusions for observational and experimental data (Tsamardinos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bareinboim and Pearl 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal inference from multiple, decentralized, dissimilarly distributed sources that cannot be combined or processed in a central site is not addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Recently, Aglietti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020), conducted randomized experiments on the source to collect data and then estimated a joint model of the interventional data from source population and the observational data from target population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our work is different in that we do not work with randomized data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' we estimate causal effects through transfers using only observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This corresponds to an important setting in real-life, where only retrospective observational data are available, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Covid-19 related case and intervention records, bank and financial transaction records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' On federated learning: Federated learning enables collaboratively learning a shared prediction model while keeping all the training data decentralized at source (McMahan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Some federated learning approaches combine federated stochastic gradient descent (Shokri and Shmatikov 2015) and federated averaging (McMahan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017) to address regression problems Álvarez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Zhe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' de Wolff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Joukov and Kuli´c (2020) and Hard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Sattler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Mohri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Recent federated learning algorithms allow collaborative learning of joint deep neural network models based on non-iid data (Sattler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' All these algorithms, however, do not directly support causal inference as the different data sources might have dissimilar distributions that would lead to biased causal effect estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Little work has been focused on federated estimation of causal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Vo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2022) proposed a Bayesian approach that estimates posterior distributions of causal effects based on Gaussian processes, which does not allow dissimilar distributions of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2021) estimated average treatment effect (ATE) and average treatment effect on the treated (ATT) and assumed that the confounders are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our work, on the other hand, estimate conditional average treatment effect (CATE) (which is also known as individual treatment effect, ITE) and average treatment effect (ATE) under the existence of latent confounders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We utilize Random Fourier 1Source code: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='com/vothanhvinh/CausalRFF 2 Features to build an integrative framework of causal inference in a federated setting that allows for dissimilar data distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 3 The Proposed Model In this section, we first detail the problem formalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We then present the causal effects of interest and the scheme to estimate them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Lastly, we describe the assumptions and the structural equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Problem Description Problem setting & notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Suppose we have m sources of data, each denoted by Ds = {(ws i, ys i, xs i)}ns i=1, where s ∈ S := {s1, s2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' , sm}, and the quantities ws i, ys i and xs i are the treatment assignments, observed outcome associated with the treatment, and covariates of individual i in source s, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These data sources Ds are located in different locations and their distributions might be completely different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' All the sources share the same causal graph as shown in Figure 1, but the data distributions may be different, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ps1(x, w, y) ̸= ps2(x, w, y), where ps1(·) and ps2(·) denote the two distributions on two sources s1 and s2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, the marginal and the conditional distributions with respect to these variables can also be different (or similar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The objective is to develop a global causal inference model that satisfies both of the following two conditions: (i) the causal inference model can be trained in a private setting where the data of each source are not shared to an outsider, and (ii) the causal inference model can incorporate data from multiple sources to improve causal effects estimation in each specific source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal effects of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Given a causal model trained under the aforementioned setting, we are interested in estimating the conditional average treatment effect (CATE)2 and average treatment effect (ATE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Y , W, X be random variables denoting the outcome, treatment, and proxy variable, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, the CATE and ATE are defined as follows (Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Madras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2019) τ(x) := E � Y |do(W=1), X=x � − E � Y |do(W=0), X=x � , τ := E[τ(X)], (1) where do(W=w) represents that a treatment w ∈ {0, 1} is given to the individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This definition is followed from Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Madras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Given a set of n new individuals whose covariates/observed proxy variables are {xi}n i=1, the CATE and ATE in this sub-population are obtained by τ(xi) and τ = �n i=1 τ(xi)/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Z Y W X Figure 1: The causal graph with latent confounder Z, treatment W, outcome Y , covariate/proxy variable X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Source (1) Source (2) Source (3) Server Figure 2: An example of our proposed model with three sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The objective function J ≃ J(1) +J(2) +J(3) is decomposed to 3 components, each associated with a source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The central task to estimate CATE and ATE is to find E[Y | do(W = w), X = x].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since the data distribution of each source might be different from (or similar to) each other, we use the notation E[Y |do(W = ws, X = xs] to denote the expectation of the outcome Y under an intervention on W of an individual in source s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' With the existence of the latent confounder Z, we can further expand this quantity using do-calculus (Pearl 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, from the backdoor adjustment formula, we have E � Y |do(W = ws), X = xs� = � E � Y |W = ws, Z = zs� ps(zs|xs)dzs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2) Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2) shows that the causal effect is identifiable if we can find the conditional distributions ps(ys|ws, zs) and ps(zs|xs) for each source s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The second distribution can be further expanded by ps(zs|xs) = � ws � ps(z|xs, ys i, ws)ps(ys|xs, ws)ps(ws|xs)dys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Following the forward sampling strategy, the remaining is to find the following distributions ps(ws|xs), ps(ys|xs, ws), ps(zs|xs, ys, ws), ps(ys|ws, zs), (3) 2Also called individual treatment effect (ITE) 3 and then systematically draw samples from these estimated distributions to obtain the empirical expectation of Y given do(W = ws) and X = xs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The CATE and ATE are identifiable if we are able to learn the distributions in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3), which involve latent confounder Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017) showed that this is possible if Z has a relationship to the observed variables X, and there are many cases that it is identifiable such as: Z is categorical and X is a Gaussian mixture model (Anandkumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2014), X includes three independent views of Z (Goodman 1974;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Allman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Anandkumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2012), Z is a multivariate binary and X are noisy functions of Z (Jernite et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017), to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Following the works by Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Madras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019), we use variational inference in the spirit of the variational auto-encoder (VAE) to recover the latent confounders, since it can learn a rich class of latent-variable models, and thus recovering the causal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Identification of our work follows closely from the literature, however our main contribution is in the federated setting of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Please refer to Appendix for the proof of identifiability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 The Causal Graph and Assumptions Since our method adopts the SCM approach with the causal graph in Figure 1, there are some implicit assumptions that follow from the axioms and properties of SCM: (A1) Consistency: W = w =⇒ Y (w) = Y , this follows from the axioms of SCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A2) No interference: the treatment on one subject does not affect the outcomes of another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This is because the outcome has only a single treatment node as its parent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A3) Positivity: every subject has some positive probability to be assigned to every treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These assumptions are standard in any causal inference algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' One can find further discussion in Pearl (2009a,b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Morgan and Winship (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For our proposed federated setting, we make two additional assumptions as follows: (A4) The individuals in all sources have the same set of common covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A5) Any individual does not exist in more than one source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Assumption (A4) has been implicitly shown in our setup since all the sources would share the same causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This is a reasonable assumption as we intend to build a unified model on all of the data sources, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', decentralized data in Choudhury et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Vaid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Flores et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020) satisfy this assumption for federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Assumption (A5) is to ensure that no individuals would dominate the other individuals when training the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, if an individual appears in all of the sources, the trained model would be biased by data of this individual (there is imbalance caused by the use of more data from this particular individual than the others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, this condition would ensure that such bias does not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In practice, Assumption (A5) sometimes does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To address such a problem, we perform a pre-training step to exclude such duplicated individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This step would use a one-way hash function to perform a secured matching procedure that identifies duplicated individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Details of the pre-training step are presented in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3 The Structural Equations This section presents how the causal relations are modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since Z is the root node in the causal graph, we model it as a multivariate normal distribution: Z ∼ N(µ, σ2 zIdz) for the all sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We now detail the structural equations of Y , W and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let V be a univariate variable that represents a node or a dimension of a node in the causal graph (Figure 1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', V can be Y , W or a dimension of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let pa(V ) be set of V ’s parent variables in the causal graph, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='e, the nodes with directed edges to V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We model the structural equation of V in two cases as follows: if V is continuous: V = fv(pa(V )) + ϵv, if V is binary: V = 1[ϕ(fv(pa(V ))) > ϵv], (4) where ϵv ∼ N(0, σ2 v) for the former case and ϵv ∼ U[0, 1] for the latter case, ϕ(·) is the logistic function and 1(·) is the indicator function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The latter case implies that V given pa(V ) follows Bernoulli distribution with p(V = 1|pa(V )) = ϕ(fv(pa(V ))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Furthermore, if W ∈ pa(V ), then we further model fv(pa(V )) = (1 − W)fv0(pa(V ) \\ {W}) + Wfv1(pa(V ) \\ {W}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (5) Example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' If Y ∈ R, W ∈ {0, 1} and Xk ∈ R (Xk is the k–th dimension of X), then the structural equations are as follows: Y = (1 − W)fy0(Z) + Wfy1(Z) + ϵy, W = 1[ϕ(fw(Z)) > ϵw], Xk = fxk(Z) + ϵXk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the subsequent sections, we present how to learn the functions fv (v ∈ {y0, y1, w, x}) in a federated setting and then use them to estimate the causal effects of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 4 4 CausalRFF: An Adaptive Federated Inference Algorithm This section presents a new federated algorithm to learn the distributions in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The central task is to decompose the objective function into multiple components, each associated with a source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Learning Distributions Involving Latent Confounder To estimate causal effects, we need to estimate the four quantities detailed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This section presents how to learn ps(zs|xs, ys, ws) and ps(ys|ws, zs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since the marginal likelihood has no analytical form, we learn the above distributions using variational inference which maximizes the evidence lower bound (ELBO) L = � s∈S ns � i=1 � Eq � log ps(ys i|ws i, zs i) + log ps(ws i|zs i) + log ps(xs i|zs i) � − KL[q(zs i)∥p(zs i)] � , (6) where q(zs) = N(zs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' fq(ys, ws, xs), σ2 qI) is the variational posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The function fq(·) is modeled as follows: fq(ys, ws, xs) = (1 − ws)fq0(ys, xs) + wsfq1(ys, xs), where fq0 and fq1 are two functions to be learned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The density functions ps(ys|ws, zs), ps(ws|zs) and ps(xs|zs) are obtained from the structural equations as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Please refer to Appendix for details on derivation of the ELBO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Adaptive modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since the observed data from each source might come from different (or similar) distributions, we would model them separately and adaptively learn their similarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, we propose a kernel-based approach to learn these distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To proceed, we first obtain the empirical loss function �L from negative of the ELBO L by generating M samples of each latent confounder Z using the reparameterization trick (Kingma and Welling 2013): zs i[l] = fq(ys i, ws i, xs i) + σqϵs i[l], where ϵs i[l] is drawn from the standard normal distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We obtain a complete dataset �Ds = M � l=1 � (ws i, ys i, xs i, zs i[l]) �ns i=1, ∀s ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (7) Using this complete dataset, we minimize the following objective function J = �L + � c∈A R(fc) (8) with respect to fc, where A = {y0, y1, w, x, q0, q1}, and R(·) denotes a regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The minimizer of J would result in the following form of fc fc(us) = � v∈S nv×M � j=1 κ(us, uv j)αv j, (9) where uv j is obtained from the j–th tuple of the dataset ˜Dv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Details are presented in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since data from the sources might come from a completely different (or similar) distribution, we would use an adaptive kernel to measure their similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, let k(us, uv) be typical kernel function such as squared exponential kernel, rational quadratic kernel, or Matérn kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The kernel used in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (9) is as follows: κ(us, uv) = λs,vk(us, uv), if s ̸= v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' otherwise, κ(us, uv) = k(us, uv), where λs,v ∈ [0, 1] is the adaptive factor and it is learned from the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (9) indicates that computing fc(us) requires collecting all data points from all sources, and so the objective function in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (8) cannot be optimized in a federated setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Next, we present a method known as Random Fourier Features to address the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Random Fourier Features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We show how to adapt Random Fourier Features (Rahimi and Recht 2007) into our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let k(u, u′) be any translation-invariant kernel (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', squared exponential kernel, rational quadratic kernel, or Matérn kernel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, by Bochner’s theorem (Wendland 2004, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6), it can be written in the following form: k(u, u′) = � eiω⊤(u−u′)s(ω)dω = � cos � ω⊤(u − u′) � s(ω)dω, (10) where s(ω) is a spectral density function associated with the kernel (please refer to Appendix for spectral density of some popular kernels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The last equality follows from the fact that the kernel function is real-valued and symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This type of kernel can be approximated by 5 k(u, u′) ≃ B−1 B � b=1 cos(ω⊤ b (u − u′)) = φ(u)⊤φ(u′), {ωb}B b=1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ∼ s(ω), (11) where φ(u) = B− 1 2 [cos(ω⊤ 1 u),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', cos(ω⊤ Bu), sin(ω⊤ 1 u),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', sin(ω⊤ Bu)]⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The last equality follows from the trigonometric identity: cos(u − v) = cos u cos v + sin u sin v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Substituting the above random Fourier Features into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (9), we obtain fc(us) ≃ � θs c + � v∈S\\{s} λs,vθv c �⊤ φ(us), (12) where θs c = �ns i=1 φ(us)αs i and λs,v (s, v ∈ S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' While optimizing the objective function J, instead of learning αs i, we can directly consider θs as parameter to be optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This has been used in several works such as Rahimi and Recht (2007);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Chaudhuri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Rajkumar and Agarwal (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This approximation allows us to rewrite the objective function J as a summation of local objective functions in each source: J ≃ � s∈S J(s), where J(s) = �L(s) + m−1 � v∈S ζ∥θv∥2 2, (13) where ζ ∈ R+ is a regularizer factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Each component J(s) is associated with the source s and it can be computed with the local data in this source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, it enables federated optimization for the objective function J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Figure 2 illustrates our proposed federated causal learning algorithm with three sources, where θ denotes the set of all parameters to be learned including θs and λs,v from all the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The federated learning algorithm can be summarized as follows: First, each source computes the local gradient, ∇θJ(s), using its own data and sends to the server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The server, then, collects these gradients from all sources and subsequently updates the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Next, the server broadcasts the new model to all the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Minimax lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We now compute the minimax lower bound of the proposed model, which gives the rate at which our estimator can converge to the population quantity of interest as the sample size increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We first state the following result that concerns the last two terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3): Lemma 1 (With presence of latent variables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let θ = {θs c : c ∈ {y0, y1, x, w}, s ∈ S} and ˆθ be its estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let ys i ∈ R and xs i ∈ Rdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let S\\s = S \\ {s}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, inf ˆθ sup P ∈P EP � ∥ˆθ − θ(P)∥2 � ≥ � m(dx + 3) log(2√m) 64 √ B � s∈S ns � 1 + � v∈S\\sλs,v�2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (14) The LHS of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (14) can be seen as the worst case of the best estimator, whereas the RHS depicts the behavior of the convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The bounds do not only depend on the number of samples (ns, training size) of each source but also the adaptive factors λs,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' When the adaptive factors are small, the lower bounds are large since data from a source s are only used to learn its own parameter θs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' When the adaptive factors are large, the lower bounds are smaller, which suggests that data from a source would help infer parameters associated with the other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This bound gives a guarantee on how data from all the sources impact the learned parameters that modulate the two distributions ps(zs|xs, ys, ws) and ps(ys|ws, zs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The proof of Lemma 1 can be found in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Learning Auxiliary Distributions The previous section has shown how to learn ps(zs|xs, ys, ws) and ps(ys|ws, zs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To compute treat- ment effects, we need to learn two more conditional distributions, namely ps(ws|xs) and ps(ys|xs, ws).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since all the variables in these two distributions are observed, we estimate them using maximum likelihood estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the following, we present a federated setting to learn ps(ws|xs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similar to the previous section, the objective function here can also be decomposed into m components as follows: Jw ≃ � s∈S J(s) w , where J(s) w = �ns i=1 ℓ(ws i, ϕ(g(xs i))) + m−1 � v∈S ζw∥ψv∥2 2 and g(xs i) = � v∈S φ(xs i)⊤(ψs + γs,vψv), γs,v ∈ [0, 1] is the adaptive factor, ψs is the parameter associ- ated with source s, and ℓ(·) denotes the cross-entropy loss function since ws i is a binary value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The first component of J(s) w is obtained from the negative log-likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Learning of ps(ys|xs, ws) is 6 similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For convenience, in the subsequent analyses, we denote the parameters and adaptive factors of this distribution as βs and ηs,v, where s, v ∈ S and s ̸= v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The next lemma shows the minimax lower bound for the first two sets of parameters ψ and β in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3), but this time without involving the latent variables: Lemma 2 (Without the presence of latent variables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let ψ = {ψs}m s=1, β = {βs}m s=1 and ˆψ, ˆβ be their estimates, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let ys i ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, (i) inf ˆψ sup P ∈P EP � ∥ ˆψ − ψ(P)∥2 � ≥ m log(2√m) 256 � s∈S ns � 1 + � v∈S\\s γs,v�, (15) (ii) inf ˆβ sup P ∈P EP � ∥ˆβ − β(P)∥2 � ≥ σ 2 9 2 � m log(2√m) B � s∈S ns � 1 + � v∈S\\s ηs,v�2 �1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (16) The proof of Lemma 2 can be found in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The bounds presented in Lemma 1 and 2 give helpful information about the number of samples to be observed and the cooperation of multiple sources of data through the transfer factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since we used variational inference and maximum likelihood to learn the parameters in our model, these methods give consistent estimation as shown in Kiefer and Wolfowitz (1956);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Van der Vaart (2000);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wang and Blei (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3 Computing Causal Effects The key to estimate causal effects in our model is to compute the outcome in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We pro- ceed by drawing samples from the distributions in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Generating samples from the con- ditional distributions ps(ws|xs), ps(ys|xs, ws), and ps(ys|ws, zs) is straightforward since they are readily available as shown in either Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' There are two options to draw samples from the posterior distribution of confounder ps(zs|xs, ys, ws).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The first one is to draw from its approximation, q(zs), since maximizing the ELBO in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 is equivalent to minimizing KL(q(zs)∥ps(zs|xs, ys, ws)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' As a second option, we note that the exact posterior of confounder can be rewritten as ps(zs|xs, ys, ws) ∝ ps(ys|zs, ws)ps(ws|zs)ps(xs|zs)p(zs), whose components on the right hand side are also available in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, we can draw from this distribution using the Metropolis-Hastings (MH) algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since Z is a multidimensional random variable, the traditional MH algorithm would require a long chain to converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We overcome this problem by using the MH with independent sampler (Liu 1996) where the proposal distribution is the variational posterior distribution q(zs) learned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The second approach would give more accurate samples since we select the samples based on exact acceptance probability of the posterior ps(zs|xs, ys, ws).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This would help estimate the CATE given xs i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The local ATE is the average of CATE of individuals in a source s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These quantities can be estimated in a local source machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To compute a global ATE, the server would collect all the local ATE in each source and then compute their weighted average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Further details are in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 5 Experiments The baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this section, we first carry out the experiments to examine the performance of CausalRFF against standard baselines such as BART (Hill 2011), TARNet (Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017), CFR- wass (CFRNet with Wasserstein distance) (Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017), CFR-mmd (CFRNet with maximum mean discrepancy distance) (Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017), CEVAE (Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2017), OrthoRF (Oprescu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2019), X-learner (Künzel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2019), R-learner (Nie and Wager 2020), and FedCI (Vo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In contrast to CausalRFF, these methods (except FedCI) do not consider causal inference within a federated setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We compare our method to these baselines trained in two ways: (a) training a global model with the combined data from all the sources, (b) using bootstrap aggregating of Breiman (1996) where m models are trained separately on each source data and then averaging the predicted treatment effects based on each trained model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Note that case (a) violates federated data setting and is only used for comparison purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In general, we expect that the performance of CausalRFF to be close to that of the performance of the baselines in case (a) when the data distribution of all the sources are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In addition, we also show that the performance of CausalRFF is better than that of the baselines in case (a) when the data distribution of all the source are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Implementation of the baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The implementation of CEVAE is from Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Implementation of TARNet, CFR-wass, and CFR-mmd are from Shalit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For these 7 1 2 3 4 5 Number of sources, m 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8 √ϵPEHE The error of CATE 1 2 3 4 5 Number of sources, m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 ϵATE The error of ATE CausalRFF Combined data Figure 3: Experimental results on DATAsame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 1 2 3 4 5 Number of sources, m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 √ϵPEHE Error of CATE 1 2 3 4 5 Number of sources, m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 ϵATE Error of ATE CausalRFF Combined data (stack) Combined data (1-hot) Figure 4: Experimental results on DATAdiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 1: Out-of-sample errors on DATAsame where top-3 performances are highlighted in bold (lower is better).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The dashes (-) in ‘ag’ (boot- strap aggregating) indicate that the numbers are the same as that of ‘cb’ (combined data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Method The error of CATE, √ϵPEHE The error of ATE, ϵATE 1 source 3 sources 5 sources 1 source 3 sources 5 sources BARTag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 X-Learnerag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 R-Learnerag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='46 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='35 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='70 OthoRFag 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 TARNetag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-wassag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-mmdag 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CEVAEag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 BARTcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 X-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 R-Learnercb 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='46 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='72 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 OthoRFcb 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='29 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 TARNetcb 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 CFR-wasscb 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-mmdcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CEVAEcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 FedCI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 CausalRFF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 methods, we use Exponential Linear Unit (ELU) activation function and fine-tune the number of nodes in each hidden later from 10 to 200 with step size of addition by 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For BART, we use package BartPy, which is readily available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For X-learner and R-learner, we use the package causalml (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For OrthoRF, we use the package econml (Microsoft Research 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For FedCI, we use the code from Vo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For all methods, the learning rate is fine-tuned from 10−4 to 10−1 with step size of multiplication by 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, the regularizer factors are also fine-tuned from 10−4 to 100 with step size of multiplication by 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We report two error metrics: ϵPEHE (precision in estimation of heterogeneous effects) and ϵATE (absolute error) to compare the methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We report the mean and standard error over 10 replicates of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Further details are presented in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Synthetic Data Data description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Obtaining ground truth for evaluating causal inference algorithm is a challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, most of the state-of-the-art methods are evaluated using synthetic or semi-synthetic datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this experiment, the synthetic data is simulated with the following distributions: zs i ∼ Cat(ρ), xs ij ∼ Bern(ϕ(aj0 + (zs i)⊤aj1)), ws i ∼ Bern(ϕ(b0 + (zs i)⊤(b1 + ∆))), ys i(0) ∼ N(sp(c0 + (zs i)⊤(c1 + ∆)), σ2 0), ys i(1) ∼ N(sp(d0 + (zs i)⊤(d1 + ∆)), σ2 1), where Cat(·), N(·), and Bern(·) denote the categorical distribution, normal distribution, and Bernoulli distribution, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ϕ(·) denotes the sigmoid function, sp(·) denotes the softplus function, and xi = [xi1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', xidx]⊤ ∈ Rdx with dx = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Herein, we convert zs i to a one-hot vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To simulate data, we randomly set the ground truth parameters as follows: ρ = [.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='34, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='26, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12]⊤, (c0, d0) = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9), (c1, d1, d1) are drawn i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='d from N(0, 2I5), aj0 and elements of aj1 are drawn i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='d from N(0, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For each source, we simulate 10 replications with ns = 1000 records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We only keep {(ys i, ws i, xs i)}ns i=1 as the observed data, where ys i = ys i(0) if ws i = 0 and ys i = ys i(1) if ws i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In each source, we use 50 data points for training, 450 for testing and 400 for validating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We report the evaluation metrics and their standard errors over the 10 replications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Result and discussion (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the first experiment, we study the performance of CausalRFF on multiple sources whose data distributions are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To do that, we simulate m = 5 sources from the same distribution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', we set the ground truth ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 for all the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We refer to this dataset as DATAsame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this experiment, we expect that the result of CausalRFF, which is trained in federated setting, is as good as training on combined data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The results in Figure 3 show that the error in two cases seem to move together in a correlated fashion, which verifies our hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In addition, to study the performance of CausalRFF on the sources whose data distributions are different, we also simulate m = 5 sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' However, the first source is with ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 and the other 8 0 1 2 3 4 5 6 7 8 Discrepancy of two sources, ∆ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5 √ϵPEHE Error of CATE 0 1 2 3 4 5 6 7 8 Discrepancy of two sources, ∆ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 ϵATE Error of ATE CausalRFF Combined data (stack) Combined data (1-hot) Figure 5: Experimental results on different levels of discrepancy, ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 2: Out-of-sample errors on DATAdiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Method The error of CATE, √ϵATE The error of ATE, ϵATE 1 source 3 sources 5 sources 1 source 3 sources 5 sources BARTag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 X-Learnerag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 R-Learnerag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 OthoRFag 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 TARNetag 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 CFR-wassag 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 CFR-mmdag 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CEVAEag 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 BARTcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 X-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 R-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 OthoRFcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 TARNetcb 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-wasscb 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 CFR-mmdcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 CEVAEcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 FedCI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 CausalRFF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='27 four sources are with ∆ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We refer to this dataset as DATAdiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We test the error of CATE and ATE on the first source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this case, we expect that the errors of CausalRFF to be lower than that of training on combined data since CausalRFF learns the adaptive factors which prevent negative impact of the other four sources to the first source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The results in Figure 4 show that CausalRFF achieves lower errors compared to training on combined data (there are two cases of combining: stacking data, and adding one-hot vectors to indicate the source of each data point), which is as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the third experiment, we study the effect of ∆ on the performance of CausalRFF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We simulate m = 2 sources with different values of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, the first source is with ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 and the second source is with ∆ varying from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We compare our CausalRFF method with that of training on combined data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Again, Figure 5 shows that CausalRFF achieves lower errors as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Result and discussion (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This section aims to compare CausalRFF with the baselines on both datasets: DATAsame and DATAdiff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Except FedCI (which is a Bayesian federated method), the other baselines are trained on two cases: combined data (cb) and bootstrap aggregating (ag) as mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' On DATAsame, we expect that the performance of the proposed method is as good as the baselines trained on combined data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The results in Table 1 show that the performance of CausalRFF is as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For DATAdiff, we report the results on Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The figures reveal that the performance of CausalRFF is as good as the baselines in predicting ATE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In terms of predicting CATE, the performance of the baselines significantly reduces as we add more data sources whose distribution are different from the first source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Meanwhile, the performance of CausalRFF in predicting CATE is slightly reduced, but it is still much better than those of the baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The reason of this is because we used adaptive factors to learn for the similarity of data distributions among the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Large-scale Synthetic Data Data description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this section, we conduct experiments on a large number of sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The set up in this section is similar to that of Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We simulate two cases: (1) DATA-LARGEsame: a dataset of 100 sources, where we set ∆ = 0 for all sources so that their distributions are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2) DATA-LARGEdiff: a dataset of 100 sources, where we draw uniformly the discrepancy factor ∆ ∼ U[0, 8] for each source so that their distributions are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In both cases, we use test set from the first 20 sources for evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Result and discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 3 shows that CausalRFF achieves competitive results in estimating ATE and CATE when the sources have the same distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 4 shows that CausalRFF outperforms the baselines when the sources have different distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These results are consistent with our discussions in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3 A Real World Dataset Data description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Infant Health and Development Program (IHDP) (Hill 2011) is a randomized study on the impact of specialist visits (the treatment) on the cognitive development of children (the 9 Table 3: Errors on DATA-LARGEsame dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Method The error of CATE, √ϵATE The error of ATE, ϵATE 20 sources 50 sources 100 sources 20 sources 50 sources 100 sources BARTcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 X-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 R-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 OthoRFcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 TARNetcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='93±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CFR-wasscb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='99±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='87±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CFR-mmdcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='98±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='87±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CEVAEcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 FedCI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='23±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CausalRFF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 Table 4: Errors on DATA-LARGEdiff dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Method The error of CATE, √ϵPEHE The error of ATE, ϵATE 20 sources 50 sources 100 sources 20 sources 50 sources 100 sources BARTcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 X-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 R-Learnercb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='88±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='88±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='86±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 OthoRFcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 TARNetcb 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-wasscb 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CFR-mmdcb 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 CEVAEcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 FedCI 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 CausalRFF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='24±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='04 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='01 outcome).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The dataset consists of 747 records with 25 covariates describing properties of the children and their mothers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The treatment group includes children who received specialist visits and control group includes children who did not receive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This dataset was ‘de-randomized’ by removing from the treated set children with non-white mothers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For each child, a treated and a control outcome are then simulated, thus allowing us to know the ‘true’ individual causal effects of the treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Further details are presented in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 5: Out-of-sample errors on IHDP dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Method The error of CATE, √ϵPEHE The error of ATE, ϵATE 1 source 2 sources 3 sources 1 source 2 sources 3 sources BARTag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='23 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 X-Learnerag 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 R-Learnerag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='34 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='24 OthoRFag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 TARNetag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='13 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 CFR-wassag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 CFR-mmdag 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 CEVAEag 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 BARTcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 X-Learnercb 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 R-Learnercb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='23 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='26 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 OthoRFcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 TARNetcb 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='59 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='61 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 CFR-wasscb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 CFR-mmdcb 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='19 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='3±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 CEVAEcb 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='22 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='9±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='07 FedCI 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09 CausalRFF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='34 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='4±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='33 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='7±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='16 Result and discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 5 reports the ex- perimental results on IHDP dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Again, we see that the proposed method gives competitive results compared to the baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particu- lar, the error of CausalRFF in predicting ATE is as low as that of the baselines, which is as we expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In addition, the errors of CausalRFF in predicting CATE are lower than those of the baselines, which verifies the efficacy of the pro- posed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Most importantly, CausalRFF is trained in a federated setting which minimizes the risk of privacy breach for the individuals stored in the local dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 6 Conclusion We have proposed a new method to learn causal effects from federated, observational data sources with dissimilar distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our method utilizes Random Fourier Features that naturally induce the decomposition of the loss function to individual components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our method allows for each component data group to inherit different distributions, and requires no prior knowledge on data discrepancy among the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have also proved statistical guarantees which show how multiple data sources are effectively incorporated in our causal model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Our work is an important step toward privacy-preserving causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Future work may include combining the proposed method with a multiparty differential privacy technique (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Rajkumar and Agarwal 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pettai and Laud 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hamm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2016), which might lead to a stronger privacy guarantee model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Another direction is to extend the proposed method with some recent ideas (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Khemakhem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2021) to study the identifiability of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Acknowledgments and Disclosure of Funding This research/project is supported by the National Research Foundation Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No: AISG2-RP-2020-016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' AB was supported by an NRF Fellowship for AI grant (NRFFAI1-2019-0002) and an Amazon Research Award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This work was conducted while YL was at Harvard University and the views expressed here do not necessarily reflect the position of Roche AG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 10 References Aglietti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Damoulas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Álvarez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and González, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Multi-task causal learning with Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 6293–6304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Alaa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and van der Schaar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Limits of estimating heterogeneous treatment effects: Guidelines for practical algorithm design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 35th International Conference on Machine Learning, pages 129–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Alaa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and van der Schaar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bayesian inference of individualized treatment effects using multi-task Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 3424–3432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Allman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Matias, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Rhodes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Identifiability of parameters in latent structure models with many observed variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Annals of Statistics, 37(6A):3099–3132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Álvarez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ward, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Guarnizo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Non-linear process convolutions for multi-output Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In The 22nd International Conference on Artificial Intelligence and Statistics, pages 1969–1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Anandkumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ge, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Hsu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Kakade, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Telgarsky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Tensor decompositions for learning latent variable models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of Machine Learning Research, 15:2773–2832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Anandkumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Hsu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Kakade, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A method of moments for mixture models and hidden markov models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 25th Annual Conference on Learning Theory, pages 33–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ge, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ma, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Risteski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Provable learning of noisy-OR networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 1057– 1066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bareinboim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal inference and the data-fusion problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Proceedings of the National Academy of Sciences, 113(27):7345–7352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Breiman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bagging predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Machine Learning, 24(2):123–140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Chaudhuri, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Monteleoni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Sarwate, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Differentially private empirical risk minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of Machine Learning Research, 12(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Harinen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Yung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' CausalML: Python package for causal machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Choudhury, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Salonidis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Gkoulalas-Divanis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Sylla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Predicting adverse drug reactions on distributed health data using federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In AMIA Annual Symposium Proceedings, volume 2019, page 313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' American Medical Informatics Association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' de Wolff, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Cuevas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Tobar, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Mogptk: The multi-output Gaussian process toolkit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv preprint arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03471.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Dorie, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Npci: Non-parametrics for causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' URL: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' com/vdorie/npci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Finkelstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Hendren, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Welfare analysis meets causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of Economic Perspectives, 34(4):146–67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Flores, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Dayan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Roth, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Zhong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Harouni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Gentili, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Abidin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Costa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Wood, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Federated learning used for predicting outcomes in SARS-COV-2 patients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Preprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' medRxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='20172809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Goodman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Exploratory latent structure analysis using both identifiable and unidentifiable models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Biometrika, 61(2):215–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Gostin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Levit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Nass, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Beyond the HIPAA Privacy Rule: Enhancing Privacy, Improving Health Through Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' National Academies Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 11 Gutman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Intrator, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Lancaster, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A Bayesian procedure for estimating the causal effects of nursing home bed-hold policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Biostatistics, 19(4):444–460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hamm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Belkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Learning privately from multiparty data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 33rd International Conference on Machine Learning, pages 555–563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Rao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Mathews, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ramaswamy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Beaufays, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Augenstein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Eichner, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Kiddon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Ramage, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Federated learning for mobile keyboard prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv preprint arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='03604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Henderson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Louis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Varadhan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bayesian analysis of heteroge- neous treatment effects for patient-centered outcomes research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Health Services and Outcomes Research Methodology, 16(4):213–233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bayesian nonparametric modeling for causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of Computational and Graphical Statistics, 20(1):217–240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Jernite, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Halpern, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Sontag, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Discovering hidden variables in noisy-OR networks using quartet tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Advances in Neural Information Processing Systems, 26:2355–2363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Joukov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Kuli´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Fast approximate multi-output Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv preprint arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='09848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Khemakhem, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Monti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Hyvarinen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Variational autoencoders and nonlinear ICA: A unifying framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics, pages 2207–2217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Kiefer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Wolfowitz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Annals of Mathematical Statistics, pages 887–906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Welling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Auto-encoding variational bayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 2nd International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Künzel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Sekhon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Bickel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Yu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Metalearners for estimating heteroge- neous treatment effects using machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Proceedings of the National Academy of Sciences, 116(10):4156–4165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Correa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Bareinboim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Generalized transportability: Synthesis of experiments from heterogeneous domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 34th AAAI Conference on Artificial Intelligence, New York, NY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' AAAI Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Metropolized independent sampling with comparisons to rejection sampling and importance sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Statistics and Computing, 6(2):113–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Louizos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Shalit, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Mooij, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Sontag, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Zemel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Welling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal effect inference with deep latent-variable models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 6446–6456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Madras, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Creager, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Pitassi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Zemel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Fairness through causal awareness: Learning causal latent-variable models for biased data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 349–358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' McMahan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Moore, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Ramage, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Hampson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and y Arcas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Communication- efficient learning of deep networks from decentralized data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, pages 1273–1282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Microsoft Research (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' EconML: A python package for ML-based heterogeneous treatment effects estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='com/microsoft/EconML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Version 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Milton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Coupland, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Giorgi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Bhatt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Spatial analysis made easy with linear regression and kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Epidemics, 29:100362.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Mohri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Sivek, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Suresh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Agnostic federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 36th International Conference on Machine Learning, pages 4615–4625.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 12 Morgan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Winship, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Counterfactuals and Causal Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Nie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Wager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Quasi-oracle estimation of heterogeneous treatment effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Biometrika.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Oprescu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Syrgkanis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Orthogonal random forest for causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 36th International Conference on Machine Learning, pages 4932–4941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pathak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Rane, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Raj, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Multiparty differential privacy via aggregation of locally trained classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Advances in Neural Information Processing Systems, 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal diagrams for empirical research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Biometrika, 82(4):669–688.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2009a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causal inference in statistics: An overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Statistics Surveys, 3:96–146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2009b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Causality: Models, Reasoning, and Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Bareinboim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Transportability of causal and statistical relations: A formal approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 25th AAAI Conference on Artificial Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Pettai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Laud, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Combining differential privacy and secure multiparty computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 31st Annual Computer Security Applications Conference, pages 421–430.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Powers, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Qian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Jung, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Schuler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Shah, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Hastie, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Tibshirani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Some methods for heterogeneous treatment effect estimation in high dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Statistics in Medicine, 37(11):1767–1787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Rahimi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Recht, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Random features for large-scale kernel machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Advances in Neural Information Processing Systems, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Rajkumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Agarwal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' A differentially private stochastic gradient descent algorithm for multiparty classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 15th International Conference on Artificial Intelligence and Statistics, pages 933–941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Rosenbaum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Rubin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The central role of the propensity score in observational studies for causal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Biometrika, 70(1):41–55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Sattler, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Wiedemann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Müller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Samek, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Robust and communication-efficient federated learning from non-iid data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' IEEE Transactions on Neural Networks and Learning Systems, 31(9):3400–3413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Sattler, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Wiedemann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Müller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Samek, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Robust and communication-efficient federated learning from non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' IEEE Transactions on Neural Networks and Learning Systems, 31(9):3400–3413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Shalit, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Johansson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Sontag, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Estimating individual treatment effect: general- ization bounds and algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 34th International Conference on Machine Learning, pages 3076–3085.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' JMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Shokri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Shmatikov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Privacy-preserving deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In ACM SIGSAC Conference on Computer and Communications Security, pages 1310–1321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Recovering latent causal factor for generalization to distributional shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Advances in Neural Information Processing Systems, 34:16846–16859.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Tsamardinos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Triantafillou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Lagani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Towards integrative causal analysis of heterogeneous data sets and studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of Machine Learning Research, 13:1097–1157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Vaid, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Jaladanki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Teng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Federated learning of electronic health records improves mortality prediction in patients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Ethnicity, 52(77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='6):0–001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Van der Vaart, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Asymptotic Statistics, volume 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 13 Vo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Hoang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Leong, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Bayesian federated estimation of causal effects from observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 38th Conference on Uncertainty in Artificial Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Kaplan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Niu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Optimizing federated learning on non-iid data with reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In IEEE INFOCOM 2020 - IEEE Conference on Computer Communications, pages 1698–1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and Blei, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Frequentist consistency of variational bayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Journal of the American Statistical Association, 114(527):1147–1161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Wendland, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Scattered Data Approximation, volume 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Xiong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Koenecke, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Powell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Shen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Vogelstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Athey, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Federated causal inference in heterogeneous observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='11732.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Pati, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Bhattacharya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' α-variational inference with statistical guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Annals of Statistics, 48(2):886–905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Huai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Representation learning for treatment effect estimation from observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 2633–2643.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Yoon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Jordon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and van der Schaar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' GANITE: Estimation of individualized treatment effects using generative adversarial nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In Proceedings of the 6th International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Lai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Suda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Civin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Chandra, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Federated learning with non-iid data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' arXiv preprint arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='00582.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Zhe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', Xing, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', and Kirby, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Scalable high-order gaussian process regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In The 22nd International Conference on Artificial Intelligence and Statistics, pages 2611–2620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 14 Appendix: An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects A Pre-training step to remove duplicated individuals As mentioned in the main text, we make five assumptions as follows: (A1) Consistency: W = w =⇒ Y (w) = Y , this follows from the axioms of structural causal model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A2) No interference: treatment on one subject does not affect the outcomes of another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This is because the outcome only has a single node for treatment as a parent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A3) Positivity (also known as Overlap): every subject has some positive probability to be assigned to every treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A4) The individuals in each source must have the same set of common covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (A5) There is no individual whose data exists in more than one source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Assumptions (A1), (A2) and (A3) are standard in any causal inference algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Assumption (A4) has been implicitly shown in our setup since all the sources would share the same causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This is a reasonable assumption as we intend to build a unified model on all of the data sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, decentralized data in Choudhury et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Vaid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Flores et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2020) (to name a few) satisfy this assumption for federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Assumption (A5) is to ensure that no individuals would dominate the other individuals when training the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, if an individual appears in all of the sources, the trained model would be biased by data of this individual (there is imbalance caused by the use of more data from this particular individual than the others).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, this condition would ensure that such bias does not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In practice, Assumption (A5) sometimes does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' To address such a problem, we propose a pre-training step to exclude such duplicated individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The pre-training step are summarized as follows: (1) Suppose that an individual can be uniquely identified via a set of features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, a pair of (national identity, nationality) can be used to uniquely identify a person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2) To identify duplicated individuals, we first encode the above features with a hash function such as MD5, SHA256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3) We then send the encoded sequences to a central server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (4) The server would collect all encoded sequences from all sources and find among them if an encoded sequence is repeated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (5) All of the repeated sequences are associated with duplicated individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, we announce the sources to exclude these individual from the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We summarize the pre-training step in Figure 6 with three sources of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' B Identification The causal effects are unidentifiable if the confounders are unobserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' However, Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2017) showed that if the joint distribution ps(xs, ys, ws, zs) can be recovered, then the causal effects are identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the following, we show how they are identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 15 L1 = List of hashed sequences for each individual in Source #1 L3 = List of hashed sequences for each individual in Source #3 L2 = List of hashed sequences for each individual in Source #2 Source #1 Source #2 Source #3 Search for duplicated individuals among the lists: L1, L2, L3 Figure 6: An illustration on how the pre-training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This step is intended to identify duplicated individuals among the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Furthermore, this step preserves privacy since each source sends only their hashed sequences of the individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The proof is adapted from Louizos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (Theorem 1, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We need to show that the distribution ps(ys|do(W = ws), xs) is identifiable from observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have ps(ys|do(W = ws), xs) = � ps(ys|do(W = ws), xs, zs)ps(zs|do(W = ws), xs)dzs = � ps(ys|ws, xs, zs)ps(zs|xs)dzs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' where the last equality is obtained by applying the do-calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The last expression, � ps(ys|ws, xs, zs)ps(zs|xs)dzs, can be identified by the joint distribution ps(xs, ys, ws, zs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In our work, ps(xs, ys, ws, zs) is recovered by its factorization with the distributions ps(ws|xs), ps(ys|xs, ws), ps(zs|xs, ys, ws), ps(ys|ws, zs), and p(zs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Adaptively learning these distributions in a federated setting is the main task of our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' C Computing CATE, local ATE, and global ATE This section gives details on how to compute CATE, local ATE and global ATE after training the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Computing the CATE and local ATE After training the model, each source can compute the CATE and the local ATE on for its own source and use it for itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' E[ys i|do(ws i =w), xs i] = � E[ys i|ws i =w, zs i]p(zs i|xs i)dzs i ≃ 1 N N � l=1 fy(ws i =w, zs i[l]) where fy(ws i =w, zs i[l]) is the mean function of ps(ys i|ws i, zs i) and {zs i[l]}N l=1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ∼ ps(zs i|xs i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The problem is to draw {zs i[l]}N l=1 from ps(zs i|xs i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We observe that ps(zs i|xs i) = � ws i∈{0,1} � ps(zs i|xs i, ys i, ws i)ps(ys i|xs i, ws i)ps(ws i|xs i) dys i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, to draw samples, we proceed in the following steps: 16 (1) Draw a sample of ws i from ps(ws i|xs i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2) Substitute the above sample of ws i to ps(ys i|xs i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (3) Draw a sample of ys i from ps(ys i|xs i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (4) Substitute the above sample of ys i to ps(zs i|xs i, ys i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (5) Draw a sample of zs i from ps(zs i|xs i, ys i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The density function of ps(ys i|xs i, ws i) and ps(ws i|xs i) are available after training the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' As described in the main text, there are two options to draw from ps(zs i|xs i, ys i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The first option is to draw from q(xs i) sine it approximates ps(zs i|xs i, ys i, ws i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The second option is to use Metropolis- Hastings algorithm with independent sampler (Liu 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For the second option, we have that ps(zs i|xs i, ys i, ws i) ∝ ps(ys i|zs i, ws i)ps(ws i|zs i)ps(xs i|zs i)p(zs i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, it can be used to compute the acceptance probability of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Note that the second option would give more exact samples since it further filters the samples based on the exact acceptance probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The above would help estimate the CATE given xs i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The local ATE is the average of CATE of individuals in a source s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These quantities can be estimated in a local source’s machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We show how to compute the global ATE in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Computing the global ATE from local ATE of each Source To compute a global ATE, the server would collect all the local ATE in each source and then compute their weighted average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For example, suppose that we have three sources whose local ATE values are 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5, and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' These local ATEs are averaged over 10, 5, and 12 individuals, in that order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, the global ATE is given as follows: global ATE = 10 × 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='0 + 8 × 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='5 + 12 × 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='8 10 + 8 + 12 = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since each source only shares their local ATE and the number of individuals, it does not leak any sensitive information about the individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' D Comparison metrics We report two error metrics in our experiments: Precision in estimation of heterogeneous effects (PEHE): ϵPEHE = n � i=1 (τ(xi) − ˆτ(xi))2/n, (17) Absolute error: ϵATE = |τ − ˆτ|, (18) where τ(xi), τ are the ground truth of ITE and ATE, and ˆτ(xi), ˆτ are their estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We report the mean and standard error over 10 replicates of the data with different random initializations of the training algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' E Derivation of the loss functions In this section, we present the loss functions and the form of functions that modulate the desired distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 17 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Learning distributions involving latent confounder The ELBO of the log marginal likelihood has the following expression logp(x, y, w) = log � p(x, y, w, z)dz ≥ � q(z) log p(x, y, w, z) q(z) dz = � s∈S ns � i=1 � Eq � log ps(ys i|ws i, zs i) + log ps(ws i|zs i) + log ps(xs i|zs i) � − KL[q(zs i)∥p(zs i)] � =: L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Using the complete dataset ˜Ds = �M l=1 � (ws i, ys i, xs i, zs i[l]) �ns i=1, ∀s ∈ S, we minimize the following loss function J: J = �L + � c∈A R(fc), A = {y0, y1, q0, qq, x, w}, where �L is the empirical loss function obtained from the negative of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the following, we find the form of fc based on the representer theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We further define fx = [fx,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', fx,dx], where fx,d is a function taking zs i as input and mapping it to a real value in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, fq0 = [fq0,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', fq0,dz] and fq1 = [fq1,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', fq1,dz].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Hc (c ∈ A) be a reproducing Kernel Hilbert space (RKHS) and κc(·, ·) be kernel function associated with Hc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We define Bc as follows: By0 = span � κy0(·, zs i[l]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' l = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', M � , By1 = span � κy1(·, zs i[l]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' l = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', M � , Bx = span {κx(·, zs i[l]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' l = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', M} , Bw = span {κw(·, zs i[l]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' l = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', M} , Bq0 = span {κq0(·, [xs i, ys i]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns} , Bq1 = span {κq1(·, [xs i, ys i]), where s ∈ S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' i = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', ns} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We posit the following regularizers: R(fy0) = reg_factory0 × ∥fy0∥2 Hy0, R(fx) = dx � d=1 reg_factorx,d × ∥fx,d∥2 Hx (d = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', dx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The regularizers R(fy1) and R(fw) are similar to that of R(fy0), and R(fq0), R(fq1) are similar to that of R(fx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We see that Bc is a subspace of Hc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We project fy0, fy1, fw, fx,d (d = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', dx), fq0,d (d = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', dz) and fq1,d (d = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', dz) onto the subspaces By0, By1, Bw, Bx, Bq0 and Bq1, respectively, and obtain f ′ y0, f ′ y1, f ′ w, f ′ x,d, f ′ q0,d and f ′ q1,d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Next, we also project them onto the perpendicular spaces of B(·) to obtain f ⊥ y0, f ⊥ y1, f ⊥ w , f ⊥ x,d, f ⊥ q0,d and f ⊥ q1,d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Note that f(·) = f ′ (·) +f ⊥ (·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, ∥f(·)∥2 H(·) = ∥f ′ (·)∥2 H(·) +∥f ⊥ (·)∥2 H(·) ≥ ∥f ′ (·)∥2 H(·), which implies that reg_factor(·) × ∥f(·)∥2 H(·) is minimized if f(·) is in its subspace B(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (I) In addition, due to the reproducing property, we have fy0(zs i[l]) = � fy0, κy0(·, zs i[l]) � Hy = � f ′ y0, κy0(·, zs i[l]) � Hy + � f ⊥ y0, κy0(·, zs i[l]) � Hy = f ′ y0(zs i[l]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, we also have fy1(zd i [l]) = f ′ y1(zd i [l]), fw(zd i [l]) = f ′ w(zd i [l]), fx,d(zl i) = f ′ x,d(zd i [l]), fq0,d(yd i , xd i ) = f ′ q0,d(yd i , xd i ) and fq1,d(yd i , xd i ) = f ′ q1,d(yd i , xd i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, �L(fy0, fy1, fq0, fq1, fx, fw) = �L(f ′ y0, f ′ y1, f ′ q0, f ′ q1, f ′ x, f ′ w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (II) (I) and (II) imply that fy0, fy1, fq0,d, fq1,d, fx,d, fw are the weighted sum of elements in their 18 corresponding subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, fc(us) = � v∈S nv×M � j=1 κ(us, uv j)αv j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Using this form with the adaptive kernel and Random Fourier Feature described in the main text (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1), we obtain the desired model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Learning auxiliary distributions The derivation of Jw, Jy and the form of functions modulated the auxiliary distributions are similar to those of J as detailed in Section E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The difference is that the empirical loss functions are obtained from the negative log-likelihood instead of the ELBO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' F Spectral distribution of some popular kernels Table 6 (adopted from Milton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (2019)) presents some popular kernels and their associated spectral density s(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Those density functions are needed to draw samples of ω for Random Fourier Features presented in Section 4 of the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In our experiments, we used Gaussian kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Table 6: Some popular kernels and their associated spectral density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Note that Kν(·) denotes the modified Bessel function of the second kind, Γ(·) is the gamma function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Kernel Kernel function, k(x1 − x2) Spectral density, s(ω) Gaussian exp � − ∥x1 − x2∥2 2 2ℓ2 � � 2π ℓ2 � −d 2 exp � − ℓ2∥ω∥2 2 2 � Laplacian exp � − ℓ∥x1 − x2∥1 � � 2 π � d 2 d � i=1 ℓ ℓ2 + ω2 i Matérn 21−ν Γ(ν) � √ 2ν ∥x1 − x2∥2 ℓ �ν Kν � √ 2ν ∥x1 − x2∥2 ℓ � 2dπ d 2 Γ(ν + d 2 )(2ν)ν Γ(ν)ℓ2ν � 2ν ℓ2 + 4π2∥ω∥2 2 �− � ν+ d 2 � G Proof of Lemma 1 Let S\\s := S \\ {s}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The model is summarized as follows: p(zs i) = N(0, σ2 zIdz), p(ws i|zs i) = Bern � ϕ �� θs w + � v∈S\\s λs,vθv w �⊤ φ(zs i) �� , p(ys i|ws i, zs i) = N �� ws i � θs y1 + � v∈S\\s λs,vθv y1 � + (1 − ws i) � θs y0 + � v∈S\\s λs,vθv y0 ��⊤ φ(zs i), σ2 y � , p(xs i|zs i) = N �� θs x + � v∈S\\s λs,vθv x �⊤ φ(zs i), σ2 xIdx � , where z(·) i ∈ Rdz, y(·) i ∈ R, w(·) i ∈ {0, 1}, x(·) i ∈ Rdx, λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let θ = {θs w, θs y0, θs y1, θs x}s∈S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Vw, Vy0, Vy1, Vx be 1/(2√m)-packing of the unit ∥ · ∥2- balls with cardinality at least (2√m)2B, (2√m)2B, (2√m)2B, (2√m)2Bdx, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Vs = δ(Vw × Vy0 × Vy1 × Vx) and V = Vs1 × Vs2 ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' × Vsm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We see that |V| ≥ (2√m)2mB(dx+3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the following, we derive the minimax bound: 19 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have that ∥θ1 − θ2∥2 = �� s∈S � c∈A ∥(θsc)1 − (θsc)2∥2 2 ≥ � � � �� s∈S 4 � δ 2√m �2 = δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The marginal distribution pθ(w, y, x) = � pθ(w, y, x, z)dz = � pθ(y|w, z)pθ(w|z)pθ(x|z)p(z)dz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Moreover, we have that DKL(pn θ1 ∥ pn θ2) = � s∈S DKL(pns θ1 ∥ pns θ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We divide the proof into three parts (I),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (II),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' and (III): (I) The upper bound of DKL(pns θ1 ∥ pns θ2) Since the data is independent,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' we have that DKL(pns θ1 ∥ pns θ2) = nsDKL(p1 θ1 ∥ p1 θ2) ≤ns � DKL � pθ1(y|w,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z)pθ1(w|z)pθ1(x|z) ���pθ2(y|w,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z′)pθ2(w|z′)pθ2(x|z′) � p(z)p(z′)dzdz′ = ns � � pθ1(w = 0|z)DKL � pθ1(y|w = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z) ��pθ2(y|w = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z′) � + pθ1(w = 1|z)DKL � pθ1(y|w = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z) ��pθ2(y|w = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' z′) � + DKL � pθ1(w|z) ��pθ2(w|z′) � + DKL � pθ1(x|z) ��pθ2(x|z′) �� p(z)p(z′)dzdz′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In the following, we find the upper bound of each component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ⋄ Upper bound of the first and second component pθ1(w = 0|z)DKL � pθ1(y|w = 0, z) ��pθ2(y|w = 0, z′) � ≤ 1 2σ2y �� (θs y0)1 + � v∈S\\s λs,v(θv y0)1 �⊤ φ(z) − � (θs y0)2 + � v∈S\\s λs,v(θv y0)2 �⊤ φ(z′) �2 ≤ 8B2δ2(1 + � v∈S\\s λs,v)2 σ2y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, we also have pθ1(w = 1|z)DKL � pθ1(y|w = 1, z) ��pθ2(y|w = 1, z′) � ≤ 8B2δ2(1 + � v∈S\\s λs,v)2 σ2y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ⋄ Upper bound of the third component DKL � pθ1(w|z) ��pθ2(w|z′) � = ϕ �� (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � log ϕ �� (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � ϕ �� (θsw)2 + � v∈S\\s λs,v(θvw)2 �⊤ φ(z′) � + ϕ � − � (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � log ϕ � − � (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � ϕ � − � (θsw)2 + � v∈S\\s λs,v(θvw)2 �⊤ φ(z′) �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For the first component,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ϕ �� (θs w)1 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)1 �⊤ φ(z) � log ϕ �� (θs w)1 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)1 �⊤ φ(z) � ϕ �� (θsw)2 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θvw)2 �⊤ φ(z′) � 20 ≤ ��� log � 1 + e − � (θs w)2+� v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)2 �⊤ φ(z)� − log � 1 + e − � (θs w)1+� v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)1 �⊤ φ(z′)���� ≤ ���(θs w)1 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)1 ��� 2∥φ(z)∥2 + ���(θs w)2 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(θv w)2 ��� 2∥φ(z′)∥2 ≤ � δ + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vδ � ∥φ(z)∥2 + � δ + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vδ � ∥φ(z′)∥2 ≤ 4Bδ � 1 + � v∈S\\s λs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, we also have ϕ � − � (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � log ϕ � − � (θs w)1 + � v∈S\\s λs,v(θv w)1 �⊤ φ(z) � ϕ � − � (θsw)2 + � v∈S\\s λs,v(θvw)2 �⊤ φ(z′) � ≤ 4Bδ � 1 + � v∈S\\s λs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, DKL � pθ1(w|z) ��pθ2(w|z′) � ≤ 8Bδ � 1 + � v∈S\\s λs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' ⋄ Upper bound of the fourth component DKL � pθ1(x|z) ��pθ2(x|z′) � = 1 2σ2x ��� � (θs x)1 + � v∈S\\s λs,v(θv x)1 �⊤ φ(z) − � (θs x)2 + � v∈S\\s λs,v(θv x)2 �⊤ φ(z′) ��� 2 2 ≤ 1 2σ2x ���� � (θs x)1 + � v∈S\\s λs,v(θv x)1 �⊤ φ(z) ��� 2 + ��� � (θs x)2 + � v∈S\\s λs,v(θv x)2 �⊤ φ(z′) ��� 2 �2 ≤ 8B2δ2� 1 + � v∈S\\s λs,v�2 σ2x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (II) Combining the results From the above upper bound of each of the components, we obtain DKL(pns θ1 ∥ pns θ2) ≤ ns � �16B2δ2(1 + � v∈S\\s λs,v)2 σ2y + 8Bδ � 1 + � v∈S\\s λs,v� + 8B2δ2(1 + � v∈S\\s λs,v)2 σ2x � p(z)p(z′)dzdz′ = ns �� 1 σ2y + 1 2σ2x � 16B2δ2� 1 + � v∈S\\s λs,v�2 + 8Bδ � 1 + � v∈S\\s λs,v�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' (III) The minimax lower bound We have that DKL(pn θ1 ∥ pn θ2) = � s∈S DKL(pns θ1 ∥ pns θ2) ≤ � s∈S ns �� 1 σ2y + 1 2σ2x � 16B2δ2� 1 + � v∈S\\s λs,v�2 + 8Bδ � 1 + � v∈S\\s λs,v�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 21 Consequently, inf ˆθn sup P ∈P EP � ∥ˆθn−θ(P)∥2 � ≥δ 2 � � � �1− � s∈S ns �� 1 σ2y + 1 2σ2x � 16B2δ2� 1+� v∈S\\s λs,v�2 +8Bδ � 1+� v∈S\\s λs,v�� +log 2 log |V| � � � � ≥δ 2 � � � �1− � s∈S ns �� 1 σ2y + 1 2σ2x � 16B2δ2� 1+� v∈S\\s λs,v�2 +8Bδ � 1+� v∈S\\s λs,v�� +log 2 2mB(dx + 3) log(2√m) � � � �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We choose δ = √ mB(dx+3) log(2√m) 4B � s∈S ns � 1+� v∈S\\s λs,v�2 , then 1 − � s∈S ns �� 1 σ2y + 1 2σ2x � 16B2δ2� 1 + � v∈S\\s λs,v�2 + 8Bδ � 1 + � v∈S\\s λs,v�� + log 2 2mB(dx + 3) log(2√m) ≥ 1 − � 1 σ2y + 1 2σ2x � log(2√m) 2 � s∈S ns � 1 + � v∈S\\s λs,v �2 − 1 � mB(dx + 3) − 1 2mB(dx + 3) ≥ 1 − � 1 σ2y + 1 2σ2x � log(2√m) 2 � s∈S ns � 1 + � v∈S\\s λs,v �2 − 1 2 − 1 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' If � s∈S ns � 1 + � v∈S\\s λs,v�2 ≥ 2 � 1 σ2y + 1 2σ2x � log(2√m), then inf ˆθn sup P ∈P EP � ∥ˆθn−θ(P)∥2 � ≥ 1 2 × � mB(dx + 3) log(2√m) 4B � s∈S ns � 1 + � v∈S\\s λs,v�2 × � 1 − 1 4 − 1 2 − 1 8 � = � m(dx + 3) log(2√m) 64 √ B � s∈S ns � 1 + � v∈S\\s λs,v�2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' H Proof of Lemma 2 The proof of Lemma 2 is divided into two parts (i) and (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We compute them separately: H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Proof of Part (i) We summarize the model as follows ws ∼ Bern � ϕ �� ψs + � v∈S\\s γs,vψv�⊤ φ(xs) �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let ψ = {ψs}s∈S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Vs be 1/(2√m)-packing of the unit ∥ · ∥2-balls with cardinality at least (2√m)2B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We now choose a set V = δ(Vs1 × Vs2 ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' × Vsm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We see that |V| ≥ (2√m)2mB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have that ∥ψ1 − ψ2∥2 = �� s∈S ∥ψs 1 − ψs 2∥2 2 ≥ δ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 22 Moreover, DKL(pn ψ1 ∥ pn ψ2) = � s∈S DKL(pns ψ1 ∥ pns ψ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We first find upper bound of DKL(pns ψ1 ∥ pns ψ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Since the data is independent, we have that DKL(pns ψ1 ∥ pns ψ2) = nsDKL(p1 ψ1 ∥ p1 ψ2) = ns � ϕ �� ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � log ϕ �� ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � ϕ �� ψs 2 + � v∈S\\s γs,vψv 2 �⊤ φ(xs) � + ϕ � − � ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � log ϕ � − � ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � ϕ � − � ψs 2 + � v∈S\\s γs,vψv 2 �⊤ φ(xs) � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The first component: ϕ �� ψs 1+ � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 1 �⊤ φ(xs) � log ϕ �� ψs 1 + � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 1 �⊤ φ(xs) � ϕ �� ψs 2 + � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 2 �⊤ φ(xs) � ≤ �����log � 1 + e − � ψs 2+� v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 2 �⊤ φ(xs)� − log � 1 + e − � ψs 1+� v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 1 �⊤ φ(xs)������ (⋆) ≤ ��� � ψs 2 + � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 2 �⊤ φ(xs) − � ψs 1 + � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='vψv 1 �⊤ φ(xs) ��� ≤ 4Bδ � 1 + � v∈S\\s γs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' where (⋆) follows from the fact that the SoftPlus function log(1 + ex) is 1-Lipschitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, �� log(1 + ex1) − log(1 + ex2) �� = ���� � x2 x1 ex 1 + ex dx ���� ≤ ���� � x2 x1 1dx ���� = ��x1 − x2 ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Similarly, for the second component, we also have ϕ � − � ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � log ϕ � − � ψs 1 + � v∈S\\s γs,vψv 1 �⊤ φ(xs) � ϕ � − � ψs 2 + � v∈S\\s γs,vψv 2 �⊤ φ(xs) � ≤ 4Bδ � 1 + � v∈S\\s γs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, DKL(pns ψ1 ∥ pns ψ2) ≤ 8Bδ � 1 + � v∈S\\s γs,v� ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Consequently, DKL(pn ψ1 ∥ pn ψ2) ≤ 8Bδ � s∈S ns � 1 + � v∈S\\s γs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' So, we have that inf ˆψn sup P ∈P EP � ∥ ˆψn − ψ(P)∥2 � ≥ δ 4 � �1 − 8Bδ � s∈S ns � 1 + � v∈S\\s γs,v� + log 2 log |V| � � 23 ≥ δ 4 � �1 − 8Bδ � s∈S ns � 1 + � v∈S\\s γs,v� + log 2 2mB log(2√m) � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We choose δ = m log(2√m) 16 � s∈S ns � 1+� v∈S\\s γs,v�, then 1 − 8Bδ � s∈S ns � 1 + � v∈S\\s γs,v� + log 2 2mB log(2√m) ≥ 1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, inf ˆψn sup P ∈P EP � ∥ ˆψn − ψ(P)∥2 � ≥ 1 4 × mB log(2√m) 16B � s∈S ns � 1 + � v∈S\\s γs,v� × 1 4 = m log(2√m) 256 � s∈S ns � 1 + � v∈S\\s γs,v�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This completes the proof of part (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Proof of Part (ii) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We summarize the model as follows ys = � (1 − ws) � βs 0 + � v∈S\\s ηs,vβv 0 � + ws� βs 1 + � v∈S\\s ηs,vβv 1 ��⊤ φ(xs) + ϵs, ϵs ∼ N(0, σ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let β = {βs 0, βs 1}s∈S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let V0s and V1s be 1/(2√m)-packing of the unit ∥ · ∥2-balls with cardinality at least (2√m)2B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Let Vs = V0s × V1s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We now choose a set V = δ(Vs1 × Vs2 ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' × Vsm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We see that |V| ≥ (2√m)4mB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have that ∥β1 − β2∥2 = �� s∈S � ∥(βs 0)1 − (βs 0)2∥2 2 + ∥(βs 1)1 − (βs 1)2∥2 2 � ≥ δ/ √ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Moreover, DKL(pn β1 ∥ pn β2) = � s∈S DKL(pns β1 ∥ pns β2) = � s∈S nsDKL(p1 β1 ∥ p1 β2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In addition,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' DKL(p1 β1 ∥ p1 β2) = 1 2σ2 �� (1 − ws) � (βs 0)1 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(βv 0)1 � + ws� (βs 1)1 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(βv 1)1 ��⊤ φ(xs) − � (1 − ws) � (βs 0)2 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(βv 0)2 � + ws� (βs 1)2 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v(βv 1)2 ��⊤ φ(xs) �2 ≤ 1 2σ2 �� (1 − ws) � 2δ + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v2δ � + ws� 2δ + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v2δ �� ∥φ(xs)∥2 �2 ≤ 8B2δ2 σ2 � 1 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v�2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 24 Thus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' DKL(pn β1 ∥ pn β2) ≤ 8B2δ2 σ2 � s∈S ns � 1 + � v∈S\\s ηs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='v�2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Consequently, inf ˆβn sup P ∈P EP � ∥ˆβn − β(P)∥2 � ≥ δ 2 √ 2 � � �1 − 8B2δ2 σ2 � s∈S ns � 1 + � v∈S\\s ηs,v�2 + log 2 log |V| � � � ≥ δ 2 √ 2 � � �1 − 8B2δ2 σ2 � s∈S ns � 1 + � v∈S\\s ηs,v�2 + log 2 4mB log(2√m) � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We choose δ2 = mB log(2√m) 4 B2 σ2 � s∈S ns � 1+� v∈S\\s ηs,v �2 , then 1 − 8B2δ2 σ2 � s∈S ns � 1 + � v∈S\\s ηs,v�2 + log 2 4mB log(2√m) = 1 − 2mB log(2√m) + log 2 4mB log(2√m) ≥ 1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, inf ˆβn sup P ∈P EP � ∥ˆβn − β(P)∥2 � ≥ 1 2 √ 2 � � � � 4mB log(2√m) 2 8B2 σ2 � s∈S ns � 1 + � v∈S\\s ηs,v �2 × 1 4 = σ 16 √ 2 � � � � m log(2√m) B � s∈S ns � 1 + � v∈S\\s ηs,v �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This completes the proof of part (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' I Further cases of the minimax lower bounds In Lemma 1 and 2, we have presented the minimax lower bounds when ys i ∈ R and xs i ∈ Rdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Here, we briefly describe the other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 Further cases of Lemma 1 In this section, we further detail the lower bound for binary outcomes and binary proxy variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In this case, we need to re-derive the upper bound of pθ1(w = j|z)DKL � pθ1(y|w = j, z) ��pθ2(y|w = j, z′) � and DKL � pθ1(x|z) ��pθ2(x|z′) � , where j = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Using similar derivations as before for the quantity DKL � pθ1(w|z) ��pθ2(w|z′) � , we have that pθ1(w = j|z)DKL � pθ1(y|w = j, z) ��pθ2(y|w = j, z′) � ≤ 8Bδ � 1 + � v∈S\\s λs,v� , and DKL � pθ1(x|z) ��pθ2(x|z′) � ≤ dx8Bδ � 1 + � v∈S\\s λs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Combining the results, we have DKL(pn θ1 ∥ pn θ2) = � s∈S DKL(pns θ1 ∥ pns θ2) ≤ � s∈S ns8(dx + 3)Bδ � 1 + � v∈S\\s λs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 25 Consequently, we have that inf ˆθn sup P ∈P EP � ∥ˆθn−θ(P)∥2 � ≥ δ 2 � �1− � s∈S ns8(dx + 3)Bδ � 1 + � v∈S\\s λs,v� +log 2 2mB(dx + 3) log(2√m) � �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We choose δ = m log(2√m) 8 � s∈S ns � 1+� v∈S\\s λs,v �, then 1 − � s∈S ns8(dx + 3)Bδ � 1 + � v∈S\\s λs,v� +log 2 2mB(dx + 3) log(2√m) ≥ 3 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Thus, inf ˆθn sup P ∈P EP � ∥ˆθn−θ(P)∥2 � ≥ 3mB log(2√m) 128 � s∈S nsB � 1 + � v∈S\\s λs,v �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Note that the derivation in this Section and in Section H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='1 give us enough tools to compute the minimax lower bounds for any further case, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', any combination of the outcomes and proxy variables (binary or continuous).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The key is to initially find the upper bound of DKL(pn θ1 ∥ pn θ2) based on the constructed packing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Then, using Fano’s method to obtain the minimax lower bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2 Further cases of Lemma 2 Note that the lower bound of Lemma 2, part (i) has only one case since we only focus on binary treatment, and it is presented in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For part (ii), consider ys i ∈ {0, 1}, then the model of the outcomes would follow a Bernoulli distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Reusing the scheme in Section H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2, we need to find the new upper bound of DKL(pn β1 ∥ pn β2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' In particular, DKL(pn β1 ∥ pn β2) = � s∈S ns � ϕ(v1) log ϕ(v1) ϕ(v2) + ϕ(−v1) log ϕ(−v1 ϕ(−v2) � , where vj = � (1 − ws) � (βs 0)j + � v∈S\\s ηs,v(βv 0)j � + ws� (βs 1)j + � v∈S\\s ηs,v(βv 1)j ��⊤ φ(xs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We have that ϕ(v1) log ϕ(v1) ϕ(v2) ≤ ����(1 − ws) � (βs 0)1 − (βs 0)2 + � v∈S\\s ηs,v[(βv 0)1 − (βv 0)2] � + ws� (βs 1)1 − (βs 1)2 + � v∈S\\s ηs,v[(βv 1)1 − (βv 1)2] ����� 2 ∥φ(xs)∥2 ≤ 4Bδ � 1 + � v∈S\\s γs,v� , Similarly, ϕ(−v1) log ϕ(−v1 ϕ(−v2) ≤ 4Bδ � 1 + � v∈S\\s γs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Hence, DKL(pn β1 ∥ pn β2) ≤ 8Bδ � s∈S ns � 1 + � v∈S\\s ηs,v� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Using similar technique in Section H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='2, we obtain inf ˆβn sup P ∈P EP � ∥ˆβn − β(P)∥2 � ≥ m log(2√m) 32 √ 2 � s∈S ns � 1 + � v∈S\\s ηs,v �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We observe that the lower bound is similar to that of Lemma 2, part (i) since they are both lower bounds of a binary response variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The constant in this bound is larger (1/(32 √ 2)) than that of Lemma 2, part (i) (1/256).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' This is expected since there are more parameters in this model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=', {βs 0, βs 1}s∈S, as compared to the model in Lemma 2, part (i) ({ψs}s∈S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' 26 J Description of IHDP data This section describe details of the IHDP data, which was skipped in the main text due to limited space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The Infant Health and Development Program (IHDP) is a randomized study on the impact of specialist visits (the treatment) on the cognitive development of children (the outcome).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The dataset consists of 747 records with 25 covariates describing properties of the children and their mothers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' The treatment group includes children who received specialist visits and control group includes children who did not receive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' Further details are presented in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For each child, a treated and a control outcome are simulated using the numerical schemes provided in the NPCI package (Dorie 2016), thus allowing us to know the true individual treatment effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We use 10 replicates of the dataset in this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For each replicate, we divide into three sources, each consists of 249 data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' For each source, we use the first 50 data points for training, the next 100 for testing and the rest 99 for validating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' We report the mean and standard error of the evaluation metrics over 10 replicates of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} +page_content=' —– END —– 27' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNAyT4oBgHgl3EQffviC/content/2301.00346v1.pdf'} diff --git a/K9A0T4oBgHgl3EQfC_82/content/2301.01996v1.pdf b/K9A0T4oBgHgl3EQfC_82/content/2301.01996v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7778dc6516d0a4cf5c810a369008a597402bfb09 --- /dev/null +++ b/K9A0T4oBgHgl3EQfC_82/content/2301.01996v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b09f0a19a55ecbbba16ad6ec2d0e77f57fe841731bf02d8b2381c680c40b7246 +size 8425672 diff --git a/KNE0T4oBgHgl3EQfSQBx/content/2301.02219v1.pdf b/KNE0T4oBgHgl3EQfSQBx/content/2301.02219v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5ceea19630e6ec60aa7970c5ccc6f1c6e9a2e194 --- /dev/null +++ b/KNE0T4oBgHgl3EQfSQBx/content/2301.02219v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d0e4b34f9a63744aced5a56df1048a9e1553867af531bbeafa9bdb2354887b0f +size 2205535 diff --git a/KNE0T4oBgHgl3EQfSQBx/vector_store/index.faiss b/KNE0T4oBgHgl3EQfSQBx/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..0bfbf2512374091d14ce0d7a934ad235999b81df --- /dev/null +++ b/KNE0T4oBgHgl3EQfSQBx/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e9965a3455428186716bac33735b8b93adbcbf05ba1b855c204b1fa52d229957 +size 6619181 diff --git a/KNE0T4oBgHgl3EQfSQBx/vector_store/index.pkl b/KNE0T4oBgHgl3EQfSQBx/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..22067c9d2059b7bf2815ff0e7d738985a1a31c5e --- /dev/null +++ b/KNE0T4oBgHgl3EQfSQBx/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2503d805e4e987a275cfb01fa8bc7feaa7dbae6de8ef6e2c2d078a7a743598c0 +size 199516 diff --git a/KtE0T4oBgHgl3EQfzgKz/vector_store/index.pkl b/KtE0T4oBgHgl3EQfzgKz/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..c1f8058841b1449706d093476884ed4e913d489e --- /dev/null +++ b/KtE0T4oBgHgl3EQfzgKz/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:698e91f2df6bc49771f5af151625fd884b4af4895a41ba50b565d5903cc4cc58 +size 305426 diff --git a/MNE3T4oBgHgl3EQfBAmd/content/2301.04263v1.pdf b/MNE3T4oBgHgl3EQfBAmd/content/2301.04263v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bdc66c1c4e29d444eb5396bd0ab9e359051f826c --- /dev/null +++ b/MNE3T4oBgHgl3EQfBAmd/content/2301.04263v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed3e666c27550ea02dffabfb7d231a02f49a097027f8e14ce8295581e8604265 +size 250245 diff --git a/MNE3T4oBgHgl3EQfBAmd/vector_store/index.pkl b/MNE3T4oBgHgl3EQfBAmd/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..3e1b3d574185f9f4e0b6b2c30c52afa044bfbb19 --- /dev/null +++ b/MNE3T4oBgHgl3EQfBAmd/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f71f8c3ecb7af3b4240ff14d69b86e722b2ef67540a170675e6e9e1adfb08d71 +size 114930 diff --git a/MNE3T4oBgHgl3EQfwQsY/vector_store/index.faiss b/MNE3T4oBgHgl3EQfwQsY/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..c03903356e2e89fd7a2b896fbd934638905e71eb --- /dev/null +++ b/MNE3T4oBgHgl3EQfwQsY/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ab194b2a5b36e464b8b554f74367c70e8441ec3b18c53a0b92c769c81c9771c3 +size 4390957 diff --git a/MNFPT4oBgHgl3EQfkjUi/content/2301.13118v1.pdf b/MNFPT4oBgHgl3EQfkjUi/content/2301.13118v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..14c3b6a608b6b945c52728d183fc468d46a9ae71 --- /dev/null +++ b/MNFPT4oBgHgl3EQfkjUi/content/2301.13118v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d092ce101c7d31ec082c756202403c84b7a397ed66a5d5a644096946a2db0618 +size 3671258 diff --git a/MNFPT4oBgHgl3EQfkjUi/vector_store/index.faiss b/MNFPT4oBgHgl3EQfkjUi/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..2ea89ee15e4005f28f72809d4b888a6a422b960f --- /dev/null +++ b/MNFPT4oBgHgl3EQfkjUi/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e24aa5d708ce6c7ccba5e5172523f4fba0f22ef0866d7909983e15cee78fefb6 +size 2883629 diff --git a/O9E2T4oBgHgl3EQfVQdj/content/2301.03821v1.pdf b/O9E2T4oBgHgl3EQfVQdj/content/2301.03821v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2367c174ad7f7b58aa407bfe1cd0dac6a59775e2 --- /dev/null +++ b/O9E2T4oBgHgl3EQfVQdj/content/2301.03821v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c3db35f13d355c2e17498ca0b6ddc6b682990bf5beea45d430e41dde8cdf10c9 +size 727904 diff --git a/O9E2T4oBgHgl3EQfVQdj/vector_store/index.pkl b/O9E2T4oBgHgl3EQfVQdj/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..a089b4a360ddcc6f4031cb9d772d9bdc6283320f --- /dev/null +++ b/O9E2T4oBgHgl3EQfVQdj/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:540e5bcc3166a381afe70c5ce52d1c456fa0cfc2fae5628255835ab688d6b76d +size 514947 diff --git a/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/2301.13309v1.pdf.txt b/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/2301.13309v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..0c60a2898121c065367a0c050fc1b63b6dc6b465 --- /dev/null +++ b/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/2301.13309v1.pdf.txt @@ -0,0 +1,928 @@ +Elastoplastic modelling of sheared colloidal glasses using Eshelby inclusions +Sagar Malik1, L. Meenakshi2, Atharva Pandit1, Antina Ghosh1, +Peter Schall3, Bhaskar Sengupta2, Vijayakumar Chikkadi1 +1 Physics Division, Indian Institute of Science Education and Research Pune, +411008 Pune, India. +2 Physics Division, Vellore Institute of Technology, +632014 Vellore, India. +3 Institute of Physics, University of Amsterdam, +1098 XH Amsterdam, The Netherlands. +We investigate spatial correlations of strain fluctuations in sheared colloidal glasses and simula- +tions of sheared amorphous solids. The correlations reveal a quadrupolar symmetry reminiscent of +the strain field due to an Eshelby’s inclusion. However, they display an algebraic decay 1/rα, where +the exponent α is close to 1 in the steady state. It takes values between 3 to 1 in the transient +stages of deformation. We explain these observations using a simple model based on interacting +Eshelby inclusions. As the system is sheared beyond the linear response to plastic flow, the density +correlations of inclusions are enhanced and it emerges as key to understanding the elastoplastic +response of the system to applied shear. +Amorphous solids are an important class of materi- +als that appear in various forms ranging from metallic +glasses to polymeric glasses and soft materials made of +emulsions, foams and granular matter [1, 2]. Even though +their mechanical properties differ significantly, they dis- +play similar elastic and plastic properties. +Therefore, +the elastoplastic deformation of amorphous solids has at- +tracted considerable attention in the past decade, and it +has been a topic of intense research [1, 3]. Due to dis- +ordered structure, the dislocation-based models of crys- +tal plasticity cannot be extended to amorphous plasticity +[1, 4]. So, several questions relating to plasticity carriers +in amorphous solids, such as their characteristics, forma- +tion, and spatiotemporal organization, are central to our +understanding of this topic. +In recent years, simulations and experiments have es- +tablished that plastic deformation in amorphous solids +occurs due to localized rearrangement of particles asso- +ciated with long-range quadrupolar strain field [5–9]. It +resembles Eshelby’s solution around a strained spheri- +cal inclusion in a homogeneous isotropic solid [10, 11]. +The overall deformation occurs due to spatiotemporal +interactions of such plastic rearrangements mediated by +elasticity. These features of amorphous plasticity have +long been an integral part of many elastoplastic models +[12–15]. Recent theoretical models have exploited these +ideas to explain the formation of shear bands and yielding +quasi-static MD simulations of sheared amorphous solids +[16, 17, 19]. Further, the mesoscopic simulations of amor- +phous plasticity based on lattice models have also incor- +porated the long-range nature of elastic strain fields aris- +ing from plastic rearrangements [20–22]. The experimen- +tal investigations along these lines are scarce [8, 9]. The +previous experiments on sheared colloidal glasses had in- +vestigated spatial correlations of strain, and non-affine +displacements in the steady state [9, 23]. Surprisingly, +the spatial correlations of non-affine displacements were +found to decay as 1/r, instead of 1/r2 as predicted by +Eshelby’s solution. +The anomalous exponent was pro- +posed to originate from the interactions of several inclu- +sions [24]. However, there is no experimental evidence. +Besides, the nature of these correlations in the transient +stages of deformation remains unclear. What is known +is that the spatial correlations of strain in quiescent col- +loidal glasses or the linear response regime decay as 1/r3 +[25]. Therefore, the nature of the strain correlations as +the system is sheared beyond the linear response to plas- +tic flow is unknown. It is natural to ask whether a simple +model based on interacting Eshelby-like inclusions can of- +fer new insights into microscopic strain fluctuations and +their correlations in the transient and steady states of +deformation of amorphous solids. +This paper presents a combined experimental and nu- +merical investigation of microscopic strain fluctuations +and their spatial correlations in 3D amorphous solids un- +der shear. The experiments are performed using dense +colloidal suspensions, and the simulations were done us- +ing low temperature, dense binary mixture using molec- +ular dynamics techniques. +The spatial correlations of +strain fluctuations reveal a familiar quadrupolar sym- +metry; however, the correlations display an anomalous +decay of 1/rα, where the exponent α ∼ 1 in the steady +state and it varies from α ∼ 3 − 1 in the transient stages +of deformation. We provide an explanation for these ob- +servations using ideas that are motivated by mesoscopic +models of amorphous plasticity. +We identify inclusion +centers based on the principal component of shear strain +ϵxz. All the particles with ϵxz larger than a threshold are +considered centers of Eshelby inclusions. +Further, the +inclusion centers are used to determine synthetic strain +maps following the simple superposition principle. The +spatial correlations of synthetic strains reveal the origin +of anomalous exponents α and further highlight the role +of spatial clustering of inclusions on the elastoplastic de- +formation of amorphous solids. +We prepare a colloidal glass by suspending sterically +arXiv:2301.13309v1 [physics.app-ph] 30 Jan 2023 + +2 +stabilized fluorescent polymethylmethacrylate particles +in a density and refractive index matching mixture of cy- +cloheptyl bromide and cis-decalin. The particles have a +diameter of σ = 1.3µm, and a polydisperity of 7% to pre- +vent crystallization. The suspension of a desired volume +fraction φ ∼ 0.60 is prepared via centrifugation, and it is +sheared using a shear cell that has two parallel bound- +aries [9]. The 3D imaging of the particles during shear +is done using a confocal microscope. The shear rate in +our experiment is ˙γ ∼ 1.5 × 10−5s−1. Further details are +included in the experimental section of supplementary +information. In our molecular dynamics simulations, we +prepare glass samples by initially equilibrating the binary +mixture in a liquid state at temperature T = 1.0 and +gradually cooling it to a final temperature of T = 0.3 at +a slow cooling rate of 10−5 to obtain well relaxed sam- +ples. The simulations are done at a density of ρ = 1.2, +a system size of N = 150000 particles, and a time step +of ∆t = 0.005 with boundary conditions in all directions. +The glassy samples are sheared along the xz plane at a +constant shear rate ˙γ = 10−4. The statistical averaging +is done using 100 realization with different initial condi- +tions. The other simulation details are provided in the +simulations section of supplementary information. +The particle coordinates are used to compute micro- +scopic strain and their spatial correlations. +Briefly, to +compute the particle level strain, the displacement of a +particle relative to its first neighbors are considered to +define a best fit affine strain tensor. The best fit ten- +sor minimizes the non-affine displacement for the par- +ticle [4]. +The principal shear strain component ϵxz is +obtained from the strain tensor. We will investigate the +correlations in the fluctuations of ϵxz using the following +expression [9]: +Cϵ(∆r) = ⟨ϵxz(r + ∆r)ϵxz(r)⟩ − ⟨ϵxz(r)⟩2 +⟨ϵxz(r)2⟩ − ⟨ϵxz(r)⟩2 +, +(1) +where angular brackets denote average over all the parti- +cles in the systems and several strain steps. Cϵ correlates +values of ϵxz at locations separated by ∆r, this way we +capture the elasto-plastic response of the system in the +steady state. +We first present the analysis of microscopic strain +and their spatial correlations in the steady state in ex- +periments. +The system is sheared at constant rate of +˙γ ∼ 1.5 × 10−5s−1, and the flow is homogeneous in the +steady state [9]. A strain interval of ∆γ ∼ 0.036 is used +to compute individual particles’ displacements and mi- +croscopic strain tensor. A reconstruction of the particle +shear strain ϵxz is shown in Fig. S1(a). +The particles +are color-coded based on ϵxz; the red color indicates de- +formation in the direction of shear, and the blue color +indicates deformation in the opposite direction. The par- +ticle scale deformation is heterogeneous with a network +of positive and negative strain regions. The spatial cor- +relations averaged over several strain steps of ∆γ ∼ 10−3 +in the steady is shown in the inset of Fig. 1. It is the +correlation in the shear plane, which is obtained when +FIG. 1: Spatial correlations of microscopic strain +averaged over all the particles in the steady state. Main +panel : the projection of strain correlations from +experiments is shown using square symbols and the +simulation results are presented using circles. The +dashed line shows a 1/∆r variation. Inset: the spatial +correlations of ϵxz in the shear plane xz obtained from +the experiments. This corresponds to the correlations in +Eq. when ∆y = 0. The quadrupolar symmetry of strain +correlations is evident. +∆r = (∆x, 0, ∆z) in Eq. 1. It has a familiar quadrupo- +lar symmetry characteristic of the strain field around an +Eshelby inclusion in homogeneous elastic materials. It +suggests that high-strain regions (blue and red zones in +Fig. S1(a)) act as strained inclusions in an elastic ma- +trix. Further, we project the correlation function onto +its corresponding circular harmonic to determine radial +correlations of strain following the expression : +C4 +ϵ (∆r) = +� 2π +0 +Cϵ(∆x, 0, ∆z) cos(4θ) dθ. +(2) +The main panel of Fig. 1 shows the radial correlations +C4 +ϵ (∆r) corresponding to the polar plot in the inset of +Fig. 1. Similar to non-affine displacements [9], the strain +correlations display an algebraic decay 1/rα, where α ∼ +1. However, this decay is slower than the 1/r3 variation +predicted by Eshelby for a strained spherical inclusion +in isotropic elastic solid [10]. +The line with circles in +Fig. 1 denotes the strain correlations obtained from finite +shear rate simulations performed at ˙γ = 10−4. A good +agreement between the curves confirms the robustness of +strain correlations in two disparate systems. It appears +that the 1/r decay stems from the strain correlations that +capture the elastoplastic response of not a single inclusion +but several interacting inclusions. This is also evident +from the heterogeneous strain map in Fig. S1(a), which +points to the formation of multiple inclusions. +Several investigations of amorphous plasticity and +mesoscopic simulations have used a minimal model based +on interacting Eshelby inclusions to understand elasto- +plastic features of sheared amorphous solids [16–21, 31]. +Motivated by these ideas, we identify the inclusion cen- + +Experiments +OSimulations +10 +C +(△r) +20 +0.1 +0.05 +10° +6 +0 +0 +-0.05 +-20 +-0.1 +-0.15 +-20 +0 +20 +10 +X/g +101 +Arl3 +FIG. 2: (a) Spatial maps of particles with shear strain ϵxz > 0.95ϵmax +xz +, where ϵmax +xz +is the maximum strain of +particles. These are considered as inclusion centers in the first case. (b) Inclusion centers are obtained from a +random selection of particles. Note that the particles in (a) and (b) are again shown in a 5µm thick region in +y−direction. (c) The normalized pair correlation function of inclusion centers. The continuous line corresponds to +inclusion centers obtained from particles with top 5% strain, and the dashed line is obtained for the random +selection of inclusion centers. +ters in our experiments using microscopic strain and use +them to generate synthetic strain fields. +All the par- +ticles with shear strain exceeding a threshold value of +|ϵi +xz| > γc. This corresponds to the top ∼ 10% of parti- +cles in our system. It was verified that the results pre- +sented here are robust and not sensitive to the strain +threshold. A spatial map of the inclusions thus identified +is shown in Fig. 2(a). Apparently, they form clusters. To +examine the effect of clustering, we also consider another +case where the inclusion centers are randomly identified, +as shown in Fig. 2(b). The pair correlation function g(r) +of the inclusions centers is presented in Fig.2(c), which +is averaged over all inclusions in the system and several +strain steps of ∆γ in the steady state. It is evident that +the structural correlations are stronger when particles +with top strains are considered as inclusion centers. In +contrast, the inclusion centers corresponding to random +selection are weakly correlated. +Next, we calculate the synthetic strain of particles due +to the inclusions. +The far-field shear strain around a +single inclusion in an isotropic homogeneous elastic solid +is εI +xz ∝ +ϵ0cos(4θ) +r3 +[1], where ϵ0 is the core strain, θ = +cos−1(z, r) is the azimuthal angle in the plane of shear +and the particle diameter is core size. The core strain of +an inclusion ϵ0 is assumed to be the shear strain of the +particle obtained from experiments. The shear strain on +any other particle in the system is a superposition of +shear strains due to all inclusions +ϵi +xy = +Ninc +� +j=1 +εI,j +xz (∆rij, θij), +(3) +where ∆rij is the distance of particle i from an inclu- +sion j, and θij = cos−1(zij, rij). The reconstructions of +shear strain when the inclusions are selected based on +high-strain particles and randomly chosen are shown in +the left column of Fig. S2. It is not surprising that the +deformation map in Figs. S2(top left) compares well with +experiments in Fig. S1. To test our approach further, we +have computed spatial correlations of synthetic strain by +averaging over several strain steps, and these results are +shown in the right column of Figs. S2 (SI). Surprisingly, +the strain correlations corresponding to high-strain in- +clusion centers display a quadrupolar symmetry in the +top right panel of Fig. S2. +On the contrary, it is ab- +sent from the one corresponding to random inclusions +in the bottom right panel of Fig. S2. In the next step, +the radial correlations for high-strain inclusions are com- +puted and are shown together with experimental results +in Figs. 2(d). There is an excellent agreement. These +results establish that strain correlation for sheared sys- +tems can be modeled as an interacting system of Eshelby +inclusions. +We next turn our attention to strain correlations in the +transient stages of deformation before the system attains +a steady state. The correlations in the steady state are +averaged over several strain intervals. However, a similar +averaging in the transient stages is not feasible in exper- +iments due to a lack of sufficient realizations. Therefore, +we exploit simulation data to investigate the transient +stages. The strain correlations are computed using Eq. 1 +at γ = 0.02, 0.05, and 0.1 and are averaged over the +azimuthal angle θ using Eq. 2. The results are shown in +Fig. 3c using thick lines. The dotted lines with slopes −1 +and −3 are shown for clarity. Surprisingly, the correla- +tions decay with different exponents 1/rα as the system +is sheared. The exponents obtained from data fitting are +shown in Fig. 3b. When the strain is small, the expo- +nent is α ∼ 3, which varies continuously with increasing +strain until α ∼ 1 in the steady state. +We elucidate +the underlying physics by analyzing the synthetic strain +fields. The first step is the identification of inclusions. +The Fig. 3a shows the count of inclusions with increas- +ing strain based on the threshold value +��ϵi +xz +�� > γc. The +threshold value is set such that the number of inclusions +in the steady state is ∼ 10% of particles in the system. +The population of inclusion centers grows monotonically +as the system is sheared. A similar rise in the population +of inclusion centers was reported by an earlier numeri- +cal study [34]. A reconstruction of inclusion centers is +shown in Fig. S3(a)-(d) at γ = 0.02, 0.04, 0.08, and 0.1, +respectively. It is clear that the inclusions begin to clus- +ter as the system is sheared towards a steady state. The +effect of clustering is also apparent in the pair correlation + +0.05 +0000 +O +60 +50 +40 +(un +30 +20 +O +10 +0.05 +20 +40 +60 +80 +100 +0 +(um)0.05 +40 +wn +30 +O +00 +0.05 +20 +40 +60 +80 +100 +X(um)-High strain particles +- Random particles +10 +g(△r) +100 +10 +101 +100Experiments +10% +Inclusions +10 +(△r +4 +100 +101 +Arlg4 +FIG. 3: Inclusion centers and strain correlations of in +the transient stages of deformation. Top left: The +number of inclusions in the system as it is sheared from +the linear elastic limit to steady plastic flow. Top right: +The exponent α with which the strain correlations +decay as the system is sheared to steady state. Bottom: +The correlations of shear strain (C4 +ϵ (∆r)) at various +stages of deformation before the system attains a steady +state is shown in the main panel. The thick lines are +the simulation results. The symbols show the results +obtained from inclusion analysis. +function g(r) of inclusions. The different symbols corre- +spond to strain values varying from γ = 0.02 − 0.1. The +enhanced peaks in the g(r) with increasing strain point +to clustering of inclusions. To explain the changing value +of the exponent α in Fig.3c, we next compute synthetic +strain fields from the inclusions. As described earlier, all +other particles’ synthetic strain is obtained from the su- +perposition of strain due to all inclusions. Further, their +angle-averaged spatial correlations are determined from +Eqs. 1 and 2. The result of these calculations is shown in +Fig. 3c. The continuous lines indicate the strain correla- +tions obtained from simulations, and the symbols are ob- +tained from the synthetic strain fields due to inclusions. +The agreement simulations and inclusion analysis is ex- +cellent. +These results firmly establish that high-strain +particles in the systems act as inclusion centers. A min- +imal model of interacting inclusions captures the strain +correlations well in the transient and steady state of de- +formation of amorphous solids. +In summary, we have investigated the elastoplas- +tic deformation of amorphous solids by investigating +the spatial correlations of microscopic strain in exper- +iments and simulations. +The correlations show a fa- +miliar quadrupolar symmetry. However, their decay is +anomalous C4 +ϵ (r) ∼ 1/rα, where α ∼ 1 in the steady +state and 1 < α < 3 in the transient stages of defor- +mation. +This behavior is described well by a simple +model of interacting inclusions. The inclusions are iden- +tified from the high-strain particles in the system. +In +the transient stages of deformation, when the strain on +the system is small, the population of inclusion centers +is low and weakly correlated. However, as the strain in- +creases, the inclusions begin to grow and saturate in the +steady state. Besides, they also form clusters, signaling a +stronger spatial correlation. Due to this enhancement in +density correlations, the correlations of synthetic strains +show a gradual change in their form. The correlations +C4 +ϵ (r) ∼ 1/rα, with the exponent taking values from 3 +in the linear regime to 1 in the steady state. The out- +comes of our study firmly establishes the universal nature +of strain correlation in sheared amorphous materials that +are independent of the interactions and microscopic scale +of the system. +ACKNOWLEDGEMENTS +V.C. acknowledges startup grant from IISER Pune. +A.G acknowledges support from Department of Sci- +ence and Technology (DST), India for a WOS grant +no.SR/WOS-A/PM-34. +[1] A. Nicolas, E.E. Ferrero, K. Martens, and J. L. Barrat, +Deformation and flow of amorphous solids: Insights from +elastoplastic models, Rev. Mod. Phys. 90, 045006 (2018). +[2] L. Berthier and G. Biroli, Theoretical perspective on +the glass transition and amorphous materials, Rev. Mod. +Phys. 83, 587 (2011). +[3] J. L. Barrat and A. Lemaitre, Dynamical Heterogeneities +in Glasses, Colloids and Granular Media (Oxford Univer- +sity Press, New York, 2011). +[4] M.L. Falk and J.S. Langer, Dynamics of viscoplastic de- +formation in amorphous solids,Phys. Rev. E 57, 7192 +(1998). +[5] C. E. Maloney and A. Lemaitre, Subextensive scaling in +the athermal, quasistatic limit of amorphous matter in +plastic shear flow, Phys. Rev. Lett. 93, 016001 (2004). +[6] C. E. Maloney and A. Lemaitre, Amorphous systems +in athermal, quasistatic shear, Phys. Rev. E 74, 016118 +(2006). +[7] A. Tanguy, F Leonforte and J. L. Barrat, Plastic response +of a 2D Lennard-Jones amorphous solid: detailed analysis +of the local rearrangements at very slow strain rate, Eur. +Phys. J. E 20, 355 (2006). +[8] P. Schall, D.A. Weitz and F. Spaepen, Structural Rear- +rangements That Govern Flow in Colloidal Glasses, Sci- + +8 +0 +TL +6 +X +n +4 +N +0.05 +0.1 +Strain()3 +2.5 +(α) +2 +1.5 +1 +0 +0.05 +0.1 +Strain()10 +10 +Inclusions +4 +-Simulations +L +C += 0.02 += 0.04 +10-2 += 0.08 +=0.10 +=0.16 +- 1/r +1/r3 +100 +101 +8 rlg5 +ence 318, 1895 (2007). +[9] V. Chikkadi, G. Wegdam, D. Bonn, B. Nienhuis, and P. +Schall, Long-Range Strain Correlations in Sheared Col- +loidal Glasses,Phys. Rev. Lett. 107, 198303 (2011). +[10] J.D. Eshelby , The determination of the elastic field of +an ellipsoidal inclusion, and related problems, Proc. Roy. +Soc. A 241, 376 (1957) +[11] J. D. Eshelby , The elastic field outside an ellipsoidal +inclusion, Proc. R. Soc. London Ser. A 252, 561 (1959) +[12] F. Spaepen, A microscopic mechanism for steady state +inhomogeneous flow in metallic glasses, Acta Metall. 25, +407 (1977). +[13] A. S. Argon, Plastic deformation in metallic glasses, Acta +Metall. 27, 47 (1979). +[14] P. Hebraud and F. Lequeux, Mode-Coupling Theory for +the Pasty Rheology of Soft Glassy Materials, Phys. Rev. +Lett. 81, 2934 (1998). +[15] G. Picard, A. Ajdari, F. Lequeux and L. Bocquet, Elastic +consequences of a single plastic event: a step towards the +microscopic modeling of the flow of yield stress fluids,Eur. +Phys. J.E 15,371 (2004 ) +[16] R. Dasgupta, H. G. E. Hentschel, and I. Procaccia, +Microscopic Mechanism of Shear Bands in Amorphous +Solids, Phys. Rev. Lett. 109, 255502 (2012). +[17] R. Dasgupta, H. G. E. Hentschel, and I. Procaccia, Yield +strain in shear banding amorphous solids, Phys. Rev. E +87, 022810 (2013). +[18] R. Dasgupta, O. Gendelman, P. Mishra, I. Procaccia, and +C. A. B. Z. Shor, Shear localization in three-dimensional +amorphous solids, Phys. Rev. E 88, 032401 (2013). +[19] V. Hieronymus-Schmidt, H. Rosner, G. Wilde, and A. +Zaccone, Shear banding in metallic glasses described by +alignments of Eshelby quadrupoles, Phys. Rev. B 95, +134111 (2017). +[20] K. A. Dahmen, Y. B. Zion, and J. T. Uhl, Microme- +chanical Model for Deformation in Solids with Universal +Predictions for Stress-Strain Curves and Slip Avalanches, +Phys. Rev. Lett. 102, 175501 (2009). +[21] Z. Budrikis1, D. F. Castellanos, S. Sandfeld, M. Zaiser +and S. Zapperi, Universal features of amorphous plastic- +ity, Commun Phys 1, 61 (2018). +[22] C. Liu, S. Dutta, P. Chaudhuri and K. Martens, Elasto- +plastic Approach Based on Microscopic Insights for the +Steady State and Transient Dynamics of Sheared Disor- +dered Solids, Phys. Rev. Lett. 126 , 138005 (2021). +[23] V. Chikkadi and P. Schall, Nonaffine measures of particle +displacements in sheared colloidal glasses, Phy. Rev. E. +85, 031402 (2012). +[24] V. Chikkadi, E. Woldhuis, M. van Hecke and P. Schall, +Correlations of strain and plasticity in a flowing foam , +Europhys. Lett. 112, 36004 (2015) +[25] M. Hassani, E. M. Zirdehi, K. Kok, P. Schall, M. Fuchs, +and F. Varnik, Long-range strain correlations in 3D qui- +escent glass forming liquids, Europhys. Lett. 124 ,8003 +(2018). +[26] A. Ghosh, Z. Budrikis, V. Chikkadi, A.L. Sellerio, S. Zap- +peri, and P. Schall, Direct Observation of Percolation in +the Yielding Transition of Colloidal Glasses, Phys. Rev. +Lett. 118, 148001 (2017). +[27] A. Lemaitre and C. Caroli, Rate-Dependent Avalanche +Size in Athermally Sheared Amorphous Solids, Phys. +Rev. Lett. 103, 065501 (2009). +[28] S. Karmakar, E. Lerner, and I. Procaccia, Statistical +physics of the yielding transition in amorphous solids, +Phys. Rev. E 82, 055103(R) (2010). +[29] A. S. Argon and L. T. Shi, Analysis of plastic flow in an +amorphous soap bubble raft by the use of an inter-bubble +potential, Philos. Mag. A 46, 275 (1982). +[30] K. E. Jensen, D. A. Weitz, and F. Spaepen, Local shear +transformations in deformed and quiescent hard-sphere +colloidal glasses, Phys. Rev. E 90, 042305 (2014). +[31] D. Rodney,A. Tanguy and D. Vandembroucq. Modeling +the mechanics of amorphous solids at different length +scale and time scale. Modelling and Simulation in Ma- +terials Science and Engineering 19.8, 083001 (2011). +[32] A. Nicolas, J. Rottler, and J. L. Barrat, Spatiotemporal +correlations between plastic events in the shear flow of +athermal amorphous solids. Eur. Phys. J. E 37, 50 (2014). +[33] T. Albaret, A. Tanguy, F. Boioli, and D. Rodney, Map- +ping between atomistic simulations and Eshelby inclu- +sions in the shear deformation of an amorphous silicon +model, Phys. Rev. E 93, 053002 (2016). +[34] T. Albaret, F. Boioli, and D. Rodney, Time-resolved +shear transformations in the transient plastic regime of +sheared amorphous silicon, Phys. Rev. E 102, 053003 +(2020). + +Supplementary information +Elastoplastic modelling of sheared amorphous solids using Eshelby inclusions +Sagar Malik1, L. Meenakshi2, Atharva Pandit1, Antina Ghosh1, +Peter Schall3, Bhaskar Sengupta2, Vijayakumar Chikkadi11 +11 Physics Division, Indian Institute of Science Education and Research Pune, Pune 411008, India. +2 Physics Division, Vellore Institute of Technology, Vellore ******, India. +3 Institute of Physics, University of Amsterdam, Amsterdam, The Netherlands. +I. +MATERIALS AND METHODS +A. +Experimental methods +We prepared a colloidal glass by suspending sterically stabilized fluorescent polymethylmethacrylate particles in a +density and refractive index matching mixture of cycloheptyl bromide and cis-decalin. The particles have a diameter +of σ = 1.3µm, and a polydisperity of 7% to prevent crystallization. The suspension was centrifuged at an elevated +temperature to obtain a dense sediment, which was subsequently diluted to get a suspension of desired volume fraction +φ ∼ 0.60. The sample was sheared using a shear cell that had two parallel boundaries separated by a distance of +∼ 50σ along the z−direction. A piezoelectric device was used to move the top boundary in the x−direction to apply +shear rates in the range 10−5 − 10−4s−1. To prevent boundary-induced crystallization in our samples, the boundaries +were coated with a layer of polydisperse particles. Confocal microscopy was used to image the individual particles +and to determine their positions in three dimensions with an accuracy of 0.03µm in the horizontal and 0.05µm in the +vertical direction. We tracked the motion of ∼ 2 × 105 particles during a 25-min time interval by acquiring image +stacks every 60 s. All the measurements presented here were made in the steady state, after the sample had been +strained to 100% at shear rate of 1.5 × 10−5s−1, as confirmed by other independent rheological measurements. +B. +Simulation methods +To prepare the thermal glass we use the well studied Kob-Anderson binary mixture model [1]. Our model consists +of N classical point particles confined in a three-dimensional simulation box in the NV T ensemble. We choose a +binary Lennard-Jones (LJ) mixture of particles which are labeled as A and B, and their number ratio is 80 : 20. For +simplicity, the mass of both types of particles m is taken to be the same and equal to unity. The interaction potential +for a pair of particles has the following form, +Uαβ(r) = 4ϵαβ +��σαβ +r +�12 +− +�σαβ +r +�6 ++ A0 + A1 +� r +σαβ +� ++ A2 +� r +σαβ +�2� +, r ≤ rcut += 0, +r>rcut, +(1) +where α, β ∈ A, B. The units of various quantities in our simulation are as follows: lengths are expressed in the unit +of σAB, energies in the unit of ϵAB, time in the unit of (mσ2 +AB/ϵAB)1/2 and temperature in the unit of ϵAB/kB. Here, +kB is the Boltzmann constant which is unity. The parameters σαβ and ϵαβ are chosen as follows: σAA = 1.0, σBB = +0.88, σAB = 0.8 and ϵAA = 1.0, ϵBB = 0.5, ϵAB = 1.5. With these set of parameters, a binary LJ mixture avoids +crystallization below Tg and forms stable glass. Tg for this model is approximately 0.44 in the reduced unit [1]. To +improve the computational efficiency, the potential is truncated at rcut = 2.5σAA. The parameters A0 = 0.040490, +A1 = −0.009702 and A2 = 0.000620 are such that the potential and its derivatives (up to second order) go to zero +smoothly at r = rcut. +To prepare the glass samples, we use MD simulation. All simulations are carried out at density ρ = 1.2 and a total +number of particles N = 150000. Position and velocity of particles are updated using the velocity-Verlet integration +technique [2] with time step ∆t = 0.005. The temperature of the system is kept fixed to the desired value by employing +the Berendsen thermostat [3]. Also, we apply periodic boundary conditions in all directions. +We begin our simulation by equilibrating the binary mixture in the liquid state at temperature T = 1.0. The system +is then cooled to the final temperature T = 0.3 below the glass transition temperature Tg = 0.43 with a slow cooling +rate 10−5 to prepare well relaxed glassy samples. For statistical averaging, the whole process is repeated 100 times +with different initial realizations. Finally, the glassy samples are sheared along the xz plane at a constant shear rate +˙γ = 10−4. During the shear process, the temperature is controlled by dissipative particle dynamics thermostat [4]. +arXiv:2301.13309v1 [physics.app-ph] 30 Jan 2023 + +2 +C. +Calculation of strain tensor and spatial correlations +To compute these quantities we follow particle trajectories and identify the nearest neighbors of each particle as +those separated by less than r0, the first minimum of the pair correlation function. We subsequently determine the +best affine deformation tensor Γ describing the transformation of the nearest neighbor vectors, di, over the strain +interval ∆γ [5], by minimizing D2 +min = (1/n)�n +i=1(di(γ + ∆γ) − Γdi(γ))2. The symmetric part of Γ is the local +strain tensor. The remaining non-affine component D2 +min has been used as a measure of plastic deformation. We +will investigate the correlations in the fluctuations of the principal shear strain component ϵxz using the following +expression [6]: +Cϵ(∆r) = ⟨ϵxz(r + ∆r)ϵ(r)⟩ − ⟨ϵxz(r)⟩2 +⟨ϵxz(r)2⟩ − ⟨ϵxz(r)⟩2 +, +(2) +where angular brackets denote average over all the particles in the systems and several strain steps. Cϵ correlates +values of ϵxz at locations separated by ∆r, this way we capture the elastic response of the system in the steady state. +II. +MICROSCOPIC SHEAR STRAIN AND SPATIAL CORRELATIONS +A. +Results from experiments in the steady state +FIG. S1. Strain map in sheared colloidal glasses at a shear rate of ˙γ ∼ 1.5 × 10−5s−1. The particles in a small section (∼ 3σ) +along y-direction are color coded based on their shear strain ϵxz values. Red color indicates deformation in direction of shear +and blue color indicates deformation in the opposite direction. +FIG. S2. The synthetic strain maps obtained from inclusions centers is shown in left panels and the right panels display their +spatial correlations. The synthetic strain values are computed based on inclusions centers that were identified from high strain +particles (top left) and selected randomly (bottom left). The spatial correlations of strain fluctuations when high strain particles +are considered as inclusions (top right) and when inclusions are selected randomly (bottom right) + +0.05 +60 +50 +40 +(un) +0 +30 +20 +10 +-0.05 +0 +40 +80 +20 +60 +0 +100 +X(μm)0.05 +60 +0.04 +0.03 +50 +0.02 +40 +0.01 +(wn) +0 +N30 +-0.01 +20 +-0.02 +-0.03 +10 +-0.04 +0 +-0.05 +0 +10 +20 +30 +40 +50 +60 +70 +80 +90 +100 +X(μm)30 +0.1 +20 +0.05 +10 +Zlg +0 +0 +-10 +-0.05 +-20 +-0.1 +-30 +-0.15 +-20 +0 +20 +X/o0.05 +60 +50 +40 +(un)Z +0 +30 +20 +10 +-0.05 +0 +20 +40 +60 +80 +100 +X(μum)30 +0.1 +20 +0.05 +10 +b +0 +N +-10 +-0.05 +-20 +-0.1 +-30 +-0.15 +-20 +0 +20 +X/g3 +B. +Results from simulations in the transient stages of deformation +FIG. S3. A spatial map of inclusion centers in the transient stages of deformation. The inclusions are identified based on a +threshold value of shear strain ϵi > γc, where γc is defined in the main text. The inclusions in a section of one particle diameter +thickness are shown at γ = 0.02 (a), γ = 0.04 (b), γ = 0.08 (c) and γ = 0.1 (d). As the system is strained, the inclusions begin +to cluster +[1] W. Kob, H. C. Andersen, Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove +correlation function, Phys. Rev. E 51, 4626 (1995). +[2] L. Verlet, Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. +159, 98 (1967). +[3] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, J. R. Haak, Molecular dynamics with coupling to +an external bath, J. Chem. Phys. 81, 3684 (1984). +[4] T. Soddemann, B. Dunweg, K. Kremer, Dissipative particle dynamics: A useful thermostat for equilibrium and nonequilib- +rium molecular dynamics simulations, Phys. Rev. E 68, 046702 (2003). +[5] M.L. Falk and J.S. Langer, Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E 57, 7192 (1998). +[6] V. Chikkadi, G. Wegdam, D. Bonn, B. Nienhuis, and P. Schall, Long-range strain correlations in sheared colloidal glasses, +Phys. Rev. Lett. 107, 198303 (2011). + + = 0.02 +45 +0.015 +40 +0.01 +35 +0.005 +30 +25 +0 +20 +-0.005 +15 +-0.01 +10 +5 +-0.015 +15 +20 +25 +30 +35 +45 +5 +10 +40 +X/g= 0.04 +45 +0.015 +40 +0.01 +35 +0.005 +30 +25 +0 +20 +-0.005 +15 +-0.01 +10 +5 +0.015 +5 +10 +15 +20 +25 +30 +35 +40 +45 +X/g0.08 +45 +0.015 +40 +0.01 +35 +0.005 +30 +25 +0 +20 +-0.005 +15 +-0.01 +10 +0.015 +5 +10 +15 +20 +25 +30 +5 +35 +40 +45 +X/g0.10 +45 +0.015 +40 +0.01 +35 +0.005 +30 +0 +20 +-0.005 +15 +-0.01 +10 +5 +0.015 +5 +10 +15 +20 +25 +30 +35 +40 +45 +X/g \ No newline at end of file diff --git a/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/load_file.txt b/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5103bb9a28d44ac37b8f49f9240b22a46d64d170 --- /dev/null +++ b/OtFQT4oBgHgl3EQfXzZD/content/tmp_files/load_file.txt @@ -0,0 +1,668 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf,len=667 +page_content='Elastoplastic modelling of sheared colloidal glasses using Eshelby inclusions Sagar Malik1, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Meenakshi2, Atharva Pandit1, Antina Ghosh1, Peter Schall3, Bhaskar Sengupta2, Vijayakumar Chikkadi1 1 Physics Division, Indian Institute of Science Education and Research Pune, 411008 Pune, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2 Physics Division, Vellore Institute of Technology, 632014 Vellore, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3 Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We investigate spatial correlations of strain fluctuations in sheared colloidal glasses and simula- tions of sheared amorphous solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The correlations reveal a quadrupolar symmetry reminiscent of the strain field due to an Eshelby’s inclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, they display an algebraic decay 1/rα, where the exponent α is close to 1 in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It takes values between 3 to 1 in the transient stages of deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We explain these observations using a simple model based on interacting Eshelby inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' As the system is sheared beyond the linear response to plastic flow, the density correlations of inclusions are enhanced and it emerges as key to understanding the elastoplastic response of the system to applied shear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Amorphous solids are an important class of materi- als that appear in various forms ranging from metallic glasses to polymeric glasses and soft materials made of emulsions, foams and granular matter [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Even though their mechanical properties differ significantly, they dis- play similar elastic and plastic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Therefore, the elastoplastic deformation of amorphous solids has at- tracted considerable attention in the past decade, and it has been a topic of intense research [1, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Due to dis- ordered structure, the dislocation-based models of crys- tal plasticity cannot be extended to amorphous plasticity [1, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' So, several questions relating to plasticity carriers in amorphous solids, such as their characteristics, forma- tion, and spatiotemporal organization, are central to our understanding of this topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In recent years, simulations and experiments have es- tablished that plastic deformation in amorphous solids occurs due to localized rearrangement of particles asso- ciated with long-range quadrupolar strain field [5–9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It resembles Eshelby’s solution around a strained spheri- cal inclusion in a homogeneous isotropic solid [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The overall deformation occurs due to spatiotemporal interactions of such plastic rearrangements mediated by elasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' These features of amorphous plasticity have long been an integral part of many elastoplastic models [12–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Recent theoretical models have exploited these ideas to explain the formation of shear bands and yielding quasi-static MD simulations of sheared amorphous solids [16, 17, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Further, the mesoscopic simulations of amor- phous plasticity based on lattice models have also incor- porated the long-range nature of elastic strain fields aris- ing from plastic rearrangements [20–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The experimen- tal investigations along these lines are scarce [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The previous experiments on sheared colloidal glasses had in- vestigated spatial correlations of strain, and non-affine displacements in the steady state [9, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Surprisingly, the spatial correlations of non-affine displacements were found to decay as 1/r, instead of 1/r2 as predicted by Eshelby’s solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The anomalous exponent was pro- posed to originate from the interactions of several inclu- sions [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, there is no experimental evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Besides, the nature of these correlations in the transient stages of deformation remains unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' What is known is that the spatial correlations of strain in quiescent col- loidal glasses or the linear response regime decay as 1/r3 [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Therefore, the nature of the strain correlations as the system is sheared beyond the linear response to plas- tic flow is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It is natural to ask whether a simple model based on interacting Eshelby-like inclusions can of- fer new insights into microscopic strain fluctuations and their correlations in the transient and steady states of deformation of amorphous solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' This paper presents a combined experimental and nu- merical investigation of microscopic strain fluctuations and their spatial correlations in 3D amorphous solids un- der shear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The experiments are performed using dense colloidal suspensions, and the simulations were done us- ing low temperature, dense binary mixture using molec- ular dynamics techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The spatial correlations of strain fluctuations reveal a familiar quadrupolar sym- metry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' however, the correlations display an anomalous decay of 1/rα, where the exponent α ∼ 1 in the steady state and it varies from α ∼ 3 − 1 in the transient stages of deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We provide an explanation for these ob- servations using ideas that are motivated by mesoscopic models of amorphous plasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We identify inclusion centers based on the principal component of shear strain ϵxz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' All the particles with ϵxz larger than a threshold are considered centers of Eshelby inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Further, the inclusion centers are used to determine synthetic strain maps following the simple superposition principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The spatial correlations of synthetic strains reveal the origin of anomalous exponents α and further highlight the role of spatial clustering of inclusions on the elastoplastic de- formation of amorphous solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We prepare a colloidal glass by suspending sterically arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='13309v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='app-ph] 30 Jan 2023 2 stabilized fluorescent polymethylmethacrylate particles in a density and refractive index matching mixture of cy- cloheptyl bromide and cis-decalin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The particles have a diameter of σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='3µm, and a polydisperity of 7% to pre- vent crystallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The suspension of a desired volume fraction φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='60 is prepared via centrifugation, and it is sheared using a shear cell that has two parallel bound- aries [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The 3D imaging of the particles during shear is done using a confocal microscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The shear rate in our experiment is ˙γ ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 × 10−5s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Further details are included in the experimental section of supplementary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In our molecular dynamics simulations, we prepare glass samples by initially equilibrating the binary mixture in a liquid state at temperature T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='0 and gradually cooling it to a final temperature of T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='3 at a slow cooling rate of 10−5 to obtain well relaxed sam- ples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The simulations are done at a density of ρ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='2, a system size of N = 150000 particles, and a time step of ∆t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 with boundary conditions in all directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The glassy samples are sheared along the xz plane at a constant shear rate ˙γ = 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The statistical averaging is done using 100 realization with different initial condi- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The other simulation details are provided in the simulations section of supplementary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The particle coordinates are used to compute micro- scopic strain and their spatial correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Briefly, to compute the particle level strain, the displacement of a particle relative to its first neighbors are considered to define a best fit affine strain tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The best fit ten- sor minimizes the non-affine displacement for the par- ticle [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The principal shear strain component ϵxz is obtained from the strain tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We will investigate the correlations in the fluctuations of ϵxz using the following expression [9]: Cϵ(∆r) = ⟨ϵxz(r + ∆r)ϵxz(r)⟩ − ⟨ϵxz(r)⟩2 ⟨ϵxz(r)2⟩ − ⟨ϵxz(r)⟩2 , (1) where angular brackets denote average over all the parti- cles in the systems and several strain steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Cϵ correlates values of ϵxz at locations separated by ∆r, this way we capture the elasto-plastic response of the system in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We first present the analysis of microscopic strain and their spatial correlations in the steady state in ex- periments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The system is sheared at constant rate of ˙γ ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 × 10−5s−1, and the flow is homogeneous in the steady state [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A strain interval of ∆γ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='036 is used to compute individual particles’ displacements and mi- croscopic strain tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A reconstruction of the particle shear strain ϵxz is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The particles are color-coded based on ϵxz;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' the red color indicates de- formation in the direction of shear, and the blue color indicates deformation in the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The par- ticle scale deformation is heterogeneous with a network of positive and negative strain regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The spatial cor- relations averaged over several strain steps of ∆γ ∼ 10−3 in the steady is shown in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It is the correlation in the shear plane, which is obtained when FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1: Spatial correlations of microscopic strain averaged over all the particles in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Main panel : the projection of strain correlations from experiments is shown using square symbols and the simulation results are presented using circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The dashed line shows a 1/∆r variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Inset: the spatial correlations of ϵxz in the shear plane xz obtained from the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' This corresponds to the correlations in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' when ∆y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The quadrupolar symmetry of strain correlations is evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' ∆r = (∆x, 0, ∆z) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It has a familiar quadrupo- lar symmetry characteristic of the strain field around an Eshelby inclusion in homogeneous elastic materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It suggests that high-strain regions (blue and red zones in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S1(a)) act as strained inclusions in an elastic ma- trix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Further, we project the correlation function onto its corresponding circular harmonic to determine radial correlations of strain following the expression : C4 ϵ (∆r) = � 2π 0 Cϵ(∆x, 0, ∆z) cos(4θ) dθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' (2) The main panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1 shows the radial correlations C4 ϵ (∆r) corresponding to the polar plot in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Similar to non-affine displacements [9], the strain correlations display an algebraic decay 1/rα, where α ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, this decay is slower than the 1/r3 variation predicted by Eshelby for a strained spherical inclusion in isotropic elastic solid [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The line with circles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1 denotes the strain correlations obtained from finite shear rate simulations performed at ˙γ = 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A good agreement between the curves confirms the robustness of strain correlations in two disparate systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It appears that the 1/r decay stems from the strain correlations that capture the elastoplastic response of not a single inclusion but several interacting inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' This is also evident from the heterogeneous strain map in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S1(a), which points to the formation of multiple inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Several investigations of amorphous plasticity and mesoscopic simulations have used a minimal model based on interacting Eshelby inclusions to understand elasto- plastic features of sheared amorphous solids [16–21, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Motivated by these ideas, we identify the inclusion cen- Experiments OSimulations 10 C (△r) 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 10° 6 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='15 20 0 20 10 X/g 101 Arl3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2: (a) Spatial maps of particles with shear strain ϵxz > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='95ϵmax xz , where ϵmax xz is the maximum strain of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' These are considered as inclusion centers in the first case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' (b) Inclusion centers are obtained from a random selection of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Note that the particles in (a) and (b) are again shown in a 5µm thick region in y−direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' (c) The normalized pair correlation function of inclusion centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The continuous line corresponds to inclusion centers obtained from particles with top 5% strain, and the dashed line is obtained for the random selection of inclusion centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' ters in our experiments using microscopic strain and use them to generate synthetic strain fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' All the par- ticles with shear strain exceeding a threshold value of |ϵi xz| > γc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' This corresponds to the top ∼ 10% of parti- cles in our system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It was verified that the results pre- sented here are robust and not sensitive to the strain threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A spatial map of the inclusions thus identified is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Apparently, they form clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To examine the effect of clustering, we also consider another case where the inclusion centers are randomly identified, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The pair correlation function g(r) of the inclusions centers is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='2(c), which is averaged over all inclusions in the system and several strain steps of ∆γ in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It is evident that the structural correlations are stronger when particles with top strains are considered as inclusion centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In contrast, the inclusion centers corresponding to random selection are weakly correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Next, we calculate the synthetic strain of particles due to the inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The far-field shear strain around a single inclusion in an isotropic homogeneous elastic solid is εI xz ∝ ϵ0cos(4θ) r3 [1], where ϵ0 is the core strain, θ = cos−1(z, r) is the azimuthal angle in the plane of shear and the particle diameter is core size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The core strain of an inclusion ϵ0 is assumed to be the shear strain of the particle obtained from experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The shear strain on any other particle in the system is a superposition of shear strains due to all inclusions ϵi xy = Ninc � j=1 εI,j xz (∆rij, θij), (3) where ∆rij is the distance of particle i from an inclu- sion j, and θij = cos−1(zij, rij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The reconstructions of shear strain when the inclusions are selected based on high-strain particles and randomly chosen are shown in the left column of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It is not surprising that the deformation map in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2(top left) compares well with experiments in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To test our approach further, we have computed spatial correlations of synthetic strain by averaging over several strain steps, and these results are shown in the right column of Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2 (SI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Surprisingly, the strain correlations corresponding to high-strain in- clusion centers display a quadrupolar symmetry in the top right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' On the contrary, it is ab- sent from the one corresponding to random inclusions in the bottom right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In the next step, the radial correlations for high-strain inclusions are com- puted and are shown together with experimental results in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' There is an excellent agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' These results establish that strain correlation for sheared sys- tems can be modeled as an interacting system of Eshelby inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We next turn our attention to strain correlations in the transient stages of deformation before the system attains a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The correlations in the steady state are averaged over several strain intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, a similar averaging in the transient stages is not feasible in exper- iments due to a lack of sufficient realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Therefore, we exploit simulation data to investigate the transient stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The strain correlations are computed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1 at γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 and are averaged over the azimuthal angle θ using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3c using thick lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The dotted lines with slopes −1 and −3 are shown for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Surprisingly, the correla- tions decay with different exponents 1/rα as the system is sheared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The exponents obtained from data fitting are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' When the strain is small, the expo- nent is α ∼ 3, which varies continuously with increasing strain until α ∼ 1 in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We elucidate the underlying physics by analyzing the synthetic strain fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The first step is the identification of inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3a shows the count of inclusions with increas- ing strain based on the threshold value ��ϵi xz �� > γc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The threshold value is set such that the number of inclusions in the steady state is ∼ 10% of particles in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The population of inclusion centers grows monotonically as the system is sheared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A similar rise in the population of inclusion centers was reported by an earlier numeri- cal study [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A reconstruction of inclusion centers is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S3(a)-(d) at γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='08, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' It is clear that the inclusions begin to clus- ter as the system is sheared towards a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The effect of clustering is also apparent in the pair correlation 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0000 O 60 50 40 (un 30 20 O 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 20 40 60 80 100 0 (um)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 40 wn 30 O 00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 20 40 60 80 100 X(um)-High strain particles Random particles 10 g(△r) 100 10 101 100Experiments 10% Inclusions 10 (△r 4 100 101 Arlg4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3: Inclusion centers and strain correlations of in the transient stages of deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Top left: The number of inclusions in the system as it is sheared from the linear elastic limit to steady plastic flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Top right: The exponent α with which the strain correlations decay as the system is sheared to steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Bottom: The correlations of shear strain (C4 ϵ (∆r)) at various stages of deformation before the system attains a steady state is shown in the main panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The thick lines are the simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The symbols show the results obtained from inclusion analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' function g(r) of inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The different symbols corre- spond to strain values varying from γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The enhanced peaks in the g(r) with increasing strain point to clustering of inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To explain the changing value of the exponent α in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='3c, we next compute synthetic strain fields from the inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' As described earlier, all other particles’ synthetic strain is obtained from the su- perposition of strain due to all inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Further, their angle-averaged spatial correlations are determined from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The result of these calculations is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The continuous lines indicate the strain correla- tions obtained from simulations, and the symbols are ob- tained from the synthetic strain fields due to inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The agreement simulations and inclusion analysis is ex- cellent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' These results firmly establish that high-strain particles in the systems act as inclusion centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A min- imal model of interacting inclusions captures the strain correlations well in the transient and steady state of de- formation of amorphous solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In summary, we have investigated the elastoplas- tic deformation of amorphous solids by investigating the spatial correlations of microscopic strain in exper- iments and simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The correlations show a fa- miliar quadrupolar symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, their decay is anomalous C4 ϵ (r) ∼ 1/rα, where α ∼ 1 in the steady state and 1 < α < 3 in the transient stages of defor- mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' This behavior is described well by a simple model of interacting inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The inclusions are iden- tified from the high-strain particles in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' In the transient stages of deformation, when the strain on the system is small, the population of inclusion centers is low and weakly correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' However, as the strain in- creases, the inclusions begin to grow and saturate in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Besides, they also form clusters, signaling a stronger spatial correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Due to this enhancement in density correlations, the correlations of synthetic strains show a gradual change in their form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The correlations C4 ϵ (r) ∼ 1/rα, with the exponent taking values from 3 in the linear regime to 1 in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The out- comes of our study firmly establishes the universal nature of strain correlation in sheared amorphous materials that are independent of the interactions and microscopic scale of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' ACKNOWLEDGEMENTS V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' acknowledges startup grant from IISER Pune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='G acknowledges support from Department of Sci- ence and Technology (DST), India for a WOS grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='SR/WOS-A/PM-34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Nicolas, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Ferrero, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Martens, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Barrat, Deformation and flow of amorphous solids: Insights from elastoplastic models, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 90, 045006 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Berthier and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 83, 587 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Barrat and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lemaitre, Dynamical Heterogeneities in Glasses, Colloids and Granular Media (Oxford Univer- sity Press, New York, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Falk and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Langer, Dynamics of viscoplastic de- formation in amorphous solids,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 57, 7192 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Maloney and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lemaitre, Subextensive scaling in the athermal, quasistatic limit of amorphous matter in plastic shear flow, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 93, 016001 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Maloney and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lemaitre, Amorphous systems in athermal, quasistatic shear, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 74, 016118 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Tanguy, F Leonforte and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Barrat, Plastic response of a 2D Lennard-Jones amorphous solid: detailed analysis of the local rearrangements at very slow strain rate, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 20, 355 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Weitz and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Spaepen, Structural Rear- rangements That Govern Flow in Colloidal Glasses, Sci- 8 0 TL 6 X n 4 N 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 Strain()3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 (α) 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 Strain()10 10 Inclusions 4 Simulations L C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04 10-2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='08 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='10 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='16 1/r 1/r3 100 101 8 rlg5 ence 318, 1895 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [9] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chikkadi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Wegdam, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Bonn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Nienhuis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, Long-Range Strain Correlations in Sheared Col- loidal Glasses,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 107, 198303 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Eshelby , The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A 241, 376 (1957) [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Eshelby , The elastic field outside an ellipsoidal inclusion, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' London Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A 252, 561 (1959) [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Spaepen, A microscopic mechanism for steady state inhomogeneous flow in metallic glasses, Acta Metall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 25, 407 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Argon, Plastic deformation in metallic glasses, Acta Metall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 27, 47 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [14] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Hebraud and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lequeux, Mode-Coupling Theory for the Pasty Rheology of Soft Glassy Materials, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 81, 2934 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Picard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Ajdari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lequeux and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Bocquet, Elastic consequences of a single plastic event: a step towards the microscopic modeling of the flow of yield stress fluids,Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='E 15,371 (2004 ) [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dasgupta, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Hentschel, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Procaccia, Microscopic Mechanism of Shear Bands in Amorphous Solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 109, 255502 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dasgupta, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Hentschel, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Procaccia, Yield strain in shear banding amorphous solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 87, 022810 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dasgupta, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Gendelman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Mishra, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Procaccia, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Shor, Shear localization in three-dimensional amorphous solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 88, 032401 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [19] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Hieronymus-Schmidt, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rosner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Wilde, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zaccone, Shear banding in metallic glasses described by alignments of Eshelby quadrupoles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' B 95, 134111 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dahmen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zion, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Uhl, Microme- chanical Model for Deformation in Solids with Universal Predictions for Stress-Strain Curves and Slip Avalanches, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 102, 175501 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [21] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Budrikis1, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Castellanos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Sandfeld, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zaiser and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zapperi, Universal features of amorphous plastic- ity, Commun Phys 1, 61 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [22] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dutta, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chaudhuri and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Martens, Elasto- plastic Approach Based on Microscopic Insights for the Steady State and Transient Dynamics of Sheared Disor- dered Solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 126 , 138005 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chikkadi and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, Nonaffine measures of particle displacements in sheared colloidal glasses, Phy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 85, 031402 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [24] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chikkadi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Woldhuis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' van Hecke and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, Correlations of strain and plasticity in a flowing foam , Europhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 112, 36004 (2015) [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Hassani, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zirdehi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Kok, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Fuchs, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Varnik, Long-range strain correlations in 3D qui- escent glass forming liquids, Europhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 124 ,8003 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Ghosh, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Budrikis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chikkadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Sellerio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Zap- peri, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, Direct Observation of Percolation in the Yielding Transition of Colloidal Glasses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 118, 148001 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lemaitre and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Caroli, Rate-Dependent Avalanche Size in Athermally Sheared Amorphous Solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 103, 065501 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Karmakar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lerner, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Procaccia, Statistical physics of the yielding transition in amorphous solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 82, 055103(R) (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Argon and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Shi, Analysis of plastic flow in an amorphous soap bubble raft by the use of an inter-bubble potential, Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A 46, 275 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Jensen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Weitz, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Spaepen, Local shear transformations in deformed and quiescent hard-sphere colloidal glasses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 90, 042305 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rodney,A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Tanguy and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Vandembroucq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Modeling the mechanics of amorphous solids at different length scale and time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Modelling and Simulation in Ma- terials Science and Engineering 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='8, 083001 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Nicolas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rottler, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Barrat, Spatiotemporal correlations between plastic events in the shear flow of athermal amorphous solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 37, 50 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [33] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Albaret, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Tanguy, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Boioli, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rodney, Map- ping between atomistic simulations and Eshelby inclu- sions in the shear deformation of an amorphous silicon model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 93, 053002 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [34] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Albaret, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Boioli, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rodney, Time-resolved shear transformations in the transient plastic regime of sheared amorphous silicon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 102, 053003 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Supplementary information Elastoplastic modelling of sheared amorphous solids using Eshelby inclusions Sagar Malik1, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Meenakshi2, Atharva Pandit1, Antina Ghosh1, Peter Schall3, Bhaskar Sengupta2, Vijayakumar Chikkadi11 11 Physics Division, Indian Institute of Science Education and Research Pune, Pune 411008, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 2 Physics Division, Vellore Institute of Technology, Vellore ******, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 3 Institute of Physics, University of Amsterdam, Amsterdam, The Netherlands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' MATERIALS AND METHODS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Experimental methods We prepared a colloidal glass by suspending sterically stabilized fluorescent polymethylmethacrylate particles in a density and refractive index matching mixture of cycloheptyl bromide and cis-decalin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The particles have a diameter of σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='3µm, and a polydisperity of 7% to prevent crystallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The suspension was centrifuged at an elevated temperature to obtain a dense sediment, which was subsequently diluted to get a suspension of desired volume fraction φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The sample was sheared using a shear cell that had two parallel boundaries separated by a distance of ∼ 50σ along the z−direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A piezoelectric device was used to move the top boundary in the x−direction to apply shear rates in the range 10−5 − 10−4s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To prevent boundary-induced crystallization in our samples, the boundaries were coated with a layer of polydisperse particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Confocal microscopy was used to image the individual particles and to determine their positions in three dimensions with an accuracy of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='03µm in the horizontal and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05µm in the vertical direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We tracked the motion of ∼ 2 × 105 particles during a 25-min time interval by acquiring image stacks every 60 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' All the measurements presented here were made in the steady state, after the sample had been strained to 100% at shear rate of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 × 10−5s−1, as confirmed by other independent rheological measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Simulation methods To prepare the thermal glass we use the well studied Kob-Anderson binary mixture model [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Our model consists of N classical point particles confined in a three-dimensional simulation box in the NV T ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We choose a binary Lennard-Jones (LJ) mixture of particles which are labeled as A and B, and their number ratio is 80 : 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' For simplicity, the mass of both types of particles m is taken to be the same and equal to unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The interaction potential for a pair of particles has the following form, Uαβ(r) = 4ϵαβ ��σαβ r �12 − �σαβ r �6 + A0 + A1 � r σαβ � + A2 � r σαβ �2� , r ≤ rcut = 0, r>rcut, (1) where α, β ∈ A, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The units of various quantities in our simulation are as follows: lengths are expressed in the unit of σAB, energies in the unit of ϵAB, time in the unit of (mσ2 AB/ϵAB)1/2 and temperature in the unit of ϵAB/kB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Here, kB is the Boltzmann constant which is unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The parameters σαβ and ϵαβ are chosen as follows: σAA = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='0, σBB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='88, σAB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='8 and ϵAA = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='0, ϵBB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5, ϵAB = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' With these set of parameters, a binary LJ mixture avoids crystallization below Tg and forms stable glass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Tg for this model is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='44 in the reduced unit [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To improve the computational efficiency, the potential is truncated at rcut = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5σAA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The parameters A0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='040490, A1 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='009702 and A2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='000620 are such that the potential and its derivatives (up to second order) go to zero smoothly at r = rcut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' To prepare the glass samples, we use MD simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' All simulations are carried out at density ρ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='2 and a total number of particles N = 150000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Position and velocity of particles are updated using the velocity-Verlet integration technique [2] with time step ∆t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The temperature of the system is kept fixed to the desired value by employing the Berendsen thermostat [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Also, we apply periodic boundary conditions in all directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We begin our simulation by equilibrating the binary mixture in the liquid state at temperature T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The system is then cooled to the final temperature T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='3 below the glass transition temperature Tg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='43 with a slow cooling rate 10−5 to prepare well relaxed glassy samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' For statistical averaging, the whole process is repeated 100 times with different initial realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Finally, the glassy samples are sheared along the xz plane at a constant shear rate ˙γ = 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' During the shear process, the temperature is controlled by dissipative particle dynamics thermostat [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='13309v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='app-ph] 30 Jan 2023 2 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Calculation of strain tensor and spatial correlations To compute these quantities we follow particle trajectories and identify the nearest neighbors of each particle as those separated by less than r0, the first minimum of the pair correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We subsequently determine the best affine deformation tensor Γ describing the transformation of the nearest neighbor vectors, di, over the strain interval ∆γ [5], by minimizing D2 min = (1/n)�n i=1(di(γ + ∆γ) − Γdi(γ))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The symmetric part of Γ is the local strain tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The remaining non-affine component D2 min has been used as a measure of plastic deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' We will investigate the correlations in the fluctuations of the principal shear strain component ϵxz using the following expression [6]: Cϵ(∆r) = ⟨ϵxz(r + ∆r)ϵ(r)⟩ − ⟨ϵxz(r)⟩2 ⟨ϵxz(r)2⟩ − ⟨ϵxz(r)⟩2 , (2) where angular brackets denote average over all the particles in the systems and several strain steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Cϵ correlates values of ϵxz at locations separated by ∆r, this way we capture the elastic response of the system in the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' MICROSCOPIC SHEAR STRAIN AND SPATIAL CORRELATIONS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Results from experiments in the steady state FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Strain map in sheared colloidal glasses at a shear rate of ˙γ ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='5 × 10−5s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The particles in a small section (∼ 3σ) along y-direction are color coded based on their shear strain ϵxz values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Red color indicates deformation in direction of shear and blue color indicates deformation in the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The synthetic strain maps obtained from inclusions centers is shown in left panels and the right panels display their spatial correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The synthetic strain values are computed based on inclusions centers that were identified from high strain particles (top left) and selected randomly (bottom left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The spatial correlations of strain fluctuations when high strain particles are considered as inclusions (top right) and when inclusions are selected randomly (bottom right) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 60 50 40 (un) 0 30 20 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0 40 80 20 60 0 100 X(μm)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='03 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 (wn) 0 N30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='03 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0 10 20 30 40 50 60 70 80 90 100 X(μm)30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 10 Zlg 0 0 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='15 20 0 20 X/o0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 60 50 40 (un)Z 0 30 20 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 0 20 40 60 80 100 X(μum)30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 10 b 0 N 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='05 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='15 20 0 20 X/g3 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Results from simulations in the transient stages of deformation FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' A spatial map of inclusion centers in the transient stages of deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The inclusions are identified based on a threshold value of shear strain ϵi > γc, where γc is defined in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' The inclusions in a section of one particle diameter thickness are shown at γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 (a), γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04 (b), γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='08 (c) and γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='1 (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' As the system is strained, the inclusions begin to cluster [1] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Kob, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Andersen, Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 51, 4626 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Verlet, Computer experiments on classical fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Thermodynamical properties of Lennard-Jones molecules, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 159, 98 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [3] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Berendsen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Postma, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' van Gunsteren, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' DiNola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Haak, Molecular dynamics with coupling to an external bath, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 81, 3684 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Soddemann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Dunweg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Kremer, Dissipative particle dynamics: A useful thermostat for equilibrium and nonequilib- rium molecular dynamics simulations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 68, 046702 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Falk and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Langer, Dynamics of viscoplastic deformation in amorphous solids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' E 57, 7192 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' [6] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Chikkadi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Wegdam, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Bonn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Nienhuis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Schall, Long-range strain correlations in sheared colloidal glasses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' 107, 198303 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='02 45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 30 25 0 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 10 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 15 20 25 30 35 45 5 10 40 X/g= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='04 45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 30 25 0 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 10 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 5 10 15 20 25 30 35 40 45 X/g0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='08 45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 30 25 0 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 5 10 15 20 25 30 5 35 40 45 X/g0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='10 45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 30 0 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='005 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='01 10 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} +page_content='015 5 10 15 20 25 30 35 40 45 X/g' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/OtFQT4oBgHgl3EQfXzZD/content/2301.13309v1.pdf'} diff --git a/P9AyT4oBgHgl3EQfUve2/vector_store/index.faiss b/P9AyT4oBgHgl3EQfUve2/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..4993f1824640129dbb86ce0e64e5f1a695218f1f --- /dev/null +++ b/P9AyT4oBgHgl3EQfUve2/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0871a36ca946a4bc9b32149deebd31e84456c1788a6731f76026c2ce325edfc7 +size 10289197 diff --git a/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/2301.02239v1.pdf.txt b/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/2301.02239v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..eed27757c6c447bf672bcc37ab31720db960a7fc --- /dev/null +++ b/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/2301.02239v1.pdf.txt @@ -0,0 +1,1545 @@ +Robust Dynamic Radiance Fields +Yu-Lun Liu2* Chen Gao1 +Andreas Meuleman3* Hung-Yu Tseng1 +Ayush Saraf1 +Changil Kim1 +Yung-Yu Chuang2 +Johannes Kopf1 +Jia-Bin Huang1,4 +1Meta +2National Taiwan University +3KAIST +4University of Maryland, College Park +https://robust-dynrf.github.io/ +Figure 1. Robust space-time synthesis from dynamic monocular videos. Our method takes a casually captured video as input and +reconstructs the camera trajectory and dynamic radiance fields. Conventional SfM system such as COLMAP fails to recover camera poses +even when using ground truth motion masks. As a result, existing dynamic radiance field methods that require accurate pose estimation +do not work on these challenging dynamic scenes. Our work tackles this robustness problem and showcases high-fidelity dynamic view +synthesis results on a wide variety of videos. +Abstract +Dynamic radiance field reconstruction methods aim to +model the time-varying structure and appearance of a dy- +namic scene. Existing methods, however, assume that ac- +curate camera poses can be reliably estimated by Structure +from Motion (SfM) algorithms. These methods, thus, are un- +reliable as SfM algorithms often fail or produce erroneous +poses on challenging videos with highly dynamic objects, +poorly textured surfaces, and rotating camera motion. We +address this robustness issue by jointly estimating the static +and dynamic radiance fields along with the camera param- +eters (poses and focal length). We demonstrate the robust- +ness of our approach via extensive quantitative and qualita- +tive experiments. Our results show favorable performance +over the state-of-the-art dynamic view synthesis methods. +*This work was done while Yu-Lun and Andreas were interns at Meta. +1. Introduction +Videos capture and preserve memorable moments of our +lives. However, when watching regular videos, viewers ob- +serve the scene from fixed viewpoints and cannot interac- +tively navigate the scene afterward. Dynamic view synthe- +sis techniques aim to create photorealistic novel views of +dynamic scenes from arbitrary camera angles and points +of view. +These systems are essential for innovative ap- +plications such as video stabilization [31, 40], virtual real- +ity [5, 13], and view interpolation [11, 79], which enable +free-viewpoint videos and let users interact with the video +sequence. It facilitates downstream applications like virtual +reality, virtual 3D teleportation, and 3D replays of live pro- +fessional sports events. +Most current dynamic view synthesis systems rely on la- +borious and expensive setups such as fixed multi-camera +capture rigs [5, 8, 13, 48, 79]. +These techniques require +simultaneous (time-synchronized) capture from multiple +cameras that is not practical for most people. +Several +methods can synthesize dynamic novel views from a sin- +1 +arXiv:2301.02239v1 [cs.CV] 5 Jan 2023 + +huft der Siegefseite ewzchjobsgle stereo or RGB camera but are specifically tailored for +human performance capture [14,26] or small animals [62]. +Recent work has relaxed these restrictions and can han- +dle unstructured video input [1, 2]. Recently, there have +been many dynamic view synthesis methods for unstruc- +tured videos [22, 23, 37, 50, 51, 54, 68, 73] and other new +methods based on deformable fields [18]. However, these +techniques require precise camera poses as input, typically +estimated via SfM systems such as COLMAP [59] (bottom +left of Table 1). +However, SfM systems are not robust to many issues, +such as noisy images from low-light conditions, motion blur +caused by users, or dynamic objects in the scene, such as +people, cars, and animals. The robustness problem of the +SfM systems causes the existing dynamic view synthesis +methods to be fragile and impractical for many challenging +videos. Recently, several NeRF-based methods [29,38,70] +have proposed jointly optimizing the camera poses with the +scene geometry. Nevertheless, these methods can only han- +dle strictly static scenes (top right of Table 1). +In this paper, we present RoDynRF — an algorithm for +reconstructing dynamic radiance fields from a casually cap- +tured video. Our method is more robust than existing ap- +proaches in the sense that we do not rely on accurate camera +poses as input. The core idea of our approach is to optimize +the camera poses in conjunction with two radiance fields +that model static and dynamic scene elements. We care- +fully design the method for joint static radiance field and +pose estimation, including a coarse-to-fine strategy, limit- +ing the effects of viewing direction, and detecting and ex- +cluding moving pixels with epipolar geometry. For mod- +eling the dynamic radiance fields, we introduce a deforma- +tion field and time-dependent appearance models. We fur- +ther leverage several auxiliary regularization losses to im- +prove the consistency of the reconstruction. We perform +an extensive experimental validation. On poses, we evalu- +ate our estimated camera trajectories quantitatively on the +Sintel dataset [7]. On view synthesis, we quantify the per- +formance on the Dynamic View Synthesis dataset [75] and +the iPhone dataset [23]. We show numerous visual com- +parisons with existing methods on the challenging DAVIS +dataset [53] and in-the-wild videos. +We summarize our core contributions as follows: +• We present a space-time synthesis algorithm from a +dynamic monocular video that does not require known +camera poses and camera intrinsics as input. +• We propose careful architecture designs and axillary +losses that improve the robustness of the camera pose +estimation and the dynamic radiance field reconstruc- +tion. +• Quantitative and qualitative evaluations demonstrate +the robustness of our method over other state-of-the- +Table 1. Catogorization of view synthesis methods. +Known camera poses +Unknown camera poses +Static +scene +NeRF [42], SVS [57], NeRF++ [76], +Mip-NeRF [3], Mip-NeRF 360 [4], DirectVoxGO [65], +Plenoxels [21], Instant-ngp [43], TensoRF [10] +NeRF - - [70], BARF [38], +SC-NeRF [29] +Dynamic +scene +NV [41], D-NeRF [54], NR-NeRF [68], +NSFF [37], DynamicNeRF [22], Nerfies [50], +HyperNeRF [51], TiNeuVox [18], T-NeRF [23] +Ours +art methods on several challenging datasets that typical +SfM systems fail to estimate camera poses. +2. Related Work +Static view synthesis. +Many view synthesis techniques +construct specific scene geometry from images captured at +various positions [6] and use local warps [9] to synthesize +high-quality novel views of a scene. Approaches to light +field rendering use implicit scene geometry to create pho- +torealistic novel views, but they require densely captured +images [25, 35]. +By using soft 3D reconstruction [52], +learning-based dense depth maps [20], multiplane images +(MPIs) [12,19,64], additional learned deep features [28,56], +or voxel-based implicit scene representations [63], several +earlier work attempt to use proxy scene geometry to en- +hance rendering quality. +Recent methods implicitly model the scene as a contin- +uous neural radiance field (NeRF) [3, 42, 76] with multi- +layer perceptrons (MLPs). However, NeRF requires days of +training time to represent a scene. Therefore, recent meth- +ods [10, 21, 43, 65] replace the implicit MLPs with explicit +voxels and significantly improve the training speed. +Several approaches synthesize novel views from a single +RGB input image. These methods often fill up holes in the +disoccluded regions and predict depth [36,47], additionally +learned features [72], multiplane images [69], and layered +depth images [32,61]. Although these techniques have pro- +duced excellent view synthesis results, they can only han- +dle static scenes. Our approach performs view synthesis +of dynamic scenes from a single monocular video, in con- +trast to existing view synthesis techniques focusing on static +scenes. +Dynamic view synthesis. +By focusing on human bod- +ies [71], using RGBD data [14], reconstructing sparse ge- +ometry [49], or producing minimal stereoscopic disparity +transitions between input views [1], many techniques re- +construct and synthesize novel views from non-rigid dy- +namic scenes. +Other techniques break down dynamic +scenes into piece-wise rigid parts using hand-crafted pri- +ors [34,58]. Many systems cannot handle scenes with com- +plicated geometry and instead require multi-view and time- +synchronized videos as input to provide interactive view +manipulation [2,5,39,79]. Yoon et al. [75] used depth from +single-view and multi-view stereo to synthesize novel views +2 + +Static +voxel +𝐕! +𝐱 = 𝑥, 𝑦, 𝑧 ! +' +Color 𝒄" +Density 𝜎" +Viewing direction 𝒅 +Dynamic +voxel +𝐕" +Color 𝒄#! +$ +Density 𝜎#! +$ +Viewing direction 𝒅 +Nonrigidity 𝑚#! +$ +𝑡% +𝐱 +𝐱′ +Time 𝑡% +Dynamic Radiance Fields +Static Radiance Fields +Coordinate +deformation +𝑅 𝑡 % +Gradients for camera poses +Stop gradients +Volume +rendering +𝜎 +Ray distance 𝛿 +Volume +rendering +𝜎 +Ray distance 𝛿 +Static RGB 𝐂! +Dynamic RGB 𝐂#! +" +Static depth 𝐃! +Dynamic depth 𝐃#! +" +Nonrigidity mask 𝐌#! +𝒅 +(a) Sampling +𝐱 = 𝐨 + 𝑡𝑑 +(b) Radiance fields +Θ&" +Θ&$ +Θ'$ +Θ( +$ +Θ$ +Summation +𝒄" × 1 − 𝑚#! +$ ++ 𝒄#! +$ × 𝑚#! +$ +𝜎" × 1 − 𝑚#! +$ ++ 𝜎#! +$ × 𝑚#! +$ +Volume +rendering +𝜎 +Ray distance 𝛿 +Combined color 𝐂#! +Combined depth 𝐃#! +P.E. +P.E. +Linear combination +Input +Input +Input +Masked +loss +Loss +Loss +Motion mask +Time-dependent MLPs +Figure 2. Overall framework. We model the dynamic scene with static and dynamic radiance fields. The static radiance fields take both +the sampled coordinates (x, y, z) and the viewing direction d as input and predict the density σs and color cs. Note that the density of the +static part is invariant to time and viewing direction, therefore, we use summation of the queried features as the density (instead of using +an MLP). We only compute the losses over the static regions. The computed gradients backpropagate not only to the static voxel field and +MLPs but also to the camera parameters. The dynamic radiance fields take the sampled coordinates and the time t to obtain the deformed +coordinates (x′, y′, z′) in the canonical space. Then we query the features using these deformed coordinates from the dynamic voxel fields +and pass the features along with the time index to a time-dependent shallow MLPs to get the color cd, density σd, and nonrigidity md of +the dynamic part. Finally, after the volume rendering, we can obtain the RGB images C{s,d} and the depth maps D{s,d} from the static +and dynamic parts along with a nonrigidity mask Md. Finally, we calculate the per-frame reconstruction loss. Note that here we only +include per-frame losses. +of dynamic scenes from a single video using explicit depth- +based 3D warping. +A recent line of work extends NeRF to handle dy- +namic scenes [18,22,37,50,51,54,68,73]. Although these +space-time synthesis results are impressive, these tech- +niques rely on precise camera pose input. Consequently, +these techniques are not applicable to challenging scenes +where COLMAP [59] or current SfM systems fail. Our ap- +proach, in contrast, can handle complex dynamic scenarios +without known camera poses. +Visual odometry and camera pose estimation. +From +a collection of images, visual odometry estimates the 3D +camera poses [16,17,44–46]. These techniques mainly fall +into two categories: direct methods that maximize photo- +metric consistency [74, 78] and feature-based methods that +rely on manually created or learned features [44, 45, 60]. +Self-supervised image reconstruction losses have recently +been used in learning-based systems to tackle visual odom- +etry [24, 33, 67, 77, 78]. Estimating camera poses from ca- +sually captured videos remains challenging. NeRF-based +techniques have been proposed to combine neural 3D rep- +resentation and camera poses for optimization [29, 38, 70], +although they are limited to static sequences. In contrast +to the visual odometry techniques outlined above, our sys- +tem simultaneously optimizes camera poses and models dy- +namic objects models. +3. Method +In this section, we first briefly introduce the background +of neural radiance fields and their extension of camera pose +estimation and dynamic scene representation in Section 3.1. +We then describe the overview of our method in Section 3.2. +Next, we discuss the details of camera pose estimation with +the static radiance field reconstruction in Section 3.3. Af- +ter that, we show how to model the dynamic scene in Sec- +tion 3.4. +Finally, we outline the implementation details +in Section 3.5. +3.1. Preliminaries +NeRF. Neural radiance fields (NeRF) [42] represent a static +3D scene with implicit MLPs parameterized by Θ and map +the 3D position (x, y, z) and viewing direction (θ, ϕ) to its +corresponding color c and density σ: +(c, σ) = MLPΘ(x, y, z, θ, ϕ). +(1) +We can compute the pixel color by applying volume render- +ing [15,30] along the ray r emitted from the camera origin: +3 + +𝑡! +𝑡!"# +𝑧 +ℒ$%&$'( +ℒ)*+& +ℒ,'-')%&./ +Optical flow 𝐟 +Volume rendered 3D +point +𝐃0!"# +1 +𝐊0!"# +2𝟏 𝐩′ +Motion mask +Epipolar +distance +thresholding +𝐩 +𝐩4 = 𝐩 + 𝐟(𝐩) +𝐃0! +1 𝐊0! +2𝟏𝐩 +Volume rendered depth 𝐃0! +1 +MiDaS depth +𝑡! +𝑡!"# +𝑧 +ℒ$%&$'( +ℒ)*+& +Optical flow 𝐟 +Volume rendered 3D +point 𝐱,! = 𝐃,! +-𝐊,! +.𝟏𝐩 +Scene flow MLP +𝑡! +𝐩 +𝐩0 = 𝐩 + 𝐟(𝐩) +𝐱,!→,!"# +𝐱,!"# = +𝐃,!"# +- +𝐊,!"# +.𝟏 𝐩′ +ℒ2'3')%&45 +Volume rendered depth 𝐃,! +6 +MiDaS depth +(a) Static radiance field reconstruction and pose estimation +(b) Dynamic radiance field reconstruction +Figure 3. Training losses. For both the (a) static and (b) dynamic parts, we introduce three auxiliary losses to encourage the consistency +of the modeling: reprojection loss, disparity loss, and monocular depth loss. The reprojection loss encourages the projection of the 3D +volume rendered points onto neighbor frames to be similar to the pre-calculated flow. The disparity loss forces the volume rendered 3D +points from two corresponding points of neighbor frames to have similar z values. Finally, the monocular depth loss calculates the scale- +and shift-invariant loss between the volume rendered depth and the pre-calculated MiDaS depth. (a) We use the motion mask to exclude +the dynamic regions from the loss calculation. (b) We use a scene flow MLP to model the 3D movement of the volume rendered 3D points. +ˆC(r) = +N +� +i=1 +T(i)(1 − exp(−σ(i)δ(i)))c(i), +T(i) = exp(− +j +� +i−1 +σ(j)δ(j)), +(2) +where δ(i) represents the distance between two consecutive +sample points along the ray, N is the number of samples +along each ray, and T(i) indicates the accumulated trans- +parency. As the volume rendering procedure is differen- +tiable, we can optimize the radiance fields by minimizing +the reconstruction error between the rendered color ˆC and +the ground truth color C: +L = +��� ˆC(r) − C(r) +��� +2 +2 . +(3) +Explicit neural voxel radiance fields. +Although with +compelling rendering quality, NeRF-based methods model +the scene with implicit representations such as MLPs for +high storage efficiency. These methods, however, are very +slow to train. To overcome this drawback, recent meth- +ods [10, 21, 43, 65] propose to model the radiance fields +with explicit voxels. Specifically, these methods replace the +mapping function with voxel grids and directly optimize the +features sampled from the voxels. They usually apply shal- +low MLPs to handle the view-dependent effects. By elim- +inating the heavy usage of the MLPs, the training time of +these methods reduces from days to hours. We also lever- +age explicit representation in this work. +3.2. Method Overview +We show our proposed framework in Figure 2. Given +an input video sequence with N frames, our method jointly +optimizes the camera poses, focal length, and static and dy- +namic radiance fields. We represent both the static and dy- +namic parts with explicit neural voxels Vs and Vd, respec- +tively. The static radiance fields are responsible for recon- +structing the static scene and estimating the camera poses +and focal length. At the same time, the goal of dynamic +radiance fields is to model the scene dynamics in the video +(usually caused by moving objects). +3.3. Camera Pose Estimation +Motion mask generation. Excluduing dynamic regions in +the video helps improve the robustness of camera pose esti- +mation. Existing methods [37] often leverage off-the-shelf +instance segmentation methods such as Mask R-CNN [27] +to mask out the common moving objects. However, many +moving objects are hard to detect/segment in the input +video, such as drifting water or swaying trees. Therefore, in +addition to the masks from Mask R-CNN, we also estimate +the fundamental matrix using the optical flow from consec- +utive frames. We then calculate and threshold the Sampson +distance (the distance of each pixel to the estimated epipolar +line) to obtain a binary motion mask. Finally, we combine +the results from Mask R-CNN and epipolar distance thresh- +olding to obtain our final motion masks. +Coarse-to-fine static scene reconstruction. The first part +of our method is reconstructing the static radiance fields +along with the camera poses. We jointly optimize the 6D +camera poses [R|t]i, i ∈ [1..N] and the focal length f +4 + +(a) w/o coarse-to-fine +(b) w/o monocular depth prior +(c) w/o late viewing direction conditioning +(d) Full model +Figure 4. Effects of design choices for camera poses estimation. +(a) Withput the coarse-to-fine strategy, the optimization often ends +up with sub-optimal solutions. (b) Without the single-image depth +prior, the optimization fails to reconstruct reasonable scene ge- +ometry with challenging camera trajectories. (c) Without the late +viewing direction conditioning, the optimization tends to minimize +the photometric loss with MLP instead of consistent voxel space, +resulting in wrong geometry and poses. (d) With all the proposed +components, our method could reconstruct reasonable scene ge- +ometry as well as the camera trajectory. +shared by all input frames simultaneously. Similar to ex- +isting pose estimation methods [38], we optimize the static +scene representation in a coarse-to-fine manner. Specifi- +cally, we start with a smaller static voxel resolution and pro- +gressively increase the voxel resolution during the training. +This coarse-to-fine strategy is essential to the camera pose +estimation as the energy surface will become smoother. +Thus, the optimizer will have less chance of getting stuck +in sub-optimal solutions (Figure 4(a) vs. Figure 4(d)). +Late viewing direction conditioning. +As our primary +supervision is the photometric consistency loss, the opti- +mization could bypass the neural voxel and directly learn +a mapping function from the viewing direction to the out- +put sample color. Therefore, we choose to fuse the viewing +direction only in the last layer of the color MLP as shown +in Figure 2. This design choice is critical because we are re- +constructing not only the scene geometry but also the cam- +era poses. Figure 4(c) shows that without the late viewing +direction conditioning, the optimization could minimize the +photometric loss by optimizing the MLP and lead to erro- +neous camera poses and geometry estimation. +Losses. +We minimize the photometric loss between the +prediction ˆCs(r) and the captured images in the static re- +gions: +Ls +c = +���( ˆCs(r) − C(r)) · (1 − M(r)) +��� +2 +2 , +(4) +where M denotes the motion mask. +To handle casually-captured but challenging camera tra- +jectories such as fast-moving or pure rotating, we introduce +auxiliary losses to regularize the training, similar to [22,37]. +(1) Reprojection loss Ls +reproj: We use 2D optical flow esti- +mated by RAFT [66] to guide the training. First, we volume +render all the sampled 3D points along a ray to generate a +surface point. We then reproject this point onto its neighbor +frame and calculate the reprojection error with the corre- +spondence estimated from RAFT. +(2) Disparity loss Ls +disp: Similar to the reprojection loss +above, we also regularize the error in the z-direction (in the +camera coordinate). We volume render the two correspond- +ing points into 3D space and calculate the error of the z +component. As we care more about the near than the far, +we compute this loss in the inverse-depth domain. +(3) Monocular depth loss Ls +monodepth: The two losses +above cannot handle pure rotating cameras and often lead to +the incorrect camera poses and geometry (Figure 4(b)). We +enforce the depth order from multiple pixels of the same +frame to match the order of a monocular depth map. We +pre-calculate the depth map using MiDaSv2.1 [55]. The +depth prediction from MiDaS is up to an unknown scale and +shift. Therefore, we use the same scale- and shift-invariant +loss in MiDaS to constrain our rendered depth values. +We illustrate these auxiliary losses in Figure 3(a). Since +the optical flow and depth map may not be accurate, we +apply annealing for the weights of these auxiliary losses +during the training. As the input frames contain dynamic +objects, we need to mask out all the dynamic regions while +applying all these losses and the L2 reconstruction loss. The +final loss for the static part is: +Ls = Ls +c + λs +reprojLs +reproj + λs +dispLs +disp + λs +monodepthLs +monodepth. +(5) +3.4. Dynamic Radiance Field Reconstruction +Handling temporal information. +To query the time- +varying features from the voxel, we first pass the 3D coor- +dinates (x, y, z) along with time index ti to a coordinate de- +formation MLP. The coordinate deformation MLP predicts +the 3D time-varying deformation vectors (∆x, ∆y, ∆z). +We then add these deformations onto the original coordi- +nates to get the deformed coordinates (x′, y′, z′). This de- +formation MLP indicates that the voxel is a canonical space +and that each corresponding 3D point from a different time +should point to the same position in this voxel space. We +design the deformation MLP to deform the 3D points from +the original camera space to the canonical voxel space. +However, using a single compact canonical voxel to rep- +resent the entire sequence along the temporal dimension +is very challenging. Therefore, we further introduce time- +dependent MLPs to enhance the queried features from the +voxel to predict time-varying color and density. Note that +the time-dependent MLPs with only two to three layers are +much shallower than the ones in other dynamic view syn- +thesis methods [22, 37] as the purpose of the MLPs here is +further to enhance the queried features from the canonical +5 + +8 +10 +12 +14 +16 +18 +26 +28 +30 +32 +34 +22 +24 +26 +28 +30 +32 +8 +10 +12 +14 +16 +18 +26 +28 +30 +32 +34 +22 +24 +26 +28 +30 +32 +8 +10 +12 +14 +16 +18 +26 +28 +30 +32 +34 +22 +24 +26 +28 +30 +32 +8 +10 +12 +14 +16 +18 +26 +28 +30 +32 +34 +22 +24 +26 +28 +30 +32 +2 +0 +2 +4 +6 +20 +22 +24 +26 +28 +20 +22 +24 +26 +2 +0 +2 +4 +6 +20 +22 +24 +26 +28 +20 +22 +24 +26 +2 +0 +2 +4 +6 +20 +22 +24 +26 +28 +20 +22 +24 +26 +2 +0 +2 +4 +6 +20 +22 +24 +26 +28 +20 +22 +24 +26 +26 25 24 23 +22 +21 +20 +19 +56 +57 +58 +59 +60 +61 +62 +63 +16 +15 +14 +13 +12 +11 +10 +9 +26 25 24 23 +22 +21 +20 +19 +56 +57 +58 +59 +60 +61 +62 +63 +16 +15 +14 +13 +12 +11 +10 +9 +26 25 24 23 +22 +21 +20 +19 +56 +57 +58 +59 +60 +61 +62 +63 +16 +15 +14 +13 +12 +11 +10 +9 +26 25 24 23 +22 +21 +20 +19 +56 +57 +58 +59 +60 +61 +62 +63 +16 +15 +14 +13 +12 +11 +10 +9 +Sample frames +ParticleSfM [77] +NeRF - - [70] +BARF [38] +Ours +Figure 5. Qualitative results of moving camera localization on +the MPI Sintel dataset. +Table 2. Quantitative evaluation of camera poses estimation on +the MPI Sintel dataset. The methods of the top block discard the +dynamic components and do not reconstruct the radiance fields; +thus they cannot render novel views. +Method +ATE (m) +RPE trans (m) +RPE rot (deg) +R-CVD [33] +0.360 +0.154 +3.443 +DROID-SLAM [67] +0.175 +0.084 +1.912 +ParticleSfM [77] +0.129 +0.031 +0.535 +NeRF - - [70] +0.433 +0.220 +3.088 +BARF [38] +0.447 +0.203 +6.353 +Ours +0.089 +0.073 +1.313 +voxel. Most of the time-varying effects are still carried out +by the coordination deformation MLP. We show the above +architecture at the bottom of Figure 2. And the photometric +training loss for the dynamic part is: +Ld +c = +��� ˆCd(r) − C(r) +��� +2 +2 , +(6) +Scene flow modeling. +We introduce three losses based +on external priors to better model the dynamic movements. +The three losses are similar to the ones in the static part, but +we need to model the movements of the 3D points. There- +fore, we introduce a scene flow MLP to compensate the 3D +motion. +(Si→i+1, Si→i−1) = MLPθsf(x, y, z, ti), +(7) +where Si→i+1 represents the 3D scene flow of the 3D point +(x, y, z) at time ti. With the 3D scene flow, we can apply +the losses for the dynamic radiance fields. We show the +training losses in Figure 3(b). +(1) Reprojection loss Ld +reproj: We induce the 2D flow us- +ing the poses, depth, and the estimated 3D scene flow from +the scene flow MLP. And we compare the error of this in- +duced flow with the one estimated by RAFT. +(2) Disparity loss Ld +disp: Similar to the disparity loss in +the static part, but here we additionally have the 3D scene +Ground truth +NeRF - - [70] +BARF [38] +Ours +Image +Depth +Image +Depth +Figure 6. +Qualitative results of static view synthesis on the +DAVIS dataset from unknown camera poses and ground truth +foreground masks. +flow. We get the corresponding points in the 3D space, add +the estimated 3D scene flow, and calculate the difference of +the z components in the inverse-depth domain. +(3) Monocular depth loss Ld +monodepth: We calculate scale- +and shift-invariant loss between the rendered depth with the +pre-calculated depth map using MiDaSv2.1. +We further regularize the 3D motion prediction from the +MLP by introducing the smooth and small scene flow loss: +Lreg +sf = ∥Si→i+1 + Si→i−1∥1 + ∥Si→i+1∥1 + ∥Si→i−1∥1 . +(8) +Note that the scene flow MLP is not part of the rendering +process but part of the losses. By representing the 3D scene +flow with an MLP and enforcing proper priors, we can make +the density prediction better and more reasonable. We also +detach the gradients from the dynamic radiance fields to the +camera poses. Finally, we supervise the nonrigidity mask +Md with motion mask M: +Ld +m = +��Md − M +�� +1 . +(9) +The overall loss of the dynamic part is: +Ld = Ld +c + λd +reprojLd +reproj + λd +dispLd +disp+ +λd +monodepthLd +monodepth + λreg +sf Lreg +sf + λd +mLd +m. +(10) +We then linearly compose the static and dynamic parts +into the final results with the predicted nonrigidity md: +ˆC(r) = +N +� +i=1 +T(i)(md(1 − exp(−σd(i)δ(i)))cd(i)+ +(1 − md)(1 − exp(−σs(i)δ(i)))cs(i)). +(11) +Total training loss. The total training loss is: +L = +��� ˆC(r) − C(r) +��� +2 +2 + Ls + Ld. +(12) +6 + +NSFF [37] +DynamicNeRF [22] +HyperNeRF [51] +TiNeuVox [18] +Ours +Ground truth +Figure 7. Novel view synthesis. Compared to other methods, our results are sharper, closer to the ground truth, and contain fewer artifacts. +Table 3. Novel view synthesis results. We report the average PSNR and LPIPS results with comparisons to existing methods on Dynamic +Scene dataset [75]. *: Numbers are adopted from DynamicNeRF [22]. +PSNR ↑ / LPIPS ↓ +Jumping +Skating +Truck +Umbrella +Balloon1 +Balloon2 +Playground +Average +NeRF* [42] +20.99 / 0.305 +23.67 / 0.311 +22.73 / 0.229 +21.29 / 0.440 +19.82 / 0.205 +24.37 / 0.098 +21.07 / 0.165 +21.99 / 0.250 +D-NeRF [54] +22.36 / 0.193 +22.48 / 0.323 +24.10 / 0.145 +21.47 / 0.264 +19.06 / 0.259 +20.76 / 0.277 +20.18 / 0.164 +21.48 / 0.232 +NR-NeRF* [68] +20.09 / 0.287 +23.95 / 0.227 +19.33 / 0.446 +19.63 / 0.421 +17.39 / 0.348 +22.41 / 0.213 +15.06 / 0.317 +19.69 / 0.323 +NSFF* [37] +24.65 / 0.151 +29.29 / 0.129 +25.96 / 0.167 +22.97 / 0.295 +21.96 / 0.215 +24.27 / 0.222 +21.22 / 0.212 +24.33 / 0.199 +DynamicNeRF* [22] +24.68 / 0.090 +32.66 / 0.035 +28.56 / 0.082 +23.26 / 0.137 +22.36 / 0.104 +27.06 / 0.049 +24.15 / 0.080 +26.10 / 0.082 +HyperNeRF [51] +18.34 / 0.302 +21.97 / 0.183 +20.61 / 0.205 +18.59 / 0.443 +13.96 / 0.530 +16.57 / 0.411 +13.17 / 0.495 +17.60 / 0.367 +TiNeuVox [18] +20.81 / 0.247 +23.32 / 0.152 +23.86 / 0.173 +20.00 / 0.355 +17.30 / 0.353 +19.06 / 0.279 +13.84 / 0.437 +19.74 / 0.285 +Ours w/ COLMAP poses +25.66 / 0.071 +28.68 / 0.040 +29.13 / 0.063 +24.26 / 0.089 +22.37 / 0.103 +26.19 / 0.054 +24.96 / 0.048 +25.89 / 0.065 +Ours w/o COLMAP poses +24.27 / 0.100 +28.71 / 0.046 +28.85 / 0.066 +23.25 / 0.104 +21.81 / 0.122 +25.58 / 0.064 +25.20 / 0.052 +25.38 / 0.079 +3.5. Implementation Details +We simultaneously estimate camera poses, focal length, +static radiance fields, and dynamic radiance fields. +For +forward-facing scenes, we parameterize the scenes with +normalized device coordinates (NDC). To handle un- +bounded scenes in the wild videos, we parameterize the +scenes using the contraction parameterization [4]. +To +encourage solid surface scene reconstruction and prevent +floaters, we add the distortion loss [4, 65]. +We set the +finest voxel resolution to 262,144,000 and 27,000,000 for +NDC and contraction, respectively. We also decompose the +voxel grid using the VM-decomposition in TensoRF [10] +for model compactness. The entire training process takes +around 28 hours with one NVIDIA V100 GPU. We provide +the detailed architecture in the supplementary material. +4. Experimental Results +Due to the space limit, we leave the experimental setup, +including datasets, compared methods, and the evaluation +metrics to the supplementary materials. +4.1. Evaluation on Camera Poses Estimation +We conduct the camera pose estimation evaluation on +the MPI Sintel dataset [7] and show the quantitative re- +sults in Table 2. Our method performs significantly bet- +ter than existing NeRF-based pose estimation methods. +Note that our method also performs favorably against ex- +isting learning-based visual odometry methods. We show +some visual comparisons of the predicted camera trajec- +tories in Figure 5. Our approach predicts accurate cam- +era poses over other NeRF-based pose estimation meth- +ods. Our method is a global optimization over the entire se- +quence instead of local registration like SLAM-based meth- +ods. Therefore, our RPE trans and rot scores are slightly +worse than ParticleSfM [77] as consecutive frames’ rotation +is less accurate. +To further reduce the effect of the dynamic parts, we +use the ground truth motion masks provided by the DAVIS +dataset to mask out the loss calculations in the dynamic re- +gions for all the NeRF-based compared methods. We show +the reconstructed images and depth maps in Figure 6. Our +approach can successfully reconstruct the detailed content +and the faithful geometry thanks to the auxiliary losses. On +the contrary, other methods often fail to reconstruct consis- +tent scene geometry and thus produce poor synthesis results. +4.2. Evaluation on Dynamic View Synthesis +Quantitative evaluation. We follow the evaluation proto- +col in DynamicNeRF [22] to synthesize the view from the +first camera and change time on the NVIDIA dynamic view +synthesis dataset. We report the PSNR and LPIPS in Ta- +ble 3. Our method performs favorably against state-of-the- +art methods. Furthermore, even without COLMAP poses, +our method can still achieve results comparable to the ones +using COLMAP poses. +We also follow the evaluation protocol in DyCheck [23] +and evaluate quantitatively on the iPhone dataset [23]. We +report the masked PSNR and SSIM in Table 4 and show that +our method performs favorably against existing methods. +Qualitative evaluation. +We show some visual com- +7 + +Table 4. Novel view synthesis results. We compare the mPSNR and mSSIM scores with existing methods on the iPhone dataset [23]. +mPSNR ↑ / mSSIM ↑ +Apple +Block +Paper-windmill +Space-out +Spin +Teddy +Wheel +Average +NSFF [37] +17.54 / 0.750 +16.61 / 0.639 +17.34 / 0.378 +17.79 / 0.622 +18.38 / 0.585 +13.65 / 0.557 +13.82 / 0.458 +15.46 / 0.569 +Nerfies [50] +17.64 / 0.743 +17.54 / 0.670 +17.38 / 0.382 +17.93 / 0.605 +19.20 / 0.561 +13.97 / 0.568 +13.99 / 0.455 +16.45 / 0.569 +HyperNeRF [51] +16.47 / 0.754 +14.71 / 0.606 +14.94 / 0.272 +17.65 / 0.636 +17.26 / 0.540 +12.59 / 0.537 +14.59 / 0.511 +16.81 / 0.550 +T-NeRF [23] +17.43 / 0.728 +17.52 / 0.669 +17.55 / 0.367 +17.71 / 0.591 +19.16 / 0.567 +13.71 / 0.570 +15.65 / 0.548 +16.96 / 0.577 +Ours +18.73 / 0.722 +18.73 / 0.634 +16.71 / 0.321 +18.56 / 0.594 +17.41 / 0.484 +14.33 / 0.536 +15.20 / 0.449 +17.09 / 0.534 +NSFF [37] +DynamicNeRF [22] +HyperNeRF [51] +TiNeuVox [18] +Ours +Figure 8. Novel space-time synthesis results on the DAVIS dataset with our estimated camera poses. COLMAP fails to produce reliable +camera poses for most of the sequences in the DAVIS dataset. With the estimated camera poses by our method, we can run other methods +and perform space-time synthesis on the scenes that are not feasible with COLMAP. Our method produces images with much better quality. +Table 5. Ablation studies. We report PSNR, SSIM and LPIPS on +the Playground sequence. +(a) Pose estimation design choices +PSNR ↑ +SSIM ↑ +LPIPS ↓ +Ours w/o coarse-to-fine +12.45 +0.4829 +0.327 +Ours w/o late viewing direction fusion +18.34 +0.5521 +0.263 +Ours w/o stopping the dynamic gradients +21.47 +0.7392 +0.211 +Ours +25.20 +0.9052 +0.052 +(b) Dynamic reconstruction achitectural designs +Dyn. model +Deform. MLP +Time-depend. MLPs +PSNR ↑ +SSIM ↑ +LPIPS ↓ +21.34 +0.8192 +0.161 +✓ +✓ +22.37 +0.8317 +0.115 +✓ +✓ +23.14 +0.8683 +0.083 +✓ +✓ +✓ +25.20 +0.9052 +0.052 +parisons on the NVIDIA dynamic view synthesis dataset +in Figure 7 and DAVIS dataset in Figure 8. COLMAP fails +to estimate the camera poses for 44 out of 50 sequences in +the DAVIS dataset. Therefore, we first run our method and +give our camera poses to other methods as input. With the +joint learning of the camera poses and radiance fields, our +method produces frames with fewer visual artifacts. Other +methods can also benefit from our estimated poses to syn- +thesize novel views. With our poses, they can reconstruct +consistent static scenes but often generate artifacts for the +dynamic parts. In contrast, our method utilizes the auxil- +iary priors and thus produces results of much better visual +quality. +(a) Fast moving camera +(b) Changing focal length +Figure 9. Failure cases. (a) In the cases that the camera is moving +fast, the flow estimation fails and leads to wrong estimated poses +and geometry. (b) Our method assumes a shared intrinsic over the +entire video and thus cannot handle changing focal length well. +4.3. Ablation Study +We analyze the design choices in Table 5. For the cam- +era poses estimation, the coarse-to-fine voxel upsampling +strategy is the most critical component. Late viewing di- +rection fusion and stopping the gradients from the dynamic +radiance field also help the optimization find better poses +and lead to higher-quality rendering results. Please refer +to Figure 4 for visual comparisons. For the dynamic ra- +diance field reconstruction, both the deformation MLP and +the time-dependent MLPs improve the final rendering qual- +ity. +4.4. Failure Cases +Even with these efforts, robust dynamic view synthesis +from a monocular video without known camera poses is still +challenging. We show some failure cases in Figure 9. +8 + +5. Conclusions +We present robust dynamic radiance fields for space- +time synthesis of casually captured monocular videos with- +out requiring camera poses as input. With the proposed +model designs, we demonstrate that our approach can re- +construct accurate dynamic radiance fields from a wide +range of challenging videos. We validate the efficacy of the +proposed method via extensive quantitative and qualitative +comparisons with the state-of-the-art. +References +[1] Luca Ballan, Gabriel J Brostow, Jens Puwein, and Marc +Pollefeys. Unstructured video-based rendering: Interactive +exploration of casually captured videos. ACM TOG, pages +1–11, 2010. 2 +[2] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and +Srinivasa Narasimhan. 4d visualization of dynamic events +from unconstrained multi-view videos. In CVPR, 2020. 2 +[3] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter +Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. +Mip-nerf: A multiscale representation for anti-aliasing neu- +ral radiance fields. In ICCV, 2021. 2 +[4] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P +Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded +anti-aliased neural radiance fields. In CVPR, 2022. 2, 7 +[5] Michael Broxton, John Flynn, Ryan Overbeck, Daniel Erick- +son, Peter Hedman, Matthew Duvall, Jason Dourgarian, Jay +Busch, Matt Whalen, and Paul Debevec. Immersive light +field video with a layered mesh representation. ACM TOG, +39:86–1, 2020. 1, 2 +[6] Chris Buehler, Michael Bosse, Leonard McMillan, Steven +Gortler, and Michael Cohen. Unstructured lumigraph ren- +dering. +In Proceedings of the 28th annual conference on +Computer graphics and interactive techniques, pages 425– +432, 2001. 2 +[7] Daniel J Butler, Jonas Wulff, Garrett B Stanley, and +Michael J Black. A naturalistic open source movie for opti- +cal flow evaluation. In ECCV, 2012. 2, 7 +[8] Joel Carranza, Christian Theobalt, Marcus A Magnor, and +Hans-Peter Seidel. Free-viewpoint video of human actors. +ACM TOG, 22:569–577, 2003. 1 +[9] Gaurav +Chaurasia, +Sylvain +Duchene, +Olga +Sorkine- +Hornung, and George Drettakis. +Depth synthesis and lo- +cal warps for plausible image-based navigation. ACM TOG, +32:1–12, 2013. 2 +[10] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and +Hao Su. Tensorf: Tensorial radiance fields. In ECCV, 2022. +2, 4, 7 +[11] Shenchang Eric Chen and Lance Williams. View interpo- +lation for image synthesis. In Proceedings of the 20th an- +nual conference on Computer graphics and interactive tech- +niques, pages 279–288, 1993. 1 +[12] Inchang Choi, Orazio Gallo, Alejandro Troccoli, Min H +Kim, and Jan Kautz. +Extreme view synthesis. +In ICCV, +2019. 2 +[13] Alvaro Collet, Ming Chuang, Pat Sweeney, Don Gillett, Den- +nis Evseev, David Calabrese, Hugues Hoppe, Adam Kirk, +and Steve Sullivan. High-quality streamable free-viewpoint +video. ACM TOG, 34:1–13, 2015. 1 +[14] Mingsong Dou, Sameh Khamis, Yury Degtyarev, Philip +Davidson, Sean Ryan Fanello, Adarsh Kowdle, Sergio Orts +Escolano, Christoph Rhemann, David Kim, Jonathan Taylor, +et al. Fusion4d: Real-time performance capture of challeng- +ing scenes. ACM TOG, 35:1–13, 2016. 2 +[15] Robert A Drebin, Loren Carpenter, and Pat Hanrahan. Vol- +ume rendering. ACM TOG, 22:65–74, 1988. 3 +[16] Jakob Engel, Vladlen Koltun, and Daniel Cremers. Direct +sparse odometry. IEEE TPAMI, 40:611–625, 2017. 3 +[17] Jakob Engel, Thomas Sch¨ops, and Daniel Cremers. +Lsd- +slam: Large-scale direct monocular slam. In ECCV, 2014. +3 +[18] Jiemin Fang, Taoran Yi, Xinggang Wang, Lingxi Xie, Xi- +aopeng Zhang, Wenyu Liu, Matthias Nießner, and Qi Tian. +Fast dynamic radiance fields with time-aware neural voxels. +ACM TOG, 2022. 2, 3, 7, 8 +[19] John Flynn, Michael Broxton, Paul Debevec, Matthew Du- +Vall, Graham Fyffe, Ryan Overbeck, Noah Snavely, and +Richard Tucker. Deepview: View synthesis with learned gra- +dient descent. In CVPR, 2019. 2 +[20] John Flynn, Ivan Neulander, James Philbin, and Noah +Snavely. Deepstereo: Learning to predict new views from +the world’s imagery. In CVPR, 2016. 2 +[21] Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong +Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: +Radiance fields without neural networks. In CVPR, 2022. 2, +4 +[22] Chen Gao, Ayush Saraf, Johannes Kopf, and Jia-Bin Huang. +Dynamic view synthesis from dynamic monocular video. In +ICCV, 2021. 2, 3, 5, 7, 8 +[23] Hang Gao, Ruilong Li, Shubham Tulsiani, Bryan Russell, +and Angjoo Kanazawa. Monocular dynamic view synthesis: +A reality check. In NeurIPS, 2022. 2, 7, 8 +[24] Cl´ement Godard, Oisin Mac Aodha, Michael Firman, and +Gabriel J Brostow. Digging into self-supervised monocular +depth estimation. In ICCV, 2019. 3 +[25] Steven J Gortler, Radek Grzeszczuk, Richard Szeliski, and +Michael F Cohen. The lumigraph. In Proceedings of the +23rd annual conference on Computer graphics and interac- +tive techniques, pages 43–54, 1996. 2 +[26] Marc Habermann, Weipeng Xu, Michael Zollhoefer, Gerard +Pons-Moll, and Christian Theobalt. Livecap: Real-time hu- +man performance capture from monocular video. ACM TOG, +38:1–17, 2019. 2 +[27] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Gir- +shick. Mask r-cnn. In ICCV, 2017. 4 +[28] Peter Hedman, Julien Philip, True Price, Jan-Michael Frahm, +George Drettakis, and Gabriel Brostow. Deep blending for +free-viewpoint image-based rendering. ACM TOG, 37:1–15, +2018. 2 +[29] Yoonwoo Jeong, Seokjun Ahn, Christopher Choy, Anima +Anandkumar, Minsu Cho, and Jaesik Park. Self-calibrating +neural radiance fields. In ICCV, 2021. 2, 3 +9 + +[30] James T Kajiya and Brian P Von Herzen. Ray tracing volume +densities. ACM TOG, 18:165–174, 1984. 3 +[31] Johannes Kopf, Michael F Cohen, and Richard Szeliski. +First-person hyper-lapse videos. ACM TOG, 33:1–10, 2014. +1 +[32] Johannes Kopf, Kevin Matzen, Suhib Alsisan, Ocean +Quigley, Francis Ge, Yangming Chong, Josh Patterson, Jan- +Michael Frahm, Shu Wu, Matthew Yu, et al. One shot 3d +photography. ACM TOG, 39:76–1, 2020. 2 +[33] Johannes Kopf, Xuejian Rong, and Jia-Bin Huang. Robust +consistent video depth estimation. In CVPR, 2021. 3, 6 +[34] Suryansh Kumar, Yuchao Dai, and Hongdong Li. Monocular +dense 3d reconstruction of a complex dynamic scene from +two perspective frames. In ICCV, 2017. 2 +[35] Marc Levoy and Pat Hanrahan. Light field rendering. In Pro- +ceedings of the 23rd annual conference on Computer graph- +ics and interactive techniques, pages 31–42, 1996. 2 +[36] Zhengqi Li, Tali Dekel, Forrester Cole, Richard Tucker, +Noah Snavely, Ce Liu, and William T Freeman. Learning +the depths of moving people by watching frozen people. In +CVPR, 2019. 2 +[37] Zhengqi Li, Simon Niklaus, Noah Snavely, and Oliver Wang. +Neural scene flow fields for space-time view synthesis of dy- +namic scenes. In CVPR, 2021. 2, 3, 4, 5, 7, 8 +[38] Chen-Hsuan Lin, Wei-Chiu Ma, Antonio Torralba, and Si- +mon Lucey. Barf: Bundle-adjusting neural radiance fields. +In ICCV, 2021. 2, 3, 5, 6 +[39] Kai-En Lin, Lei Xiao, Feng Liu, Guowei Yang, and Ravi +Ramamoorthi. Deep 3d mask volume for view synthesis of +dynamic scenes. In ICCV, 2021. 2 +[40] Yu-Lun Liu, Wei-Sheng Lai, Ming-Hsuan Yang, Yung-Yu +Chuang, and Jia-Bin Huang. Hybrid neural fusion for full- +frame video stabilization. In ICCV, 2021. 1 +[41] Stephen Lombardi, Tomas Simon, Jason Saragih, Gabriel +Schwartz, Andreas Lehrmann, and Yaser Sheikh. Neural vol- +umes: Learning dynamic renderable volumes from images. +ACM TOG, 38:65:1–65:14, 2019. 2 +[42] Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, +Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: +Representing scenes as neural radiance fields for view syn- +thesis. In ECCV, 2020. 2, 3, 7 +[43] Thomas M¨uller, Alex Evans, Christoph Schied, and Alexan- +der Keller. Instant neural graphics primitives with a multires- +olution hash encoding. ACM TOG, 41:102:1–102:15, 2022. +2, 4 +[44] Raul Mur-Artal, Jose Maria Martinez Montiel, and Juan D +Tardos. Orb-slam: a versatile and accurate monocular slam +system. IEEE transactions on robotics, 31:1147–1163, 2015. +3 +[45] Raul Mur-Artal and Juan D Tard´os. Orb-slam2: An open- +source slam system for monocular, stereo, and rgb-d cam- +eras. IEEE transactions on robotics, 33:1255–1262, 2017. +3 +[46] Richard A Newcombe, Steven J Lovegrove, and Andrew J +Davison. DTAM: Dense tracking and mapping in real-time. +In ICCV, 2011. 3 +[47] Simon Niklaus, Long Mai, Jimei Yang, and Feng Liu. 3d ken +burns effect from a single image. ACM TOG, 38:1–15, 2019. +2 +[48] Sergio Orts-Escolano, Christoph Rhemann, Sean Fanello, +Wayne Chang, Adarsh Kowdle, Yury Degtyarev, David +Kim, Philip L. Davidson, Sameh Khamis, Mingsong Dou, +Vladimir Tankovich, Charles Loop, Qin Cai, Philip A. Chou, +Sarah Mennicken, Julien Valentin, Vivek Pradeep, Shenlong +Wang, Sing Bing Kang, Pushmeet Kohli, Yuliya Lutchyn, +Cem Keskin, and Shahram Izadi. Holoportation: Virtual 3d +teleportation in real-time. In Proceedings of the 29th annual +symposium on user interface software and technology, pages +741–754, 2016. 1 +[49] Hyun Soo Park, Takaaki Shiratori, Iain Matthews, and Yaser +Sheikh. 3d reconstruction of a moving point from a series of +2d projections. In ECCV, 2010. 2 +[50] Keunhong Park, Utkarsh Sinha, Jonathan T Barron, Sofien +Bouaziz, Dan B Goldman, Steven M Seitz, and Ricardo +Martin-Brualla. Nerfies: Deformable neural radiance fields. +In CVPR, 2021. 2, 3, 8 +[51] Keunhong Park, Utkarsh Sinha, Peter Hedman, Jonathan T +Barron, Sofien Bouaziz, Dan B Goldman, Ricardo Martin- +Brualla, and Steven M Seitz. +Hypernerf: +A higher- +dimensional representation for topologically varying neural +radiance fields. ACM TOG, 40, 2021. 2, 3, 7, 8 +[52] Eric Penner and Li Zhang. Soft 3d reconstruction for view +synthesis. ACM TOG, 36:1–11, 2017. 2 +[53] Federico Perazzi, Jordi Pont-Tuset, Brian McWilliams, Luc +Van Gool, Markus Gross, and Alexander Sorkine-Hornung. +A benchmark dataset and evaluation methodology for video +object segmentation. In CVPR, 2016. 2 +[54] Albert Pumarola, Enric Corona, Gerard Pons-Moll, and +Francesc Moreno-Noguer. D-nerf: Neural radiance fields for +dynamic scenes. In CVPR, 2021. 2, 3, 7 +[55] Ren´e Ranftl, +Katrin Lasinger, +David Hafner, +Konrad +Schindler, and Vladlen Koltun. Towards robust monocular +depth estimation: Mixing datasets for zero-shot cross-dataset +transfer. IEEE TPAMI, 44, 2020. 5 +[56] Gernot Riegler and Vladlen Koltun. Free view synthesis. In +ECCV, 2020. 2 +[57] Gernot Riegler and Vladlen Koltun. Stable view synthesis. +In CVPR, 2021. 2 +[58] Chris Russell, Rui Yu, and Lourdes Agapito. Video pop-up: +Monocular 3d reconstruction of dynamic scenes. In ECCV, +2014. 2 +[59] Johannes +Lutz +Sch¨onberger +and +Jan-Michael +Frahm. +Structure-from-motion revisited. In CVPR, 2016. 2, 3 +[60] Johannes L Schonberger and Jan-Michael Frahm. Structure- +from-motion revisited. In CVPR, 2016. 3 +[61] Meng-Li Shih, Shih-Yang Su, Johannes Kopf, and Jia-Bin +Huang. 3d photography using context-aware layered depth +inpainting. In CVPR, 2020. 2 +[62] Samarth Sinha, Roman Shapovalov, Jeremy Reizenstein, Ig- +nacio Rocco, Natalia Neverova, Andrea Vedaldi, and David +Novotny. +Common pets in 3d: Dynamic new-view syn- +thesis of real-life deformable categories. +arXiv preprint +arXiv:2211.03889, 2022. 2 +10 + +[63] Vincent Sitzmann, Michael Zollh¨ofer, and Gordon Wet- +zstein. +Scene representation networks: +Continuous 3d- +structure-aware neural scene representations. +In NeurIPS, +2019. 2 +[64] Pratul P Srinivasan, Richard Tucker, Jonathan T Barron, +Ravi Ramamoorthi, Ren Ng, and Noah Snavely. Pushing the +boundaries of view extrapolation with multiplane images. In +CVPR, 2019. 2 +[65] Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel +grid optimization: Super-fast convergence for radiance fields +reconstruction. In CVPR, 2022. 2, 4, 7 +[66] Zachary Teed and Jia Deng. Raft: Recurrent all-pairs field +transforms for optical flow. In ECCV, 2020. 5 +[67] Zachary Teed and Jia Deng. Droid-slam: Deep visual slam +for monocular, stereo, and rgb-d cameras. In NeurIPS, 2021. +3, 6 +[68] Edgar Tretschk, Ayush Tewari, Vladislav Golyanik, Michael +Zollh¨ofer, Christoph Lassner, and Christian Theobalt. Non- +rigid neural radiance fields: Reconstruction and novel view +synthesis of a dynamic scene from monocular video. +In +ICCV, 2021. 2, 3, 7 +[69] Richard Tucker and Noah Snavely. Single-view view syn- +thesis with multiplane images. In CVPR, 2020. 2 +[70] Zirui Wang, +Shangzhe Wu, +Weidi Xie, +Min Chen, +and Victor Adrian Prisacariu. +Nerf–: +Neural radiance +fields without known camera parameters. +arXiv preprint +arXiv:2102.07064, 2021. 2, 3, 6 +[71] Chung-Yi Weng, +Brian Curless, +Pratul P Srinivasan, +Jonathan T Barron, and Ira Kemelmacher-Shlizerman. Hu- +mannerf: Free-viewpoint rendering of moving people from +monocular video. In CVPR, 2022. 2 +[72] Olivia Wiles, Georgia Gkioxari, Richard Szeliski, and Justin +Johnson. Synsin: End-to-end view synthesis from a single +image. In CVPR, 2020. 2 +[73] Wenqi Xian, Jia-Bin Huang, Johannes Kopf, and Changil +Kim. Space-time neural irradiance fields for free-viewpoint +video. In CVPR, 2021. 2, 3 +[74] Zhichao Yin and Jianping Shi. Geonet: Unsupervised learn- +ing of dense depth, optical flow and camera pose. In CVPR, +2018. 3 +[75] Jae Shin Yoon, Kihwan Kim, Orazio Gallo, Hyun Soo Park, +and Jan Kautz. +Novel view synthesis of dynamic scenes +with globally coherent depths from a monocular camera. In +CVPR, 2020. 2, 7 +[76] Kai Zhang, Gernot Riegler, Noah Snavely, and Vladlen +Koltun. Nerf++: Analyzing and improving neural radiance +fields. arXiv preprint arXiv:2010.07492, 2020. 2 +[77] Wang Zhao, Shaohui Liu, Hengkai Guo, Wenping Wang, and +Yong-Jin Liu. Particlesfm: Exploiting dense point trajecto- +ries for localizing moving cameras in the wild. In ECCV, +2022. 3, 6, 7 +[78] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G +Lowe. Unsupervised learning of depth and ego-motion from +video. In CVPR, 2017. 3 +[79] C Lawrence Zitnick, Sing Bing Kang, Matthew Uyttendaele, +Simon Winder, and Richard Szeliski. +High-quality video +view interpolation using a layered representation. +ACM +TOG, 23:600–608, 2004. 1, 2 +11 + diff --git a/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/load_file.txt b/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..b7ce7720d446c6c8e1cfb08978134b4f913d6329 --- /dev/null +++ b/PNE0T4oBgHgl3EQfTwAQ/content/tmp_files/load_file.txt @@ -0,0 +1,1075 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf,len=1074 +page_content='Robust Dynamic Radiance Fields Yu-Lun Liu2* Chen Gao1 Andreas Meuleman3* Hung-Yu Tseng1 Ayush Saraf1 Changil Kim1 Yung-Yu Chuang2 Johannes Kopf1 Jia-Bin Huang1,4 1Meta 2National Taiwan University 3KAIST 4University of Maryland, College Park https://robust-dynrf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='io/ Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Robust space-time synthesis from dynamic monocular videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method takes a casually captured video as input and reconstructs the camera trajectory and dynamic radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Conventional SfM system such as COLMAP fails to recover camera poses even when using ground truth motion masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' As a result, existing dynamic radiance field methods that require accurate pose estimation do not work on these challenging dynamic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our work tackles this robustness problem and showcases high-fidelity dynamic view synthesis results on a wide variety of videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Abstract Dynamic radiance field reconstruction methods aim to model the time-varying structure and appearance of a dy- namic scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Existing methods, however, assume that ac- curate camera poses can be reliably estimated by Structure from Motion (SfM) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These methods, thus, are un- reliable as SfM algorithms often fail or produce erroneous poses on challenging videos with highly dynamic objects, poorly textured surfaces, and rotating camera motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We address this robustness issue by jointly estimating the static and dynamic radiance fields along with the camera param- eters (poses and focal length).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We demonstrate the robust- ness of our approach via extensive quantitative and qualita- tive experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our results show favorable performance over the state-of-the-art dynamic view synthesis methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' This work was done while Yu-Lun and Andreas were interns at Meta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Introduction Videos capture and preserve memorable moments of our lives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, when watching regular videos, viewers ob- serve the scene from fixed viewpoints and cannot interac- tively navigate the scene afterward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic view synthe- sis techniques aim to create photorealistic novel views of dynamic scenes from arbitrary camera angles and points of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These systems are essential for innovative ap- plications such as video stabilization [31, 40], virtual real- ity [5, 13], and view interpolation [11, 79], which enable free-viewpoint videos and let users interact with the video sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' It facilitates downstream applications like virtual reality, virtual 3D teleportation, and 3D replays of live pro- fessional sports events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Most current dynamic view synthesis systems rely on la- borious and expensive setups such as fixed multi-camera capture rigs [5, 8, 13, 48, 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These techniques require simultaneous (time-synchronized) capture from multiple cameras that is not practical for most people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Several methods can synthesize dynamic novel views from a sin- 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='02239v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='CV] 5 Jan 2023 huft der Siegefseite ewzchjobsgle stereo or RGB camera but are specifically tailored for human performance capture [14,26] or small animals [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Recent work has relaxed these restrictions and can han- dle unstructured video input [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Recently, there have been many dynamic view synthesis methods for unstruc- tured videos [22, 23, 37, 50, 51, 54, 68, 73] and other new methods based on deformable fields [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, these techniques require precise camera poses as input, typically estimated via SfM systems such as COLMAP [59] (bottom left of Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, SfM systems are not robust to many issues, such as noisy images from low-light conditions, motion blur caused by users, or dynamic objects in the scene, such as people, cars, and animals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The robustness problem of the SfM systems causes the existing dynamic view synthesis methods to be fragile and impractical for many challenging videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Recently, several NeRF-based methods [29,38,70] have proposed jointly optimizing the camera poses with the scene geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Nevertheless, these methods can only han- dle strictly static scenes (top right of Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In this paper, we present RoDynRF — an algorithm for reconstructing dynamic radiance fields from a casually cap- tured video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method is more robust than existing ap- proaches in the sense that we do not rely on accurate camera poses as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The core idea of our approach is to optimize the camera poses in conjunction with two radiance fields that model static and dynamic scene elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We care- fully design the method for joint static radiance field and pose estimation, including a coarse-to-fine strategy, limit- ing the effects of viewing direction, and detecting and ex- cluding moving pixels with epipolar geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' For mod- eling the dynamic radiance fields, we introduce a deforma- tion field and time-dependent appearance models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We fur- ther leverage several auxiliary regularization losses to im- prove the consistency of the reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We perform an extensive experimental validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' On poses, we evalu- ate our estimated camera trajectories quantitatively on the Sintel dataset [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' On view synthesis, we quantify the per- formance on the Dynamic View Synthesis dataset [75] and the iPhone dataset [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show numerous visual com- parisons with existing methods on the challenging DAVIS dataset [53] and in-the-wild videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We summarize our core contributions as follows: We present a space-time synthesis algorithm from a dynamic monocular video that does not require known camera poses and camera intrinsics as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We propose careful architecture designs and axillary losses that improve the robustness of the camera pose estimation and the dynamic radiance field reconstruc- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Quantitative and qualitative evaluations demonstrate the robustness of our method over other state-of-the- Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Catogorization of view synthesis methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Known camera poses Unknown camera poses Static scene NeRF [42], SVS [57], NeRF++ [76], Mip-NeRF [3], Mip-NeRF 360 [4], DirectVoxGO [65], Plenoxels [21], Instant-ngp [43], TensoRF [10] NeRF - - [70], BARF [38], SC-NeRF [29] Dynamic scene NV [41], D-NeRF [54], NR-NeRF [68], NSFF [37], DynamicNeRF [22], Nerfies [50], HyperNeRF [51], TiNeuVox [18], T-NeRF [23] Ours art methods on several challenging datasets that typical SfM systems fail to estimate camera poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Related Work Static view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Many view synthesis techniques construct specific scene geometry from images captured at various positions [6] and use local warps [9] to synthesize high-quality novel views of a scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Approaches to light field rendering use implicit scene geometry to create pho- torealistic novel views, but they require densely captured images [25, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' By using soft 3D reconstruction [52], learning-based dense depth maps [20], multiplane images (MPIs) [12,19,64], additional learned deep features [28,56], or voxel-based implicit scene representations [63], several earlier work attempt to use proxy scene geometry to en- hance rendering quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Recent methods implicitly model the scene as a contin- uous neural radiance field (NeRF) [3, 42, 76] with multi- layer perceptrons (MLPs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, NeRF requires days of training time to represent a scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, recent meth- ods [10, 21, 43, 65] replace the implicit MLPs with explicit voxels and significantly improve the training speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Several approaches synthesize novel views from a single RGB input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These methods often fill up holes in the disoccluded regions and predict depth [36,47], additionally learned features [72], multiplane images [69], and layered depth images [32,61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Although these techniques have pro- duced excellent view synthesis results, they can only han- dle static scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our approach performs view synthesis of dynamic scenes from a single monocular video, in con- trast to existing view synthesis techniques focusing on static scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' By focusing on human bod- ies [71], using RGBD data [14], reconstructing sparse ge- ometry [49], or producing minimal stereoscopic disparity transitions between input views [1], many techniques re- construct and synthesize novel views from non-rigid dy- namic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Other techniques break down dynamic scenes into piece-wise rigid parts using hand-crafted pri- ors [34,58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Many systems cannot handle scenes with com- plicated geometry and instead require multi-view and time- synchronized videos as input to provide interactive view manipulation [2,5,39,79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Yoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' [75] used depth from single-view and multi-view stereo to synthesize novel views 2 Static voxel 𝐕!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝐱 = 𝑥, 𝑦, 𝑧 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' \' Color 𝒄" Density 𝜎" Viewing direction 𝒅 Dynamic voxel 𝐕" Color 𝒄#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ Density 𝜎#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ Viewing direction 𝒅 Nonrigidity 𝑚#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ 𝑡% 𝐱 𝐱′ Time 𝑡% Dynamic Radiance Fields Static Radiance Fields Coordinate deformation 𝑅 𝑡 % Gradients for camera poses Stop gradients Volume rendering 𝜎 Ray distance 𝛿 Volume rendering 𝜎 Ray distance 𝛿 Static RGB 𝐂!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic RGB 𝐂#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' " Static depth 𝐃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic depth 𝐃#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' " Nonrigidity mask 𝐌#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝒅 (a) Sampling 𝐱 = 𝐨 + 𝑡𝑑 (b) Radiance fields Θ&" Θ&$ Θ\'$ Θ( $ Θ$ Summation 𝒄" × 1 − 𝑚#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ + 𝒄#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ × 𝑚#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ 𝜎" × 1 − 𝑚#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ + 𝜎#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ × 𝑚#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' $ Volume rendering 𝜎 Ray distance 𝛿 Combined color 𝐂#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Combined depth 𝐃#!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Linear combination Input Input Input Masked loss Loss Loss Motion mask Time-dependent MLPs Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Overall framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We model the dynamic scene with static and dynamic radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The static radiance fields take both the sampled coordinates (x, y, z) and the viewing direction d as input and predict the density σs and color cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Note that the density of the static part is invariant to time and viewing direction, therefore, we use summation of the queried features as the density (instead of using an MLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We only compute the losses over the static regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The computed gradients backpropagate not only to the static voxel field and MLPs but also to the camera parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The dynamic radiance fields take the sampled coordinates and the time t to obtain the deformed coordinates (x′, y′, z′) in the canonical space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Then we query the features using these deformed coordinates from the dynamic voxel fields and pass the features along with the time index to a time-dependent shallow MLPs to get the color cd, density σd, and nonrigidity md of the dynamic part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, after the volume rendering, we can obtain the RGB images C{s,d} and the depth maps D{s,d} from the static and dynamic parts along with a nonrigidity mask Md.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, we calculate the per-frame reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Note that here we only include per-frame losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' of dynamic scenes from a single video using explicit depth- based 3D warping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' A recent line of work extends NeRF to handle dy- namic scenes [18,22,37,50,51,54,68,73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Although these space-time synthesis results are impressive, these tech- niques rely on precise camera pose input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Consequently, these techniques are not applicable to challenging scenes where COLMAP [59] or current SfM systems fail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our ap- proach, in contrast, can handle complex dynamic scenarios without known camera poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Visual odometry and camera pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' From a collection of images, visual odometry estimates the 3D camera poses [16,17,44–46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These techniques mainly fall into two categories: direct methods that maximize photo- metric consistency [74, 78] and feature-based methods that rely on manually created or learned features [44, 45, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Self-supervised image reconstruction losses have recently been used in learning-based systems to tackle visual odom- etry [24, 33, 67, 77, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Estimating camera poses from ca- sually captured videos remains challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' NeRF-based techniques have been proposed to combine neural 3D rep- resentation and camera poses for optimization [29, 38, 70], although they are limited to static sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In contrast to the visual odometry techniques outlined above, our sys- tem simultaneously optimizes camera poses and models dy- namic objects models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Method In this section, we first briefly introduce the background of neural radiance fields and their extension of camera pose estimation and dynamic scene representation in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We then describe the overview of our method in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Next, we discuss the details of camera pose estimation with the static radiance field reconstruction in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Af- ter that, we show how to model the dynamic scene in Sec- tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, we outline the implementation details in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Preliminaries NeRF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Neural radiance fields (NeRF) [42] represent a static 3D scene with implicit MLPs parameterized by Θ and map the 3D position (x, y, z) and viewing direction (θ, ϕ) to its corresponding color c and density σ: (c, σ) = MLPΘ(x, y, z, θ, ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (1) We can compute the pixel color by applying volume render- ing [15,30] along the ray r emitted from the camera origin: 3 𝑡!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝑡!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 𝑧 ℒ$%&$\'( ℒ)*+& ℒ,\'-\')%&.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='/ Optical flow 𝐟 Volume rendered 3D point 𝐃0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 1 𝐊0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 2𝟏 𝐩′ Motion mask Epipolar distance thresholding 𝐩 𝐩4 = 𝐩 + 𝐟(𝐩) 𝐃0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 𝐊0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2𝟏𝐩 Volume rendered depth 𝐃0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 MiDaS depth 𝑡!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝑡!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 𝑧 ℒ$%&$\'( ℒ)*+& Optical flow 𝐟 Volume rendered 3D point 𝐱,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' = 𝐃,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝐊,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='𝟏𝐩 Scene flow MLP 𝑡!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 𝐩 𝐩0 = 𝐩 + 𝐟(𝐩) 𝐱,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='→,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 𝐱,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# = 𝐃,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# 𝐊,!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' "# .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content="𝟏 𝐩′ ℒ2'3')%&45 Volume rendered depth 𝐃,!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 6 MiDaS depth (a) Static radiance field reconstruction and pose estimation (b) Dynamic radiance field reconstruction Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Training losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' For both the (a) static and (b) dynamic parts, we introduce three auxiliary losses to encourage the consistency of the modeling: reprojection loss, disparity loss, and monocular depth loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The reprojection loss encourages the projection of the 3D volume rendered points onto neighbor frames to be similar to the pre-calculated flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The disparity loss forces the volume rendered 3D points from two corresponding points of neighbor frames to have similar z values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, the monocular depth loss calculates the scale- and shift-invariant loss between the volume rendered depth and the pre-calculated MiDaS depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (a) We use the motion mask to exclude the dynamic regions from the loss calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (b) We use a scene flow MLP to model the 3D movement of the volume rendered 3D points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ˆC(r) = N � i=1 T(i)(1 − exp(−σ(i)δ(i)))c(i), T(i) = exp(− j � i−1 σ(j)δ(j)), (2) where δ(i) represents the distance between two consecutive sample points along the ray, N is the number of samples along each ray, and T(i) indicates the accumulated trans- parency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' As the volume rendering procedure is differen- tiable, we can optimize the radiance fields by minimizing the reconstruction error between the rendered color ˆC and the ground truth color C: L = ��� ˆC(r) − C(r) ��� 2 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (3) Explicit neural voxel radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Although with compelling rendering quality, NeRF-based methods model the scene with implicit representations such as MLPs for high storage efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' These methods, however, are very slow to train.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To overcome this drawback, recent meth- ods [10, 21, 43, 65] propose to model the radiance fields with explicit voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Specifically, these methods replace the mapping function with voxel grids and directly optimize the features sampled from the voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' They usually apply shal- low MLPs to handle the view-dependent effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' By elim- inating the heavy usage of the MLPs, the training time of these methods reduces from days to hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We also lever- age explicit representation in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Method Overview We show our proposed framework in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Given an input video sequence with N frames, our method jointly optimizes the camera poses, focal length, and static and dy- namic radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We represent both the static and dy- namic parts with explicit neural voxels Vs and Vd, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The static radiance fields are responsible for recon- structing the static scene and estimating the camera poses and focal length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' At the same time, the goal of dynamic radiance fields is to model the scene dynamics in the video (usually caused by moving objects).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Camera Pose Estimation Motion mask generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Excluduing dynamic regions in the video helps improve the robustness of camera pose esti- mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Existing methods [37] often leverage off-the-shelf instance segmentation methods such as Mask R-CNN [27] to mask out the common moving objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, many moving objects are hard to detect/segment in the input video, such as drifting water or swaying trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, in addition to the masks from Mask R-CNN, we also estimate the fundamental matrix using the optical flow from consec- utive frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We then calculate and threshold the Sampson distance (the distance of each pixel to the estimated epipolar line) to obtain a binary motion mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, we combine the results from Mask R-CNN and epipolar distance thresh- olding to obtain our final motion masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Coarse-to-fine static scene reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The first part of our method is reconstructing the static radiance fields along with the camera poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We jointly optimize the 6D camera poses [R|t]i, i ∈ [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='.N] and the focal length f 4 (a) w/o coarse-to-fine (b) w/o monocular depth prior (c) w/o late viewing direction conditioning (d) Full model Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Effects of design choices for camera poses estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (a) Withput the coarse-to-fine strategy, the optimization often ends up with sub-optimal solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (b) Without the single-image depth prior, the optimization fails to reconstruct reasonable scene ge- ometry with challenging camera trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (c) Without the late viewing direction conditioning, the optimization tends to minimize the photometric loss with MLP instead of consistent voxel space, resulting in wrong geometry and poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (d) With all the proposed components, our method could reconstruct reasonable scene ge- ometry as well as the camera trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' shared by all input frames simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Similar to ex- isting pose estimation methods [38], we optimize the static scene representation in a coarse-to-fine manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Specifi- cally, we start with a smaller static voxel resolution and pro- gressively increase the voxel resolution during the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' This coarse-to-fine strategy is essential to the camera pose estimation as the energy surface will become smoother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Thus, the optimizer will have less chance of getting stuck in sub-optimal solutions (Figure 4(a) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Figure 4(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Late viewing direction conditioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' As our primary supervision is the photometric consistency loss, the opti- mization could bypass the neural voxel and directly learn a mapping function from the viewing direction to the out- put sample color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, we choose to fuse the viewing direction only in the last layer of the color MLP as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' This design choice is critical because we are re- constructing not only the scene geometry but also the cam- era poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Figure 4(c) shows that without the late viewing direction conditioning, the optimization could minimize the photometric loss by optimizing the MLP and lead to erro- neous camera poses and geometry estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We minimize the photometric loss between the prediction ˆCs(r) and the captured images in the static re- gions: Ls c = ���( ˆCs(r) − C(r)) · (1 − M(r)) ��� 2 2 , (4) where M denotes the motion mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To handle casually-captured but challenging camera tra- jectories such as fast-moving or pure rotating, we introduce auxiliary losses to regularize the training, similar to [22,37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (1) Reprojection loss Ls reproj: We use 2D optical flow esti- mated by RAFT [66] to guide the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' First, we volume render all the sampled 3D points along a ray to generate a surface point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We then reproject this point onto its neighbor frame and calculate the reprojection error with the corre- spondence estimated from RAFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (2) Disparity loss Ls disp: Similar to the reprojection loss above, we also regularize the error in the z-direction (in the camera coordinate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We volume render the two correspond- ing points into 3D space and calculate the error of the z component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' As we care more about the near than the far, we compute this loss in the inverse-depth domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (3) Monocular depth loss Ls monodepth: The two losses above cannot handle pure rotating cameras and often lead to the incorrect camera poses and geometry (Figure 4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We enforce the depth order from multiple pixels of the same frame to match the order of a monocular depth map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We pre-calculate the depth map using MiDaSv2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='1 [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The depth prediction from MiDaS is up to an unknown scale and shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, we use the same scale- and shift-invariant loss in MiDaS to constrain our rendered depth values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We illustrate these auxiliary losses in Figure 3(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Since the optical flow and depth map may not be accurate, we apply annealing for the weights of these auxiliary losses during the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' As the input frames contain dynamic objects, we need to mask out all the dynamic regions while applying all these losses and the L2 reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The final loss for the static part is: Ls = Ls c + λs reprojLs reproj + λs dispLs disp + λs monodepthLs monodepth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (5) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic Radiance Field Reconstruction Handling temporal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To query the time- varying features from the voxel, we first pass the 3D coor- dinates (x, y, z) along with time index ti to a coordinate de- formation MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The coordinate deformation MLP predicts the 3D time-varying deformation vectors (∆x, ∆y, ∆z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We then add these deformations onto the original coordi- nates to get the deformed coordinates (x′, y′, z′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' This de- formation MLP indicates that the voxel is a canonical space and that each corresponding 3D point from a different time should point to the same position in this voxel space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We design the deformation MLP to deform the 3D points from the original camera space to the canonical voxel space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' However, using a single compact canonical voxel to rep- resent the entire sequence along the temporal dimension is very challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, we further introduce time- dependent MLPs to enhance the queried features from the voxel to predict time-varying color and density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Note that the time-dependent MLPs with only two to three layers are much shallower than the ones in other dynamic view syn- thesis methods [22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 37] as the purpose of the MLPs here is ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='further to enhance the queried features from the canonical ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 25 24 23 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='57 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='58 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='62 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='63 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 25 24 23 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='57 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='58 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='62 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='63 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 25 24 23 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='57 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='58 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='62 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='63 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 25 24 23 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='57 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='58 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='62 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='63 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='Sample frames ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='ParticleSfM [77] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='NeRF - - [70] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='BARF [38] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='Ours ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Qualitative results of moving camera localization on the MPI Sintel dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Quantitative evaluation of camera poses estimation on the MPI Sintel dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The methods of the top block discard the dynamic components and do not reconstruct the radiance fields;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' thus they cannot render novel views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Method ATE (m) RPE trans (m) RPE rot (deg) R-CVD [33] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='360 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='154 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='443 DROID-SLAM [67] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='084 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='912 ParticleSfM [77] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='129 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='031 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='535 NeRF - - [70] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='433 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='220 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='088 BARF [38] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='447 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='203 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='353 Ours 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='073 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='313 voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Most of the time-varying effects are still carried out by the coordination deformation MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show the above architecture at the bottom of Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' And the photometric training loss for the dynamic part is: Ld c = ��� ˆCd(r) − C(r) ��� 2 2 , (6) Scene flow modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We introduce three losses based on external priors to better model the dynamic movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The three losses are similar to the ones in the static part, but we need to model the movements of the 3D points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' There- fore, we introduce a scene flow MLP to compensate the 3D motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (Si→i+1, Si→i−1) = MLPθsf(x, y, z, ti), (7) where Si→i+1 represents the 3D scene flow of the 3D point (x, y, z) at time ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' With the 3D scene flow, we can apply the losses for the dynamic radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show the training losses in Figure 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (1) Reprojection loss Ld reproj: We induce the 2D flow us- ing the poses, depth, and the estimated 3D scene flow from the scene flow MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' And we compare the error of this in- duced flow with the one estimated by RAFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (2) Disparity loss Ld disp: Similar to the disparity loss in the static part, but here we additionally have the 3D scene Ground truth NeRF - - [70] BARF [38] Ours Image Depth Image Depth Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Qualitative results of static view synthesis on the DAVIS dataset from unknown camera poses and ground truth foreground masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We get the corresponding points in the 3D space, add the estimated 3D scene flow, and calculate the difference of the z components in the inverse-depth domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (3) Monocular depth loss Ld monodepth: We calculate scale- and shift-invariant loss between the rendered depth with the pre-calculated depth map using MiDaSv2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We further regularize the 3D motion prediction from the MLP by introducing the smooth and small scene flow loss: Lreg sf = ∥Si→i+1 + Si→i−1∥1 + ∥Si→i+1∥1 + ∥Si→i−1∥1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (8) Note that the scene flow MLP is not part of the rendering process but part of the losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' By representing the 3D scene flow with an MLP and enforcing proper priors, we can make the density prediction better and more reasonable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We also detach the gradients from the dynamic radiance fields to the camera poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Finally, we supervise the nonrigidity mask Md with motion mask M: Ld m = ��Md − M �� 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (9) The overall loss of the dynamic part is: Ld = Ld c + λd reprojLd reproj + λd dispLd disp+ λd monodepthLd monodepth + λreg sf Lreg sf + λd mLd m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (10) We then linearly compose the static and dynamic parts into the final results with the predicted nonrigidity md: ˆC(r) = N � i=1 T(i)(md(1 − exp(−σd(i)δ(i)))cd(i)+ (1 − md)(1 − exp(−σs(i)δ(i)))cs(i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (11) Total training loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The total training loss is: L = ��� ˆC(r) − C(r) ��� 2 2 + Ls + Ld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (12) 6 NSFF [37] DynamicNeRF [22] HyperNeRF [51] TiNeuVox [18] Ours Ground truth Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Novel view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Compared to other methods, our results are sharper, closer to the ground truth, and contain fewer artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Novel view synthesis results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We report the average PSNR and LPIPS results with comparisons to existing methods on Dynamic Scene dataset [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' *: Numbers are adopted from DynamicNeRF [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' PSNR ↑ / LPIPS ↓ Jumping Skating Truck Umbrella Balloon1 Balloon2 Playground Average NeRF* [42] 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='99 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='305 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='67 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='311 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='73 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='229 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='29 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='440 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='82 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='205 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='37 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='098 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='07 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='165 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='99 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='250 D-NeRF [54] 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='36 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='193 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='48 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='323 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='145 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='47 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='264 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='06 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='259 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='76 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='277 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='18 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='164 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='48 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='232 NR-NeRF* [68] 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='09 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='287 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='95 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='227 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='33 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='446 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='63 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='421 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='39 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='348 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='41 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='213 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='06 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='317 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='69 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='323 NSFF* [37] 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='65 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='151 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='29 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='129 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='96 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='167 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='97 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='295 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='96 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='215 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='27 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='222 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='22 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='212 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='33 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='199 DynamicNeRF* [22] 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='68 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='090 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='66 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='035 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='082 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='137 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='36 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='104 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='06 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='049 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='15 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='080 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='10 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='082 HyperNeRF [51] 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='302 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='97 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='183 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='205 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='443 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='96 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='530 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='57 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='411 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='17 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='495 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='60 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='367 TiNeuVox [18] 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='81 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='247 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='32 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='152 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='86 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='173 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='00 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='355 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='30 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='353 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='06 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='279 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='84 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='437 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='74 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='285 Ours w/ COLMAP poses 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='66 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='071 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='68 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='040 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='13 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='063 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='089 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='37 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='103 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='19 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='054 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='96 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='048 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='89 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='065 Ours w/o COLMAP poses 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='27 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='100 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='71 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='046 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='85 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='066 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='25 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='104 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='81 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='122 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='58 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='064 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='052 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='38 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='079 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Implementation Details We simultaneously estimate camera poses, focal length, static radiance fields, and dynamic radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' For forward-facing scenes, we parameterize the scenes with normalized device coordinates (NDC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To handle un- bounded scenes in the wild videos, we parameterize the scenes using the contraction parameterization [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To encourage solid surface scene reconstruction and prevent floaters, we add the distortion loss [4, 65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We set the finest voxel resolution to 262,144,000 and 27,000,000 for NDC and contraction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We also decompose the voxel grid using the VM-decomposition in TensoRF [10] for model compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The entire training process takes around 28 hours with one NVIDIA V100 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We provide the detailed architecture in the supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Experimental Results Due to the space limit, we leave the experimental setup, including datasets, compared methods, and the evaluation metrics to the supplementary materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Evaluation on Camera Poses Estimation We conduct the camera pose estimation evaluation on the MPI Sintel dataset [7] and show the quantitative re- sults in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method performs significantly bet- ter than existing NeRF-based pose estimation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Note that our method also performs favorably against ex- isting learning-based visual odometry methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show some visual comparisons of the predicted camera trajec- tories in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our approach predicts accurate cam- era poses over other NeRF-based pose estimation meth- ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method is a global optimization over the entire se- quence instead of local registration like SLAM-based meth- ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, our RPE trans and rot scores are slightly worse than ParticleSfM [77] as consecutive frames’ rotation is less accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' To further reduce the effect of the dynamic parts, we use the ground truth motion masks provided by the DAVIS dataset to mask out the loss calculations in the dynamic re- gions for all the NeRF-based compared methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show the reconstructed images and depth maps in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our approach can successfully reconstruct the detailed content and the faithful geometry thanks to the auxiliary losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' On the contrary, other methods often fail to reconstruct consis- tent scene geometry and thus produce poor synthesis results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Evaluation on Dynamic View Synthesis Quantitative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We follow the evaluation proto- col in DynamicNeRF [22] to synthesize the view from the first camera and change time on the NVIDIA dynamic view synthesis dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We report the PSNR and LPIPS in Ta- ble 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method performs favorably against state-of-the- art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Furthermore, even without COLMAP poses, our method can still achieve results comparable to the ones using COLMAP poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We also follow the evaluation protocol in DyCheck [23] and evaluate quantitatively on the iPhone dataset [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We report the masked PSNR and SSIM in Table 4 and show that our method performs favorably against existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Qualitative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show some visual com- 7 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Novel view synthesis results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We compare the mPSNR and mSSIM scores with existing methods on the iPhone dataset [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' mPSNR ↑ / mSSIM ↑ Apple Block Paper-windmill Space-out Spin Teddy Wheel Average NSFF [37] 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='54 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='750 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='61 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='639 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='378 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='79 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='622 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='38 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='585 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='65 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='557 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='82 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='458 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='46 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='569 Nerfies [50] 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='64 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='743 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='54 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='670 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='38 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='382 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='93 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='605 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='561 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='97 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='568 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='99 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='455 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='45 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='569 HyperNeRF [51] 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='47 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='754 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='71 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='606 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='94 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='272 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='65 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='636 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='26 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='540 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='537 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='59 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='511 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='81 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='550 T-NeRF [23] 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='43 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='728 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='52 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='669 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='55 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='367 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='71 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='591 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='16 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='567 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='71 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='570 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='65 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='548 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='96 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='577 Ours 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='73 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='722 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='73 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='634 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='71 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='321 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='56 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='594 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='41 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='484 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='33 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='536 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='449 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='09 / 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='534 NSFF [37] DynamicNeRF [22] HyperNeRF [51] TiNeuVox [18] Ours Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Novel space-time synthesis results on the DAVIS dataset with our estimated camera poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' COLMAP fails to produce reliable camera poses for most of the sequences in the DAVIS dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' With the estimated camera poses by our method, we can run other methods and perform space-time synthesis on the scenes that are not feasible with COLMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Our method produces images with much better quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Ablation studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We report PSNR, SSIM and LPIPS on the Playground sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (a) Pose estimation design choices PSNR ↑ SSIM ↑ LPIPS ↓ Ours w/o coarse-to-fine 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='327 Ours w/o late viewing direction fusion 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='5521 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='263 Ours w/o stopping the dynamic gradients 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='7392 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='211 Ours 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9052 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='052 (b) Dynamic reconstruction achitectural designs Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' model Deform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' MLP Time-depend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' MLPs PSNR ↑ SSIM ↑ LPIPS ↓ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8192 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='161 ✓ ✓ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='115 ✓ ✓ 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='8683 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='083 ✓ ✓ ✓ 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='9052 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='052 parisons on the NVIDIA dynamic view synthesis dataset in Figure 7 and DAVIS dataset in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' COLMAP fails to estimate the camera poses for 44 out of 50 sequences in the DAVIS dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Therefore, we first run our method and give our camera poses to other methods as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' With the joint learning of the camera poses and radiance fields, our method produces frames with fewer visual artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Other methods can also benefit from our estimated poses to syn- thesize novel views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' With our poses, they can reconstruct consistent static scenes but often generate artifacts for the dynamic parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In contrast, our method utilizes the auxil- iary priors and thus produces results of much better visual quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (a) Fast moving camera (b) Changing focal length Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Failure cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (a) In the cases that the camera is moving fast, the flow estimation fails and leads to wrong estimated poses and geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' (b) Our method assumes a shared intrinsic over the entire video and thus cannot handle changing focal length well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Ablation Study We analyze the design choices in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' For the cam- era poses estimation, the coarse-to-fine voxel upsampling strategy is the most critical component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Late viewing di- rection fusion and stopping the gradients from the dynamic radiance field also help the optimization find better poses and lead to higher-quality rendering results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Please refer to Figure 4 for visual comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' For the dynamic ra- diance field reconstruction, both the deformation MLP and the time-dependent MLPs improve the final rendering qual- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Failure Cases Even with these efforts, robust dynamic view synthesis from a monocular video without known camera poses is still challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We show some failure cases in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 8 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Conclusions We present robust dynamic radiance fields for space- time synthesis of casually captured monocular videos with- out requiring camera poses as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' With the proposed model designs, we demonstrate that our approach can re- construct accurate dynamic radiance fields from a wide range of challenging videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' We validate the efficacy of the proposed method via extensive quantitative and qualitative comparisons with the state-of-the-art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' References [1] Luca Ballan, Gabriel J Brostow, Jens Puwein, and Marc Pollefeys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Unstructured video-based rendering: Interactive exploration of casually captured videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, pages 1–11, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [2] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and Srinivasa Narasimhan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4d visualization of dynamic events from unconstrained multi-view videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [3] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Mip-nerf: A multiscale representation for anti-aliasing neu- ral radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [4] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Mip-nerf 360: Unbounded anti-aliased neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 7 [5] Michael Broxton, John Flynn, Ryan Overbeck, Daniel Erick- son, Peter Hedman, Matthew Duvall, Jason Dourgarian, Jay Busch, Matt Whalen, and Paul Debevec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Immersive light field video with a layered mesh representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 39:86–1, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1, 2 [6] Chris Buehler, Michael Bosse, Leonard McMillan, Steven Gortler, and Michael Cohen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Unstructured lumigraph ren- dering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 425– 432, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [7] Daniel J Butler, Jonas Wulff, Garrett B Stanley, and Michael J Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' A naturalistic open source movie for opti- cal flow evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 7 [8] Joel Carranza, Christian Theobalt, Marcus A Magnor, and Hans-Peter Seidel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Free-viewpoint video of human actors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 22:569–577, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [9] Gaurav Chaurasia, Sylvain Duchene, Olga Sorkine- Hornung, and George Drettakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Depth synthesis and lo- cal warps for plausible image-based navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 32:1–12, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [10] Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Tensorf: Tensorial radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 4, 7 [11] Shenchang Eric Chen and Lance Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' View interpo- lation for image synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In Proceedings of the 20th an- nual conference on Computer graphics and interactive tech- niques, pages 279–288, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [12] Inchang Choi, Orazio Gallo, Alejandro Troccoli, Min H Kim, and Jan Kautz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Extreme view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [13] Alvaro Collet, Ming Chuang, Pat Sweeney, Don Gillett, Den- nis Evseev, David Calabrese, Hugues Hoppe, Adam Kirk, and Steve Sullivan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' High-quality streamable free-viewpoint video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 34:1–13, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [14] Mingsong Dou, Sameh Khamis, Yury Degtyarev, Philip Davidson, Sean Ryan Fanello, Adarsh Kowdle, Sergio Orts Escolano, Christoph Rhemann, David Kim, Jonathan Taylor, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Fusion4d: Real-time performance capture of challeng- ing scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 35:1–13, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [15] Robert A Drebin, Loren Carpenter, and Pat Hanrahan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Vol- ume rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 22:65–74, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [16] Jakob Engel, Vladlen Koltun, and Daniel Cremers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Direct sparse odometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' IEEE TPAMI, 40:611–625, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [17] Jakob Engel, Thomas Sch¨ops, and Daniel Cremers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Lsd- slam: Large-scale direct monocular slam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [18] Jiemin Fang, Taoran Yi, Xinggang Wang, Lingxi Xie, Xi- aopeng Zhang, Wenyu Liu, Matthias Nießner, and Qi Tian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Fast dynamic radiance fields with time-aware neural voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 7, 8 [19] John Flynn, Michael Broxton, Paul Debevec, Matthew Du- Vall, Graham Fyffe, Ryan Overbeck, Noah Snavely, and Richard Tucker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Deepview: View synthesis with learned gra- dient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [20] John Flynn, Ivan Neulander, James Philbin, and Noah Snavely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Deepstereo: Learning to predict new views from the world’s imagery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [21] Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Plenoxels: Radiance fields without neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 4 [22] Chen Gao, Ayush Saraf, Johannes Kopf, and Jia-Bin Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Dynamic view synthesis from dynamic monocular video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 5, 7, 8 [23] Hang Gao, Ruilong Li, Shubham Tulsiani, Bryan Russell, and Angjoo Kanazawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Monocular dynamic view synthesis: A reality check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In NeurIPS, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 7, 8 [24] Cl´ement Godard, Oisin Mac Aodha, Michael Firman, and Gabriel J Brostow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Digging into self-supervised monocular depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [25] Steven J Gortler, Radek Grzeszczuk, Richard Szeliski, and Michael F Cohen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' The lumigraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In Proceedings of the 23rd annual conference on Computer graphics and interac- tive techniques, pages 43–54, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [26] Marc Habermann, Weipeng Xu, Michael Zollhoefer, Gerard Pons-Moll, and Christian Theobalt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Livecap: Real-time hu- man performance capture from monocular video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 38:1–17, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [27] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Gir- shick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Mask r-cnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 4 [28] Peter Hedman, Julien Philip, True Price, Jan-Michael Frahm, George Drettakis, and Gabriel Brostow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Deep blending for free-viewpoint image-based rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 37:1–15, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [29] Yoonwoo Jeong, Seokjun Ahn, Christopher Choy, Anima Anandkumar, Minsu Cho, and Jaesik Park.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Self-calibrating neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3 9 [30] James T Kajiya and Brian P Von Herzen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Ray tracing volume densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 18:165–174, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [31] Johannes Kopf, Michael F Cohen, and Richard Szeliski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' First-person hyper-lapse videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 33:1–10, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [32] Johannes Kopf, Kevin Matzen, Suhib Alsisan, Ocean Quigley, Francis Ge, Yangming Chong, Josh Patterson, Jan- Michael Frahm, Shu Wu, Matthew Yu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' One shot 3d photography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 39:76–1, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [33] Johannes Kopf, Xuejian Rong, and Jia-Bin Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Robust consistent video depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3, 6 [34] Suryansh Kumar, Yuchao Dai, and Hongdong Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Monocular dense 3d reconstruction of a complex dynamic scene from two perspective frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [35] Marc Levoy and Pat Hanrahan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Light field rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In Pro- ceedings of the 23rd annual conference on Computer graph- ics and interactive techniques, pages 31–42, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [36] Zhengqi Li, Tali Dekel, Forrester Cole, Richard Tucker, Noah Snavely, Ce Liu, and William T Freeman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Learning the depths of moving people by watching frozen people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [37] Zhengqi Li, Simon Niklaus, Noah Snavely, and Oliver Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Neural scene flow fields for space-time view synthesis of dy- namic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 4, 5, 7, 8 [38] Chen-Hsuan Lin, Wei-Chiu Ma, Antonio Torralba, and Si- mon Lucey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Barf: Bundle-adjusting neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 5, 6 [39] Kai-En Lin, Lei Xiao, Feng Liu, Guowei Yang, and Ravi Ramamoorthi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Deep 3d mask volume for view synthesis of dynamic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [40] Yu-Lun Liu, Wei-Sheng Lai, Ming-Hsuan Yang, Yung-Yu Chuang, and Jia-Bin Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Hybrid neural fusion for full- frame video stabilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [41] Stephen Lombardi, Tomas Simon, Jason Saragih, Gabriel Schwartz, Andreas Lehrmann, and Yaser Sheikh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Neural vol- umes: Learning dynamic renderable volumes from images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 38:65:1–65:14, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [42] Ben Mildenhall, Pratul P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Srinivasan, Matthew Tancik, Jonathan T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Barron, Ravi Ramamoorthi, and Ren Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' NeRF: Representing scenes as neural radiance fields for view syn- thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 7 [43] Thomas M¨uller, Alex Evans, Christoph Schied, and Alexan- der Keller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Instant neural graphics primitives with a multires- olution hash encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 41:102:1–102:15, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 4 [44] Raul Mur-Artal, Jose Maria Martinez Montiel, and Juan D Tardos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Orb-slam: a versatile and accurate monocular slam system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' IEEE transactions on robotics, 31:1147–1163, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [45] Raul Mur-Artal and Juan D Tard´os.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Orb-slam2: An open- source slam system for monocular, stereo, and rgb-d cam- eras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' IEEE transactions on robotics, 33:1255–1262, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [46] Richard A Newcombe, Steven J Lovegrove, and Andrew J Davison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' DTAM: Dense tracking and mapping in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [47] Simon Niklaus, Long Mai, Jimei Yang, and Feng Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3d ken burns effect from a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 38:1–15, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [48] Sergio Orts-Escolano, Christoph Rhemann, Sean Fanello, Wayne Chang, Adarsh Kowdle, Yury Degtyarev, David Kim, Philip L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Davidson, Sameh Khamis, Mingsong Dou, Vladimir Tankovich, Charles Loop, Qin Cai, Philip A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Chou, Sarah Mennicken, Julien Valentin, Vivek Pradeep, Shenlong Wang, Sing Bing Kang, Pushmeet Kohli, Yuliya Lutchyn, Cem Keskin, and Shahram Izadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Holoportation: Virtual 3d teleportation in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In Proceedings of the 29th annual symposium on user interface software and technology, pages 741–754, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1 [49] Hyun Soo Park, Takaaki Shiratori, Iain Matthews, and Yaser Sheikh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3d reconstruction of a moving point from a series of 2d projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [50] Keunhong Park, Utkarsh Sinha, Jonathan T Barron, Sofien Bouaziz, Dan B Goldman, Steven M Seitz, and Ricardo Martin-Brualla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Nerfies: Deformable neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 8 [51] Keunhong Park, Utkarsh Sinha, Peter Hedman, Jonathan T Barron, Sofien Bouaziz, Dan B Goldman, Ricardo Martin- Brualla, and Steven M Seitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Hypernerf: A higher- dimensional representation for topologically varying neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 40, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 7, 8 [52] Eric Penner and Li Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Soft 3d reconstruction for view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 36:1–11, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [53] Federico Perazzi, Jordi Pont-Tuset, Brian McWilliams, Luc Van Gool, Markus Gross, and Alexander Sorkine-Hornung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' A benchmark dataset and evaluation methodology for video object segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [54] Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francesc Moreno-Noguer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' D-nerf: Neural radiance fields for dynamic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 7 [55] Ren´e Ranftl, Katrin Lasinger, David Hafner, Konrad Schindler, and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Towards robust monocular depth estimation: Mixing datasets for zero-shot cross-dataset transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' IEEE TPAMI, 44, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 5 [56] Gernot Riegler and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Free view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [57] Gernot Riegler and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Stable view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [58] Chris Russell, Rui Yu, and Lourdes Agapito.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Video pop-up: Monocular 3d reconstruction of dynamic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [59] Johannes Lutz Sch¨onberger and Jan-Michael Frahm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Structure-from-motion revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3 [60] Johannes L Schonberger and Jan-Michael Frahm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Structure- from-motion revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [61] Meng-Li Shih, Shih-Yang Su, Johannes Kopf, and Jia-Bin Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3d photography using context-aware layered depth inpainting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [62] Samarth Sinha, Roman Shapovalov, Jeremy Reizenstein, Ig- nacio Rocco, Natalia Neverova, Andrea Vedaldi, and David Novotny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Common pets in 3d: Dynamic new-view syn- thesis of real-life deformable categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='03889, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 10 [63] Vincent Sitzmann, Michael Zollh¨ofer, and Gordon Wet- zstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Scene representation networks: Continuous 3d- structure-aware neural scene representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In NeurIPS, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [64] Pratul P Srinivasan, Richard Tucker, Jonathan T Barron, Ravi Ramamoorthi, Ren Ng, and Noah Snavely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Pushing the boundaries of view extrapolation with multiplane images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [65] Cheng Sun, Min Sun, and Hwann-Tzong Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 4, 7 [66] Zachary Teed and Jia Deng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Raft: Recurrent all-pairs field transforms for optical flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 5 [67] Zachary Teed and Jia Deng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Droid-slam: Deep visual slam for monocular, stereo, and rgb-d cameras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3, 6 [68] Edgar Tretschk, Ayush Tewari, Vladislav Golyanik, Michael Zollh¨ofer, Christoph Lassner, and Christian Theobalt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Non- rigid neural radiance fields: Reconstruction and novel view synthesis of a dynamic scene from monocular video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 7 [69] Richard Tucker and Noah Snavely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Single-view view syn- thesis with multiplane images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [70] Zirui Wang, Shangzhe Wu, Weidi Xie, Min Chen, and Victor Adrian Prisacariu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Nerf–: Neural radiance fields without known camera parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='07064, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3, 6 [71] Chung-Yi Weng, Brian Curless, Pratul P Srinivasan, Jonathan T Barron, and Ira Kemelmacher-Shlizerman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Hu- mannerf: Free-viewpoint rendering of moving people from monocular video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [72] Olivia Wiles, Georgia Gkioxari, Richard Szeliski, and Justin Johnson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Synsin: End-to-end view synthesis from a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [73] Wenqi Xian, Jia-Bin Huang, Johannes Kopf, and Changil Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Space-time neural irradiance fields for free-viewpoint video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 3 [74] Zhichao Yin and Jianping Shi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Geonet: Unsupervised learn- ing of dense depth, optical flow and camera pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [75] Jae Shin Yoon, Kihwan Kim, Orazio Gallo, Hyun Soo Park, and Jan Kautz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Novel view synthesis of dynamic scenes with globally coherent depths from a monocular camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2, 7 [76] Kai Zhang, Gernot Riegler, Noah Snavely, and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Nerf++: Analyzing and improving neural radiance fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content='07492, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 2 [77] Wang Zhao, Shaohui Liu, Hengkai Guo, Wenping Wang, and Yong-Jin Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Particlesfm: Exploiting dense point trajecto- ries for localizing moving cameras in the wild.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In ECCV, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3, 6, 7 [78] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G Lowe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' Unsupervised learning of depth and ego-motion from video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' In CVPR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 3 [79] C Lawrence Zitnick, Sing Bing Kang, Matthew Uyttendaele, Simon Winder, and Richard Szeliski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' High-quality video view interpolation using a layered representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' ACM TOG, 23:600–608, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} +page_content=' 1, 2 11' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE0T4oBgHgl3EQfTwAQ/content/2301.02239v1.pdf'} diff --git a/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.faiss b/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..4efb5bbad3a9b11ad038a5043012cccbf8d33981 --- /dev/null +++ b/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:87b3e72903ed2fd4ad0fea938f29bdbe8eaa7b8c1e7b053bf38a35e1ce152789 +size 2621485 diff --git a/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.pkl b/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..68d708d89b5cb3643b3eed92a07f9e2ea644d596 --- /dev/null +++ b/Q9E4T4oBgHgl3EQfKgxv/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8f2361dc4c9a9cc518f19bc33393aa9be191b20c34998363385e64bd81b9f420 +size 101303 diff --git a/TdAyT4oBgHgl3EQfuflV/vector_store/index.faiss b/TdAyT4oBgHgl3EQfuflV/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..52353884906017dfc28fe5b5ed64e88d201776ec --- /dev/null +++ b/TdAyT4oBgHgl3EQfuflV/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0e2b7cfc839eaa61b175619fa2c2989bd9502edab48b530f03b6add4976020e5 +size 2555949 diff --git a/TtAzT4oBgHgl3EQf0v7t/content/2301.01790v1.pdf b/TtAzT4oBgHgl3EQf0v7t/content/2301.01790v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..72034948969b147554ea757e7f6df8a043268713 --- /dev/null +++ b/TtAzT4oBgHgl3EQf0v7t/content/2301.01790v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e2cec21b4e43082b523d147dc30283e541c5c0d4232c680c6ed9f9692d145dee +size 497805 diff --git a/TtAzT4oBgHgl3EQf0v7t/vector_store/index.faiss b/TtAzT4oBgHgl3EQf0v7t/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..95a309da1551a2234508aa177b2f809f73fd79aa --- /dev/null +++ b/TtAzT4oBgHgl3EQf0v7t/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:449f04ed27cc6ce1c2d214a6164b93a627997e9c77b643101581c9b28ad22eb2 +size 2424877 diff --git a/TtAzT4oBgHgl3EQf0v7t/vector_store/index.pkl b/TtAzT4oBgHgl3EQf0v7t/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..12085cf0307a09a87ec917435eb246b3e104d155 --- /dev/null +++ b/TtAzT4oBgHgl3EQf0v7t/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:18f91a9a713a71144b3f49c19e4021553267c7ae351c205c77ad0eec94a6765b +size 91152 diff --git a/UNAyT4oBgHgl3EQf8fqv/content/2301.00858v1.pdf b/UNAyT4oBgHgl3EQf8fqv/content/2301.00858v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1b6a82f224ee6972717243dd379b5cb335f611b9 --- /dev/null +++ b/UNAyT4oBgHgl3EQf8fqv/content/2301.00858v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0f26cdda470aafe285dca6dca5674bae54b1d6cd10c224245c96d7d74a11b104 +size 751980 diff --git a/UNAyT4oBgHgl3EQf8fqv/vector_store/index.pkl b/UNAyT4oBgHgl3EQf8fqv/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..cecc987a8d38d36a9acfbe23e37f6add1ac55ed4 --- /dev/null +++ b/UNAyT4oBgHgl3EQf8fqv/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ad08e8997e1c1628bcea05189b8ead7ddee325e9f16cfa83986f5e8ed77d99b7 +size 219246 diff --git a/UdE1T4oBgHgl3EQfuwU5/content/2301.03391v1.pdf b/UdE1T4oBgHgl3EQfuwU5/content/2301.03391v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5f258b30bb09efda228a51bde1861d17efc6ba49 --- /dev/null +++ b/UdE1T4oBgHgl3EQfuwU5/content/2301.03391v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5228e8bb67a32f326b85d4565d22895b85c94d13fa7aaea212d51da55ec238c5 +size 712493 diff --git a/UdE1T4oBgHgl3EQfuwU5/vector_store/index.faiss b/UdE1T4oBgHgl3EQfuwU5/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..ec7ec3f953bcba96357f98f733cd6ca5003d86ab --- /dev/null +++ b/UdE1T4oBgHgl3EQfuwU5/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:163d00303f129dee741f1de6928467fc73739e8bffbb60a28786ea8acc330ac5 +size 3866669 diff --git a/UdE1T4oBgHgl3EQfuwU5/vector_store/index.pkl b/UdE1T4oBgHgl3EQfuwU5/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..e6f3cbae30d0a562bd271652fdc11f207ed6d53b --- /dev/null +++ b/UdE1T4oBgHgl3EQfuwU5/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9b019941e5a60bfd21e1d905c1c57f3cab603385690e9da365c2fbe75845aedb +size 145651 diff --git a/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/2301.02029v1.pdf.txt b/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/2301.02029v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..73676db102e6b1b6a21befc3506b4dfbd7fd48fb --- /dev/null +++ b/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/2301.02029v1.pdf.txt @@ -0,0 +1,617 @@ +arXiv:2301.02029v1 [math.GT] 5 Jan 2023 +LIMITS OF MANIFOLDS IN THE +GROMOV-HAUSDORFF METRIC SPACE +FRIEDRICH HEGENBARTH AND DUŠAN D. REPOVŠ +Abstract. We apply the Gromov-Hausdorff metric dG for char- +acterization of certain generalized manifolds. Previously, we have +proved that with respect to the metric dG, generalized n-manifolds +are limits of spaces which are obtained by gluing two topological +n-manifolds by a controlled homotopy equivalence (the so-called +2-patch spaces). In the present paper, we consider the so-called +manifold-like generalized n-manifolds Xn, introduced in 1966 by +Mardešić and Segal, which are characterized by the existence of δ- +mappings fδ of Xn onto closed manifolds M n +δ , for arbitrary small +δ > 0, i.e. there exist onto maps fδ : Xn → M n +δ such that for every +u ∈ M n +δ , f −1 +δ +(u) has diameter less than δ. We prove that with re- +spect to the metric dG, manifold-like generalized n-manifolds Xn +are limits of topological n-manifolds M n +i . Moreover, if topologi- +cal n-manifolds M n +i satisfy a certain local contractibility condition +M(̺, n), we prove that generalized n-manifold Xn is resolvable. +1. Introduction +This paper is a continuation of our systematic study of the charac- +terization problem for generalized n-manifolds, n ≥ 5, (see Cavicchioli +et al. [5, 6] and Hegenbarth and Repovš [23, 24, 25, 26, 27, 28]). This is +a very important class of spaces which in the algebraic sense strongly +resemble topological manifolds, whereas in the geometric sense they +can fail to be locally Euclidean at any point (see e.g., Cannon [4], +Edwards [11], and Repovš [42, 43, 44]). +Definition 1.1. A generalized n-manifold Xn is an n-dimensional met- +ric absolute neighborhood retract (ANR) Xn with local homology +H∗(Xn, Xn \ {x}; Z) ∼= H∗(Rn, Rn \ {0}; Z), for every x ∈ X. +2020 Mathematics Subject Classification. Primary 53C23, 55R20, 57P10, 57R65 +57R67; Secondary 55M05, 55N99, 57P05, 57P99. +Key words and phrases. Gromov-Hausdorff metric, Gromov topological moduli +space, manifold-like generalized manifold, absolute neighborhood retract, cell-like +map, δ-map, structure map, controlled surgery sequence, ε-homotopy equivalence, +2-patch space, periodic surgery spectrum L. +1 + +2 +F. HEGENBARTH AND D.D. REPOVŠ +We shall only consider oriented generalized n-manifolds without bound- +ary (i.e. Hn(Xn, Xn \ {x}; Z) ∼= Z, for every x ∈ Xn). Throughout the +paper, we shall be assuming that n ≥ 5. +Definition 1.2. Given any δ > 0, a continuous map fδ : X → Y of a +metric space X onto a topological space Y is called a δ-map if for every +point y ∈ Y, the preimage f −1 +δ (y) has diameter < δ. +More than half a century ago, Mardešić and Segal [30, Theorem 1] +proved the following very nice characterization result for generalized +manifolds in terms of δ-maps. +Theorem 1.3. Let Xn be a compact n-dimensional metric ANR such +that for every δ > 0, there exists a δ-map fδ : Xn → Mn +δ of Xn onto +some (triangulated) oriented closed topological n-manifold Mn +δ . Then +Xn is a generalized n-manifold. +Definition 1.4. Mardešić and Segal called such a generalized n-manifold +Xn manifold-like. We shall call such maps fδ : Xn → Mn +δ structure +maps. +Remark 1.5. Since every topological n-manifold (except for nonsmooth- +able 4-manifolds), admits a handlebody decomposition (see Quinn [37]), +we shall hereafter neglect "triangulated". +Let dG be the Gromov-Hausdorff distance which is a complete metric +on the set of all isometry classes of compact metric spaces. (Details +will be given in Section 2, for an overview see Ferry [14, §29].) +In +our previous paper Hegenbarth-Repovš [25, §4.3], we proved that with +respect to metric dG, every generalized n-manifold Xn is the limit of +2-patch spaces, defined by Bryant et al. [3]. +In this paper we shall prove the following new characterization re- +sult for manifold-like generalized n-manifolds - an approximation by +topological n-manifolds in terms of the Gromov-Hausdorff metric dG. +Theorem 1.6 (Approximation Theorem). For every manifold-like gen- +eralized n-manifold Xn and every δ > 0, there exists a topological n- +manifold Mn +δ such that dG(Xn, Mn +δ ) < δ. +Remark 1.7. The metric on generalzed n-manifold Xn is induced by +a fixed embedding Xn ֒→ Rm of Xn into some Euclidean m-space Rm, +for a sufficiently large dimension m ∈ N. The metric on topological +n-manifold Mn +δ is then induced by an embedding Mn +δ ֒→ Nm +Xn of Mn +δ +into a small neighbourhood Nm +Xn ⊂ Rm of Xn in Rm (see Section 2 for +more details). + +LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE +3 +Edwards [11] obtained a fundamental criterion for a generalized n- +manifold Xn to be a topological n-manifold. The first (sufficient) con- +dition is the existence of a cell-like map f : Mn → Xn, where Mn is +a closed topological n-manifold, also called the (cell-like) resolution of +Xn (see e.g., Mitchell and Repovš [32]). By the uniqueness result of +Quinn ([36, Proposition 3.2.3]), any two resolutions f1 : Mn +1 → Xn and +f2: Mn +2 → Xn of Xn are equivalent, i.e. for every ε > 0, there exists +a homeomorphism hε : Mn +1 → Mn +2 such that d(f1, f2 ◦ hε) < ε. The +second (sufficient) condition is a general position type of property, the +so-called disjoint disks property of Xn (see e.g., Cavicchioli et al. [6]). +Quinn [38, 39] developed a controlled surgery theory and constructed +a surgery obstruction i(Xn) ∈ Z to the existence of resolutions of gener- +alized n-manifolds Xn. It is convenient to consider I(Xn) := 1+8i(Xn), +called the resolution index (this appears naturally, passing from the +quadratic L-spectrum to the symmetric L-spectrum, see Ranicki [40]). +So I(Xn) = 1 if and only if Xn admits a (cell-like) resolution. +There are no known general methods for calculating Quinn’s resolu- +tion index I(Xn), like there are for other invariants. In this paper we +shall show that it vanishes for a certain class of manifold-like general- +ized n-manifolds, and thus we shall prove that they are resolvable (see +Theorem 1.9 below). First, we need some more notations (see Ferry +[14, §29]). +Definition 1.8. A function ̺: [0, R) → [0, ∞) is called contractible if +for every t, ̺(t) ≥ t, and ̺ is continuous at 0. Let M(̺, n) denote the +set of all compact metric spaces M of dimension ≤ n, such that for +every x ∈ M, the r-ball Br(x) = {y ∈ M | d(x, y) ≤ r} contracts to +{x} inside the ̺(r)-ball B̺(r)(x). +The following is the second main result of our paper. +Theorem 1.9 (Resolution Theorem). Let Xn be a generalized n-ma- +nifold and fix an embedding i: Xn ֒→ Rm for some m ≥ n ≥ 5. Let +̺: [0, R) → [0, ∞) be a contractible function and suppose that for every +small δ > 0, there is a structure map fδ : Xn → Mn +δ such that Mn +δ ∈ +M(̺, n) with respect to the metric defined in Theorem 1.6. Then Xn +is resolvable. +Remark 1.10. We recall that the metric on generalized n-manifold +Xn (resp. +topological n-manifold Mn +δ ) is induced by the embedding +Xn ֒→ Rm (resp. Mn +δ ֒→ Nm +Xn ⊂ Rm). +As an application, consider the following nice result of Ferry [14, +Proposition 29.38]. + +4 +F. HEGENBARTH AND D.D. REPOVŠ +Theorem 1.11. Suppose that X = lim +−→{Mn +i }, where {Mn +i } ⊂ M(̺, n), +in the Gromov-Hausdorff metric. If dimX < ∞, then X is a general- +ized n-manifold. +It now follows by our Theorem 1.9 that the space X in Theorem 1.11 +is in fact, a resolvable generalized n-manifold X. For some related pre- +vious results on limits in the Gromov-Hausdorff metric space see Dran- +ishnikov and Ferry [7, 8] Dranishnikov et al. [9], Engel [12], Ferry [13, +15, 16], Ferry and Okun [18], Grove et al. [22], Kawamura [29], and +Moore [33]. +We conclude the introduction with the following very interesting +open problem related to our Theorem 1.9. Recall that there are plenty +of nonresolvable generalized n-manifolds - see e.g., Cavicchioli et al. +[5]. How about manifold-like generalized n-manifolds? +Question 1.12. Does there exist, for any n ≥ 5, a nonresolvable +manifold-like generalized n-manifold? +2. Proof of Theorem 1.6 +Let Xn be a manifold-like generalized n-manifold. +For any δ > +0, let fδ : Xn → Mn +δ be a structure map from Definition 1.4. +We +shall invoke the following result due to Eilenberg (see e.g. Ferry [14, +Corollary 29.10]). +Proposition 2.1. For every δ > 0, there exist a structure map fδ : Xn → +Mn +δ and a continuous map gδ : Mn +δ → Xn such that gδ ◦ fδ : Xn → Xn +is δ-homotopic to IdXn : Xn → Xn. +This is a special case where also the following fact holds. +Supplement 2.2. The structure map fδ : Xn → Mn +δ from Proposi- +tion 2.1 is a homotopy equivalence with the inverse gδ : Mn +δ → Xn. +Proof of Proposition 2.1: The induced map +(fδ)∗ : H∗(Xn; Z) → H∗(Mn +δ ; Z) +is injective since gδ ◦ fδ ∼ IdXn. Therefore the composition +Hn(Xn; Z) +(fδ)∗ +→ Hn(Mn +δ ; Z) +(gδ)∗ +→ Hn(Xn; Z) +is the identity, (gδ)∗ ◦ (fδ)∗ = (IdXn)∗, and we have +Hn(Mn +δ ; Z) ∼= Z, +(gδ)∗([Mn +δ ]) = [Xn], +if we choose the fundamental class appropriately. It follows by duality +that the induced map +(fδ)∗ : H∗(Xn; Z) → H∗(Mn +δ ; Z) + +LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE +5 +is also surjective and that fδ : Xn → Mn +δ and gδ : Mn +δ → Xn are both +of degree 1. In particular, since the map fδ : Xn → Mn +δ is of degree 1, +it now follows that the induced map +(fδ)∗: π1(Xn) → π1(Mn +δ ) +is surjective (see Browder [1, Proposition 1.2]). Since (fδ)∗: π1(Xn) → +π1(Mn +δ ) is also injective, it is in fact, an isomorphism. +Now, arguing as above, we can show that fδ : Xn → Mn +δ induces +isomorphisms in homology with coefficients in group rings. It therefore +follows by Ferry [13, Theorem 7.4] that fδ : Xn → Mn +δ is indeed a +homotopy equivalence with the inverse gδ : Mn +δ → Xn. This completes +the proof of Proposition 2.1. +□ +Definition 2.3. The Gromov-Hausdorff distance between any compact +metric spaces X and Y is defined as follows: For any closed subsets X +and Y of a compact metric space (Z, d), and any δ > 0, define their +neighborhoods +Nδ(X) := {z ∈ Z | d(z, X) < δ}, +and +Nδ(Y ) := {z ∈ Z | d(z, Y ) < δ} +and define the following distances +dZ(X, Y ) := inf{δ > 0 | X ⊂ Nδ(Y ) and Y ⊂ Nδ(X)} +and +dG(X, Y ) := inf{dZ(X, Y ) | X, Y are isometrically embedded in Z}, +where Z ranges over all compact metric spaces. +Remark 2.4. The Gromov-Hausdorff convergence is a notion of con- +vergence of metric spaces which is a generalization of the classical Haus- +dorff convergence. The Gromov-Hausdorff distance was introduced in +1975 by Edwards [10] and then rediscovered and generalized in 1981 by +Gromov [21] (see also Tuzhilin [46]). +To determine dG(Xn, Mn +δ ) for a structure map fδ : Xn → Mn +δ , the +choice of the metric is important. We choose an embedding Xn ֒→ Rm, +and take on Xn the metric induced from Rm. It is important to note +that the property of fδ : Xn → Mn +δ being a structure map does not +depend on the choice of the metric on Mn +δ . It will be appropriately +chosen below. +Let fδ : Xn → Mn +δ be a structure map with the inverse gδ : Mn +δ → +Xn, such that gδ ◦ fδ is δ-homotopic to IdXn for a given small δ > 0 +(see Proposition 2.1). In the sequel, let +i: Xn ֒→ Nδ := Nδ(Xn ֒→ Rm) + +6 +F. HEGENBARTH AND D.D. REPOVŠ +denote the inclusion of Xn into a δ-neighbourhood Nδ of Xn in Rm. +Since by hypothesis, Xn is manifold-like, it follows that for arbitrary +small δ′ > 0, there exists an embedding j : Mn +δ ֒→ Nδ with d(i◦gδ, j) < +δ′ (see Rourke and Sanderson [45, General Position Theorem for Maps +5.4]). These maps can be represented by the following diagram +(2.1) +Xn +Mn +δ +Nδ +gδ +fδ +i +j +We choose on Mn +δ the metric induced on j(Mn +δ ) ⊂ Rm. Since +d(i ◦ gδ, j) < δ′, +we can deduce the following +d(i(x), j(Mn +δ )) ≤ d(i(x), (i◦gδ◦fδ)(x))+d((i◦gδ◦fδ)(x), j(Mn +δ )) < δ+δ′, +i.e., +i(Xn) ⊂ Nδ+δ′(j(Mn +δ ) ⊂ Rm) +(see also Remark 2.5 below). +Of course, Nδ and Nδ+δ′(j(Mn +δ ) ⊂ Rm) belong to a compact subset +Z of Rm with the induced metric. We obtain the following +dG(Xn, Mn +δ ) ≤ dZ(Xn, Mn +δ ) < δ + δ′. +Now δ and δ′ can be chosen to be arbitrarily small, thus we have com- +pleted the proof of Theorem 1.6. +□ +Remark 2.5. Recall that +d(z, A) := inf{d(z, a) | a ∈ A}, +where A ⊂ Z is a compact subset of the metric space Z. For z, z′ ∈ Z, +the inequality +d(z′, a) ≤ d(z, z′) + d(z, a) +implies the inequality +d(z′, A) ≤ d(z′, z) + d(z, A), +which was used above. + +LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE +7 +3. Proof of Theorem 1.9 +In this section, we shall apply the controlled surgery sequence to +prove Theorem 1.9. For more details on this important subject we re- +fer to Bryant et al. [2], Cavicchioli el at. [6], Ferry [17, 19, 20], Mio [31], +Pedersen et al. [34], Pedersen and Yamasaki [35], Quinn [38, 39], Ran- +icki and Yamasaki [41], and Yamasaki [47]. +Let L denote the periodic L-spectrum, i. e. L0 = Z × G/TOP, and +L+ is its connected covering spectrum with L+ +0 = G/TOP. Now, if +Sε + + +Xn +↓ Id +Xn + + ̸= ∅, then there exists an exact sequence +· · · → Hn+1(Xn; L+) → Hn+1(Xn; L) → Sε + + +Xn +↓ Id +Xn + + → Hn(Xn; L+) → . . . +Elements of Sε + + +Xn +↓ Id +Xn + + are equivalence classes of ε-homotopy equiv- +alences Mn +h→ Xn (measured in Xn), with Mn a closed (oriented) +topological n-manifold. +Definition 3.1. Two elements +Mn +1 +h1 +→ Xn, Mn +2 +h2 +→ Xn ∈ Sε + + +Xn +↓ Id +Xn + + +are said to be ε-related if there exists a homeomorphism ϕ: Mn +1 → Mn +2 +such that h2 ◦ ϕ is ε-homotopic to h1. +Remark 3.2. Being ε-related does not define an equivalence relation, +but it is a part of the following assertion: There exists an ε0 > 0 +depending only on Xn, such that for every ε ≤ ε0, this becomes an +equivalence relation. +For p + q = n + 1, it follows from the spectral sequences +E2 +pq = Hp(Xn; πq(L)) ⇒ Hp+q(Xn; L) +and +E+2 +pq = Hp(Xn; πq(L+)) ⇒ Hp+q(Xn; L+) +that +E+2 +pq = E2 +pq, +hence +Hn+1(Xn; L+) ∼= Hn+1(Xn; L). + +8 +F. HEGENBARTH AND D.D. REPOVŠ +Moreover, Hn(Xn; L+) → Hn(Xn; L) must be injective. It follows that +if +Sε + + +Xn +↓ Id +Xn + + ̸= ∅. +then it consists of only one element +card + +Sε + + +Xn +↓ Id +Xn + + + + = 1. +Proposition 3.3. Let Xn be a generalized n-manifold. Then I(Xn) = +1 if and only if +Sε + + +Xn +↓ Id +Xn + + ̸= ∅, +i.e. for every ε ≤ ε0, there exists an ε-homotopy equivalence Mn +h→ Xn. +Proof. The proof is standard, see e.g., Mio [31, §3] or Bryant et al. [2, +p. 444]. +□ +In order to prove Theorem 1.9, we have to show that for each ε ≤ +ε0, there exists for every M(̺, n)-like generalized manifold Xn, an ε- +homotopy equivalence hε: Mn → Xn. This follows from Theorem 1.6 +and Ferry [14, Theorem 29.20]. +Theorem 3.4. Let ̺: [0, R) → [0, ∞) be a contractible function and +let Y and Z be any compact metric spaces. Then for every ε > 0, there +exists δ > 0 such that if Y, Z ∈ M(̺, n) and dG(Y, Z) < δ, then Y and +Z are ε-homotopy equivalent. Here, δ = δ(ε, ̺) depends on ε and ̺, +but not on Y, Z. +Let us provide some more details: We equip generalized n-manifold +Xn with the metric given by an embedding Xn ֒→ Rm of Xn into some +Rm, for a sufficiently large m ∈ N, see Theorem 1.6 and Remark 1.7. +By Ferry [14, Theorem 29.14], Xn with this metric belongs to M(̺, n) +for some contractible function ̺: [0, R) → [0, ∞). +By hypothesis, we can now choose a sequence {εi > 0}i∈N such that +lim +i→+∞ εi = 0, +∞ +� +i=1 +εi < ∞, +and then invoking Theorem 3.4, obtain a sequence +{δi := δi(εi, ̺) > 0}i∈N. + +LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE +9 +By Theorem 1.6, then there exists a sequence of closed topological +n-manifolds {Mn +δi}i∈N ⊂ M(̺, n), with respect to the metric obtained +by embedding Mn +δi ֒→ Nm +Xn ⊂ Rm each Mn +δi into a small neighbourhood +Nm +Xn of generalized n-manifold Xn in Rm, such that +dG(Mn +δi, Xn) < δi, +for every i ∈ N. +Therefore every topological n-manifold Mn +δi is εi-homotopy equiva- +lent to Xn. This proves Theorem 1.9. +□ +Acknowledgements +This research was supported by the Slovenian Research Agency grants +P1-0292, J1-4031, J1-4001, N1-0278, N1-0114, and N1-0083. We thank +the referee for comments and suggestions. +References +[1] F. Browder, Poincaré spaces, their normal fibrations and surgery, Invent. +Math. 17 (1972), 191-202. MR 0326743 +[2] J.L. Bryant, S. Ferry, W. Mio, and S. Weinberger, Topology of homology +manifolds, Ann. of Math. 143 (2) (1996), 435-467. MR 1394965 +[3] J.L. Bryant, S. Ferry, W. Mio, and S. Weinberger, Desingularizing homology +manifolds, Geom. and Topol. 11 (2007), 1289-1314. MR 2326946 +[4] J.W. Cannon, The recognition problem: what is a topological manifold? Bull. +Amer. Math. Soc. 84 (1978), no. 5, 832-866. MR 0494113 +[5] A. Cavicchioli, F. Hegenbarth, and D. Repovš, On the construction of +4k-dimensional generalized manifolds, High-Dimensional Manifold Topology, +F.T. Farrell and W. Lueck, Eds., World Scientific, Singapore 2003, pp. 103- +124. MR 2048717 +[6] A. Cavicchioli, F. Hegenbarth, and D. Repovš, Higher-Dimensional General- +ized Manifolds: Surgery and Constructions, EMS Series of Lectures in Math- +ematics 23, European Math. Soc., Zürich, 2016. MR 3558558 +[7] A.N. Dranishnikov and S.C. Ferry, Cell-like images of topological manifolds +and limits of manifolds in Gromov-Hausdorff space, preprint, State University +of New York at Binghamton, 1994. +[8] A.N. Dranishnikov and S.C. Ferry, Cell-like maps and topological structure +groups on manifolds, preprint, State University of New York at Binghamton, +2007. +[9] A.N. Dranishnikov, S.C. Ferry and S. Weinberger, An infinite-dimensional +phenomenon in finite-dimensional metric topology, Camb. J. Math. 8 (2020), +no. 1, 95-147. MR 4085433 +[10] D.A. Edwards, The structure of superspace, Studies in Topology, Proc. Conf., +Univ. North Carolina, Charlotte, N. C., 1974, Academic Press, New York +1975, pp. 121-133. MR 0401069 +[11] R.D. Edwards, Topology of manifolds and cell-like maps, Proceedings of the +International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fen- +nica, Helsinki, 1980.pp. 111-127. MR 0562601 + +10 +F. HEGENBARTH AND D.D. REPOVŠ +[12] T.L. Engel, Deformation and rigidity along paths of manifolds, State Univer- +sity of New York at Binghamton Dissertation, 1991. ProQuest Dissertations +& Theses Global (303991612). +[13] S.C. Ferry, Mapping manifolds to polyhedra, preprint, State University of +New York at Binghamton, 2003. +[14] S.C. Ferry, Geometric Topology Notes, preprint, Rutgers Univ., Piscataway, +NJ, 1992-1993. https://sites.math.rutgers.edu/∼sferry/ps/geotop.pdf +[15] S. Ferry, Topological finiteness theorems for manifolds in Gromov-Hausdorff +space, Duke Math. J. 74 (1994), no. 1, 95-106. MR 1271464 +[16] S. Ferry, Limits of polyhedra in Gromov-Hausdorff space, Topology 37 (1998), +1325-1338. MR 1632944 +[17] S.C. Ferry, Epsilon-delta surgery over Z, Geom. Dedicata 148 (2010), 71-101. +MR 2011m:57030 +[18] S.C. Ferry and B.L. Okun, Approximating topological metrics by Riemannian +metrics, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1865-1872. MR1246524 +[19] S.C. Ferry and E.K. Pedersen, Squeezing structures, preprint, State Univer- +sity of New York at Binghamton, 1992. +[20] S.C. Ferry and E.K. Pedersen, Epsilon surgery theory, Novikov Conjectures, +Index Theorems and Rigidity, Vol. 2 (Oberwolfach, 1993), London Math. +Soc. Lecture Note Ser., 227, Cambridge Univ. Press, Cambridge, 1995, pp. +167-226. MR 1388311 +[21] M. Gromov, Structures métriques pour les variétés riemanniennes, Ed. by J. +Lafontaine and P. Pansu, Textes Mathématiques, CEDIC, Paris, 1981. MR +0682063 +[22] K. Grove, P. Petersen and J. Wu, Geometric finiteness theorems via controlled +topology, Invent. Math. 99 (1990), 205-213; Correction, Invent. Math. 104 +(1991), 222-223. MR1029396 +[23] F. Hegenbarth and D. Repovš, The Bryant-Ferry-Mio-Weinberger construc- +tion of generalized manifolds, Exotic Homology Manifolds, Oberwolfach 2003, +Geom. Topol. Monogr. 9, Geom. Topol. Publ., Coventry, 2006, pp. 17-32. MR +2222488 +[24] F. Hegenbarth and D. Repovš, Controlled homotopy equivalences and struc- +ture sets of manifolds, Proc. Amer. Math. Soc. 142 (2014), 3987-3999. MR +3251739 +[25] F. Hegenbarth and D. Repovš, The relationship of generalized manifolds to +Poincaré duality complexes and topological manifolds, Topology Appl. 239 +(2018), 126-141. +[26] F. Hegenbarth and D. Repovš, Controlled surgery and L-homology, Mediterr. +J. Math. 16 (2019), no. 3, art. 79, 22 pp. MR 3945264 +[27] F. Hegenbarth and D. Repovš, On Steenrod L-homology, generalized mani- +folds, and surgery, Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 579-607. MR +4085040 +[28] F. Hegenbarth and D. Repovš, Generalized manifolds, normal invarints, and +L-homology, Proc. Edinb. Math. Soc. (2) 64 (2021), no. 3, 574-589. MR +4330277 +[29] K. Kawamura, A characterization of LCn compacta in terms of Gromov- +Hausdorff convergence, Canad. Math. Bull. 37 (1994), no. 4, 505-513. MR +1303678 + +LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 11 +[30] S. Mardešić and J. Segal, ε-mappings and generalized manifolds, Michigan +Math. J. 13 (4) (1967), 171-182. MR 0211407 +[31] W. Mio, Homology manifolds, Surveys on Surgery Theory, Vol. 1, Ann. of +Math. Stud., 145, Princeton Univ. Press, Princeton, NJ, 2000. pp. 323-343. +MR 1747540 +[32] W.J.R. Mitchell and D. Repovš, The topology of cell-like mappings, Rend. +Fac. Sci. Univ. Cagliari, Suppl. 58 (1988), 265-300. MR 92f:54012 +[33] T.E. Moore, Gromov-Hausdorff convergence to nonmanifolds, J. Geom. Anal. +5 (1995), no. 3, 411-418. MR 1360828 +[34] E.K. Pedersen, F. Quinn, and A. Ranicki, Controlled surgery with trivial local +fundamental groups, High-Dimensional Manifold Topology, F.T. Farrell and +W. Lück, Eds., World Sci. Publishing, River Edge, N.J., 2003, pp. 421-426. +MR 2005e:57077 +[35] E.K. Pedersen and M. Yamasaki, Stability in controlled L-theory, Exotic Ho- +mology Manifolds, Oberwolfach 2003, Geom. Topol. Monogr., 9, Geom. Topol. +Publ., Coventry, 2006, pp. 67-86. MR 2222491 +[36] F.S. Quinn, Ends of maps, I, Ann. of Math. (2) 110 (1979), no. 2, 275-331. +MR 0549490 +[37] F.S. Quinn, Ends of maps, III. Dimensions 4 and 5. J. Diff. Geo. 17 (1982), +no. 2, 503-521. MR 0679069 +[38] F.S. Quinn, Resolutions of homology manifolds and the topological charac- +terization of manifolds, Invent. Math. 72 (2) (1983), 267-284; Corrigendum, +Invent. Math. 85 (3) (1986), 653. MR 85b:57023, MR 87g:57031 +[39] F.S. Quinn, An obstruction to the resolution of homology manifolds, Michigan +Math. J. 34 (2) (1987), 285-291. MR 88j:57016 +[40] A.A. Ranicki, Algebraic L-Theory and Topological Manifolds, Cambridge +Tracts in Math. 102, Cambridge Univ. Press, Cambridge, 1992. MR 1211640 +[41] A. Ranicki and M. Yamasaki, Controlled L-theory, Exotic Homology Man- +ifolds, Oberwolfach 2003, Geom. Topol. Monogr., 9, Geom. Topol. Publ., +Coventry, 2006, pp. 105-153. MR 2222493 +[42] D. Repovš, The recognition problem for topological manifolds, Geometric +and Algebraic Topology, J. Krasinkiewicz, S. Spież, and H. Toruñczyk, Eds., +PWN, Warsaw 1986, pp. 77-108. MR 89d:57024 +[43] D. Repovš, Detection of higher dimensional topological manifolds among +topological spaces, Giornate di Topologia e Geometria Delle Varietá, Bologna +1990, M. Ferri, Ed., Univ. degli Studi di Bologna 1992, pp. 113-143. MR +1196725 +[44] D. Repovš, The recognition problem for topological manifolds: A survey, +Kodai Math. J. 17:3 (1994), 538-548. MR 96d:57024 +[45] C. Rourke, B. Sanderson, Introduction to Piecewise-linear Topology, Ergeb- +nisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New +York-Heidelberg, 1972. MR 0350744 +[46] A. +Tuzhilin, +Who +invented +the +Gromov-Hausdorff +distance?, +arXiv:1612.00728 [math.MG] +[47] M. Yamasaki, Controlled surgery theory, Sugaku Exp. 13 (2000), no. 1, 113- +124. MR 1755658 + +12 +F. HEGENBARTH AND D.D. REPOVŠ +Dipartimento di Matematica "Federigo Enriques", Università degli +studi di Milano, 20133 Milano, Italy +Email address: friedrich.hegenbarth@unimi.it +Faculty of Education and Faculty of Mathematics and Physics, Uni- +versity of Ljubljana & Institute of Mathematics, Physics and Mechan- +ics, 1000 Ljubljana, Slovenia +Email address: dusan.repovs@guest.arnes.si + diff --git a/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/load_file.txt b/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f39169690a96a163efc46d9172e5c4a2283f508 --- /dev/null +++ b/W9A0T4oBgHgl3EQfFP9S/content/tmp_files/load_file.txt @@ -0,0 +1,605 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf,len=604 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='02029v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='GT] 5 Jan 2023 LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE FRIEDRICH HEGENBARTH AND DUŠAN D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We apply the Gromov-Hausdorff metric dG for char- acterization of certain generalized manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Previously, we have proved that with respect to the metric dG, generalized n-manifolds are limits of spaces which are obtained by gluing two topological n-manifolds by a controlled homotopy equivalence (the so-called 2-patch spaces).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' In the present paper, we consider the so-called manifold-like generalized n-manifolds Xn, introduced in 1966 by Mardešić and Segal, which are characterized by the existence of δ- mappings fδ of Xn onto closed manifolds M n δ , for arbitrary small δ > 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' there exist onto maps fδ : Xn → M n δ such that for every u ∈ M n δ , f −1 δ (u) has diameter less than δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We prove that with re- spect to the metric dG, manifold-like generalized n-manifolds Xn are limits of topological n-manifolds M n i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Moreover, if topologi- cal n-manifolds M n i satisfy a certain local contractibility condition M(̺, n), we prove that generalized n-manifold Xn is resolvable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Introduction This paper is a continuation of our systematic study of the charac- terization problem for generalized n-manifolds, n ≥ 5, (see Cavicchioli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [5, 6] and Hegenbarth and Repovš [23, 24, 25, 26, 27, 28]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' This is a very important class of spaces which in the algebraic sense strongly resemble topological manifolds, whereas in the geometric sense they can fail to be locally Euclidean at any point (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Cannon [4], Edwards [11], and Repovš [42, 43, 44]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' A generalized n-manifold Xn is an n-dimensional met- ric absolute neighborhood retract (ANR) Xn with local homology H∗(Xn, Xn \\ {x};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) ∼= H∗(Rn, Rn \\ {0};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z), for every x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Primary 53C23, 55R20, 57P10, 57R65 57R67;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Secondary 55M05, 55N99, 57P05, 57P99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Gromov-Hausdorff metric, Gromov topological moduli space, manifold-like generalized manifold, absolute neighborhood retract, cell-like map, δ-map, structure map, controlled surgery sequence, ε-homotopy equivalence, 2-patch space, periodic surgery spectrum L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1 2 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ We shall only consider oriented generalized n-manifolds without bound- ary (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hn(Xn, Xn \\ {x};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) ∼= Z, for every x ∈ Xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Throughout the paper, we shall be assuming that n ≥ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Given any δ > 0, a continuous map fδ : X → Y of a metric space X onto a topological space Y is called a δ-map if for every point y ∈ Y, the preimage f −1 δ (y) has diameter < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' More than half a century ago, Mardešić and Segal [30, Theorem 1] proved the following very nice characterization result for generalized manifolds in terms of δ-maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let Xn be a compact n-dimensional metric ANR such that for every δ > 0, there exists a δ-map fδ : Xn → Mn δ of Xn onto some (triangulated) oriented closed topological n-manifold Mn δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Then Xn is a generalized n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mardešić and Segal called such a generalized n-manifold Xn manifold-like.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We shall call such maps fδ : Xn → Mn δ structure maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Since every topological n-manifold (except for nonsmooth- able 4-manifolds), admits a handlebody decomposition (see Quinn [37]), we shall hereafter neglect "triangulated".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let dG be the Gromov-Hausdorff distance which is a complete metric on the set of all isometry classes of compact metric spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' (Details will be given in Section 2, for an overview see Ferry [14, §29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=') In our previous paper Hegenbarth-Repovš [25, §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='3], we proved that with respect to metric dG, every generalized n-manifold Xn is the limit of 2-patch spaces, defined by Bryant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' In this paper we shall prove the following new characterization re- sult for manifold-like generalized n-manifolds - an approximation by topological n-manifolds in terms of the Gromov-Hausdorff metric dG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6 (Approximation Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For every manifold-like gen- eralized n-manifold Xn and every δ > 0, there exists a topological n- manifold Mn δ such that dG(Xn, Mn δ ) < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The metric on generalzed n-manifold Xn is induced by a fixed embedding Xn ֒→ Rm of Xn into some Euclidean m-space Rm, for a sufficiently large dimension m ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The metric on topological n-manifold Mn δ is then induced by an embedding Mn δ ֒→ Nm Xn of Mn δ into a small neighbourhood Nm Xn ⊂ Rm of Xn in Rm (see Section 2 for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 3 Edwards [11] obtained a fundamental criterion for a generalized n- manifold Xn to be a topological n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The first (sufficient) con- dition is the existence of a cell-like map f : Mn → Xn, where Mn is a closed topological n-manifold, also called the (cell-like) resolution of Xn (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Mitchell and Repovš [32]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' By the uniqueness result of Quinn ([36, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='3]), any two resolutions f1 : Mn 1 → Xn and f2: Mn 2 → Xn of Xn are equivalent, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' for every ε > 0, there exists a homeomorphism hε : Mn 1 → Mn 2 such that d(f1, f2 ◦ hε) < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The second (sufficient) condition is a general position type of property, the so-called disjoint disks property of Xn (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Cavicchioli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn [38, 39] developed a controlled surgery theory and constructed a surgery obstruction i(Xn) ∈ Z to the existence of resolutions of gener- alized n-manifolds Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It is convenient to consider I(Xn) := 1+8i(Xn), called the resolution index (this appears naturally, passing from the quadratic L-spectrum to the symmetric L-spectrum, see Ranicki [40]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' So I(Xn) = 1 if and only if Xn admits a (cell-like) resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' There are no known general methods for calculating Quinn’s resolu- tion index I(Xn), like there are for other invariants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' In this paper we shall show that it vanishes for a certain class of manifold-like general- ized n-manifolds, and thus we shall prove that they are resolvable (see Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' First, we need some more notations (see Ferry [14, §29]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' A function ̺: [0, R) → [0, ∞) is called contractible if for every t, ̺(t) ≥ t, and ̺ is continuous at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let M(̺, n) denote the set of all compact metric spaces M of dimension ≤ n, such that for every x ∈ M, the r-ball Br(x) = {y ∈ M | d(x, y) ≤ r} contracts to {x} inside the ̺(r)-ball B̺(r)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The following is the second main result of our paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9 (Resolution Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let Xn be a generalized n-ma- nifold and fix an embedding i: Xn ֒→ Rm for some m ≥ n ≥ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let ̺: [0, R) → [0, ∞) be a contractible function and suppose that for every small δ > 0, there is a structure map fδ : Xn → Mn δ such that Mn δ ∈ M(̺, n) with respect to the metric defined in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Then Xn is resolvable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We recall that the metric on generalized n-manifold Xn (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' topological n-manifold Mn δ ) is induced by the embedding Xn ֒→ Rm (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mn δ ֒→ Nm Xn ⊂ Rm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' As an application, consider the following nice result of Ferry [14, Proposition 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 4 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Suppose that X = lim −→{Mn i }, where {Mn i } ⊂ M(̺, n), in the Gromov-Hausdorff metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' If dimX < ∞, then X is a general- ized n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It now follows by our Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9 that the space X in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='11 is in fact, a resolvable generalized n-manifold X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For some related pre- vious results on limits in the Gromov-Hausdorff metric space see Dran- ishnikov and Ferry [7, 8] Dranishnikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [9], Engel [12], Ferry [13, 15, 16], Ferry and Okun [18], Grove et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [22], Kawamura [29], and Moore [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We conclude the introduction with the following very interesting open problem related to our Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Recall that there are plenty of nonresolvable generalized n-manifolds - see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Cavicchioli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' How about manifold-like generalized n-manifolds?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Question 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Does there exist, for any n ≥ 5, a nonresolvable manifold-like generalized n-manifold?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6 Let Xn be a manifold-like generalized n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For any δ > 0, let fδ : Xn → Mn δ be a structure map from Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We shall invoke the following result due to Eilenberg (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry [14, Corollary 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For every δ > 0, there exist a structure map fδ : Xn → Mn δ and a continuous map gδ : Mn δ → Xn such that gδ ◦ fδ : Xn → Xn is δ-homotopic to IdXn : Xn → Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' This is a special case where also the following fact holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Supplement 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The structure map fδ : Xn → Mn δ from Proposi- tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1 is a homotopy equivalence with the inverse gδ : Mn δ → Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1: The induced map (fδ)∗ : H∗(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) → H∗(Mn δ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) is injective since gδ ◦ fδ ∼ IdXn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Therefore the composition Hn(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) (fδ)∗ → Hn(Mn δ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) (gδ)∗ → Hn(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) is the identity, (gδ)∗ ◦ (fδ)∗ = (IdXn)∗, and we have Hn(Mn δ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) ∼= Z, (gδ)∗([Mn δ ]) = [Xn], if we choose the fundamental class appropriately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It follows by duality that the induced map (fδ)∗ : H∗(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) → H∗(Mn δ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Z) LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 5 is also surjective and that fδ : Xn → Mn δ and gδ : Mn δ → Xn are both of degree 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' In particular, since the map fδ : Xn → Mn δ is of degree 1, it now follows that the induced map (fδ)∗: π1(Xn) → π1(Mn δ ) is surjective (see Browder [1, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Since (fδ)∗: π1(Xn) → π1(Mn δ ) is also injective, it is in fact, an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Now, arguing as above, we can show that fδ : Xn → Mn δ induces isomorphisms in homology with coefficients in group rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It therefore follows by Ferry [13, Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4] that fδ : Xn → Mn δ is indeed a homotopy equivalence with the inverse gδ : Mn δ → Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' This completes the proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' □ Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The Gromov-Hausdorff distance between any compact metric spaces X and Y is defined as follows: For any closed subsets X and Y of a compact metric space (Z, d), and any δ > 0, define their neighborhoods Nδ(X) := {z ∈ Z | d(z, X) < δ}, and Nδ(Y ) := {z ∈ Z | d(z, Y ) < δ} and define the following distances dZ(X, Y ) := inf{δ > 0 | X ⊂ Nδ(Y ) and Y ⊂ Nδ(X)} and dG(X, Y ) := inf{dZ(X, Y ) | X, Y are isometrically embedded in Z}, where Z ranges over all compact metric spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The Gromov-Hausdorff convergence is a notion of con- vergence of metric spaces which is a generalization of the classical Haus- dorff convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The Gromov-Hausdorff distance was introduced in 1975 by Edwards [10] and then rediscovered and generalized in 1981 by Gromov [21] (see also Tuzhilin [46]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' To determine dG(Xn, Mn δ ) for a structure map fδ : Xn → Mn δ , the choice of the metric is important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We choose an embedding Xn ֒→ Rm, and take on Xn the metric induced from Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It is important to note that the property of fδ : Xn → Mn δ being a structure map does not depend on the choice of the metric on Mn δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It will be appropriately chosen below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let fδ : Xn → Mn δ be a structure map with the inverse gδ : Mn δ → Xn, such that gδ ◦ fδ is δ-homotopic to IdXn for a given small δ > 0 (see Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' In the sequel, let i: Xn ֒→ Nδ := Nδ(Xn ֒→ Rm) 6 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ denote the inclusion of Xn into a δ-neighbourhood Nδ of Xn in Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Since by hypothesis, Xn is manifold-like, it follows that for arbitrary small δ′ > 0, there exists an embedding j : Mn δ ֒→ Nδ with d(i◦gδ, j) < δ′ (see Rourke and Sanderson [45, General Position Theorem for Maps 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' These maps can be represented by the following diagram (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1) Xn Mn δ Nδ gδ fδ i j We choose on Mn δ the metric induced on j(Mn δ ) ⊂ Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Since d(i ◦ gδ, j) < δ′, we can deduce the following d(i(x), j(Mn δ )) ≤ d(i(x), (i◦gδ◦fδ)(x))+d((i◦gδ◦fδ)(x), j(Mn δ )) < δ+δ′, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', i(Xn) ⊂ Nδ+δ′(j(Mn δ ) ⊂ Rm) (see also Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='5 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Of course, Nδ and Nδ+δ′(j(Mn δ ) ⊂ Rm) belong to a compact subset Z of Rm with the induced metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We obtain the following dG(Xn, Mn δ ) ≤ dZ(Xn, Mn δ ) < δ + δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Now δ and δ′ can be chosen to be arbitrarily small, thus we have com- pleted the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' □ Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Recall that d(z, A) := inf{d(z, a) | a ∈ A}, where A ⊂ Z is a compact subset of the metric space Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For z, z′ ∈ Z, the inequality d(z′, a) ≤ d(z, z′) + d(z, a) implies the inequality d(z′, A) ≤ d(z′, z) + d(z, A), which was used above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9 In this section, we shall apply the controlled surgery sequence to prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For more details on this important subject we re- fer to Bryant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [2], Cavicchioli el at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [6], Ferry [17, 19, 20], Mio [31], Pedersen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [34], Pedersen and Yamasaki [35], Quinn [38, 39], Ran- icki and Yamasaki [41], and Yamasaki [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let L denote the periodic L-spectrum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L0 = Z × G/TOP, and L+ is its connected covering spectrum with L+ 0 = G/TOP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Now, if Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 ̸= ∅, then there exists an exact sequence · · → Hn+1(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L+) → Hn+1(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L) → Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 → Hn(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L+) → .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Elements of Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 are equivalence classes of ε-homotopy equiv- alences Mn h→ Xn (measured in Xn), with Mn a closed (oriented) topological n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Two elements Mn 1 h1 → Xn, Mn 2 h2 → Xn ∈ Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 are said to be ε-related if there exists a homeomorphism ϕ: Mn 1 → Mn 2 such that h2 ◦ ϕ is ε-homotopic to h1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Being ε-related does not define an equivalence relation, but it is a part of the following assertion: There exists an ε0 > 0 depending only on Xn, such that for every ε ≤ ε0, this becomes an equivalence relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' For p + q = n + 1, it follows from the spectral sequences E2 pq = Hp(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' πq(L)) ⇒ Hp+q(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L) and E+2 pq = Hp(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' πq(L+)) ⇒ Hp+q(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L+) that E+2 pq = E2 pq, hence Hn+1(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L+) ∼= Hn+1(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 8 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ Moreover, Hn(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L+) → Hn(Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' L) must be injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' It follows that if Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' then it consists of only one element card \uf8ee \uf8f0Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 \uf8f9 \uf8fb = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let Xn be a generalized n-manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Then I(Xn) = 1 if and only if Sε \uf8eb \uf8ed Xn ↓ Id Xn \uf8f6 \uf8f8 ̸= ∅, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' for every ε ≤ ε0, there exists an ε-homotopy equivalence Mn h→ Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' The proof is standard, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Mio [31, §3] or Bryant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 444].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' □ In order to prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9, we have to show that for each ε ≤ ε0, there exists for every M(̺, n)-like generalized manifold Xn, an ε- homotopy equivalence hε: Mn → Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' This follows from Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6 and Ferry [14, Theorem 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let ̺: [0, R) → [0, ∞) be a contractible function and let Y and Z be any compact metric spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Then for every ε > 0, there exists δ > 0 such that if Y, Z ∈ M(̺, n) and dG(Y, Z) < δ, then Y and Z are ε-homotopy equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Here, δ = δ(ε, ̺) depends on ε and ̺, but not on Y, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Let us provide some more details: We equip generalized n-manifold Xn with the metric given by an embedding Xn ֒→ Rm of Xn into some Rm, for a sufficiently large m ∈ N, see Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6 and Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' By Ferry [14, Theorem 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='14], Xn with this metric belongs to M(̺, n) for some contractible function ̺: [0, R) → [0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' By hypothesis, we can now choose a sequence {εi > 0}i∈N such that lim i→+∞ εi = 0, ∞ � i=1 εi < ∞, and then invoking Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='4, obtain a sequence {δi := δi(εi, ̺) > 0}i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 9 By Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='6, then there exists a sequence of closed topological n-manifolds {Mn δi}i∈N ⊂ M(̺, n), with respect to the metric obtained by embedding Mn δi ֒→ Nm Xn ⊂ Rm each Mn δi into a small neighbourhood Nm Xn of generalized n-manifold Xn in Rm, such that dG(Mn δi, Xn) < δi, for every i ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Therefore every topological n-manifold Mn δi is εi-homotopy equiva- lent to Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' This proves Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' □ Acknowledgements This research was supported by the Slovenian Research Agency grants P1-0292, J1-4031, J1-4001, N1-0278, N1-0114, and N1-0083.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' We thank the referee for comments and suggestions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' References [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Browder, Poincaré spaces, their normal fibrations and surgery, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 17 (1972), 191-202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0326743 [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Bryant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mio, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Weinberger, Topology of homology manifolds, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 143 (2) (1996), 435-467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1394965 [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Bryant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mio, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Weinberger, Desingularizing homology manifolds, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' and Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 11 (2007), 1289-1314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2326946 [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Cannon, The recognition problem: what is a topological manifold?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 84 (1978), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 5, 832-866.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0494113 [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Cavicchioli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, On the construction of 4k-dimensional generalized manifolds, High-Dimensional Manifold Topology, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Farrell and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Lueck, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', World Scientific, Singapore 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 103- 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2048717 [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Cavicchioli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, Higher-Dimensional General- ized Manifolds: Surgery and Constructions, EMS Series of Lectures in Math- ematics 23, European Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Zürich, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 3558558 [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Dranishnikov and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Cell-like images of topological manifolds and limits of manifolds in Gromov-Hausdorff space, preprint, State University of New York at Binghamton, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Dranishnikov and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Cell-like maps and topological structure groups on manifolds, preprint, State University of New York at Binghamton, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Dranishnikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Weinberger, An infinite-dimensional phenomenon in finite-dimensional metric topology, Camb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 8 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1, 95-147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 4085433 [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Edwards, The structure of superspace, Studies in Topology, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' North Carolina, Charlotte, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 1974, Academic Press, New York 1975, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 121-133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0401069 [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Edwards, Topology of manifolds and cell-like maps, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Fen- nica, Helsinki, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 111-127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0562601 10 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Engel, Deformation and rigidity along paths of manifolds, State Univer- sity of New York at Binghamton Dissertation, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' ProQuest Dissertations & Theses Global (303991612).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Mapping manifolds to polyhedra, preprint, State University of New York at Binghamton, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Geometric Topology Notes, preprint, Rutgers Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Piscataway, NJ, 1992-1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='rutgers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='edu/∼sferry/ps/geotop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='pdf [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Topological finiteness theorems for manifolds in Gromov-Hausdorff space, Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 74 (1994), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1, 95-106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1271464 [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Limits of polyhedra in Gromov-Hausdorff space, Topology 37 (1998), 1325-1338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1632944 [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry, Epsilon-delta surgery over Z, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Dedicata 148 (2010), 71-101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2011m:57030 [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Okun, Approximating topological metrics by Riemannian metrics, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 123 (1995), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 6, 1865-1872.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR1246524 [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Pedersen, Squeezing structures, preprint, State Univer- sity of New York at Binghamton, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferry and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Pedersen, Epsilon surgery theory, Novikov Conjectures, Index Theorems and Rigidity, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2 (Oberwolfach, 1993), London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Lecture Note Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 227, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Press, Cambridge, 1995, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 167-226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1388311 [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Gromov, Structures métriques pour les variétés riemanniennes, Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Lafontaine and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Pansu, Textes Mathématiques, CEDIC, Paris, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0682063 [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Grove, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Petersen and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Wu, Geometric finiteness theorems via controlled topology, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 99 (1990), 205-213;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Correction, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 104 (1991), 222-223.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR1029396 [23] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, The Bryant-Ferry-Mio-Weinberger construc- tion of generalized manifolds, Exotic Homology Manifolds, Oberwolfach 2003, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Monogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 9, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Coventry, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 17-32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2222488 [24] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, Controlled homotopy equivalences and struc- ture sets of manifolds, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 142 (2014), 3987-3999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 3251739 [25] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, The relationship of generalized manifolds to Poincaré duality complexes and topological manifolds, Topology Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 239 (2018), 126-141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' [26] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, Controlled surgery and L-homology, Mediterr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 16 (2019), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 3, art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 79, 22 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 3945264 [27] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, On Steenrod L-homology, generalized mani- folds, and surgery, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Edinb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' (2) 63 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2, 579-607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 4085040 [28] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Hegenbarth and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, Generalized manifolds, normal invarints, and L-homology, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Edinb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' (2) 64 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 3, 574-589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 4330277 [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Kawamura, A characterization of LCn compacta in terms of Gromov- Hausdorff convergence, Canad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 37 (1994), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 4, 505-513.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1303678 LIMITS OF MANIFOLDS IN THE GROMOV-HAUSDORFF METRIC SPACE 11 [30] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mardešić and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Segal, ε-mappings and generalized manifolds, Michigan Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 13 (4) (1967), 171-182.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0211407 [31] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mio, Homology manifolds, Surveys on Surgery Theory, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Stud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 145, Princeton Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Press, Princeton, NJ, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 323-343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1747540 [32] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Mitchell and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, The topology of cell-like mappings, Rend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Fac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Cagliari, Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 58 (1988), 265-300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 92f:54012 [33] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Moore, Gromov-Hausdorff convergence to nonmanifolds, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 5 (1995), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 3, 411-418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1360828 [34] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Pedersen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ranicki, Controlled surgery with trivial local fundamental groups, High-Dimensional Manifold Topology, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Farrell and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Lück, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Publishing, River Edge, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 421-426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2005e:57077 [35] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Pedersen and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Yamasaki, Stability in controlled L-theory, Exotic Ho- mology Manifolds, Oberwolfach 2003, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Monogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 9, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Coventry, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 67-86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2222491 [36] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn, Ends of maps, I, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' (2) 110 (1979), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2, 275-331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0549490 [37] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn, Ends of maps, III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Dimensions 4 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Geo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 17 (1982), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 2, 503-521.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0679069 [38] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn, Resolutions of homology manifolds and the topological charac- terization of manifolds, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 72 (2) (1983), 267-284;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Corrigendum, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 85 (3) (1986), 653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 85b:57023, MR 87g:57031 [39] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Quinn, An obstruction to the resolution of homology manifolds, Michigan Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 34 (2) (1987), 285-291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 88j:57016 [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ranicki, Algebraic L-Theory and Topological Manifolds, Cambridge Tracts in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 102, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Press, Cambridge, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1211640 [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ranicki and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Yamasaki, Controlled L-theory, Exotic Homology Man- ifolds, Oberwolfach 2003, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Monogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', 9, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Coventry, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 105-153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 2222493 [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, The recognition problem for topological manifolds, Geometric and Algebraic Topology, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Krasinkiewicz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Spież, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Toruñczyk, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', PWN, Warsaw 1986, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 77-108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 89d:57024 [43] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, Detection of higher dimensional topological manifolds among topological spaces, Giornate di Topologia e Geometria Delle Varietá, Bologna 1990, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Ferri, Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' degli Studi di Bologna 1992, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 113-143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1196725 [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Repovš, The recognition problem for topological manifolds: A survey, Kodai Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 17:3 (1994), 538-548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 96d:57024 [45] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Rourke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Sanderson, Introduction to Piecewise-linear Topology, Ergeb- nisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 0350744 [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Tuzhilin, Who invented the Gromov-Hausdorff distance?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=', arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='00728 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='MG] [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' Yamasaki, Controlled surgery theory, Sugaku Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 13 (2000), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' 1, 113- 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' MR 1755658 12 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' HEGENBARTH AND D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content=' REPOVŠ Dipartimento di Matematica "Federigo Enriques", Università degli studi di Milano, 20133 Milano, Italy Email address: friedrich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='hegenbarth@unimi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='it Faculty of Education and Faculty of Mathematics and Physics, Uni- versity of Ljubljana & Institute of Mathematics, Physics and Mechan- ics, 1000 Ljubljana, Slovenia Email address: dusan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='repovs@guest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='arnes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} +page_content='si' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/W9A0T4oBgHgl3EQfFP9S/content/2301.02029v1.pdf'} diff --git a/W9FLT4oBgHgl3EQfTS_4/content/2301.12045v1.pdf b/W9FLT4oBgHgl3EQfTS_4/content/2301.12045v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..463100cfc3d4b92e4189b2a5f69547365469e059 --- /dev/null +++ b/W9FLT4oBgHgl3EQfTS_4/content/2301.12045v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:155f8a36a40e765d833b8e9f670749f7b60e604688770a42c8f90254b213df8f +size 798295 diff --git a/W9FLT4oBgHgl3EQfTS_4/vector_store/index.pkl b/W9FLT4oBgHgl3EQfTS_4/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..5377edc7644c0a02f4160b8d249de30ac6499f77 --- /dev/null +++ b/W9FLT4oBgHgl3EQfTS_4/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fe0c51442b1773bd6017fe3e999b2b8ed4a36a9d64f955f6839b2c96c3c4c888 +size 265460 diff --git a/WdAzT4oBgHgl3EQfKPti/content/tmp_files/2301.01093v1.pdf.txt b/WdAzT4oBgHgl3EQfKPti/content/tmp_files/2301.01093v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bdfb47ac609d0db4bc3535b6e3dbc4c59be2726 --- /dev/null +++ b/WdAzT4oBgHgl3EQfKPti/content/tmp_files/2301.01093v1.pdf.txt @@ -0,0 +1,671 @@ +Draft version January 4, 2023 +Typeset using LATEX default style in AASTeX631 +Photochemical hazes can trace the C/O ratio in exoplanet atmospheres +L´ıa Corrales +,1 Lisseth Gavilan +,2, 3 D. J. Teal +,4 and Eliza M.-R. Kempton +4 +1University of Michigan, Dept. of Astronomy, 1085 S University Ave, Ann Arbor, MI 48109, USA +2NASA Ames Research Center, Space Science & Astrobiology Division, Moffett Field, CA 94035, USA +3Bay Area Environmental Research Institute (BAERI), Sonoma, CA 95476, USA +4University of Maryland, Department of Astronomy, 4296 Stadium Dr, College Park, MD 20742, USA +ABSTRACT +Photochemical hazes are suspected to obscure molecular features, such as water, from detection +in the transmission spectra of exoplanets with atmospheric temperatures < 800 K. The opacities of +laboratory produced organic compounds (tholins) from Khare et al. (1984) have become a standard +for modeling haze in exoplanet atmospheres. However, these tholins were grown in an oxygen-free, +Titan-like environment that is very different from typical assumptions for exoplanets, where C/O∼ 0.5. +This work presents the 0.13 − 10 µm complex refractive indices derived from laboratory transmission +measurements of tholins grown in environments with different oxygen abundances. With the increasing +uptake of oxygen, absorption increases across the entire wavelength range, and a scattering feature +around 6 µm shifts towards shorter wavelengths and becomes more peaked around 5.8 µm, due to a +C=O stretch resonance. Using GJ 1214 b as a test-case, we examine the transmission spectra of a sub- +Neptune planet with C/O ratios of solar, 1, and 1000 to evaluate the effective differences between our +opacities and those of Khare. For an atmosphere with solar hydrogen and helium abundances, we find +a difference of 200-1500 ppm, but for high-metallicity (Z=1000) environments, the difference may only +be 20 ppm. The 1 − 2 µm transmission data for GJ 1214 b rule out the Titan-like haze model, and are +more consistent with C/O= 1 and C/O=solar haze models. This work demonstrates that using haze +opacities that are more consistent with underlying assumptions about bulk atmospheric composition +are important for building self-consistent models that appropriately constrain the atmospheric C/O +ratio, even when molecular features are obscured. +Keywords: Exoplanet atmospheric composition (487) — Laboratory astrophysics (2004) — Astrochem- +istry (75) — Exoplanet evolution (491) +1. INTRODUCTION +Approximately 75% of the over 5,000 exoplanets known today were discovered via the transit method, where the +chance alignment of an extra-solar planet’s orbit with Earth’s vantage point causes the planet to pass in front of the +star, blocking ∼ 0.1 − 1% of its light. Observing a transit at multiple wavelengths builds a transmission spectrum, on +which the contents of the exoplanet’s atmosphere are imprinted via their unique spectroscopic fingerprints in absorption +and scattering. The depth of an exoplanet transit, as a function of wavelength, depends jointly on the transmission +properties of the atmospheric contents as well as their vertical distribution. In this letter, we investigate whether the +spectral features of atmospheric hazes on an exoplanet can provide key markers of the bulk content of the gas in which +they form. +Aerosols – whether condensing directly from atmospheric gas (clouds) or through photochemical reactions (hazes) – +are known to affect nearly every type of exoplanet atmosphere. Even hot Jupiters, across a wide range of temperatures +(1000 − 2000 K), have spectral features that are muted as a result of aerosol obscuration (Sing et al. 2016) and steep +Corresponding author: L. Corrales +liac@umich.edu +arXiv:2301.01093v1 [astro-ph.EP] 3 Jan 2023 + +ID2 +Corrales & Gavilan et al. +optical slopes that are suspected to arise from a combination of clouds and hazes (Sing et al. 2011; Pont et al. 2013; +McCullough et al. 2014; S´anchez-L´opez et al. 2020; Steinrueck et al. 2021). Theoretical models predict that the infrared +opacity of hot Jupiters with Teq ∼ 900 − 2200 K will be dominated by mineral condensates rich in refractory elements +(Helling et al. 2019, 2016; Powell et al. 2018; Gao et al. 2020). Only below about 800 K are photochemically produced +organic hazes expected to form and dominate the infrared opacity (Morley et al. 2015; Gao et al. 2020). +Photochemical hazes are also suspected to be a key source of opacity for more temperate, smaller planets such as +sub-Neptunes and super-Earths. One such planet is GJ 1214 b, which has a mass of 6.55 ME and radius of 2.68 RE, +consistent with a variety of composition models that suggest it hosts an atmosphere comprising ∼ 0.5 to a few percent of +the planet’s mass (Charbonneau et al. 2009; Rogers & Seager 2010). Transmission measurements from 0.7−4.5 µm can +be reproduced by models employing some combination of a high mean molecular weight atmosphere and an optically +thick aerosol layer at altitudes ∼ 10 mbar (Bean et al. 2010; D´esert et al. 2011; Miller-Ricci Kempton et al. 2012; Fraine +et al. 2013; Morley et al. 2013; Kreidberg et al. 2014). The chemical composition and origin of the obscuration is not +well-known, and models of cloud condensation in exoplanet atmospheres can require strong loft and low sedimentation +efficiency to reproduce the flat spectrum of GJ 1214 b (Morley et al. 2013; Gao & Benneke 2018; Ohno & Okuzumi +2018). Since hazes are produced photochemically at higher altitudes, they are also under investigation to explain the +flat 1−2 µm transmission through the atmosphere of this planet (Morley et al. 2015; Kawashima & Ikoma 2018, 2019; +Lavvas et al. 2019; Ohno et al. 2020). +We examine the ability of hazes to mute molecular signals and contribute their own features to the mid-IR transmis- +sion spectra of warm exoplanet atmospheres. As of now, the dominant opacities used to incorporate the transmission +effects of photochemical hazes in models of exoplanet atmospheres mainly come from Khare et al. (1984, hereafter +referred to as K84), which was obtained from laboratory grown compounds (tholins) in a simulated Titan atmosphere +– a majority N2 environment with trace CH4. The broad wavelength range covered by the K84 model has made it +particularly useful for the exoplanet community, but it has fundamental limitations. K84 tholins exhibit a clear trans- +mission window around 0.5 − 3 µm, but in-situe measurements of Titan hazes show more uniform absorption across +0.5 − 1.5 µm (Brass´e et al. 2015), in agreement with more recent laboratory measurements (Tran et al. 2003; Lavvas +et al. 2010; Rannou et al. 2010; Gavilan et al. 2018). This demonstrates the need for a larger variety of lab-measured +aerosol optical properties, which are important for planning and interpreting observations of exoplanet atmospheres. +In this work, we showcase the attenuation properties of tholins grown in different mixtures of N2, CO2, and CH4, +providing benchmark spectral features of hazes from a variety of oxidation states. We apply the optical properties +derived from this work to simulate the 0.3 − 10 µm transmission spectrum of sub-Neptune GJ 1214 b under different +C/O and H+He abundance fractions to identify spectral features from hazes that provide markers for the C/O ratio +of the atmosphere. The C/O ratio is a key tracer of atmospheric composition and can also be an indicator of where +the planet formed in the protoplanetary disk, and whether its atmosphere is primordial or secondary (e.g., ¨Oberg & +Bergin 2021). With this work, we are releasing the lab-measured optical constants and attenuation cross-sections for +tholins produced at three C/O ratios, which are of broad relevance to the exoplanet community. +2. OVERVIEW OF LABORATORY MEASUREMENTS +Computing the attenuation properties of aerosols requires knowledge of the substance’s dielectric properties, which +are conveniently encoded by the real and imaginary parts of the complex index of refraction: n∗(λ) = n(λ) + ik(λ). +In applying n∗ to the wave equations for light propagation through a medium, the imaginary k component causes the +electric field to decay exponentially with distance (absorption) and the real part n induces a phase shift (scattering). +Throughout this section, we compare the n and k spectrum of tholins as proxies for the significance of scattering and +absorption, respectively. Generally, experiments that form tholins with CO or CO2 agree on the overall impact of +increasing Oxygen: the real optical index n increases towards shorter wavelengths, while k makes them more absorbing +in the UV-Vis (Hasenkopf et al. 2010; Ugelow et al. 2018; Gavilan et al. 2017, 2018; Jovanovi´c et al. 2021). +Gavilan et al. (2017, G17) and Gavilan et al. (2018, G18 hereafter) investigated the role of atmospheric CO2 on +the optical properties of tholins prepared using the PAMPRE chamber (Szopa et al. 2006) located at LATMOS (U. +Paris-Saclay, France). In this chamber, the neutral gas remains at room temperature (∼300 K) while the electrons +have a mean energy of 1-2 eV (∼ 104 K, Alcouffe et al. 2010). These temperatures span the range of estimated +atmospheric temperature profiles for GJ 1214 b (Miller-Ricci & Fortney 2010; Kawashima & Ikoma 2019). For these +experiments, an increasingly oxygenated atmosphere was created by increasing the CO2/CH4 ratio from 0 to 4, while +keeping a constant molar fraction of N2. G17 used the ellipsometry technique to measure both the n and k values in the + +Hazes as a probe of C/O ratio +3 +2 +4 +6 +8 +10 +Wavelength (micron) +0.00 +0.01 +0.10 +1.00 +k +NH/NH2 +NH +C +N +C=O +C=N +Khare+ 1984 +C/O = inf +C/O = 1.0 +C/O = 0.625 +2 +4 +6 +8 +10 +Wavelength (micron) +0.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +4.0 +4.5 +n +NH/NH2 +NH +C +N +C=O +C=N +Figure 1. +The imaginary (k, left) and real (n, right) parts of the complex index of refraction as measured for hazes produced +from laboratory gas mixtures with different C/O ratios (G18). +The optical constants derived from the laboratory work of +(Khare et al. 1984) are overlaid for reference. The resonant wavelength for various molecular stretching and vibrational bands, +suspected to underlie the main infrared absorption features, are identified with dash vertical lines in each plot. +270 − 600 nm wavelength range. Through UV-MIR transmission spectroscopy, G18 obtained a direct measurement of +the k values from the broader wavelength range of 130 nm to 10 µm. This latter study revealed absorption resonances +spanning the vacuum-ultraviolet (VUV) to the mid-infrared (MIR). Electronic transitions in the 200 − 500 nm range +were attributed to amine groups and, as the CO2/CH4 ratio increases, to electronic transitions from hydroxyl (-OH) +and carboxyl (-COOH) groups. For the most oxygen-rich samples, absorption is greatest in the 0.13 − 0.3 µm and +6 − 10 µm regions. +2.1. Derivation of optical constants +We present the complex refractive indices of three tholin samples from G18: those produced in an N2:CO2:CH4 +mixture of 95:0:5 (C/O=∞), 90:5:5 (C/O= 1), and 90:8:2 (C/O= 0.625, which is near-solar). The imaginary part of +the complex of index of refraction was derived from transmission measurements obtained in four wavelength ranges: +the vacuum-ultraviolet to UV (130 − 250 nm), the UV-Vis (210 − 1000 nm), the near-infrared (1.05 − 2.7 µm), and +the mid-infrared (1.43 − 10 µm). For the region with no data (1 − 1.05 µm) we interpolated between the visible and +near-IR data. Due to the different spectral resolution of each wavelength range, data was interpolated onto a new +regularized grid of 1000 wavenumber values, logarithmically spaced from 0.13 − 10 µm. +The final composite k spectrum was used to calculate the n spectrum, via the Kramers-Kronig relations (de L. Kronig +1926; Dale Keefe 2002; Lucarini et al. 2005). We use OpC1, which is based on the FORTRAN program LZKKTB +(also known as KKTRANS, Bertie & Zhang 1992), and is modified to include the non-constant electronic contribution +to the real refractive index discussed in (Bertie & Lan 1995). As part of the OpC calculation, the k spectrum is +linearly extrapolated down to 0 at the wavenumber of 0 (Bertie & Zhang 1992). It uses the Maclaurin method to +numerically calculate the Cauchy principal value of the integral which improves the accuracy of the transform near +intense absorption peaks Ohta & Ishida (1988). The transform requires an “anchor” value for the real part of the +complex index of refraction at high wavenumber. Because we lack a precise measurement of n(λ > 10 µm), we use +n(600nm) calculated from the ellipsometry experiment in G17. The direct transmission measurements are considered +highly reliable, and the n values scale linearly with the choice of the anchor value, so we estimate an uncertainty of +±2.5% on k and ±5% on most of the n values. The uncertainty on n is likely higher at the endpoints of the wavelength +range, ±15%, due to the extrapolations employed by OpC. +Figure 1 shows the results of the OpC calculation for the real (n) part of the complex index of refraction, given +the imaginary part (k) measured in the lab. To remove a few zero values in the k curve, we smoothed all optical +constants using the Savitzky-Golay algorithm, employing a fourth order polynomial least-squares fit across 11 adjacent +bins at every data point (Savitzky & Golay 1964; Press et al. 2007). To mimic the growth of hazes in the oxygen-free +1 https://github.com/zmeri/opC + +4 +Corrales & Gavilan et al. +(C/O= ∞) environment of Titan, K84 used slightly different gas abundances, N2:CH4 = 90:10 (K84) versus 95:5 (G18). +Nonetheless, the optical constants of the hazes produced in a C/O=∞ environment by G18 are within agreement with +K84 at a level that is consistent with the variations found throughout the literature and within the environment of +Titan, itself (Brass´e et al. 2015; Lavvas et al. 2010; Rannou et al. 2010). +Figure 1 also identifies some of the major mid-infrared vibrational absorption bands. The intensities and positions +of the vibrational bands observed from the hazes change as CO2 is added to the haze-growing environment. As the +oxygen content increases in the laboratory environment, the oxygen content of the hazes also appears to increase, as +evidenced by the strong C=O features. Meanwhile, the overall contrast of the NH and C=N features around 3 µm and +4.6 µm, respectively, becomes less prevalent when the hazes are grown in a more oxygen rich environment. Adding a +moderate amount of CO2 (C/O= 1) causes a shift the of the mid-infrared absorption peak towards a C=O stretching +mode at 5.88 µm. Adding even more CO2 (C/O= 0.625) greatly enhances the haze absorptivity across all wavelengths +considered. For this near-Solar C/O environment, a variety of stretching and bending modes from C=N, C=O, and +C=C overlap, resulting in relatively flat continuum absorption for wavelengths longer than 6 µm. This feature of +the spectrum creates strong scattering resonances near 6 µm, due to anomalous dispersion. For a more complete +identification and comparison of the spectral features found in the tholins shown here, we refer the reader to the +original paper by G18. +2.2. Calculation of particle cross-sections +The n and k values calculated in Section 2.1 are used as inputs for calculating the absorption and scattering cross- +sections. We employ the Bohren & Huffman (1983) algorithm for the general Mie solution for computing the absorption +and scattering of spherical particles, using the newdust Python library for generic multi-wavelength extinction by +astrophysical particulates (Corrales et al. 2016; Corrales 2023)2 We find that scattering is generally negligible for the +small particles around 1−10 nm, making it so that their extinction cross-sections roughly follow the absorption profile +exactly, displaying all the features of Figure 1. For larger ∼ 0.1 µm particles, scattering dominates over absorption at +wavelengths shorter than 2 µm, leading to roughly featureless transmission. However, extinction features from 3.4 µm +to 6 µm may still be used to identify haze species from these larger particles. +We calculated the attenuation efficiency, which relates the cross-section for a physical interaction to the projected +geometric cross-section of the particle (Q = σ/πa2, where a is the particle radius), for a range of particle sizes between +1 nm and 10 µm over the wavelength range of 130 nm to 10 µm. The scattering, absorption, and total extinction +(absorption plus scattering) efficiencies are publicly available in ASCII and FITS file format.3 +This archive also +provides the geometric scattering factor, g = ⟨cos θ⟩, for each particle size and wavelength. Pure forward scattering +is characterized by g = 1 and isotropic scattering is characterized by g = 0. The g value is relevant for deciding +how much light is effectively removed from the path of incident radiation, which determines whether or not scattering +contributes to the effective opacity of a medium. +A value of g ≥ 0.8 could lead to a 10% difference in the transmission properties for some hot Jupiter or sub-Neptune +sized planets that are accessible for transit measurements today (Roberts et al. 2017). We find that this condition +is mainly satisfied for particles > 1 µm at wavelengths < 500 nm. In Section 3 of this work, we use the vertical +haze particle distributions of (Kawashima & Ikoma 2019), computed for GJ 1214 b, and simulate its transmission +properties from 300 nm to 10 µm using a version of ExoTransmit that is modified for aerosols (Kempton et al. 2017; +Teal et al. 2022). We find that the majority of haze particles for these simulations have radii < 1 µm for the region +of the atmosphere that is not optically thick (P < 1 mbar) at short wavelength. Furthermore, the focus of this work +is to identify NIR-MIR spectroscopic features of aerosols that could provide a marker of the atmosphere’s C/O ratio. +For all these reasons, we use the total extinction cross-section (Qabs + Qsca) to compute the transmission properties +for GJ 1214 b. +3. TRANSMISSION PROPERTIES OF GJ 1214 b WITH DIFFERENT C/O RATIOS +We model the transmission of GJ 1214 b’s atmosphere using a modified version of ExoTransmit (Kempton et al. 2017) +that incorporates the vertical profile of a single haze species, given number density and particle radius as a function +of pressure in the atmosphere (Teal et al. 2022). The background atmosphere is composed of gas in thermochemical +2 This code employs a vector-based computation of the original Bohren & Huffman (1983) algorithm. It is open source and publicly available +at https://github.com/eblur/newdust +3 https://doi.org/10.5281/zenodo.7500026 + +Hazes as a probe of C/O ratio +5 +Table 1. ExoTransmit calculation inputs +This work +Chemical Profile +Haze Profile +Haze Opacities +Name +C/O +Z (solar) +KI19 model +G18 setup +Solar +0.5 +1 +Fiducial +C/O = 0.625 +High-Z +0.5 +1000 +1000 × solar +C/O = 0.625 +C/O = 1 +1 +1 +C/O = 1 +C/O = 1 +C/O = 1000 +1000 +1 +C/O = 1000 +C/O = ∞ +equilibrium. The volume mixing ratios of the gas species are computed using the chemical equilibrium code of Mbarek +& Kempton (2016), given a set of elemental abundances defined by the metallicity and C/O ratio of the atmosphere. +The atmosphere is modeled with an isothermal temperature of 500 K across the pressure range of 100 to 10−9 bar. +Gas phase absorption is calculated using the default opacity tables provided with ExoTransmit. Table 1 describes the +input parameters for each set of models, defined by the metallicity, C/O ratio, and haze inputs. We use the vertical +haze profiles computed by (Kawashima & Ikoma 2019, hereafter referred to as KI19), which examined the growth of +hazes in a simulated GJ 1214 b atmosphere under the influence of a variety of C/O ratios and metallicities (their +Table 1). For simulations that utilized non-solar C/O ratios, the remaining metal abundances were set to their solar +values relative to hydrogen. For all cases, we compare the modeled transmission under the effect of no haze, K84 haze, +and the G18 haze described in Table 1. +There is a fundamental limitation in the sub-Neptune model assumptions that make it difficult to provide physical +consistency between the molecular abundances and haze composition in the simulated spectra. None of the chemical +profiles used in this work provided the 90% N2 atmospheric environment used to grow tholins. However, our goal is +to examine how transmission features might change as a result of increasing oxygen uptake by the hazes, making the +relative abundances of CO2 and CH4 of particular interest. We examined the vertical profiles of the CO2/CH4 ratio +from both our chemical equilibrium models and the models of KI19 to see how they compared with the molecular +abundances used by G18. In the Solar and C/O=1 models, CO2/CH4 ≈ 4 and 1, respectively, at pressures around +10−7 bar, where haze particles begin to form. In the High-Z model, CO2/CH4 ≈ 4 at 10−7 bar and deeper, maintaining +the appropriate ratio where hazes form and continue to grow. We examined the vertical profiles from a contrived +mixture of C:N:O=10:180:16, designed to mimic the bulk abundances from the G18 experiment with C/O=0.625. +In this case, CO2/CH4 < 10−5 across all pressure scales. Since we are unable to produce a model atmosphere of +GJ 1214 b that is identical to the laboratory setup, which would also be difficult to compare with KI19, we opt to use +the chemical profiles built from solar C/N abundances, which yield CO2/CH4 ratios that are closer to those used in +the laboratory environment. +Figures 2–3 showcase the ExoTransmit results. Even with hazes, some molecular line features present themselves +when modeled with the highest spectral resolution possible (R = 1000 for the default ExoTransmit opacity tables). +For ease of visual comparison between this work and KI19, each spectrum has been smoothed via the Savitzky-Golay +algorithm to remove the high resolution line features. +Figure 2 demonstrates that, despite many differences in the model complexities implemented by KI19 and this work, +we were able to reproduce the transmission spectrum from the KI19 fiducial model (dash cyan curve), utilizing K84 +haze opacities (peach curve), to sufficient agreement.4 +KI19 did not implement an isothermal temperature profile +and included the effects of photochemistry, making it so that the majority of molecular species were dissociated above +pressures of 10−7 bar. We tested the impact of this difference by computing the ExoTransmit spectrum with a pressure +cut-off of 10−7 bar, and found no appreciable difference. KI19 also assume a different set of haze precursor molecules +– HCN, C2H2, and CH4 – than the G18 experiments, which utilized N2, CH4, and CO2. This leads the KI19 vertical +profiles of volume mixing ratios for molecules like HCN and C2H2, in comparison to our chemical equilibrium models, +to differ by orders of magnitude, where KI19 abundances were generally higher. This might explain the differences +between the transmission spectrum continuum in Figure 2. Fortunately, the ∼ 300 ppm differences between the KI19 +fiducial and Solar (K84 haze) transmission spectrum are not a subject of concern for this work, which seeks only to +4 The normalization of the KI19 model was adjusted by 20% to agree around 4.3 µm. This adjustment is necessary to account for minor +differences between this work and KI19 in the assumed radius, mass, and temperature profile for GJ 1214 b. + +6 +Corrales & Gavilan et al. +1.4 +1.5 +1.6 +1.7 +1.8 +1.9 +2.0 +Transit depth (%) +Solar +High-Z +Clear +K84 haze +G18 haze +KI19 Fiducial +0.00 +0.05 +0.10 +0.15 +% +G18-K84 (Solar) +2 +4 +6 +8 +10 +Wavelength (micron) +0 +10 +20 +ppm +G18-K84 (High-Z) +Figure 2. +Transmission spectra of GJ 1214 b for the fiducial case of a solar C/O ratio. Top: The transmission spectrum +of GJ 1214 b was computed under the assumption of solar metallicity relative to hydrogen (Solar, top curves) and for Z=1000 +× solar metallicity (High-Z, bottom curves). The transmission spectrum produced by KI19 for their fiducial haze case, which +utilized K84 opacities, is shown for comparison (dash cyan curve). This curve was scaled up by a factor of 20% to match the +K84 haze spectrum around 4.3 µm, which accounts for slight differences in the assumed planet parameters. Middle: Using the +optical constants of lab-grown tholins (Gavilan et al. 2018, G18) with a C/O ratio close to solar leads to significantly enhanced +attenuation, increasing the transit depth of GJ 1214 b by 0.5 − 0.15% across the wavelength range of 1 − 6 µm, relative to +models computed with the optical constants of (Khare et al. 1984, K84). Bottom: In the High-Z atmosphere, which is highly +depleted of Hydrogen and Helium, the differences between using the G18 and K84 optical properties are more subtle. Using the +optical properties of G18 tholins leads to a 10 − 20 ppm difference in the predicted transit depth. +compare the results of modeling transmission with different haze species. Haze is the leading order effect in shaping +the transmission spectra computed in this work. +Figure 2 showcases the transmission spectrum results for the Solar and High-Z models described in Table 1. The +transmission spectrum computed with the optical constants from the G18 tholins produced in a near-solar C/O ratio +environment is significantly higher, flatter, and contains different spectral features from the transmission model that +uses K84 tholin properties. In particular, the absorption and scattering resonances induced by abundant C=O bonds +produce, in effect, a transit depth feature that is enhanced by 0.15% around 5.8 µm. Continuum absorption also + +Hazes as a probe of C/O ratio +7 +1.7 +1.8 +1.9 +Transit Depth (%) +C/O = 1 +G18 haze +K84 haze +0 +200 +400 +ppm +G18-K84 (C/O=1) +1.8 +1.9 +2.0 +Transit Depth (%) +C/O = 1000 +G18 haze +K84 haze +2 +4 +6 +8 +10 +Wavelength (micron) +0 +200 +ppm +G18-K84 (C/O=1000) +Figure 3. +Transmission spectra of GJ 1214 b for non-Solar C/O ratios. Top two panels: The transmission spectrum of +GJ 1214 b computed under the assumption of solar metallicity relative to hydrogen and C/O= 1, using the K84 and G18 tholin +opacities. Using the optical constants from tholins grown in a C/O= 1 environment suggest a deeper transit than expected +when using K84 opacities, especially across 2 − 6 µm, by about 200 − 400 ppm. Bottom two panels: The transmission spectrum +of GJ 1214 b computed under the assumption of solar metallicity relative to hydrogen and C/O= 1000, using the K84 and +G18 tholin opacities. Since both sets of tholins were grown in a Titan-like C/O= ∞ environment, the two curves agree within +200 ppm. +enhances the transit depth by about 0.05 − 0.10% across 1 − 5 µm and by 0.05% around 9 − 10 µm. It’s particularly +interesting that the G18 tholin opacities produce flatter transmission spectra overall, which may help to interpret the +stronlgy featureless observed transmission spectrum of GJ 1214 b (Section 4). +Our fiducial Solar model assumes that GJ 1214 b has a substantial H and He envelope. If GJ 1214 b is depleted of H +and He (the High-Z model), no matter what haze species is implemented, the transmission spectrum is relatively flat +and featureless due to the high mean molecular weight of the atmosphere. The bottom panel of Figure 2 shows that +it would require 20 ppm level precision to distinguish between haze species of different C/O ratios, using the 5.8 µm +C=O resonance feature. +Figure 3 demonstrates that, as the elemental abundance of oxygen falls, the differences between the optical constants +derived from G18 and K84 tholins become less dramatic (also seen in Figure 1). In the case of C/O= 1, using G18 + +8 +Corrales & Gavilan et al. +2 +4 +6 +8 +10 +Wavelength (micron) +1.300 +1.325 +1.350 +1.375 +1.400 +1.425 +1.450 +Transit depth (%) +Solar +C/O = 1.0 +C/O = 1000 +High-Z +1.1 +1.2 +1.3 +1.4 +1.5 +1.6 +1.7 +Wavelength (micron) +1.33 +1.34 +1.35 +1.36 +1.37 +Transit depth (%) +Figure 4. The transmission spectrum of GJ 1214 b, with light grey squares (Bean et al. 2010, 2011; D´esert et al. 2011) and +dark grey circles (Fraine et al. 2013; Kreidberg et al. 2014), overlaid with the three ExoTransmit models utilizing the new optical +constants derived from the laboratory measurements of G18. Each ExoTransmit model has been renormalized to match the +mean 1 − 2 µm transit depth so that the shape of the spectral features can be compared. The more precise 1 − 2 µm data are +consistent with C/O ratios of Solar and 1 assuming significant Solar H/He abundances (bottom panel), but the Spitzer data +points are more consistent with the Z = 1000 model. +tholins in the model predict a transit depth that is enhanced by up to 400 ppm (0.04%) across the 1− 6 µm range and +again at 10 µm, compared to K84. Even though both K84 and G18 optical properties were determined from tholins +grown in an environment free of oxygen, we used the chemical and haze vertical profiles computed with C/O= 1000 +in order to match the KI19 models. We find that the optical properties derived from G18 tholins still differ from the +results obtained with K84 opacities, producing ∼ ±250 ppm differences in the modeled transmission depths (Figure 3). +4. CONCLUSIONS +This work examines how spectral signatures of photochemical hazes, as informed by laboratory measurements, +might constrain the C/O ratio of the atmosphere in which they formed. The pioneering work of Khare et al. (1984) +provided broad-band optical properties for tholins, grown in an oxygen-free environment, and is a dominant template +for photochemical haze widely in use for exoplanet transmission models today. Employing these optical properties +in models of exoplanet atmospheric transmission comes with a biased assumption that those atmospheres are nearly +devoid of oxygen. In Section 2, we present the 0.3 − 10 µm optical properties of tholins grown in a gas chamber +with increasing amounts of oxygen (Gavilan et al. 2017, 2018). These tholins exhibit infrared spectral shapes around +1 − 3 µm, 6 µm, and 10 µm that are distinct from each other and from K84. +In Section 3, we employ the new lab-measured tholin opacities to model the transmission spectrum of sub-Neptune +GJ 1214 b, finding that these haze species are distinguishable from the K84 model by 200-1500 ppm, assuming Solar +abundances of H and He. Figure 4 shows the observed optical-IR transmission spectrum of GJ 1214 b (Bean et al. +2010, 2011; D´esert et al. 2011; Fraine et al. 2013; Kreidberg et al. 2014) with the three ExoTransmit models of +different C/O ratios. The transmission models have been renormalized to match the average 1 − 2 µm transit depth, +for the sake of comparing the spectral shapes. In the optical-IR (0.3 − 2 µm), lab-grown tholins exhibit a relatively + +Hazes as a probe of C/O ratio +9 +clear transmission (low k) window that shifts towards longer wavelengths as the C/O ratio increases. However, the +transmission spectrum in this wavelength range appears smooth, because scattering by 0.1 µm scale particles dominates. +At longer wavelenghts, hazes in a near-solar C/O atmosphere are predicted to exhibit a strong and narrow peak in the +transmission spectrum around 5.8 µm. As the abundance of oxygen decreases, this feature broadens and shifts redder +by approximately 0.3 µm. The relatively flat 6 − 8 µm absorption profile of the tholin species examined here makes +it so that molecular features dominate the observed spectral shape around 8 µm. Thus overall, transmission spectra +captured across the infrared wavelength range of 3 − 10 µm will be more suitable for identifying haze species and C/O +ratios in GJ 1214 b. +While Figure 4 does not demonstrate a real fit to the GJ 1214 b transit data, a few trends are visible. The 0.5−2 µm +data are more consistent with the near-Solar and C/O= 1 transmission models than those that employ haze opacities +from tholins grown in Titan-like environments, where C/O= ∞. However, the Spitzer data are more consistent with +our high metallicity Z = 1000 calculation, while the high precision 1 − 2 µm data are not (Figure 4, bottom). This +is consistent with the findings of Lavvas et al. (2019), who then require a haze formation yield ∼ 10 − 20% in order +to match the transmission wavelength at shorter wavelengths. The Kawashima & Ikoma (2018) models used in this +work are more consistent with 1% haze formation efficiency scenarios from Lavvas et al. (2019), with the caveat that +average particle sizes from K19 are a factor of 3-10 larger. The JWST observations of GJ 1214 b (Greene et al. 2017; +Bean et al. 2021) are likely to provide firmer insight for distinguishing among haze formation models and C/O ratios. +As noted in Section 3, the expected molecular abundances in sub-Neptune atmospheres are not identical to the +laboratory environment in most tholin experiments, which are designed to mimic Titan and early-Earth conditions. +The presence of particular molecules, not just bulk C:N:O ratios, affects the optical properties of photochemical hazes, +their production efficiency, and particle size distribution (H¨orst & Tolbert 2014; Brass´e et al. 2015; H¨orst 2017; Ugelow +et al. 2018). Recent experiments that simulate photochemical conditions in hot Jupiters with T > 1000 K inject doubt +that hazes can form from CO and H2O in an H2 dominated atmosphere (Fleury et al. 2019, 2020). Our transmission +spectrum models rely on the theoretical predictions of Kawashima & Ikoma (2019), where hazes do form from HCN, +C2H2, and CH4 in an H2 dominated atmosphere and temperatures spanning 500-1200 K. Other aerosol production +models also predict that Jupiter-like planets can form hazes from CH4 at Teq < 950 K (Gao et al. 2020). Despite these +nuances, the optical properties of K84 are widely used as a template for chemical hazes in non-terrestrial environments. +While the optical constants provided by this work are similarly imperfect for use with gas giants and sub-Neptunes, +they provide a necessary advancement that is an improvement over the current practice. +Based on the laboratory data, we expect to be able to distinguish among hazes grown in different C/O ratio +environments via strong C=O resonances observable around 6 µm, arising from the enhanced uptake of oxygen into +the solid phase. If present, distinguishing among haze species in the atmosphere of a cool (< 800 K) planet with a H/He +rich envelope is most plausible with the current generation of telescopes. We demonstrate that a model GJ 1214 b +atmosphere that employs K84 optical constants to predict transmission spectra under the influence of haze obscuration +could differ by 200-1500 ppm and, in the case of a solar C/O atmosphere, be underestimated by as much as 10%. If +the atmosphere of GJ 1214 b has a high mean molecular weight, represented by our Z=1000 simulation, ∼ 20 ppm +sensitivity is required to distinguish among haze species. This level of precision may be achievable with JWST for a +select number of transiting sub-Neptunes. Based on the experimental setup, the optical properties for these lab-grown +tholins are even more relevant for temperate terrestrial planets, which will only be accessible by future generations of +ground and space-based telescopes. The optical constants and size-dependent cross-sections of the tholins used in this +work are publicly available in several formats that can be adapted for use by other open source transmission modeling +tools. A static version of eblur/newdust and the custom version of ExoTransmit, used to compute the cross-sections +and transmission spectra, are also provided with this data release (doi:10.5281/zenodo.7500026). +REFERENCES +Alcouffe, G., Cavarroc, M., Cernogora, G., et al. 2010, +Plasma Sources Science Technology, 19, 015008, +doi: 10.1088/0963-0252/19/1/015008 +Bean, J. L., Miller-Ricci Kempton, E., & Homeier, D. 2010, +Nature, 468, 669, doi: 10.1038/nature09596 +Bean, J. L., D´esert, J.-M., Kabath, P., et al. 2011, ApJ, +743, 92, doi: 10.1088/0004-637X/743/1/92 +Bean, J. L., Kempton, E. M. R., Fu, G., et al. 2021, +Unlocking the Mysteries of the Archetype Sub-Neptune +GJ1214b with a Full-Orbit Phase Curve, JWST +Proposal. Cycle 1, ID. #1803 + +10 +Corrales & Gavilan et al. +Bertie, J. E., & Lan, Z. 1995, JChPh, 103, 10152, +doi: 10.1063/1.469917 +Bertie, J. E., & Zhang, S. L. 1992, Canadian Journal of +Chemistry, 70, 520, doi: 10.1139/v92-074 +Bohren, C. F., & Huffman, D. R. 1983, Absorption and +scattering of light by small particles +Brass´e, C., Mu˜noz, O., Coll, P., & Raulin, F. 2015, +Planet. Space Sci., 109, 159, +doi: 10.1016/j.pss.2015.02.012 +Charbonneau, D., Berta, Z. K., Irwin, J., et al. 2009, +Nature, 462, 891, doi: 10.1038/nature08679 +Corrales, L. 2023, eblur/newdust: Python extinction and +scattering halo calculations for astrophysical particulates, +1.0, Zenodo, doi: 10.5281/zenodo.7500048 +Corrales, L. R., Garc´ıa, J., Wilms, J., & Baganoff, F. 2016, +MNRAS, 458, 1345, doi: 10.1093/mnras/stw376 +Dale Keefe, C. 2002, Journal of Molecular Structure, 641, +165, doi: https://doi.org/10.1016/S0022-2860(02)00184-9 +de L. Kronig, R. 1926, J. Opt. Soc. Am., 12, 547, +doi: 10.1364/JOSA.12.000547 +D´esert, J.-M., Bean, J., Miller-Ricci Kempton, E., et al. +2011, ApJL, 731, L40, doi: 10.1088/2041-8205/731/2/L40 +Fleury, B., Gudipati, M. S., Henderson, B. L., & Swain, M. +2019, ApJ, 871, 158, doi: 10.3847/1538-4357/aaf79f +—. 2020, ApJ, 899, 147, doi: 10.3847/1538-4357/aba828 +Fraine, J. D., Deming, D., Gillon, M., et al. 2013, ApJ, 765, +127, doi: 10.1088/0004-637X/765/2/127 +Gao, P., & Benneke, B. 2018, ApJ, 863, 165, +doi: 10.3847/1538-4357/aad461 +Gao, P., Thorngren, D. P., Lee, G. K. H., et al. 2020, +Nature Astronomy, 4, 951, +doi: 10.1038/s41550-020-1114-3 +Gavilan, L., Carrasco, N., Vrønning Hoffmann, S., Jones, +N. C., & Mason, N. J. 2018, ApJ, 861, 110, +doi: 10.3847/1538-4357/aac8df +Gavilan, L., Remusat, L., Roskosz, M., et al. 2017, ApJ, +840, 35, doi: 10.3847/1538-4357/aa6bfc +Greene, T. P., Beatty, T. G., Rieke, M. J., & Schlawin, E. +2017, Transit Spectroscopy of Mature Planets, JWST +Proposal. Cycle 1, ID. #1185 +Hasenkopf, C. A., Beaver, M. R., Trainer, M. G., et al. +2010, Icarus, 207, 903, doi: 10.1016/j.icarus.2009.12.015 +Helling, C., Lee, G., Dobbs-Dixon, I., et al. 2016, MNRAS, +460, 855, doi: 10.1093/mnras/stw662 +Helling, C., Iro, N., Corrales, L., et al. 2019, A&A, 631, +A79, doi: 10.1051/0004-6361/201935771 +H¨orst, S. M. 2017, Journal of Geophysical Research +(Planets), 122, 432, doi: 10.1002/2016JE005240 +H¨orst, S. M., & Tolbert, M. A. 2014, ApJ, 781, 53, +doi: 10.1088/0004-637X/781/1/53 +Jovanovi´c, L., Gautier, T., Broch, L., et al. 2021, Icarus, +362, 114398, +doi: https://doi.org/10.1016/j.icarus.2021.114398 +Kawashima, Y., & Ikoma, M. 2018, ApJ, 853, 7, +doi: 10.3847/1538-4357/aaa0c5 +—. 2019, ApJ, 877, 109, doi: 10.3847/1538-4357/ab1b1d +Kempton, E. M. R., Lupu, R., Owusu-Asare, A., Slough, +P., & Cale, B. 2017, PASP, 129, 044402, +doi: 10.1088/1538-3873/aa61ef +Khare, B. N., Sagan, C., Arakawa, E. T., et al. 1984, +Icarus, 60, 127, doi: 10.1016/0019-1035(84)90142-8 +Kreidberg, L., Bean, J. L., D´esert, J.-M., et al. 2014, +Nature, 505, 69, doi: 10.1038/nature12888 +Lavvas, P., Koskinen, T., Steinrueck, M. E., Garc´ıa Mu˜noz, +A., & Showman, A. P. 2019, ApJ, 878, 118, +doi: 10.3847/1538-4357/ab204e +Lavvas, P., Yelle, R. V., & Griffith, C. A. 2010, Icarus, 210, +832, doi: 10.1016/j.icarus.2010.07.025 +Lucarini, V., Saarinen, J. J., Peiponen, K.-E., & Vartiainen, +E. M. 2005, Kramers-Kronig relations in optical materials +research, Vol. 110 (Springer Science & Business Media) +Mbarek, R., & Kempton, E. M. R. 2016, ApJ, 827, 121, +doi: 10.3847/0004-637X/827/2/121 +McCullough, P. R., Crouzet, N., Deming, D., & +Madhusudhan, N. 2014, ApJ, 791, 55, +doi: 10.1088/0004-637X/791/1/55 +Miller-Ricci, E., & Fortney, J. J. 2010, ApJL, 716, L74, +doi: 10.1088/2041-8205/716/1/L74 +Miller-Ricci Kempton, E., Zahnle, K., & Fortney, J. J. +2012, ApJ, 745, 3, doi: 10.1088/0004-637X/745/1/3 +Morley, C. V., Fortney, J. J., Kempton, E. M. R., et al. +2013, ApJ, 775, 33, doi: 10.1088/0004-637X/775/1/33 +Morley, C. V., Fortney, J. J., Marley, M. S., et al. 2015, +ApJ, 815, 110, doi: 10.1088/0004-637X/815/2/110 +¨Oberg, K. I., & Bergin, E. A. 2021, PhR, 893, 1, +doi: 10.1016/j.physrep.2020.09.004 +Ohno, K., & Okuzumi, S. 2018, ApJ, 859, 34, +doi: 10.3847/1538-4357/aabee3 +Ohno, K., Okuzumi, S., & Tazaki, R. 2020, ApJ, 891, 131, +doi: 10.3847/1538-4357/ab44bd +Ohta, K., & Ishida, H. 1988, Appl. Spectrosc., 42, 952. +http://as.osa.org/abstract.cfm?URI=as-42-6-952 +Pont, F., Sing, D. K., Gibson, N. P., et al. 2013, MNRAS, +432, 2917, doi: 10.1093/mnras/stt651 +Powell, D., Zhang, X., Gao, P., & Parmentier, V. 2018, +ApJ, 860, 18, doi: 10.3847/1538-4357/aac215 +Press, W. H., Teukolsky, S. A., Vetterling, W. T., & +Flannery, B. P. 2007, Numerical Recipes 3rd Edition: +The Art of Scientific Computing (Cambridge University +Press) + +Hazes as a probe of C/O ratio +11 +Rannou, P., Cours, T., Le Mou´elic, S., et al. 2010, Icarus, +208, 850, doi: 10.1016/j.icarus.2010.03.016 +Roberts, S. R., Jiang, Y.-F., Wang, Q. D., & Ostriker, J. P. +2017, MNRAS, 466, 1477, doi: 10.1093/mnras/stw2995 +Rogers, L. A., & Seager, S. 2010, ApJ, 716, 1208, +doi: 10.1088/0004-637X/716/2/1208 +S´anchez-L´opez, A., L´opez-Puertas, M., Snellen, I. A. G., +et al. 2020, A&A, 643, A24, +doi: 10.1051/0004-6361/202038629 +Savitzky, A., & Golay, M. J. E. 1964, Analytical +Chemistry, 36, 1627 +Sing, D. K., Pont, F., Aigrain, S., et al. 2011, MNRAS, 416, +1443, doi: 10.1111/j.1365-2966.2011.19142.x +Sing, D. K., Fortney, J. J., Nikolov, N., et al. 2016, Nature, +529, 59, doi: 10.1038/nature16068 +Steinrueck, M. E., Showman, A. P., Lavvas, P., et al. 2021, +MNRAS, 504, 2783, doi: 10.1093/mnras/stab1053 +Szopa, C., Cernogora, G., Boufendi, L., Correia, J. J., & +Coll, P. 2006, Planet. Space Sci., 54, 394, +doi: 10.1016/j.pss.2005.12.012 +Teal, D. J., Kempton, E. M. R., Bastelberger, S., +Youngblood, A., & Arney, G. 2022, ApJ, 927, 90, +doi: 10.3847/1538-4357/ac4d99 +Tran, B. N., Joseph, J. C., Ferris, J. P., Persans, P. D., & +Chera, J. J. 2003, Icarus, 165, 379, +doi: 10.1016/S0019-1035(03)00209-4 +Ugelow, M. S., De Haan, D. O., H¨orst, S. M., & Tolbert, +M. A. 2018, ApJL, 859, L2, +doi: 10.3847/2041-8213/aac2c7 + diff --git a/WdAzT4oBgHgl3EQfKPti/content/tmp_files/load_file.txt b/WdAzT4oBgHgl3EQfKPti/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..98f4d2da768b0271bed67c89c2720e1cfc8a5a48 --- /dev/null +++ b/WdAzT4oBgHgl3EQfKPti/content/tmp_files/load_file.txt @@ -0,0 +1,858 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf,len=857 +page_content='Draft version January 4, 2023 Typeset using LATEX default style in AASTeX631 Photochemical hazes can trace the C/O ratio in exoplanet atmospheres L´ıa Corrales ,1 Lisseth Gavilan ,2, 3 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Teal ,4 and Eliza M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kempton 4 1University of Michigan, Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1085 S University Ave,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Ann Arbor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' MI 48109,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' USA 2NASA Ames Research Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Space Science & Astrobiology Division,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Moffett Field,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' CA 94035,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' USA 3Bay Area Environmental Research Institute (BAERI),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Sonoma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' CA 95476,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' USA 4University of Maryland,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 4296 Stadium Dr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' College Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' MD 20742,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' USA ABSTRACT Photochemical hazes are suspected to obscure molecular features,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' such as water,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' from detection in the transmission spectra of exoplanets with atmospheric temperatures < 800 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The opacities of laboratory produced organic compounds (tholins) from Khare et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (1984) have become a standard for modeling haze in exoplanet atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' However, these tholins were grown in an oxygen-free, Titan-like environment that is very different from typical assumptions for exoplanets, where C/O∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This work presents the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='13 − 10 µm complex refractive indices derived from laboratory transmission measurements of tholins grown in environments with different oxygen abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' With the increasing uptake of oxygen, absorption increases across the entire wavelength range, and a scattering feature around 6 µm shifts towards shorter wavelengths and becomes more peaked around 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 µm, due to a C=O stretch resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Using GJ 1214 b as a test-case, we examine the transmission spectra of a sub- Neptune planet with C/O ratios of solar, 1, and 1000 to evaluate the effective differences between our opacities and those of Khare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For an atmosphere with solar hydrogen and helium abundances, we find a difference of 200-1500 ppm, but for high-metallicity (Z=1000) environments, the difference may only be 20 ppm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The 1 − 2 µm transmission data for GJ 1214 b rule out the Titan-like haze model, and are more consistent with C/O= 1 and C/O=solar haze models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This work demonstrates that using haze opacities that are more consistent with underlying assumptions about bulk atmospheric composition are important for building self-consistent models that appropriately constrain the atmospheric C/O ratio, even when molecular features are obscured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Keywords: Exoplanet atmospheric composition (487) — Laboratory astrophysics (2004) — Astrochem- istry (75) — Exoplanet evolution (491) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' INTRODUCTION Approximately 75% of the over 5,000 exoplanets known today were discovered via the transit method, where the chance alignment of an extra-solar planet’s orbit with Earth’s vantage point causes the planet to pass in front of the star, blocking ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1 − 1% of its light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Observing a transit at multiple wavelengths builds a transmission spectrum, on which the contents of the exoplanet’s atmosphere are imprinted via their unique spectroscopic fingerprints in absorption and scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The depth of an exoplanet transit, as a function of wavelength, depends jointly on the transmission properties of the atmospheric contents as well as their vertical distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In this letter, we investigate whether the spectral features of atmospheric hazes on an exoplanet can provide key markers of the bulk content of the gas in which they form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Aerosols – whether condensing directly from atmospheric gas (clouds) or through photochemical reactions (hazes) – are known to affect nearly every type of exoplanet atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Even hot Jupiters, across a wide range of temperatures (1000 − 2000 K), have spectral features that are muted as a result of aerosol obscuration (Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016) and steep Corresponding author: L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Corrales liac@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='edu arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='01093v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='EP] 3 Jan 2023 ID2 Corrales & Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' optical slopes that are suspected to arise from a combination of clouds and hazes (Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Pont et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' McCullough et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' S´anchez-L´opez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Steinrueck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Theoretical models predict that the infrared opacity of hot Jupiters with Teq ∼ 900 − 2200 K will be dominated by mineral condensates rich in refractory elements (Helling et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Only below about 800 K are photochemically produced organic hazes expected to form and dominate the infrared opacity (Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Photochemical hazes are also suspected to be a key source of opacity for more temperate, smaller planets such as sub-Neptunes and super-Earths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' One such planet is GJ 1214 b, which has a mass of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='55 ME and radius of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='68 RE, consistent with a variety of composition models that suggest it hosts an atmosphere comprising ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 to a few percent of the planet’s mass (Charbonneau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Rogers & Seager 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Transmission measurements from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 µm can be reproduced by models employing some combination of a high mean molecular weight atmosphere and an optically thick aerosol layer at altitudes ∼ 10 mbar (Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D´esert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Miller-Ricci Kempton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Fraine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kreidberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The chemical composition and origin of the obscuration is not well-known, and models of cloud condensation in exoplanet atmospheres can require strong loft and low sedimentation efficiency to reproduce the flat spectrum of GJ 1214 b (Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gao & Benneke 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Ohno & Okuzumi 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Since hazes are produced photochemically at higher altitudes, they are also under investigation to explain the flat 1−2 µm transmission through the atmosphere of this planet (Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kawashima & Ikoma 2018, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Lavvas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Ohno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We examine the ability of hazes to mute molecular signals and contribute their own features to the mid-IR transmis- sion spectra of warm exoplanet atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' As of now, the dominant opacities used to incorporate the transmission effects of photochemical hazes in models of exoplanet atmospheres mainly come from Khare et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (1984, hereafter referred to as K84), which was obtained from laboratory grown compounds (tholins) in a simulated Titan atmosphere – a majority N2 environment with trace CH4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The broad wavelength range covered by the K84 model has made it particularly useful for the exoplanet community, but it has fundamental limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K84 tholins exhibit a clear trans- mission window around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 − 3 µm, but in-situe measurements of Titan hazes show more uniform absorption across 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 µm (Brass´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015), in agreement with more recent laboratory measurements (Tran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Lavvas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Rannou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This demonstrates the need for a larger variety of lab-measured aerosol optical properties, which are important for planning and interpreting observations of exoplanet atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In this work, we showcase the attenuation properties of tholins grown in different mixtures of N2, CO2, and CH4, providing benchmark spectral features of hazes from a variety of oxidation states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We apply the optical properties derived from this work to simulate the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 − 10 µm transmission spectrum of sub-Neptune GJ 1214 b under different C/O and H+He abundance fractions to identify spectral features from hazes that provide markers for the C/O ratio of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The C/O ratio is a key tracer of atmospheric composition and can also be an indicator of where the planet formed in the protoplanetary disk, and whether its atmosphere is primordial or secondary (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', ¨Oberg & Bergin 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' With this work, we are releasing the lab-measured optical constants and attenuation cross-sections for tholins produced at three C/O ratios, which are of broad relevance to the exoplanet community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' OVERVIEW OF LABORATORY MEASUREMENTS Computing the attenuation properties of aerosols requires knowledge of the substance’s dielectric properties, which are conveniently encoded by the real and imaginary parts of the complex index of refraction: n∗(λ) = n(λ) + ik(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In applying n∗ to the wave equations for light propagation through a medium, the imaginary k component causes the electric field to decay exponentially with distance (absorption) and the real part n induces a phase shift (scattering).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Throughout this section, we compare the n and k spectrum of tholins as proxies for the significance of scattering and absorption, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Generally, experiments that form tholins with CO or CO2 agree on the overall impact of increasing Oxygen: the real optical index n increases towards shorter wavelengths, while k makes them more absorbing in the UV-Vis (Hasenkopf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Ugelow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Jovanovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (2017, G17) and Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (2018, G18 hereafter) investigated the role of atmospheric CO2 on the optical properties of tholins prepared using the PAMPRE chamber (Szopa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2006) located at LATMOS (U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Paris-Saclay, France).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In this chamber, the neutral gas remains at room temperature (∼300 K) while the electrons have a mean energy of 1-2 eV (∼ 104 K, Alcouffe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' These temperatures span the range of estimated atmospheric temperature profiles for GJ 1214 b (Miller-Ricci & Fortney 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kawashima & Ikoma 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For these experiments, an increasingly oxygenated atmosphere was created by increasing the CO2/CH4 ratio from 0 to 4, while keeping a constant molar fraction of N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' G17 used the ellipsometry technique to measure both the n and k values in the Hazes as a probe of C/O ratio 3 2 4 6 8 10 Wavelength (micron) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='00 k NH/NH2 NH C N C=O C=N Khare+ 1984 C/O = inf C/O = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 C/O = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625 2 4 6 8 10 Wavelength (micron) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 n NH/NH2 NH C N C=O C=N Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The imaginary (k, left) and real (n, right) parts of the complex index of refraction as measured for hazes produced from laboratory gas mixtures with different C/O ratios (G18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The optical constants derived from the laboratory work of (Khare et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1984) are overlaid for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The resonant wavelength for various molecular stretching and vibrational bands, suspected to underlie the main infrared absorption features, are identified with dash vertical lines in each plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 270 − 600 nm wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Through UV-MIR transmission spectroscopy, G18 obtained a direct measurement of the k values from the broader wavelength range of 130 nm to 10 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This latter study revealed absorption resonances spanning the vacuum-ultraviolet (VUV) to the mid-infrared (MIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Electronic transitions in the 200 − 500 nm range were attributed to amine groups and, as the CO2/CH4 ratio increases, to electronic transitions from hydroxyl (-OH) and carboxyl (-COOH) groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For the most oxygen-rich samples, absorption is greatest in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='13 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 µm and 6 − 10 µm regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Derivation of optical constants We present the complex refractive indices of three tholin samples from G18: those produced in an N2:CO2:CH4 mixture of 95:0:5 (C/O=∞), 90:5:5 (C/O= 1), and 90:8:2 (C/O= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625, which is near-solar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The imaginary part of the complex of index of refraction was derived from transmission measurements obtained in four wavelength ranges: the vacuum-ultraviolet to UV (130 − 250 nm), the UV-Vis (210 − 1000 nm), the near-infrared (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='05 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7 µm), and the mid-infrared (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='43 − 10 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For the region with no data (1 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='05 µm) we interpolated between the visible and near-IR data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Due to the different spectral resolution of each wavelength range, data was interpolated onto a new regularized grid of 1000 wavenumber values, logarithmically spaced from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='13 − 10 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The final composite k spectrum was used to calculate the n spectrum, via the Kramers-Kronig relations (de L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kronig 1926;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Dale Keefe 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Lucarini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We use OpC1, which is based on the FORTRAN program LZKKTB (also known as KKTRANS, Bertie & Zhang 1992), and is modified to include the non-constant electronic contribution to the real refractive index discussed in (Bertie & Lan 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' As part of the OpC calculation, the k spectrum is linearly extrapolated down to 0 at the wavenumber of 0 (Bertie & Zhang 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' It uses the Maclaurin method to numerically calculate the Cauchy principal value of the integral which improves the accuracy of the transform near intense absorption peaks Ohta & Ishida (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The transform requires an “anchor” value for the real part of the complex index of refraction at high wavenumber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Because we lack a precise measurement of n(λ > 10 µm), we use n(600nm) calculated from the ellipsometry experiment in G17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The direct transmission measurements are considered highly reliable, and the n values scale linearly with the choice of the anchor value, so we estimate an uncertainty of ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5% on k and ±5% on most of the n values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The uncertainty on n is likely higher at the endpoints of the wavelength range, ±15%, due to the extrapolations employed by OpC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 1 shows the results of the OpC calculation for the real (n) part of the complex index of refraction, given the imaginary part (k) measured in the lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' To remove a few zero values in the k curve, we smoothed all optical constants using the Savitzky-Golay algorithm, employing a fourth order polynomial least-squares fit across 11 adjacent bins at every data point (Savitzky & Golay 1964;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Press et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' To mimic the growth of hazes in the oxygen-free 1 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='com/zmeri/opC 4 Corrales & Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (C/O= ∞) environment of Titan, K84 used slightly different gas abundances, N2:CH4 = 90:10 (K84) versus 95:5 (G18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Nonetheless, the optical constants of the hazes produced in a C/O=∞ environment by G18 are within agreement with K84 at a level that is consistent with the variations found throughout the literature and within the environment of Titan, itself (Brass´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Lavvas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Rannou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 1 also identifies some of the major mid-infrared vibrational absorption bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The intensities and positions of the vibrational bands observed from the hazes change as CO2 is added to the haze-growing environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' As the oxygen content increases in the laboratory environment, the oxygen content of the hazes also appears to increase, as evidenced by the strong C=O features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Meanwhile, the overall contrast of the NH and C=N features around 3 µm and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='6 µm, respectively, becomes less prevalent when the hazes are grown in a more oxygen rich environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Adding a moderate amount of CO2 (C/O= 1) causes a shift the of the mid-infrared absorption peak towards a C=O stretching mode at 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='88 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Adding even more CO2 (C/O= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625) greatly enhances the haze absorptivity across all wavelengths considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For this near-Solar C/O environment, a variety of stretching and bending modes from C=N, C=O, and C=C overlap, resulting in relatively flat continuum absorption for wavelengths longer than 6 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This feature of the spectrum creates strong scattering resonances near 6 µm, due to anomalous dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For a more complete identification and comparison of the spectral features found in the tholins shown here, we refer the reader to the original paper by G18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Calculation of particle cross-sections The n and k values calculated in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1 are used as inputs for calculating the absorption and scattering cross- sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We employ the Bohren & Huffman (1983) algorithm for the general Mie solution for computing the absorption and scattering of spherical particles, using the newdust Python library for generic multi-wavelength extinction by astrophysical particulates (Corrales et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Corrales 2023)2 We find that scattering is generally negligible for the small particles around 1−10 nm, making it so that their extinction cross-sections roughly follow the absorption profile exactly, displaying all the features of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For larger ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1 µm particles, scattering dominates over absorption at wavelengths shorter than 2 µm, leading to roughly featureless transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' However, extinction features from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='4 µm to 6 µm may still be used to identify haze species from these larger particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We calculated the attenuation efficiency, which relates the cross-section for a physical interaction to the projected geometric cross-section of the particle (Q = σ/πa2, where a is the particle radius), for a range of particle sizes between 1 nm and 10 µm over the wavelength range of 130 nm to 10 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The scattering, absorption, and total extinction (absorption plus scattering) efficiencies are publicly available in ASCII and FITS file format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 This archive also provides the geometric scattering factor, g = ⟨cos θ⟩, for each particle size and wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Pure forward scattering is characterized by g = 1 and isotropic scattering is characterized by g = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The g value is relevant for deciding how much light is effectively removed from the path of incident radiation, which determines whether or not scattering contributes to the effective opacity of a medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A value of g ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 could lead to a 10% difference in the transmission properties for some hot Jupiter or sub-Neptune sized planets that are accessible for transit measurements today (Roberts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We find that this condition is mainly satisfied for particles > 1 µm at wavelengths < 500 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In Section 3 of this work, we use the vertical haze particle distributions of (Kawashima & Ikoma 2019), computed for GJ 1214 b, and simulate its transmission properties from 300 nm to 10 µm using a version of ExoTransmit that is modified for aerosols (Kempton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Teal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We find that the majority of haze particles for these simulations have radii < 1 µm for the region of the atmosphere that is not optically thick (P < 1 mbar) at short wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Furthermore, the focus of this work is to identify NIR-MIR spectroscopic features of aerosols that could provide a marker of the atmosphere’s C/O ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For all these reasons, we use the total extinction cross-section (Qabs + Qsca) to compute the transmission properties for GJ 1214 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' TRANSMISSION PROPERTIES OF GJ 1214 b WITH DIFFERENT C/O RATIOS We model the transmission of GJ 1214 b’s atmosphere using a modified version of ExoTransmit (Kempton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017) that incorporates the vertical profile of a single haze species, given number density and particle radius as a function of pressure in the atmosphere (Teal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The background atmosphere is composed of gas in thermochemical 2 This code employs a vector-based computation of the original Bohren & Huffman (1983) algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' It is open source and publicly available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='com/eblur/newdust 3 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7500026 Hazes as a probe of C/O ratio 5 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' ExoTransmit calculation inputs This work Chemical Profile Haze Profile Haze Opacities Name C/O Z (solar) KI19 model G18 setup Solar 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 1 Fiducial C/O = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625 High-Z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 1000 1000 × solar C/O = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625 C/O = 1 1 1 C/O = 1 C/O = 1 C/O = 1000 1000 1 C/O = 1000 C/O = ∞ equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The volume mixing ratios of the gas species are computed using the chemical equilibrium code of Mbarek & Kempton (2016), given a set of elemental abundances defined by the metallicity and C/O ratio of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The atmosphere is modeled with an isothermal temperature of 500 K across the pressure range of 100 to 10−9 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Gas phase absorption is calculated using the default opacity tables provided with ExoTransmit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Table 1 describes the input parameters for each set of models, defined by the metallicity, C/O ratio, and haze inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We use the vertical haze profiles computed by (Kawashima & Ikoma 2019, hereafter referred to as KI19), which examined the growth of hazes in a simulated GJ 1214 b atmosphere under the influence of a variety of C/O ratios and metallicities (their Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For simulations that utilized non-solar C/O ratios, the remaining metal abundances were set to their solar values relative to hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For all cases, we compare the modeled transmission under the effect of no haze, K84 haze, and the G18 haze described in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' There is a fundamental limitation in the sub-Neptune model assumptions that make it difficult to provide physical consistency between the molecular abundances and haze composition in the simulated spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' None of the chemical profiles used in this work provided the 90% N2 atmospheric environment used to grow tholins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' However, our goal is to examine how transmission features might change as a result of increasing oxygen uptake by the hazes, making the relative abundances of CO2 and CH4 of particular interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We examined the vertical profiles of the CO2/CH4 ratio from both our chemical equilibrium models and the models of KI19 to see how they compared with the molecular abundances used by G18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In the Solar and C/O=1 models, CO2/CH4 ≈ 4 and 1, respectively, at pressures around 10−7 bar, where haze particles begin to form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In the High-Z model, CO2/CH4 ≈ 4 at 10−7 bar and deeper, maintaining the appropriate ratio where hazes form and continue to grow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We examined the vertical profiles from a contrived mixture of C:N:O=10:180:16, designed to mimic the bulk abundances from the G18 experiment with C/O=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='625.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In this case, CO2/CH4 < 10−5 across all pressure scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Since we are unable to produce a model atmosphere of GJ 1214 b that is identical to the laboratory setup, which would also be difficult to compare with KI19, we opt to use the chemical profiles built from solar C/N abundances, which yield CO2/CH4 ratios that are closer to those used in the laboratory environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figures 2–3 showcase the ExoTransmit results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Even with hazes, some molecular line features present themselves when modeled with the highest spectral resolution possible (R = 1000 for the default ExoTransmit opacity tables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' For ease of visual comparison between this work and KI19, each spectrum has been smoothed via the Savitzky-Golay algorithm to remove the high resolution line features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 2 demonstrates that, despite many differences in the model complexities implemented by KI19 and this work, we were able to reproduce the transmission spectrum from the KI19 fiducial model (dash cyan curve), utilizing K84 haze opacities (peach curve), to sufficient agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='4 KI19 did not implement an isothermal temperature profile and included the effects of photochemistry, making it so that the majority of molecular species were dissociated above pressures of 10−7 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We tested the impact of this difference by computing the ExoTransmit spectrum with a pressure cut-off of 10−7 bar, and found no appreciable difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' KI19 also assume a different set of haze precursor molecules – HCN, C2H2, and CH4 – than the G18 experiments, which utilized N2, CH4, and CO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This leads the KI19 vertical profiles of volume mixing ratios for molecules like HCN and C2H2, in comparison to our chemical equilibrium models, to differ by orders of magnitude, where KI19 abundances were generally higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This might explain the differences between the transmission spectrum continuum in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Fortunately, the ∼ 300 ppm differences between the KI19 fiducial and Solar (K84 haze) transmission spectrum are not a subject of concern for this work, which seeks only to 4 The normalization of the KI19 model was adjusted by 20% to agree around 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This adjustment is necessary to account for minor differences between this work and KI19 in the assumed radius, mass, and temperature profile for GJ 1214 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 6 Corrales & Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 Transit depth (%) Solar High-Z Clear K84 haze G18 haze KI19 Fiducial 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='15 % G18-K84 (Solar) 2 4 6 8 10 Wavelength (micron) 0 10 20 ppm G18-K84 (High-Z) Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Transmission spectra of GJ 1214 b for the fiducial case of a solar C/O ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Top: The transmission spectrum of GJ 1214 b was computed under the assumption of solar metallicity relative to hydrogen (Solar, top curves) and for Z=1000 × solar metallicity (High-Z, bottom curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The transmission spectrum produced by KI19 for their fiducial haze case, which utilized K84 opacities, is shown for comparison (dash cyan curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This curve was scaled up by a factor of 20% to match the K84 haze spectrum around 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 µm, which accounts for slight differences in the assumed planet parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Middle: Using the optical constants of lab-grown tholins (Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, G18) with a C/O ratio close to solar leads to significantly enhanced attenuation, increasing the transit depth of GJ 1214 b by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='15% across the wavelength range of 1 − 6 µm, relative to models computed with the optical constants of (Khare et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1984, K84).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Bottom: In the High-Z atmosphere, which is highly depleted of Hydrogen and Helium, the differences between using the G18 and K84 optical properties are more subtle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Using the optical properties of G18 tholins leads to a 10 − 20 ppm difference in the predicted transit depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' compare the results of modeling transmission with different haze species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Haze is the leading order effect in shaping the transmission spectra computed in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 2 showcases the transmission spectrum results for the Solar and High-Z models described in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The transmission spectrum computed with the optical constants from the G18 tholins produced in a near-solar C/O ratio environment is significantly higher, flatter, and contains different spectral features from the transmission model that uses K84 tholin properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In particular, the absorption and scattering resonances induced by abundant C=O bonds produce, in effect, a transit depth feature that is enhanced by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='15% around 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Continuum absorption also Hazes as a probe of C/O ratio 7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='9 Transit Depth (%) C/O = 1 G18 haze K84 haze 0 200 400 ppm G18-K84 (C/O=1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 Transit Depth (%) C/O = 1000 G18 haze K84 haze 2 4 6 8 10 Wavelength (micron) 0 200 ppm G18-K84 (C/O=1000) Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Transmission spectra of GJ 1214 b for non-Solar C/O ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Top two panels: The transmission spectrum of GJ 1214 b computed under the assumption of solar metallicity relative to hydrogen and C/O= 1, using the K84 and G18 tholin opacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Using the optical constants from tholins grown in a C/O= 1 environment suggest a deeper transit than expected when using K84 opacities, especially across 2 − 6 µm, by about 200 − 400 ppm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Bottom two panels: The transmission spectrum of GJ 1214 b computed under the assumption of solar metallicity relative to hydrogen and C/O= 1000, using the K84 and G18 tholin opacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Since both sets of tholins were grown in a Titan-like C/O= ∞ environment, the two curves agree within 200 ppm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' enhances the transit depth by about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='05 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='10% across 1 − 5 µm and by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='05% around 9 − 10 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' It’s particularly interesting that the G18 tholin opacities produce flatter transmission spectra overall, which may help to interpret the stronlgy featureless observed transmission spectrum of GJ 1214 b (Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Our fiducial Solar model assumes that GJ 1214 b has a substantial H and He envelope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' If GJ 1214 b is depleted of H and He (the High-Z model), no matter what haze species is implemented, the transmission spectrum is relatively flat and featureless due to the high mean molecular weight of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The bottom panel of Figure 2 shows that it would require 20 ppm level precision to distinguish between haze species of different C/O ratios, using the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 µm C=O resonance feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 3 demonstrates that, as the elemental abundance of oxygen falls, the differences between the optical constants derived from G18 and K84 tholins become less dramatic (also seen in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In the case of C/O= 1, using G18 8 Corrales & Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2 4 6 8 10 Wavelength (micron) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='300 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='325 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='350 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='375 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='400 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='425 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='450 Transit depth (%) Solar C/O = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0 C/O = 1000 High-Z 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7 Wavelength (micron) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='33 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='34 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='35 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='36 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='37 Transit depth (%) Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The transmission spectrum of GJ 1214 b, with light grey squares (Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D´esert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011) and dark grey circles (Fraine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kreidberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014), overlaid with the three ExoTransmit models utilizing the new optical constants derived from the laboratory measurements of G18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Each ExoTransmit model has been renormalized to match the mean 1 − 2 µm transit depth so that the shape of the spectral features can be compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The more precise 1 − 2 µm data are consistent with C/O ratios of Solar and 1 assuming significant Solar H/He abundances (bottom panel), but the Spitzer data points are more consistent with the Z = 1000 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' tholins in the model predict a transit depth that is enhanced by up to 400 ppm (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='04%) across the 1− 6 µm range and again at 10 µm, compared to K84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Even though both K84 and G18 optical properties were determined from tholins grown in an environment free of oxygen, we used the chemical and haze vertical profiles computed with C/O= 1000 in order to match the KI19 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We find that the optical properties derived from G18 tholins still differ from the results obtained with K84 opacities, producing ∼ ±250 ppm differences in the modeled transmission depths (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' CONCLUSIONS This work examines how spectral signatures of photochemical hazes, as informed by laboratory measurements, might constrain the C/O ratio of the atmosphere in which they formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The pioneering work of Khare et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (1984) provided broad-band optical properties for tholins, grown in an oxygen-free environment, and is a dominant template for photochemical haze widely in use for exoplanet transmission models today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Employing these optical properties in models of exoplanet atmospheric transmission comes with a biased assumption that those atmospheres are nearly devoid of oxygen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In Section 2, we present the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 − 10 µm optical properties of tholins grown in a gas chamber with increasing amounts of oxygen (Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' These tholins exhibit infrared spectral shapes around 1 − 3 µm, 6 µm, and 10 µm that are distinct from each other and from K84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In Section 3, we employ the new lab-measured tholin opacities to model the transmission spectrum of sub-Neptune GJ 1214 b, finding that these haze species are distinguishable from the K84 model by 200-1500 ppm, assuming Solar abundances of H and He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Figure 4 shows the observed optical-IR transmission spectrum of GJ 1214 b (Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D´esert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Fraine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kreidberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014) with the three ExoTransmit models of different C/O ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The transmission models have been renormalized to match the average 1 − 2 µm transit depth, for the sake of comparing the spectral shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' In the optical-IR (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 − 2 µm), lab-grown tholins exhibit a relatively Hazes as a probe of C/O ratio 9 clear transmission (low k) window that shifts towards longer wavelengths as the C/O ratio increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' However, the transmission spectrum in this wavelength range appears smooth, because scattering by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1 µm scale particles dominates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' At longer wavelenghts, hazes in a near-solar C/O atmosphere are predicted to exhibit a strong and narrow peak in the transmission spectrum around 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='8 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' As the abundance of oxygen decreases, this feature broadens and shifts redder by approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The relatively flat 6 − 8 µm absorption profile of the tholin species examined here makes it so that molecular features dominate the observed spectral shape around 8 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Thus overall, transmission spectra captured across the infrared wavelength range of 3 − 10 µm will be more suitable for identifying haze species and C/O ratios in GJ 1214 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' While Figure 4 does not demonstrate a real fit to the GJ 1214 b transit data, a few trends are visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5−2 µm data are more consistent with the near-Solar and C/O= 1 transmission models than those that employ haze opacities from tholins grown in Titan-like environments, where C/O= ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' However, the Spitzer data are more consistent with our high metallicity Z = 1000 calculation, while the high precision 1 − 2 µm data are not (Figure 4, bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This is consistent with the findings of Lavvas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (2019), who then require a haze formation yield ∼ 10 − 20% in order to match the transmission wavelength at shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The Kawashima & Ikoma (2018) models used in this work are more consistent with 1% haze formation efficiency scenarios from Lavvas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' (2019), with the caveat that average particle sizes from K19 are a factor of 3-10 larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The JWST observations of GJ 1214 b (Greene et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021) are likely to provide firmer insight for distinguishing among haze formation models and C/O ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' As noted in Section 3, the expected molecular abundances in sub-Neptune atmospheres are not identical to the laboratory environment in most tholin experiments, which are designed to mimic Titan and early-Earth conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The presence of particular molecules, not just bulk C:N:O ratios, affects the optical properties of photochemical hazes, their production efficiency, and particle size distribution (H¨orst & Tolbert 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Brass´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' H¨orst 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Ugelow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Recent experiments that simulate photochemical conditions in hot Jupiters with T > 1000 K inject doubt that hazes can form from CO and H2O in an H2 dominated atmosphere (Fleury et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Our transmission spectrum models rely on the theoretical predictions of Kawashima & Ikoma (2019), where hazes do form from HCN, C2H2, and CH4 in an H2 dominated atmosphere and temperatures spanning 500-1200 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Other aerosol production models also predict that Jupiter-like planets can form hazes from CH4 at Teq < 950 K (Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Despite these nuances, the optical properties of K84 are widely used as a template for chemical hazes in non-terrestrial environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' While the optical constants provided by this work are similarly imperfect for use with gas giants and sub-Neptunes, they provide a necessary advancement that is an improvement over the current practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Based on the laboratory data, we expect to be able to distinguish among hazes grown in different C/O ratio environments via strong C=O resonances observable around 6 µm, arising from the enhanced uptake of oxygen into the solid phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' If present, distinguishing among haze species in the atmosphere of a cool (< 800 K) planet with a H/He rich envelope is most plausible with the current generation of telescopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' We demonstrate that a model GJ 1214 b atmosphere that employs K84 optical constants to predict transmission spectra under the influence of haze obscuration could differ by 200-1500 ppm and, in the case of a solar C/O atmosphere, be underestimated by as much as 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' If the atmosphere of GJ 1214 b has a high mean molecular weight, represented by our Z=1000 simulation, ∼ 20 ppm sensitivity is required to distinguish among haze species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' This level of precision may be achievable with JWST for a select number of transiting sub-Neptunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Based on the experimental setup, the optical properties for these lab-grown tholins are even more relevant for temperate terrestrial planets, which will only be accessible by future generations of ground and space-based telescopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' The optical constants and size-dependent cross-sections of the tholins used in this work are publicly available in several formats that can be adapted for use by other open source transmission modeling tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A static version of eblur/newdust and the custom version of ExoTransmit, used to compute the cross-sections and transmission spectra, are also provided with this data release (doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7500026).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' REFERENCES Alcouffe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Cavarroc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Cernogora, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, Plasma Sources Science Technology, 19, 015008, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0963-0252/19/1/015008 Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Miller-Ricci Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Homeier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, Nature, 468, 669, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1038/nature09596 Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', D´esert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Kabath, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011, ApJ, 743, 92, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/743/1/92 Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Fu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021, Unlocking the Mysteries of the Archetype Sub-Neptune GJ1214b with a Full-Orbit Phase Curve, JWST Proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Cycle 1, ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' #1803 10 Corrales & Gavilan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Bertie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Lan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1995, JChPh, 103, 10152, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='469917 Bertie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1992, Canadian Journal of Chemistry, 70, 520, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1139/v92-074 Bohren, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Huffman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1983, Absorption and scattering of light by small particles Brass´e, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Mu˜noz, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Coll, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Raulin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', 109, 159, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='pss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='012 Charbonneau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Berta, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Irwin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2009, Nature, 462, 891, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1038/nature08679 Corrales, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2023, eblur/newdust: Python extinction and scattering halo calculations for astrophysical particulates, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='0, Zenodo, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='7500048 Corrales, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Garc´ıa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Wilms, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Baganoff, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016, MNRAS, 458, 1345, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1093/mnras/stw376 Dale Keefe, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2002, Journal of Molecular Structure, 641, 165, doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/S0022-2860(02)00184-9 de L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Kronig, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1926, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', 12, 547, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1364/JOSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='000547 D´esert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Miller-Ricci Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011, ApJL, 731, L40, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/2041-8205/731/2/L40 Fleury, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Gudipati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Henderson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Swain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, ApJ, 871, 158, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aaf79f —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020, ApJ, 899, 147, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aba828 Fraine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Gillon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013, ApJ, 765, 127, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/765/2/127 Gao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Benneke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJ, 863, 165, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aad461 Gao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Thorngren, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020, Nature Astronomy, 4, 951, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1038/s41550-020-1114-3 Gavilan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Carrasco, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Vrønning Hoffmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Jones, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Mason, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJ, 861, 110, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aac8df Gavilan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Remusat, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Roskosz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, ApJ, 840, 35, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aa6bfc Greene, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Beatty, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Rieke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Schlawin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, Transit Spectroscopy of Mature Planets, JWST Proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Cycle 1, ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' #1185 Hasenkopf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Beaver, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Trainer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, Icarus, 207, 903, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='015 Helling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Dobbs-Dixon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016, MNRAS, 460, 855, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1093/mnras/stw662 Helling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Iro, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Corrales, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, A&A, 631, A79, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1051/0004-6361/201935771 H¨orst, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, Journal of Geophysical Research (Planets), 122, 432, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1002/2016JE005240 H¨orst, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Tolbert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014, ApJ, 781, 53, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/781/1/53 Jovanovi´c, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Gautier, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Broch, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021, Icarus, 362, 114398, doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='114398 Kawashima, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Ikoma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJ, 853, 7, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aaa0c5 —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, ApJ, 877, 109, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/ab1b1d Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Lupu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Owusu-Asare, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Slough, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Cale, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, PASP, 129, 044402, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/1538-3873/aa61ef Khare, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Sagan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Arakawa, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1984, Icarus, 60, 127, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/0019-1035(84)90142-8 Kreidberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', D´esert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014, Nature, 505, 69, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1038/nature12888 Lavvas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Koskinen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Steinrueck, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Garc´ıa Mu˜noz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Showman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2019, ApJ, 878, 118, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/ab204e Lavvas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Yelle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Griffith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, Icarus, 210, 832, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='025 Lucarini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Saarinen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Peiponen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Vartiainen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2005, Kramers-Kronig relations in optical materials research, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 110 (Springer Science & Business Media) Mbarek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016, ApJ, 827, 121, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/0004-637X/827/2/121 McCullough, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Crouzet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2014, ApJ, 791, 55, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/791/1/55 Miller-Ricci, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, ApJL, 716, L74, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/2041-8205/716/1/L74 Miller-Ricci Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Zahnle, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2012, ApJ, 745, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/745/1/3 Morley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013, ApJ, 775, 33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/775/1/33 Morley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Marley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2015, ApJ, 815, 110, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/815/2/110 ¨Oberg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Bergin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021, PhR, 893, 1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='physrep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='004 Ohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Okuzumi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJ, 859, 34, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aabee3 Ohno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Okuzumi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Tazaki, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020, ApJ, 891, 131, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/ab44bd Ohta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Ishida, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1988, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', 42, 952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' http://as.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='osa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='org/abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='cfm?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='URI=as-42-6-952 Pont, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Gibson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2013, MNRAS, 432, 2917, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1093/mnras/stt651 Powell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Gao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Parmentier, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJ, 860, 18, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/aac215 Press, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Teukolsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Vetterling, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Flannery, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2007, Numerical Recipes 3rd Edition: The Art of Scientific Computing (Cambridge University Press) Hazes as a probe of C/O ratio 11 Rannou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Cours, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Le Mou´elic, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, Icarus, 208, 850, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='016 Roberts, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Ostriker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2017, MNRAS, 466, 1477, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1093/mnras/stw2995 Rogers, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Seager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2010, ApJ, 716, 1208, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1088/0004-637X/716/2/1208 S´anchez-L´opez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', L´opez-Puertas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Snellen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2020, A&A, 643, A24, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1051/0004-6361/202038629 Savitzky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Golay, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 1964, Analytical Chemistry, 36, 1627 Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Pont, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Aigrain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2011, MNRAS, 416, 1443, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='19142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='x Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Nikolov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2016, Nature, 529, 59, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1038/nature16068 Steinrueck, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Showman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Lavvas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2021, MNRAS, 504, 2783, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1093/mnras/stab1053 Szopa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Cernogora, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Boufendi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Correia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Coll, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2006, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', 54, 394, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='pss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='012 Teal, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Bastelberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Youngblood, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Arney, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2022, ApJ, 927, 90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/1538-4357/ac4d99 Tran, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Joseph, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Ferris, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', Persans, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Chera, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2003, Icarus, 165, 379, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='1016/S0019-1035(03)00209-4 Ugelow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', De Haan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', H¨orst, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=', & Tolbert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content=' 2018, ApJL, 859, L2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} +page_content='3847/2041-8213/aac2c7' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfKPti/content/2301.01093v1.pdf'} diff --git a/WtE1T4oBgHgl3EQfJAP_/content/2301.02948v1.pdf b/WtE1T4oBgHgl3EQfJAP_/content/2301.02948v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ff0ce1f2dce24d4c0ccbe6baffa4acd395a9e6a0 --- /dev/null +++ b/WtE1T4oBgHgl3EQfJAP_/content/2301.02948v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c7d1180ab18e697f6b8ff98a890f585ab8a903adc4d01c74f961cc80102023d8 +size 1455715 diff --git a/WtE1T4oBgHgl3EQfJAP_/vector_store/index.pkl b/WtE1T4oBgHgl3EQfJAP_/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..b4d253a4f30d0415630acd0ab072d417daeb137c --- /dev/null +++ b/WtE1T4oBgHgl3EQfJAP_/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:820631eaa388c4488684ceb208c93c5fe67ec979030fadc837fa0936708700b6 +size 203294 diff --git a/XtE4T4oBgHgl3EQfNgyO/content/2301.04957v1.pdf b/XtE4T4oBgHgl3EQfNgyO/content/2301.04957v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..51151df3892a6d0eacd0cc4452d3a35d809b1989 --- /dev/null +++ b/XtE4T4oBgHgl3EQfNgyO/content/2301.04957v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1c83df327390e75c3e516a5b8bb6dd4cbae888117173cc9a4a2b6b9243763af2 +size 1807983 diff --git a/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/2301.11294v1.pdf.txt b/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/2301.11294v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d8c62bf00187f1a8e69d2fb113b19104a7f68c36 --- /dev/null +++ b/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/2301.11294v1.pdf.txt @@ -0,0 +1,3154 @@ +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +Louis Sharrock 1 Christopher Nemeth 1 +Abstract +In recent years, particle-based variational infer- +ence (ParVI) methods such as Stein variational +gradient descent (SVGD) have grown in popular- +ity as scalable methods for Bayesian inference. +Unfortunately, the properties of such methods in- +variably depend on hyperparameters such as the +learning rate, which must be carefully tuned by +the practitioner in order to ensure convergence +to the target measure at a suitable rate. In this +paper, we introduce a suite of new particle-based +methods for scalable Bayesian inference based on +coin betting, which are entirely learning-rate free. +We illustrate the performance of our approach on +a range of numerical examples, including several +high-dimensional models and datasets, demon- +strating comparable performance to other ParVI +algorithms. +1. Introduction +The task of sampling from complex, high-dimensional +probability distributions is of fundamental importance to +Bayesian inference (Robert & Casella, 2004; Gelman et al., +2013), machine learning (Neal, 1996; Andrieu et al., 2003; +Welling & Teh, 2011; Wilson & Izmailov, 2020), molecular +dynamics (Krauth, 2006; Leli`evre & Stoltz, 2016; Leimkuh- +ler & Matthews, 2016), and scientific computing (MacKay, +2003; Liu, 2009). In this paper, we consider the canonical +task of sampling from a probability distribution π(dx) on +Rd with density π(x) with respect to the Lebesgue measure +of the form1 +π(x) := exp (−U(x)) +Z +(1) +where U : Rd → R is a measurable, continuously dif- +ferentiable function known as the potential, and Z = +� +Rd exp(−U(x))dx is an unknown normalising constant. +1Department of Mathematics, Lancaster University, UK. Corre- +spondence to: Louis Sharrock . +1In a slight abuse of notation, we use π to denote both the +measure and its density. +Recently, there has been growing interest in hybrid methods +which combine the non-parametric nature of Markov chain +Monte Carlo (MCMC) sampling with parameteric approxi- +mations using optimisation-based variational inference (VI). +In particular, particle based variational inference (ParVI) +methods (Liu & Wang, 2016; Chen et al., 2018a; Liu et al., +2019a; Chewi et al., 2020; Korba et al., 2021) approximate +the target distribution using an ensemble of interacting par- +ticles, which are deterministically updated by minimising +the Kullback-Leibler (KL) divergence. +Perhaps the most well known of these methods is Stein vari- +ational gradient descent (SVGD). This algorithm iteratively +updates the particles according to a form of gradient descent +on the KL divergence, with the descent direction restricted +to belong to a unit ball in a reproducing kernel Hilbert space +(RKHS) (Liu & Wang, 2016). This approach has since given +rise to several variants (Liu, 2017; Han & Liu, 2018; Liu & +Zhu, 2018; Zhuo et al., 2018; Chen et al., 2018b; Detom- +maso et al., 2018; Futami et al., 2019a;b; Wang et al., 2019; +Chen & Ghattas, 2020; Ye et al., 2020; Liu et al., 2022; Sun +& Richt´arik, 2022); and found success in a range of prob- +lems, including uncertainty quantification (Zhu & Zabaras, +2018), reinforcement learning (Haarnoja et al., 2017; Liu +et al., 2017; Zhang et al., 2018), learning deep probabilistic +models (Pu et al., 2017; Wang & Liu, 2017), and Bayesian +meta-learning (Feng et al., 2017; Yoon et al., 2018). +In order to construct and analyse sampling algorithms of this +type, one popular approach is to reformulate the sampling +problem as an optimisation problem in the space of measures +(Jordan et al., 1998; Liu, 2017; Wibisono, 2018; Cheng & +Bartlett, 2018; Durmus et al., 2019). In this setting, one +views the target π as the solution of an optimisation problem +π = arg min +µ∈P2(Rd) +F(µ), +(2) +where P2(Rd) denotes the set of probability measures {µ : +� +Rd ||x||2µ(dx) < ∞}, and F : P(Rd) → R is a functional +which is uniquely minimised at π. A general strategy for +solving this problem is then to simulate a time-discretisation +of the gradient flow of F over P2(Rd), having equipped this +space with a suitable metric (Ambrosio et al., 2008). +Many popular sampling algorithms can be understood from +this perspective. +For example, Langevin Monte Carlo +(LMC), a popular MCMC algorithm, corresponds to the +arXiv:2301.11294v1 [stat.ML] 26 Jan 2023 + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +2 +(a) Bivariate Gaussian +(b) Mixture of Bivariate Gaussians +(c) ‘Donut’ Distribution +(d) Rosenbrock Distribution +(e) ‘Squiggle’ Distribution +(f) ‘Funnel’ Distribution +Figure 1. A comparison between SVGD (Liu & Wang, 2016) and its learning-rate free analogue, Coin SVGD (Algorithm 2). We +plot the samples generated by both methods for several two-dimensional target distributions. Further details are provided in Section 4.1 +and Appendix E.1. +so-called forward-flow discretisation of the gradient flow of +the KL divergence with respect to the quadratic Wasserstein +metric (Wibisono, 2018; Durmus et al., 2019).2 Meanwhile, +SVGD can be viewed as the explicit Euler discretisation of +the gradient flow of the KL divergence with respect to a ker- +nelised Wasserstein metric (Liu, 2017; Duncan et al., 2019). +Other more recent examples, designed with this perspec- +tive in mind, include maximum mean discrepancy (MMD) +gradient descent (Arbel et al., 2019), the Wasserstein prox- +imal gradient algorithm (Salim et al., 2020), kernel Stein +discrepancy descent (KSDD) (Korba et al., 2021), Laplacian +adjusted Wasserstein gradient descent (LAWGD) (Chewi +et al., 2020), mollified energy interaction descent (MEID) +(Li et al., 2022), and the various other ParVI methods de- +scribed in (Chen et al., 2018a; Liu et al., 2019a;b). +One feature common to all of these approaches is the need +to specify an appropriate learning rate (i.e., step size) γ, or +a learning rate schedule (γt)t≥1. This learning rate must be +sufficiently small to ensure convergence to the target mea- +sure, or a close approximation thereof, but also large enough +to ensure convergence within a reasonable time period. In +theory, for a given target π, existing non-asymptotic conver- +gence rates allow one to derive an optimal learning rate (see, +e.g., Korba et al., 2020; Salim et al., 2022; Sun & Richt´arik, +2022 for SVGD; Dalalyan, 2017a;b; Durmus & Moulines, +2017; Dalalyan & Karagulyan, 2019; Durmus & Moulines, +2The connection between the law of the overdamped Langevin +diffusion (i.e., the continuous-time dynamics of LMC) and the +gradient flow of the KL divergence dates back to Otto et al. (Jordan +et al., 1998; Otto, 2001; Otto & Westdickenberg, 2005). +2019 for LMC). Invariably, however, the optimal learning +rate is a function of the unknown target measure (e.g., Corol- +lary 6 in Korba et al., 2020; Theorem 9 in Durmus et al., +2019) and thus, in practice, cannot be computed. +With these considerations in mind, a natural question is +whether one can obtain a gradient-based sampling method +which does not require a learning rate. In this paper, we an- +swer this question in the affirmative. In particular, inspired +by the parameter-free optimisation methods developed by +Orabona and coworkers (Orabona, 2014; Orabona & Pal, +2016; Orabona & Tommasi, 2017; Cutkosky & Orabona, +2018; Jun & Orabona, 2019; Chen et al., 2022a), and lever- +aging the view of sampling as an optimisation problem in +the space of measures (Wibisono, 2018), we obtain a new +suite of particle-based algorithms for scalable Bayesian in- +ference which are entirely learning rate free. Similar to other +ParVIs, our algorithms deterministically update an ensem- +ble of interacting particles in order to approximate the target +distribution. However, unlike other ParVIs, our algorithms +do not correspond to the time-discretisation of any gradient +flow, and thus bear little resemblance to existing methods. +Under the assumption of log-concavity, we outline how to +establish convergence to the target measure in the infinite- +particle regime, and how to obtain a non-asymptotic con- +vergence rate. We then illustrate the performance of our +approach on a range of numerical examples, including both +convex and non-convex targets. Our results indicate that the +proposed methodology achieves comparable performance +to existing particle-based sampling algorithms in a range of +tasks, with no need to tune a learning rate. + +SVGD +Coin-SVGDSVGD +Coin-SVGDSVGD +Coin-SVGDSVGD +Coin-SVGDSVGD +Coin-SVGDSVGD +Coin-SVGDCoin Sampling: Gradient-Based Bayesian Inference without Learning Rates +3 +2. Preliminaries +2.1. Optimisation in Euclidean Space +We begin by reviewing optimisation in Euclidean spaces, +focusing on the learning-rate free stochastic optimisation +method introduced by Orabona & Pal (2016). This will later +provide the foundation for our learning-rate free sampling +method. +2.1.1. NOTATION +Let X ⊆ Rd, and write ||·|| and ⟨·, ·⟩ for the Euclidean norm +and inner product in Rd. Let f : X → R ∪ {−∞, ∞}, and +let f ∗ : X ∗ → R ∪ {−∞, ∞} denote the Fenchel conjugate +of f, so that f ∗(u) = supx∈X [⟨u, x⟩ − f(x)]. +Suppose that f is m-strongly convex, for some m ≥ 0. Let +x ∈ X. We say that g ∈ X is a subgradient of f at x, and +write g ∈ ∂f(x) if, for any z ∈ X, +f(z) − f(x) ≥ ⟨g, z − x⟩ + m +2 ||z − x||2 +(3) +If f is differentiable at x, then the differential set ∂f(x) con- +tains a single element, ∂f(x) = {∇f(x)}, where ∇f(x) +denotes the gradient of f at x. +2.1.2. EUCLIDEAN GRADIENT FLOWS +Suppose we are interested in the optimisation problem +x∗ = arg min +x∈X +f(x), +(4) +where f : X → R is m-strongly convex. We can solve this +problem using the gradient flow of f, defined as the solution +x : [0, ∞) → Rd of the following differential inclusion +˙xt ∈ −∂f(xt), +(5) +with initial condition x0 = xinit. This inclusion admits a +unique, absolutely continuous solution for almost all t ≥ 0 +(e.g., Theorem 3.1 in Br´ezis, 1973, Theorem 2.7 in Pey- +pouquet & Sorin, 2010; Proposition 2.1 in Santambrogio, +2017). Moreover, the function t �→ f(xt) is decreasing, +with limt→∞ f(xt) = infx∈X f(x) (Peypouquet & Sorin, +2010, Proposition 3.1). +In practice, it is necessary to use a time-discretisation of +this gradient flow. One standard choice is a backward Euler +discretisation, which results in the proximal point algorithm +(G¨uler, 1991; De Giorgi, 1993) Alternatively, one can utilise +a forward Euler discretisation, which results in the standard +subgradient descent algorithm (Shor, 1985) +xt+1 = xt + γ∇gt , +gt ∈ ∂f(xt). +(6) +The properties of this algorithm depend, necessarily, on +the choice of learning rate γ > 0. For example, given +an L-Lipschitz function, it is well known that the average +of the algorithm iterates ¯xT = +1 +T +�T +t=1 xt satisfies (e.g., +Zinkevich, 2003) +f (¯xT ) − f(x∗) ≤ 1 +T +�||x1 − x∗||2 +2γ ++ L2Tγ +2 +� +. +(7) +Using this expression, one can obtain the ‘ideal’ learning +rate as γideal = ||x1−x∗|| +L +√ +T +, which implies the optimal error +bound +f(¯xT ) − f(x∗) ≤ L||x1 − x∗|| +√ +T +. +(8) +In practice, however, it is not possible to achieve this bound. +Indeed, even in hindsight, one cannot compute the ideal +learning rate γideal, since it depends on the unknown ||x1 − +x∗||. +2.1.3. LEARNING-RATE FREE GRADIENT DESCENT +Following Orabona & Pal (2016), we now outline an al- +ternative approach for solving the stochastic optimisation +problem in (4) which is entirely learning-rate free. Consider +a gambler who bets on the outcomes of a series of adver- +sarial coin flips. Suppose that the gambler starts with an +initial wealth w0 = ε > 0. In the tth round, the gambler +bets on the outcome of a coin flip ct ∈ {−1, 1}, where +1 +denotes heads and −1 denotes tails. For now, we make no +assumptions on how ct is generated. +We will encode the gambler’s bet in the tth round by xt ∈ R. +In particular, sign(xt) ∈ {−1, 1} will denote whether the +bet is on heads or tails, and |xt| ∈ R will denote the size +of the bet. Thus, in the tth round, the gambler wins xtct if +sign(ct) = sign(xt); and loses xtct otherwise. Finally, we +will write wt for the wealth of the gambler at the end of the +tth round. Clearly, we then have that +wt = ε + +t +� +i=1 +cixi. +(9) +We will restrict our attention to the case in which the gam- +bler’s bets satisfy xt = βtwt−1, for some betting fraction +βt ∈ [−1, 1]. This is equivalent to the assumption that the +gambler cannot borrow any money. +We will now outline how to solve the convex optimisation +problem x∗ = arg minx∈R f(x) using a coin-betting algo- +rithm. For simplicity, we will restrict our attention to the +simple one-dimensional function f(x) = |x − 10|. We +note, however, that this approach can easily be extended to +any convex function f : Rd → R (Orabona & Pal, 2016). +Suppose we define the outcome of a coin flip ct ∈ {−1, 1} +to be equal to −gt ∈ ∂[−f(xt)], the negative subgradient +of f(xt). In this case, under a certain assumption on the +betting strategy (βt)T +t=1, Orabona & Pal (2016) show that +the average of bets f(¯xT ) converges to f(x∗), with a rate +which depends on the quality of the betting strategy. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +4 +Lemma 2.1. Suppose that the betting strategy (βt)T +t=1 guar- +antees that, for any sequence of coin flips (ct)T +t=1 ∈ [−1, 1], +there exists a function h : R → R such that the wealth after +T rounds satisfies wT ≥ h(�T +t=1 ct). Then +f +� +1 +T +T +� +t=1 +xt +� +− f(x∗) ≤ h∗(x∗) + ε +T +(10) +Proof. See Appendix B. +We can thus use any suitable coin-betting algorithm to obtain +x∗ = arg minx∈R f(x), given access to the subgradients of +f. Any such algorithm will be entirely learning-rate free. +There are various betting strategies which satisfy the inequal- +ity wT ≥ h(�T +t=1 ct) (e.g., Orabona & Pal, 2016; Orabona +& Tommasi, 2017; Chen et al., 2022a). Perhaps the simplest +such strategy is one based on the Krichevsky-Trofimov (KT) +estimator (Krichevsky & Trofimov, 1981), which defines +the betting strategy to be equal to βt = �t−1 +i=1 ci/t. This +results in the coin betting algorithm +xt = − +�t−1 +i=1 gi +t +� +ε − +t−1 +� +i=1 +gixi +� +. +(11) +In this case, it is possible to show (Orabona & Pal, 2016, +Lemma 14) that the wealth is lower bounded by +h +� T +� +t=1 +ct +� += +ε +K +√ +T +exp +���T +t=1 ct +�2 +2T +� +, +(12) +where K is a universal constant. Thus, using Lemma 2.1 +and an appropriate bound on the convex conjugate of h, one +obtains (Orabona & Pal, 2016, Corollary 5) +f(¯xT ) − f(x∗) ≤ K +||x∗|| +� +log(1 + 24T 2||x∗||2 +ε2 +) + ε +√ +T +. +(13) +It is instructive to compare this bound with (8), the corre- +sponding bound for subgradient descent with an optimally +chosen learning rate. Although the coin-betting approach +does not quite achieve the optimal bound in (8), it comes +close, containing only an additional log-factor. This can be +viewed as the trade-off for the fact that the algorithm is now +learning-rate free. +3. Coin Sampling for Bayesian Inference +Our approach, summarised in Algorithm 1, can be viewed +as a natural extension of the learning-rate free optimisa- +tion methods introduced in Section 2.1.3 to the Wasserstein +space. In particular, coin sampling utilises Wasserstein gra- +dients, approximated via a set of interacting particles, within +the coin-betting framework, to obtain a learning-rate free +Bayesian inference algorithm. +3.1. Optimisation in Wasserstein Space +To extend coin betting to our setting, we will require some +basic concepts from optimal transport, including the defini- +tion of the Wasserstein space and Wasserstein gradient flow. +We provide additional details on geodesic convexity and +subdifferential calculus in Appendix A; see also the books +of Ambrosio et al. (2008) and Villani (2008). +3.1.1. THE WASSERSTEIN SPACE +For p ≥ 1, let Pp(Rd) denote the set of probability measures +on Rd with finite pth moment: +� +Rd ||x||pµ(dx) < ∞. For +any µ ∈ Pp(Rd), let Lp(µ) denote the set of measurable +functions f : Rd → Rd such that +� +Rd ||f(x)||pµ(dx) < ∞. +We will write ||·||2 +L2(µ) and ⟨·, ·⟩L2(µ) to denote, respectively, +the norm and the inner product of this space. +Given a probability measure µ ∈ P2(Rd) and a mea- +surable function T : Rd → Rd, we write T#µ for the +pushforward measure of µ under T, that is, the measure +such that T#µ(B) = µ(T −1(B)) for all Borel measurable +B ∈ B(Rd). For every µ, ν ∈ Pp(Rd), let Γ(µ, ν) be the +set of couplings (or transport plans) between µ and ν, de- +fined as Γ(µ, ν) = {γ ∈ Pp(Rd) : Q1 +#γ = µ, Q2 +#γ = ν}, +where Q1 and Q2 denote the projections onto the first and +second components of Rd × Rd. The Wasserstein p-distance +between µ and ν is then defined according to +W p +p (µ, ν) = +inf +γ∈Γ(µ,ν) +� +Rd×Rd ||x − y||pγ(dx, dy). +(14) +The Wasserstein distance W2 is a distance over P2(Rd). +Thus (P2(Rd), W2) is a metric space of probability mea- +sures, known as the Wasserstein space. One important +property of W2 is that, under certain regularity conditions, +there exists a unique optimal coupling γ∗ ∈ Γ(µ, ν) which +minimises the transport cost +� +Rd×Rd ||x − y||pγ∗(dx, dy). +This optimal coupling is of the form γ = (id × tν +µ)#µ, +where id : Rd → Rd is the identity map, and tν +µ is +known as the optimal transport map (Brenier, 1991; Gigli, +2011). +It follows that (tν +µ)#µ = ν and W 2 +2 (µ, ν) = +� +Rd ||x − y||2γ∗(dx, dy) = +� +Rd ||x − tν +µ(x)||2dx. +3.1.2. WASSERSTEIN GRADIENT FLOWS +Recall the optimisation problem from Section 1, +π = arg min +µ∈P2(Rd) +F(µ), +(15) +where F : P2(Rd) → (−∞, ∞] is a proper, lower semi- +continuous functional uniquely minimised at π. There are +various possible choices for the functional F (see, e.g., +Simon-Gabriel, 2018). In the context of Bayesian inference, +perhaps the most common choice is KL(µ|π), the Kullback- +Leibler (KL) divergence of µ with respect to π. Other + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +5 +possibilities include the chi-squared divergence X 2(µ|π) +(Chewi et al., 2020), and the maximum mean discrepancy +MMD(µ|π) (Arbel et al., 2019), of which the kernel Stein +discrepancy KSD(µ|π) (Korba et al., 2021) is a special case. +Similarly to the Euclidean case, typical solutions to (15) +are based on the use of a gradient flow. In particular, we +now consider the Wasserstein gradient flow of F, defined +as the weak solution µ : [0, ∞) → P2(Rd) of the continuity +equation (Ambrosio et al., 2008, Chapter 11) +∂tµt + ∇ · (vtµt) = 0 , +vt ∈ −∂F(µt). +(16) +where ∂F(µ) denotes the Fr´echet subdifferential ∂F(µ) +of F at µ (see Appendix A). Under mild conditions, this +equation admits a unique solution for any initial condi- +tion (e.g., Theorem 11.1.4 and Theorem 11.2.1 in Ambro- +sio et al., 2008; Proposition 4.13 in Santambrogio, 2017). +In addition, the function t �→ F(µt) is decreasing, so +that limt→∞ F(µt) = infµ∈P2(Rd) F(µ) (Ambrosio et al., +2008, Chapter 11). +3.1.3. DISCRETISED WASSERSTEIN GRADIENT FLOWS +For practical purposes, it is once more necessary to discre- +tise the gradient flow in (16). Several popular approaches ex- +ist, including the backward Euler discretisation, which cor- +responds to the minimising movement scheme (MMS) (Am- +brosio et al., 2008, Definition 2.0.6) or Jordan-Kinderlehrer- +Otto (JKO) scheme (Jordan et al., 1998). Another natu- +ral choice for discretising (16) is a forward Euler scheme, +which yields the Wasserstein (sub)gradient descent algo- +rithm (e.g., Guo et al., 2022) +µt+1 = (id − γξt)# µt , +ξt ∈ ∂F(µt). +(17) +For different choices of the functional F, this discretisation +yields the population limit of several existing particle-based +algorithms. These include MMD gradient descent (Arbel +et al., 2019), KSDD (Korba et al., 2021), and, replacing the +Wasserstein gradient (17) by a kernel approximation, SVGD +(Liu & Wang, 2016) and LAWGD (Chewi et al., 2020). +Regardless of the choice of numerical discretisation, the +properties of the resulting algorithm depend, necessarily, on +the choice of learning rate γ > 0. To illustrate this point, we +recall the following bound for the Wasserstein subgradient +descent algorithm (Guo et al., 2022, Theorem 8) +F +� +1 +T +T +� +t=1 +µt +� +− F(π) ≤ 1 +T +�W 2 +2 (µ1, π) +2γ ++ L2Tγ +2 +� +, +(18) +which holds under the assumption that the Wasserstein sub- +gradients ||ξt||L2(µt) ≤ L. We note that a similar bound +also holds for the Langevin Monte Carlo (LMC) algorithm +(Durmus et al., 2019, Section 3). +Based on (18), the optimal worst case learning rate is given +by γideal = W2(µ1,π) +L +√ +T +, and thus the optimal error bound as +F +� 1 +T +T +� +t=1 +µt +� +− F(π) ≤ LW2(µ1, π) +√ +T +. +(19) +Similar to the Euclidean case, however, this rate cannot be +achieved in practice. In particular, computing γideal now +depends on the unknown Wasserstein distance W2(µ1, π). +3.2. Coin Wasserstein Gradient Descent +We now introduce an alternative approach to solving the +optimisation problem in (15), which is entirely learning rate +free. Consider an infinite set of gamblers, indexed by x0 ∈ +Rd. We will assume that the gamblers have initial wealth +w0 := w0(x0), where w0 : Rd → R≥ε, ε > 0. Similar to +before, in the tth round, each gambler bets xt(x0) ∈ Rd on +the outcome ct(x0) ∈ Rd, and earns ⟨xt(x0), ct(x0)⟩. Once +again, we assume the bets satisfy xt(x0) = βtwt−1(x0), +for some betting fraction βt(x0) ∈ [−1, 1]d. +Importantly, will now view xt : Rd → Rd as a function, +which defines the bets associated with gambler x0 ∈ Rd. +Similarly, wt : Rd → Rε, ct : Rd → Rd, and βt : Rd → +[−1, 1]d are now all to be viewed as functions. We also now +introduce a betting distribution µx +t ∈ P2(Rd), defined as the +push-forward of some initial betting distribution, µx +0, under +the betting function xt : Rd → Rd. This definitions is quite +natural. In particular, it implies that, for a gambler x0 ∼ µx +0, +the bet xt := xt(x0) made by this gambler are distributed +according to the betting distribution µx +t . +To obtain the parameter-free Wasserstein gradient descent +algorithm, we will assume that the outcomes observed +by the gambler x0 ∈ Rd, are given by the normalised +Wasserstein gradients ct(x0) = − 1 +L∇W2F(µt)(xt(x0)), +where L is the constant defined in Assumption 3.2. We +will also suppose that this gambler’s betting fraction is +βt(x0) = 1 +t +�t−1 +s=1 cs(x0). This leads to Algorithm 1. +3.3. Main Results +We will establish convergence of Algorithm 1 under the +following general assumptions, in addition to a technical +assumption in Appendix B. +Assumption 3.1. The functional F : P2(Rd) → (−∞, ∞] +is (i) proper and lower semi-continuous, and (ii) geodesi- +cally convex. +Assumption 3.2. There exists L > 0 such that, for all +u ∈ Rd, ||∇W2F(µx +t )(u)|| ≤ L. +Assumption 3.1(i) is a general technical condition satisfied +in all relevant cases (e.g., Ambrosio et al., 2008, Section 10). +Assumption 3.1(ii) is a standard condition used in the analy- +sis of existing sampling algorithms such as LMC (Wibisono, + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +6 +Algorithm 1 Coin Wasserstein Gradient Descent +Input: initial measure µx +0 ∈ P2(Rd), initial parameter x0 ∼ µx +0 or x0 ∈ Rd, initial wealth function w0 : Rd → R≥ε +satisfying w0 ∈ L2(µx +0), functional F : P2(Rd) → (−∞, ∞], constant L. +for t = 1 to T do +Compute +xt(x0) = − +�t−1 +s=1 ∇W2F(µx +s)(xs(x0)) +Lt +� +w0(x0) − +t−1 +� +s=1 +⟨ 1 +L∇W2F(µx +s)(xs(x0)), xs(x0)⟩ +� +. +(20) +Define µx +t = (xt)#µx +0. +Output: µx +T or 1 +T +�T +t=1 µx +t . +2018; Durmus & Moulines, 2019).3 This assumptions holds +if F(µ) = KL(µ|π), and the potential U : Rd → R is +convex (Ambrosio et al., 2008, Section 9.4). +To our knowledge, Assumption 3.2 has also only explicitly +appeared in the analysis of the Wasserstein subgradient +descent algorithm in Guo et al. (2022). However, similar +conditions have also been used to analyse the convergence +of SVGD to its population limit (Liu et al., 2017, Theorem +3.2; Korba et al., 2020, Proposition 7). On the other hand, +convergence rates for SVGD (in the infinite particle regime) +can be established under boundedness assumptions for the +kernel function and either the KSD of the algorithm iterates +(Liu et al., 2017), the Stein Fisher information (Korba et al., +2020), or the Hessian of the potential (Salim et al., 2022; +Shi et al., 2022). +Theorem 3.3. Let Assumptions 3.1 - 3.2 and Assumption +B.1 (see Appendix B) hold. Then +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +� � +Rd w0(x)µx +0(dx) +(21) ++ +� +Rd ||x|| +� +� +� +�T ln +� +1 + 24K2 +1T 2 ||x||2 +ε2 +� +π(dx) +� +. +Proof. See Appendix B. +The proof of Theorem 3.3 closely follows the proof used +to establish the convergence rate of the parameter-free opti- +misation algorithm in Orabona & Pal (2016). In our case, +however, it is no longer evident how to convert a lower +bound on the wealth into an upper bound on the regret (see +Lemma 2.1). In Appendix B, we provide a technical con- +dition (Assumption B.1) which allow us to obtain the rate +in Theorem 3.3. It remains an interesting direction for fu- +ture work to obtain more easily verifiable conditions under +which this result still holds. +3We note that one can establish convergence rates for LMC +under weaker conditions, such as the log-Sobolev inequality (LSI) +or the Poincar´e inequality (PI) (Vempala & Wibisono, 2019). Simi- +larly, convergence of SVGD can be established using the Stein LSI +(Duncan et al., 2019; Korba et al., 2020), Talagrand’s inequality +(Salim et al., 2022; Shi et al., 2022), or the PI (Chewi et al., 2020). +3.4. Practical Implementation +In practice, we do not directly observe the vector fields +∇W2F(µx +t ). Indeed, these quantities depend on knowl- +edge of the measures µx +t , which typically we cannot +compute in closed form. +Following existing ParVIs, a +standard approach is to approximate these quantities us- +ing a set of interacting particles. +In particular, sup- +pose we initialise (xi +0)N +i=1 +i.i.d. +∼ µx +0(dx), with empirical law +µN +0 = 1 +N +�n +i=1 δxi +0. We can then update the particles ac- +cording to an empirical version of (20). This yields, after +each iteration, particles (xi +t)N +i=1, with empirical distribution +µx,N +t += 1 +N +�N +i=1 δxi +t. +This approach relies, crucially, on being able to compute, or +approximate ∇W2{F(µx,N +t +)}t∈[0,T ], the Wasserstein gradi- +ents of F evaluated at {µx,N +t +}t∈[0,T ]. Fortunately, a similar +step is also central to existing particle-based sampling al- +gorithms, including SVGD (Liu & Wang, 2016), KSDD +(Korba et al., 2020), and LAWGD (Chewi et al., 2020). We +can thus use existing methods to compute these terms. In +fact, as outlined in Appendix C, we can obtain learning-rate +free versions of SVGD (Section C.1), LAWGD (Section +C.2), and KSDD (Section C.3). We refer to these algorithms +as Coin SVGD, Coin LAWGD, and Coin KSD, respectively. +In principle, our approach also requires knowledge of a +bound on the Wasserstein gradients (see Assumption 3.2). +In practice, we will adaptively estimate this constant using a +similar approach to the one outlined in Orabona & Tommasi +(2017). We provide full details in Appendix D. +4. Numerical Results +In this section, we evaluate the numerical performance of +Coin SVGD (Algorithm 2), Coin LAWGD (Algorithm 3), +and Coin KSDD (Algorithm 4). In all cases, we implement +the adaptive versions of these algorithms (see Appendix D). +We use the RBF kernel k(x, x′) = exp(− 1 +h||x−x′||2 +2), with +bandwidth chosen using the median heuristic in Liu & Wang +(2016). The code to reproduce all results will be available +on GitHub post-review. Additional implementation +details and results are provided in Appendix E. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +7 +4.1. Toy Examples +We begin by illustrating the performance of Coin SVGD +on a series of toy examples (see Appendix E.1 for details). +In the interest of space, results for Coin LAWGD and Coin +KSDD are deferred to Appendices E.2 and E.3. +In Figure 1 (see Section 1), we plot the sampling approx- +imations generated by SVGD and Coin SVGD after 1000 +iterations, using 20 particles. Encouragingly, Coin SVGD +converges to the target distribution in all cases, even those +which do not satisfy the assumptions of our theorem (e.g., +convexity). In fact, further simulations indicate that the +performance of Coin SVGD is competitive with the best +performance of SVGD, when using the optimal but a priori +unknown learning rate (see Figure 7 in Appendix E.1). +4.2. Bayesian Independent Component Analysis +We next consider a Bayesian independent component analy- +sis (ICA) model (e.g., Comon, 1994). Suppose we observe +x ∈ Rp. The task of ICA is to infer the ‘unmixing ma- +trix’ W ∈ Rp×p such that x = W−1s, where s ∈ Rp +denote the latent independent sources. We will assume each +component si has the same density: si ∼ ps. The log- +likelihood of this model is then given by log p(x|W) = +log |W| + �p +i=1 ps([Wx]i). For the prior, we assume that +the entries of W are i.i.d., with law N(0, 1). The posterior +is then p(W|x) ∝ p(x|W)p(W), with +∇W log p(W|x) = (W−1)T − p′ +s(Wx) +ps(Wx)xT − W (22) +where ps is chosen such that p′ +s(·) +ps(·) = tanh(·). We are in- +terested in sampling from p(W|x). In our experiments, +we generate 1000 samples of x from the ICA model, for +p ∈ {2, 4, 8, 16}. We use N = 10 particles, and repeat each +experiment 50 times. To assess convergence, we compute +the Amari distance (Amari et al., 1995) between the true W +and the estimates { ¯ +Wi}10 +i=1 generated by each algorithm. +We run SVGD for three learning rate: the optimal rate, tuned +when p = 2, and a smaller and larger learning rate. +Our results are plotted in Figure 2. For p = 2, the per- +formance of Coin SVGD is similar to the performance of +SVGD with the optimal learning rate. For p ∈ {4, 8, 16}, +the gap between the performance of Coin SVGD and SVGD +increases. In particular, as we increase the dimension, Coin +SVGD increasingly outperforms SVGD with the original +optimal learning rate. In some sense, these results are unsur- +prising. The learning rate for SVGD was tuned with p = 2, +and it should not necessarily perform well for p ∈ {4, 8, 16}. +At the same time, these results illustrate the advantages of +our algorithm: Coin SVGD requires no tuning, yet still +performs robustly across all of these experiments. +0 +100 +200 +300 +400 +500 +Sample +10 +5 +10 +4 +10 +3 +10 +2 +10 +1 +100 +Amari Distance +SVGD ('good' step) +SVGD ('small' step) +SVGD ('large' step) +Coin SVGD +Random +(a) p = 2 +0 +100 +200 +300 +400 +500 +Sample +100 +Amari Distance +SVGD ('good' step) +SVGD ('small' step) +SVGD ('large' step) +Coin SVGD +Random +(b) p = 4 +0 +100 +200 +300 +400 +500 +Sample +2 × 100 +3 × 100 +4 × 100 +6 × 100 +Amari Distance +SVGD ('good' step) +SVGD ('small' step) +SVGD ('large' step) +Coin SVGD +Random +(c) p = 8 +0 +100 +200 +300 +400 +500 +Sample +10 +1 +100 +Amari Distance +SVGD ('good' step) +SVGD ('small' step) +SVGD ('large' step) +Coin SVGD +Random +(d) p = 16 +Figure 2. Results for the Bayesian ICA model: Amari distances +between the true unmixing matrix and the estimated unmixing +matrices output by SVGD and Coin SVGD (lower is better). +4.3. Bayesian Logistic Regression +We next consider the Bayesian logistic regression model +for binary classification, as described in Gershman et al. +(2012). Let D = {xi, yi}N +i=1 be a dataset with feature +vectors xi ∈ Rp, and binary labels yi ∈ {−1, 1}. We +assume that p(yi = 1|xi, w) = (1 + exp(−wT xi))−1, +for some w ∈ Rp. We place a Gaussian prior p(w|α) = +N(w|0, α−1) on the regression weights w, and a Gamma +prior p(α) = Gamma(α|1, 0.01) on α ∈ R+. +We would like to sample from p(θ|D), where the parameter +of interest is given by θ = [w, log α]T ∈ Rp+1. We test our +algorithm using the Covertype dataset, which consists of +581,012 data points and 54 features. We randomly partition +the data into a training dataset (70%), validation dataset +(10%), and testing dataset (20%). We compute stochastic +gradients using mini-batches of size 100. +Our results are plotted in Figures 3 and 4. Similar to be- +fore, the performance of Coin SVGD is similar to the best +10 +4 +10 +3 +10 +2 +10 +1 +Step Size +0.50 +0.55 +0.60 +0.65 +0.70 +0.75 +Predictive Accuracy +SVGD +Coin SVGD +(a) Test Accuracy +10 +4 +10 +3 +10 +2 +10 +1 +Step Size +0.525 +0.550 +0.575 +0.600 +0.625 +0.650 +0.675 +0.700 +Negative Log-Likelihood +SVGD +Coin SVGD +(b) Negative Log-Likelihood +Figure 3. Results for the Bayesian logistic regression model: +test-accuracy and the log-likelihood for SVGD and Coin SVGD. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +8 +0 +500 +1000 +1500 +2000 +2500 +Iterations +0.50 +0.55 +0.60 +0.65 +0.70 +0.75 +Predictive Accuracy +SVGD (optimal step) +SVGD (small step) +SVGD (big step) +Coin SVGD +(a) Test Accuracy +0 +500 +1000 +1500 +2000 +2500 +Iterations +0.55 +0.60 +0.65 +0.70 +0.75 +0.80 +0.85 +Negative Log-Likelihood +SVGD (optimal step) +SVGD (small step) +SVGD (big step) +Coin SVGD +(b) Negative Log-Likelihood +Figure 4. Results for the Bayesian logistic regression model: +test-accuracy and the log-likelihood for SVGD (three learning +rates) and Coin SVGD as a function of the number of iterations. +performance of SVGD. On the other hand, when the learn- +ing rate is too small or too large, Coin SVGD significantly +outperforms SVGD. +4.4. Bayesian Neural Network +We next consider a Bayesian neural network model. Our +settings are identical to those given in Liu & Wang (2016); +see also (Hernandez-Lobato & Adams, 2015). In particular, +we use a two-layer neural network with 50 hidden units +with RELU(x) = max(0, x) as the activation function. We +assume the output is normal, and place a Gamma(1, 0.1) +prior on the inverse covariance. Meanwhile, we assign an +isotropic Gaussian prior to the neural network weights. +In Figure 5, we plot the performance of our algorithm on +4 UCI datasets. In all cases, we randomly partition the +data into 90% for training and 10% for testing. Our results +indicate that SVGD typically outperforms Coin SVGD for +well chosen learning rates, but significantly under-performs +Coin SVGD when the learning rate is too small or too large. +For certain datasets, the performance of Coin SVGD is very +close to the optimal performance of SVGD, while for others, +there remains a reasonable performance gap. This gap could +be further reduced using recent advancements in parameter- +free stochastic optimisation (e.g. Chen et al., 2022a;b). +4.5. Bayesian Probabilistic Matrix Factorisation +Finally, we consider a Bayesian probabilistic matrix factori- +sation (PMF) model (Salakhutdinov & Mnih, 2008). Let +R ∈ RN×M be a matrix of ratings for N users and M +movies, where Rij is the rating user i gave to movie j. De- +fine matrices U and V for users and movies, respectively, +where Ui ∈ Rd and Vj ∈ Rd are d-dimensional latent fea- +ture vectors for user i and movie j. The likelihood for the +rating matrix is given by +p(R|U, V, α) = +N +� +i=1 +M +� +j=1 +� +N(Rij|UT +i Vj, α−1�Iij +(23) +where Iij denotes an indicator variable which equals 1 if +users i gave rating for movie j. The priors for the users and +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +3 +4 +5 +6 +7 +8 +9 +Test RMSE +SVGD +Coin SVGD +(a) Boston +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +6 +8 +10 +12 +14 +16 +18 +Test RMSE +SVGD +Coin SVGD +(b) Concrete +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +2 +4 +6 +8 +10 +Test RMSE +SVGD +Coin SVGD +(c) Energy +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +0.100 +0.125 +0.150 +0.175 +0.200 +0.225 +0.250 +0.275 +Test RMSE +SVGD +Coin SVGD +(d) Kin8nm +Figure 5. Results for the Bayesian neural network: test RMSE +for SVGD and Coin SVGD after T = 1000 iterations for four UCI +benchmark datasets. +movies are p(U|µU, ΛU) = �N +i=1 N(Ui|µU, Λ−1 +U ) and +p(V|µV, ΛV) = �M +j=1 N(Vj|µU, Λ−1 +U ), with prior distri- +butions on the hyper-parameters, for W = U or V, given by +µW ∼ N(µW|µ0, ΛW) and ΛW ∼ Γ(a0, b0). The param- +eters of interest are then θ = (U, µU, ΛU, V, µV, ΛV). In +our experiments, we use hyper-parameters (α, µ0, a0, b0) = +(3, 0, 4, 5), and set the latent dimension d = 20. +We test our algorithm on the MovieLens dataset (Harper & +Konstan, 2015), which consists of 100,000 ratings, taking +values {1,2,3,4,5}, for 1,682 movies from 943 users. The +data are split into 80% for training and 20% for testing. We +use N = 10 particles, and a batch size of 1000. We average +our results over 5 random seeds. +Our results are shown in Figure 6, where we plot the root +mean squared error (RMSE) for SVGD and Coin SVGD, as +a function of the learning rate, after 1000 and 2000 iterations. +We also compare against the stochastic gradient Langevin +dynamics (SGLD) algorithm (Welling & Teh, 2011). In +this case, Coin SVGD outperforms SVGD for almost all +learning rates, and significantly outperforms SGLD. +10 +8 +10 +7 +10 +6 +10 +5 +10 +4 +10 +3 +Step Size +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +Test RMSE +SVGD +Coin SVGD +SGLD +(a) T = 1000. +10 +8 +10 +7 +10 +6 +10 +5 +10 +4 +10 +3 +Step Size +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +Test RMSE +SVGD +Coin SVGD +SGLD +(b) T = 2000. +Figure 6. Results for the Bayesian probabilistic matrix factori- +sation model: RMSE for SGLD, SVGD, and Coin SVGD. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +9 +References +Amari, S., Cichocki, A., and Yang, H. H. A New Learning +Algorithm for Blind Signal Separation. In Proceedings of +the 8th International Conference on Neural Information +Processing Systems (NIPS 1995), pp. 757–763, Denver, +CO, 1995. doi: 10.5555/2998828.2998935. +Ambrosio, L., Gigli, N., and Giuseppe Savar´e. Gradient +Flows: In Metric Spaces and in the Space of Probability +Measures. Birkh¨auser, Basel, 2008. ISBN 978-3-7643- +8721-1. doi: 10.1007/978-3-7643-8722-8. +Andrieu, C., de Freitas, N., Doucet, A., and Jordan, M. I. An +Introduction to MCMC for Machine Learning. Machine +Learning, 50(1):5–43, 2003. ISSN 1573-0565. doi: 10. +1023/A:1020281327116. +Arbel, M., Korba, A., Salim, A., and Gretton, A. Maximum +Mean Discrepancy Gradient Flow. In Proceedings of +the 33rd International Conference on Neural Information +Processing Systems (NeurIPS 2019), Vancouver, Canada, +2019. +Bauschke, H. H. and Combettes, P. L. Convex Analysis and +Monotone Operator Theory in Hilbert Spaces. Springer, +New York, NY, 2011. doi: 10.1007/978-1-4419-9467-7. +Brenier, Y. Polar factorization and monotone rearrangement +of vector-valued functions. Communications on Pure and +Applied Mathematics, 44(4):375–417, jun 1991. ISSN +0010-3640. doi: 10.1002/cpa.3160440402. +Br´ezis, H. +Op´erateurs maximaux monotones et semi- +groupes de contractions dans les espaces de Hilbert. El- +sevier Science, Burlington, MA, 1973. +Chen, C., Zhang, R., Wang, W., Li, B., and Chen, L. A +Unified Particle Optimization Framework for Scalable +Bayesian Sampling. In Uncertainty in Artificial Intelli- +gence, Monterey, CA, 2018a. +Chen, K., Cutkosky, A., and Orabona, F. Implicit Parameter- +free Online Learning with Truncated Linear Models. In +Proceedings of the 33rd International Conference on Al- +gorithmic Learning Theory (ALT 2022), Paris, France, +2022a. +Chen, K., Langford, J., and Orabona, F. Better Parameter- +Free Stochastic Optimization with ODE Updates for Coin- +Betting. In Proceedings of the Thirty-Sixth AAAI Confer- +ence on Artificial Intelligence (AAAI-22), Online, 2022b. +Chen, P. and Ghattas, O. Projected Stein Variational Gra- +dient Descent. In Proceedings of the 34th International +Conference on Neural Information Processing Systems +(NeurIPS 2020), Vancouver, Canada, 2020. +Chen, W. Y., Mackey, L., Gorham, J., Briol, F.-X., and +Oates, C. Stein Points. In Proceedings of the 35th Inter- +national Conference on Machine Learning (ICML 2018), +Stockholm, Sweden, 2018b. +Cheng, X. and Bartlett, P. Convergence of Langevin MCMC +in KL-divergence. Algorithmic Learning Theory, pp. 186– +211, 2018. +Chewi, S., Le Gouic, T., Lu, C., Maunu, T., and Rigollet, P. +SVGD as a kernelized Wasserstein gradient flow of the +chi-squared divergence. In Proceedings of the 34th Inter- +national Conference on Neural Information Processing +Systems (NeurIPS 2020), pp. 2098–2109, 2020. +Chwialkowski, K., Strathmann, H., and Gretton, A. +A +Kernel Test of Goodness of Fit. In Proceedings of the 33rd +International Conference on Machine Learning (ICML +2016), New York, NY, 2016. +Comon, P. Independent component analysis, A new con- +cept? Signal Processing, 36(3):287–314, 1994. ISSN +0165-1684. doi: 10.1016/0165-1684(94)90029-9. +Cutkosky, A. and Orabona, F. Black-Box Reductions for +Parameter-free Online Learning in Banach Spaces. In +Proceedings of the 31st Annual Conference on Learning +Theory (COLT 2018), Stockholm, Sweden, 2018. +Dalalyan, A. S. Further and stronger analogy between sam- +pling and optimization: Langevin Monte Carlo and gra- +dient descent. In Proceedings of the 30th Conference on +Learning Theory (COLT 2017), Amsterdam, The Nether- +lands, 2017a. +Dalalyan, A. S. Theoretical guarantees for approximate +sampling from smooth and log-concave densities. Jour- +nal of the Royal Statistical Society. Series B (Statisti- +cal Methodology), 79(3):651–676, sep 2017b. +ISSN +13697412, 14679868. +Dalalyan, A. S. and Karagulyan, A. User-friendly guar- +antees for the Langevin Monte Carlo with inaccurate +gradient. Stochastic Processes and their Applications, +129(12):5278–5311, 2019. +ISSN 0304-4149. +doi: +10.1016/j.spa.2019.02.016. +De Giorgi, E. New problems on minimizing movements. In +Boundary Value Problems for PDE and Applications, pp. +81–98. Masson, Paris, 1993. +Detommaso, G., Cui, T., Spantini, A., Marzouk, Y., and +Scheichl, R. A Stein variational Newton method. In Pro- +ceedings of the 32nd International Conference on Neural +Information Processing Systems (NIPS 2018), Montreal, +Canada, 2018. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +10 +Duncan, A., Nusken, N., and Szpruch, L. On the geometry +of Stein variational gradient descent. arXiv preprint, 2019. +doi: 10.48550/arXiv.1912.00894. +Durmus, A. and Moulines, ´E. Nonasymptotic convergence +analysis for the unadjusted Langevin algorithm. The An- +nals of Applied Probability, 27(3):1551–1587, jun 2017. +doi: 10.1214/16-AAP1238. +Durmus, +A. and Moulines, +´E. +High-dimensional +Bayesian inference via the unadjusted Langevin algo- +rithm. Bernoulli, 25(4A):2854–2882, nov 2019. doi: +10.3150/18-BEJ1073. +Durmus, A., Majewski, S., and Miasojedow, B. Analysis of +Langevin Monte Carlo via Convex Optimization. Journal +of Machine Learning Research, 20(1):2666–2711, 2019. +Feng, Y., Wang, D., and Liu, Q. Learning to Draw Samples +with Amortized Stein Variational Gradient Descent. In +Proceedings of the Conference on Uncertainty In Artifi- +cial Intelligence (UAI 2017), Sydney, Australia, 2017. +Futami, F., Cui, Z., Sato, I., and Sugiyama, M. Frank-Wolfe +Stein Sampling. arXiv preprint, 2019a. doi: 10.48550/ +arXiv.1805.07912. +Futami, F., Cui, Z., Sato, I., and Sugiyama, M. Bayesian +Posterior Approximation via Greedy Particle Optimiza- +tion. In Proceedings of the 33rd AAAI Conference on +Artificial Intelligence, Honolulu, HI, 2019b. +Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., +Vehtari, A., and Rubin, D. B. Bayesian Data Analysis. +Chapman and Hall/CRC, New York, 3rd edition, 2013. +doi: 10.1201/b16018. +Gershman, S. J., Hoffman, M. D., and Blei, D. M. Nonpara- +metric Variational Inference. In Proceedings of the 29th +International Conference on Machine Learning (ICML +2012), Edinburgh, UK, 2012. +Gigli, N. On the inverse implication of Brenier-Mccann +theorems and the structure of (P2(M),W2). Methods and +Applications of Analysis, 18(2), 2011. doi: 10.4310/MAA. +2011.v18.n2.a1. +Gorham, J. and Mackey, L. Measuring Sample Quality +with Kernels. In Proceedings of the 34th International +Conference on Machine Learning (ICML 2017), Sydney, +Australia, 2017. +G¨uler, O. On the Convergence of the Proximal Point Algo- +rithm for Convex Minimization. SIAM Journal on Con- +trol and Optimization, 29(2):403–419, mar 1991. ISSN +0363-0129. doi: 10.1137/0329022. +Guo, W., Hur, Y., Liang, T., and Ryan, C. T. Online Learning +to Transport via the Minimal Selection Principle. +In +Proceedings of the 35th Annual Conference on Learning +Theory (COLT 2022), London, UK, 2022. +Haario, H., Saksman, E., and Tamminen, J. Adaptive pro- +posal distribution for random walk Metropolis algorithm. +Computational Statistics, 14(3):375–395, 1999. ISSN +1613-9658. doi: 10.1007/s001800050022. +Haarnoja, T., Tang, H., Abbeel, P., and Levine, S. Rein- +forcement Learning with Deep Energy-Based Policies. In +Proceedings of the 34th International Conference on Ma- +chine Learning (ICML 2017), Sydney, Australia, 2017. +Han, J. and Liu, Q. Stein Variational Gradient Descent +Without Gradient. In Proceedings of the 35th Interna- +tional Conference on Machine Learning (ICML 2018), +Stockholm, Sweden, 2018. +Harper, F. M. and Konstan, J. A. The MovieLens Datasets: +History and Context. ACM Transactions on Interactive +Intelligent Systems, 5(4), 2015. ISSN 2160-6455. doi: +10.1145/2827872. +Hartmann, M., Girolami, M., and Klami, A. Lagrangian +Manifold Monte Carlo on Monge Patches. In Proceed- +ings of the 25th International Conference on Aritificial +Intelligence and Statistics (AISTATS 2022), Online, 2022. +Hernandez-Lobato, J. M. and Adams, R. P. Probabilistic +Backpropagation for Scalable Learning of Bayesian Neu- +ral Networks. In Proceedings of the 32nd International +Conference on Machine Learning (ICML 2015), Lille, +France, 2015. +Jordan, R., Kinderlehrer, D., and Otto, F. The Variational +Formulation of the Fokker–Planck Equation. SIAM Jour- +nal on Mathematical Analysis, 29(1):1–17, 1998. doi: +10.1137/S0036141096303359. +Jun, K.-S. and Orabona, F. Parameter-Free Online Convex +Optimization with Sub-Exponential Noise. In Proceed- +ings of the 32nd Annual Conference on Learning Theory +(COLT 2019), Phoenix, AZ, 2019. +Korba, A., Salim, A., Arbel, M., Luise, G., and Gretton, A. +A Non-Asymptotic Analysis for Stein Variational Gra- +dient Descent. In Proceedings of the 34th International +Conference on Neural Information Processing Systems +(NeurIPS 2020), Vancouver, Canada, 2020. +Korba, A., Pierre-Cyril, Aubin-Frankowski, Majewski, S., +and Ablin, P. Kernel Stein Discrepancy Descent. In +Proceedings of the 38th International Conference on Ma- +chine Learning (ICML 2021), Online, 2021. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +11 +Krauth, W. Statistical Mechanics: Algorithms and Com- +putations. +Oxford University Press, 2006. +ISBN +9780198515364. +Krichevsky, R. and Trofimov, V. The performance of univer- +sal encoding. IEEE Transactions on Information Theory, +27(2):199–207, 1981. doi: 10.1109/TIT.1981.1056331. +Leimkuhler, B. and Matthews, C. Efficient molecular dy- +namics using geodesic integration and solvent–solute +splitting. Proceedings of the Royal Society A: Mathe- +matical, Physical and Engineering Sciences, 472(2189): +20160138, may 2016. doi: 10.1098/rspa.2016.0138. +Leli`evre, T. and Stoltz, G. Partial differential equations +and stochastic methods in molecular dynamics. Acta +Numerica, 25:681–880, 2016. ISSN 0962-4929. doi: +DOI:10.1017/S0962492916000039. +Li, L., Liu, Q., Korba, A., Yurochkin, M., and Solomon, +J. Sampling with Mollified Interaction Energy Descent. +arXiv preprint, 2022. doi: 10.48550/arXiv.2210.13400. +Liu, C. and Zhu, J. Riemannian Stein Variational Gradient +Descent for Bayesian Inference. In Proceedings of the +32nd AAAI Conference on Artificial Intelligence, New +Orleans, LA, 2018. +Liu, C., Zhuo, J., Cheng, P., Zhang, R., Zhu, J., and Carin, +L. Understanding and Accelerating Particle-Based Varia- +tional Inference. In Proceedings of the 36th International +Conference on Machine Learning (ICML 2019), Long +Beach, CA, 2019a. +Liu, C., Zhuo, J., and Zhu, J. Understanding MCMC Dynam- +ics as Flows on the Wasserstein Space. In Proceedings of +the 36th International Conference on Machine Learning +(ICML 2019), Long Beach, CA, 2019b. +Liu, D. C. and Nocedal, J. On the limited memory BFGS +method for large scale optimization. Mathematical Pro- +gramming, 45(1):503–528, 1989. ISSN 1436-4646. doi: +10.1007/BF01589116. +Liu, J. S. +Monte Carlo Strategies in Scientific Com- +puting. +Springer-Verlag, New York, 2009. +ISBN +9780387763699. +Liu, Q. Stein variational gradient descent as gradient flow. +In Proceedings of the 31st International Conference on +Neural Information Processing Systems (NIPS 2017), pp. +3118–3126, Red Hook, NY, 2017. ISBN 9781510860964. +Liu, Q. and Wang, D. Stein Variational Gradient Descent: +A General Purpose Bayesian Inference Algorithm. In +Proceedings of the 30th Conference on Neural Informa- +tion Processings Systems (NIPS 2016), Barcelona, Spain, +2016. +Liu, Q., Lee, J. D., and Jordan, M. A Kernelized Stein +Discrepancy for Goodness-of-fit Tests. In Proceedings of +the 33rd International Conference on Machine Learning +(ICML 2016), New York, NY, 2016. +Liu, X., Zhu, H., Ton, J.-F., Wynne, G., and Duncan, A. +Grassmann Stein Variational Gradient Descent. In Pro- +ceedings of the 25th International Conference on Aritifi- +cial Intelligence and Statistics (AISTATS 2022), Online, +2022. +Liu, Y., Ramachandran, P., Liu, Q., and Peng, J. Stein Varia- +tional Policy Gradient. In Proceedings of the Conference +on Uncertainty In Artificial Intelligence (UAI 2017), Syd- +ney, Australia, 2017. +Ma, Y.-A., Chen, T., and Fox, E. B. A complete recipe for +stochastic gradient MCMC. In Proceedings of the 28th In- +ternational Conference on Neural Information Processing +Systems (NIPS 2015), pp. 2917–2925, Montreal, Canada, +2015. doi: 10.5555/2969442.2969566. +MacKay, D. J. Information Theory, Inference, and Learning +Algorithms. Cambridge University Press, 2003. ISBN +9780521642989. +Neal, +R. M. +Bayesian Learning for Neural Net- +works. +Springer, New York, 1996. +doi: 10.1007/ +978-1-4612-0745-0. +Neal, R. M. Slice sampling. The Annals of Statistics, 31(3): +705–767, jun 2003. doi: 10.1214/aos/1056562461. +Orabona, F. Simultaneous Model Selection and Optimiza- +tion through Parameter-free Stochastic Learning. In Pro- +ceedings of the 28th International Conference on Neural +Information Processing Systems (NIPS 2014), Montreal, +Canada, 2014. +Orabona, F. A Modern Introduction to Online Learning. +arXiv preprint, 2022. doi: 10.48550/arXiv.1912.13213. +Orabona, F. and Cutkosky, A. Tutorial on Parameter-Free +Online Learning. In Proceedings of the 37th International +Conference on Machine Learning (ICML 2020), Online, +2020. +Orabona, F. and Pal, D. Coin Betting and Parameter-Free +Online Learning. In Proceedings of the 30th Conference +on Neural Information Processings Systems (NIPS 2016), +Barcelona, Spain, 2016. +Orabona, F. and Tommasi, T. Training Deep Networks with- +out Learning Rates Through Coin Betting. In Proceedings +of the 31st International Conference on Neural Informa- +tion Processing Systems (NIPS 2017), Long Beach, CA, +2017. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +12 +Otto, F. The Geometry of Dissipative Evolution Equations: +The Porous Medium Equation. Communications in Par- +tial Differential Equations, 26(1-2):101–174, jan 2001. +ISSN 0360-5302. doi: 10.1081/PDE-100002243. +Otto, F. and Westdickenberg, M. Eulerian Calculus for the +Contraction in the Wasserstein Distance. SIAM Journal +on Mathematical Analysis, 37(4):1227–1255, 2005. doi: +10.1137/050622420. +Pagani, F., Wiegand, M., and Nadarajah, S. +An n- +dimensional Rosenbrock distribution for Markov chain +Monte Carlo testing. Scandinavian Journal of Statis- +tics, 49(2):657–680, jun 2022. ISSN 0303-6898. doi: +10.1111/sjos.12532. +Peypouquet, J. and Sorin, S. Evolution Equations for Maxi- +mal Monotone Operators: Asymptotic Analysis in Con- +tinuous and Discrete Time. Journal of Convex Analysis, +17(3-4):1113–1163, 2010. +Pu, Y., Gan, Z., Henao, R., Li, C., Han, S., and Carin, L. +VAE Learning via Stein Variational Gradient Descent. In +Proceedings of the 31st International Conference on Neu- +ral Information Processing Systems (NIPS 2017), Long +Beach, CA, 2017. +Robert, C. P. and Casella, G. Monte Carlo Statistical Meth- +ods. Springer-Verlag, New York, 2 edition, 2004. doi: +10.1007/978-1-4757-4145-22. +Salakhutdinov, R. and Mnih, A. Bayesian Probabilistic +Matrix Factorization Using Markov Chain Monte Carlo. +In Proceedings of the 25th International Conference on +Machine Learning (ICML 2008), pp. 880–887, New York, +NY, 2008. ISBN 9781605582054. doi: 10.1145/1390156. +1390267. +Salim, A., Korba, A., and Luise, G. The Wasserstein Prox- +imal Gradient Algorithm. In Proceedings of the 34th +International Conference on Neural Information Process- +ing Systems (NeurIPS 2020), Vancouver, Canada, 2020. +Salim, A., Sun, L., and Peter Richt´arik. A Convergence The- +ory for SVGD in the Population Limit under Talagrand’s +Inequality T1. In Proceedings of the 39th International +Conference on Machine Learning (ICML 2022), Online, +2022. +Santambrogio, F. Euclidean, metric, and Wasserstein gra- +dient flows: an overview. +Bulletin of Mathematical +Sciences, 7(1):87–154, 2017. ISSN 1664-3615. doi: +10.1007/s13373-017-0101-1. +Shi, Y., Bortoli, V. D., Deligiannidis, G., and Doucet, +A. Conditional Simulation Using Diffusion Schr¨odinger +Bridges. In Proceedings of the 10th International Confer- +ence on Learning Representations (ICLR 2022), Online, +2022. +Shor, N. Z. Minimization Methods for Non-Differentiable +Functions. Springer, Berlin, Heidelberg, 1985. doi: 10. +1007/978-3-642-82118-9. +Simon-Gabriel, C.-J. Distribution-Dissimilarities in Ma- +chine Learning. +Phd, Eberhard Karls Universit¨at +T¨ubingen, Germany, 2018. +Sun, L. and Richt´arik, P. Improved Stein Variational Gra- +dient Descent with Importance Weights. arXiv preprint, +2022. doi: 10.48550/arXiv.2210.00462. +Vempala, S. S. and Wibisono, A. Rapid Convergence of the +Unadjusted Langevin Algorithm: Isoperimetry Suffices. +In Proceedings of the 33rd International Conference on +Neural Information Processing Systems (NeurIPS 2019), +Vancouver, Canada, 2019. +Villani, C. Optimal Transport: Old and New. Springer- +Verlag, Berlin, 2008. ISBN 978-3-540-71049-3. doi: +10.1007/978-3-540-71050-9. +Wang, D. and Liu, Q. Learning to Draw Samples: With +Application to Amortized MLE for Generative Adver- +sarial Learning. In Proceedings of the 5th International +Conference on Learning Representations (ICLR 2017), +Toulon, France, 2017. +Wang, D., Tang, Z., Bajaj, C., and Liu, Q. Stein Variational +Gradient Descent with Matrix-Valued Kernels. In Pro- +ceedings of the 33rd International Conference on Neural +Information Processing Systems (NeurIPS 2019), Van- +couver, Canada, 2019. +Welling, M. and Teh, Y. W. Bayesian Learning via Stochas- +tic Gradient Langevin Dynamics. +In Proceedings of +the 28th International Conference on Machine Learning +(ICML 2011), Bellevue, WA, 2011. +Wenliang, L. K. and Kanagawa, H. Blindness of score-based +methods to isolated components and mixing proportions. +In arXiv preprint, 2021. doi: arXiv.2008.10087. +Wibisono, A. Sampling as optimization in the space of +measures: The Langevin dynamics as a composite op- +timization problem. In Proceedings of the 31st Annual +Conference on Learning Theory (COLT 2018), Stock- +holm, Sweden, 2018. +Wilson, A. G. and Izmailov, P. Bayesian Deep Learning +and a Probabilistic Perspective of Generalization. In Pro- +ceedings of the 34th International Conference on Neural +Information Processing Systems (NeurIPS 2020), Van- +couver, Canada, 2020. +Ye, M., Ren, T., and Liu, Q. Stein Self-Repulsive Dynamics: +Benefits from Past Samples. In Proceedings of the 34th +International Conference on Neural Information Process- +ing Systems (NeurIPS 2020), Vancouver, Canada, 2020. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +13 +Yoon, J., Kim, T., Dia, O., Kim, S., Bengio, Y., and Ahn, +S. Bayesian Model-Agnostic Meta-Learning. In Pro- +ceedings of the 32nd International Conference on Neural +Information Processing Systems (NIPS 2018), Montreal, +Canada, 2018. +Zhang, R., Chen, C., Li, C., and Carin, L. Policy Optimiza- +tion as Wasserstein Gradient Flows. In Proceedings of +the 35th International Conference on Machine Learning +(ICML 2018), Stockholm, Sweden, 2018. +Zhu, Y. and Zabaras, N. +Bayesian deep convolutional +encoder–decoder networks for surrogate modeling and +uncertainty quantification. Journal of Computational +Physics, 366:415–447, 2018. +ISSN 0021-9991. +doi: +10.1016/j.jcp.2018.04.018. +Zhuo, J., Liu, C., Shi, J., Zhu, J., Chen, N., and Zhang, +B. Message Passing Stein Variational Gradient Descent. +In Proceedings of the 35th International Conference on +Machine Learning (ICML 2018), Stockholm, Sweden, +2018. +Zinkevich, M. Online Convex Programming and General- +ized Infinitesimal Gradient Ascent. In Proceedings of +the 20th International Conference on Machine Learn- +ing (ICML 2003), ICML’03, pp. 928–935, Washing- +ton DC, 2003. AAAI Press. ISBN 1577351894. doi: +10.5555/3041838.3041955. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +14 +A. Background +A.1. Geodesic Convexity +In this section, we define a rigorous notion of convexity on the Wasserstein space. Let µ, ν ∈ P2(Rd). We define a constant +speed geodesic between µ and ν as a curve (λµ→ν +η +)η∈[0,1] such that λ0 = µ, λ1 = ν, and W2(λι, λη) = (η − ι)W2(µ, ν) +for all ι, η ∈ [0, 1]. If ην +µ is the optimal transport map between µ and ν, then a constant speed geodesic is given by +λµ→ν +η += +� +(1 − η)id + ηtν +µ +� +# µ. +(24) +Let F : P2(Rd) → (−∞, ∞]. The functional F is said to be lower semi-continuous if, for all M ∈ R, {F ≤ M} is a +closed subset of P2(Rd). For m ≥ 0, we say that F is m-geodesically convex if, for any µ, ν ∈ P2(Rd), there exists a +constant speed geodesic (λµ→ν +η +)η∈[0,1] between µ and ν such that, for all η ∈ [0, 1], +F(λµ→ν +η +) ≤ (1 − η)F(µ) + ηF(ν) − m +2 η(1 − η)W 2 +2 (µ, ν). +(25) +In the case that this inequality holds for m = 0, we will simply say that F is geodesically convex. +A.2. Subdifferential Calculus +We are now ready to introduce some basic concepts relating to subdifferential calculus in W2. This will provide us with +the machinery to develop parameter-free methods for solving optimisation problems over P2(Rd). Let µ ∈ P2(Rd), and +let ξ ∈ L2(µ). Let F be a proper and lower semi-continuous functional on P2(Rd). We say that ξ ∈ L2(µ) belongs to the +Fr´echet subdifferential of F at µ, and write ξ ∈ ∂F(µ) if, for any ν ∈ P2(Rd), +lim inf +ν→µ +F(ν) − F(µ) − +� +Rd⟨ξ(x), tν +µ(x) − x⟩µ(dx) +W2(ν, µ) +≥ 0. +(26) +Suppose, in addition, that F is m-geodesically convex. Then ξ ∈ L2(µ) belongs to the Fr´echet subdifferential ∂F(µ) if and +only if, for all ν ∈ P2(Rd), +F(ν) − F(µ) ≥ +� +Rd⟨ξ(x), tν +µ(x) − x⟩µ(dx) + m +2 W 2 +2 (µ, ν). +(27) +For certain functionals F, and under certain regularity conditions, (see Lemma 10.4.13 in Ambrosio et al., 2008), one has +that ∂F(µ) = {∇W2F(µ)}, where ∇W2F(µ) ∈ L2(µ) is given by +∇W2F(µ) = ∇∂F(µ) +∂µ +(x) for µ-a.e. x ∈ Rd, +(28) +and ∂F(µ) +∂µ +: Rd → R denotes the first variation of F at µ, that is, the unique function such that +lim +ε→0 +1 +ε (F(µ + εζ) − F(µ)) = +� +Rd +∂F(µ) +∂µ +(x)ζ(dx), +(29) +where ζ = ν − µ, and ν ∈ P2(Rd). We will refer to ∇W2F(µ) as the Wasserstein gradient of F at µ. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +15 +B. Theoretical Results +B.1. Lemma 2.1 +Lemma 2.1. This result is well known; see, e.g., Lemma 1 in Orabona & Pal (2016); Theorem 9.6 in Orabona (2022); +Section 4 in Orabona & Tommasi (2017); Part 2 in (Orabona & Cutkosky, 2020). In particular, we have +f +� +1 +T +T +� +t=1 +xt +� +− f(x∗) ≤ 1 +T +T +� +t=1 +� +f(xt) − f(x∗) +� +(Jensen’s inequality) +≤ 1 +T +� T +� +t=1 +ctx∗ − +T +� +t=1 +ctxt +� +(convexity) +≤ 1 +T +�� T +� +t=1 +ct +� +x∗ − h +� T +� +t=1 +ct +� ++ ε +� +(definition of h(·)) +≤ 1 +T +� +max +v +[vx∗ − h (v)] + ε +� +(maximum over v = �T +t=1 ct) += h∗(x∗) + ε +T +. +(definition of h∗(·)) +B.2. Theorem 3.3 +In this section, we outline how to prove Theorem 3.3. This proof relies on a rather technical assumption, which we state +below (Assumption B.1). The task of establishing more easily verifiable conditions under which this assumption holds +remains an interesting direction for future work. +B.2.1. PROOF UNDER ASSUMPTION B.1 +Assumption B.1. Let xt : Rd → Rd and µx +t ∈ P2(Rd) be defined as in Algorithm 1. For t = 0, . . . , T, let tπ +µx +t : Rd → Rd +and tµx +t +π : Rd → Rd denote the optimal transport maps from µx +t �→ π and from π �→ µx +t , respectively. In addition, let +˜tµx +t +π,t := xt ◦ tµx +0 +π : Rd → Rd denote the transport map from π to µx +t , defined as the composition of xt and tµx +0 +π . Define the +functions v : Rd → Rd and ˜v : Rd → Rd according to +v(x) = +T +� +t=1 +−∇W2F(µx +t )(tµx +t +π (x)), +˜v(x) = +T +� +t=1 +−∇W2F(µx +t )(˜tµx +t +π (x)). +(30) +Then there exists a constant K1 > 0 such that, for all x ∈ Rd, +1 +4L2T +� +||v(x)||2 − ||˜v(x)||2� +≤ ln K1. +(31) +Proof. Our proof begins in much the same fashion as the proof of Lemma 2.1. On this occasion, we consider +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ 1 +T +T +� +t=1 +F (µx +t ) − F(π) +(32) +≤ 1 +T +T +� +t=1 +� +Rd⟨−∇W2F(µx +t )(x), tπ +µx +t (x) − x⟩µx +t (dx) +(33) +≤ L +T +� +Rd +� +T +� +t=1 +−∇W2 ˆF(µx +t )(tµx +t +π (x)), x +� +π(dx) +(34) +− L +T +� +Rd +T +� +t=1 +� +− ∇W2 ˆF(µx +t )(xt(x)), xt(x) +� +µx +0(dx) + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +16 +where in the first line we have used Jensen’s inequality, in the second line we have used the definition of geodesic convexity +(see Section A), and in the third line we have substituted x �→ tµx +t +π (x) and x �→ xt(x) in the first and second integrals, +respectively, used the fact that (tµx +t +π )#π = µx +t and (xt)#µx +0 = µx +t (see Algorithm 1), and introduced the notation ˆF = 1 +LF. +By construction, the betting strategy in Algorithm 1 guarantees that, for any x ∈ Rd, initial wealth function w0 : Rd → R≥ε, +and for any arbitrary sequence c1(x), . . . , cT (x) ∈ Rd, such that ||ct(x)|| ≤ 1, there exists an even, logarithmically convex +function hx : R → R+, the ‘coin betting potential’, such that the ‘wealth’ is lower bounded as (Orabona & Pal, 2016, Proof +of Theorem 3, Appendix C) +wT (x) = w0(x) + +T +� +t=1 +⟨ct(x), xt(x)⟩ ≥ hx +������ +����� +T +� +t=1 +ct(x) +����� +����� +� +, +(35) +where we include the subscript x in hx(·) to emphasise that this function depends on the parameter x via the initial wealth +w0(x). In particular, the betting strategy in Algorithm 1 guarantees that this inequality holds with (Orabona & Pal, 2016, +Appendix F.1, Proof of Corollary 5) +hx (u) = w0(x)2T Γ(1)Γ( T +1 +2 ++ u +2 ) · Γ( T +1 +2 +− u +2 ) +Γ2( 1 +2)Γ(T + 1) +. +(36) +Due to Lemma 16 in Orabona & Pal (2016), we also have that +hx(u) ≥ ix(u) := w0(x) +K +√ +T +exp +� u2 +2T +� +, +(37) +where K = e√π is a universal constant. We will apply the inequality in (35) for the sequence ct(x) = −∇W2 ˆF(µt)(xt(x)). +In particular, substituting this sequence into (35), and using also the inequality in (37), we have that +w0(x) − +T +� +t=1 +� +−∇W2 ˆF(µt)(xt(x)), xt(x) +� +≥ −ix +������ +����� +T +� +t=1 +−∇W2 ˆF(µt)(xt(x)) +����� +����� +� +. +(38) +Suppose, for each x ∈ Rd, we define the function ix : Rd → (−∞, ∞] according to Ix(u) = ix(||u||). By substituting this +definition into (38), and then substituting (38) into (32) - (34), we then have +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +� T +� +t=1 +� +Rd +� +−∇W2 ˆF(µx +t )(tµx +t +π (x)), x +� +π(dx) +− +� +Rd Ix +� T +� +t=1 +−∇W2 ˆF(µx +t )(xt(x)) +� +µx +0(dx) + +� +Rd w0(x)µx +0(dx) +� +(39) += L +T +�� +Rd +� T +� +t=1 +−∇W2 ˆF(µx +t )(tµx +t +π (x)), x +� +π(dx) +− +� +Rd Jx +� T +� +t=1 +−∇W2 ˆF(µx +t )(˜tµx +t +π (x)) +� +π(dx) + +� +Rd w0(x)µx +0(dx) +� +, +(40) +where, in the second line, we have substituted x �→ tµx +0 +π (x), used the definition of ˜tµx +t +π (·), used the fact that (tµx +0 +π )#π = µx +0, +and defined the function Jx : Rd → (−∞, ∞] according to Jx(u) = It +µx +0 +π (x)(u). Suppose we also now define +u(x) = +T +� +t=1 +−∇W2 ˆF(µx +t )(tµx +t +π (x)) , +˜u(x) = +T +� +t=1 +−∇W2 ˆF(µx +t )(˜tµx +t +π (x)) , +A = +� +Rd Jx (˜u(x)) π(dx) +� +Rd Jx (u(x))) π(dx) +(41) +Using this notation, we can now rewrite the previous inequality as +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +�� +Rd ⟨u(x), x⟩ π(dx) − +� +Rd Jx (˜u(x)) π(dx) + +� +Rd w0(x)µx +0(dx) +� +(42) += L +T +�� +Rd A +� +⟨u(x), x +A⟩ − Jx(u(x)) +� +π(dx) + +� +Rd w0(x)µx +0(dx) +� +. +(43) + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +17 +Let us fix x ∈ Rd, and write θ = u(x), F(·) = Jx(·), and x∗ = x +A. Using this notation, for fixed x ∈ Rd, we can rewrite the +first integrand in (43) as +� +u(x), x +A +� +− Jx(u(x)) := ⟨θ, x∗⟩ − F(θ). +(44) +Taking the supremum over θ ∈ Rd and using the definition of the convex conjugate, we can easily upper bound this +expression by +⟨θ, x∗⟩ − F(θ) ≤ sup +θ∈Rd (⟨θ, x⟩ − F(θ)) ≤ F ∗(x∗), +(45) +where, as elsewhere, F ∗ denotes the Fenchel conjugate of F. Returning to our previous notation, and using the fact that +x ∈ Rd was chosen arbitrarily, we thus have that +⟨u(x), x +A⟩ − Jx(u(x)) ≤ J∗ +x +� x +A +� +, +for all x ∈ Rd. +(46) +Substituting this expression into (42) - (43), it now follows straightforwardly that +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +�� +Rd AJ∗ +x +� x +A +� +π(dx) + +� +Rd w0(x)µx +0(dx) +� +(47) += L +T +� +� +� +Rd AI∗ +x +� +� +��� +���tπ +µx +0 (x) +��� +��� +A +� +� µx +0(dx) + +� +Rd w0(x)µx +0(dx) +� +� +(48) += L +T +� +� +� +Rd Ai∗ +x +� +� +��� +���tπ +µx +0 (x) +��� +��� +A +� +� µx +0(dx) + +� +Rd w0(x)µx +0(dx) +� +� , +(49) +where in the second line we have substituted x �→ tπ +µx +0 (x), used the fact that (tπ +µx +0 )#µx +0 = π, and used the definition of Ix; +and, in the final line, we have used the fact that the Fenchel conjugate of ix(|| · ||) is i∗ +x(|| · ||) since i∗ +x is an even function +(Bauschke & Combettes, 2011, Example 13.7). Now, Lemma 18 of Orabona & Pal (2016) allows to bound this Fenchel +conjugate as +i∗ +x(u) ≤ |u| +� +T ln +� +1 + 24T 2u2 +w2 +0(x) +� +− w0(x) +K +√ +T +. +(50) +Substituting this into our previous bound (49), we finally arrive at +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +� � +Rd ||tπ +µx +0 (x)|| +� +� +� +�T ln +� +1 + +24T 2||tπ +µx +0 (x)||2 +A2w2 +0(x) +� +µx +0(dx) + +� +Rd w0(x) +� +1 − +A +K +√ +T +� +µx +0(dx) +� +≤ L +T +� � +Rd ||x|| +� +T ln +� +1 + 24T 2||x||2 +A2ε2 +� +π(dx) + +� +Rd w0(x)µx +0(dx) +� +, +(51) +where in the second line we have used our assumption on µx +0. It remains to bound the constant A from below, or, equivalently, +the constant A−1 from above. The required bound will follow directly from our technical assumption. In particular, +simplifying the definition given in (41), we have that +A−1 = +� +Rd w0(tµx +0 +π (x)) exp +�||v(x)||2 +2L2T +� +π(dx) +� +Rd w0(tµx +0 +π (x)) exp +�||˜v(x)||2 +2L2T +� +π(dx) +≤ +� +Rd w0(tµx +0 +π (x)) exp +�||v(x)||2 +2L2T +� +π(dx) +� +Rd +1 +K1 +w0(tµx +0 +π (x)) exp +�||v(x)||2 +2L2T +� +π(dx) += K1, +(52) +where the second inequality follows from the bound in Assumption B.1. Substituting this into (51), we finally arrive at +F +� +1 +T +T +� +t=1 +µx +t +� +− F(π) ≤ L +T +� � +Rd ||x|| +� +� +� +�T ln +� +1 + 24K2 +1T 2 ||x||2 +ε2 +� +π(dx) + +� +Rd w0(x)µx +0(dx) +� +. +(53) + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +18 +C. Coin ParVI Algorithms +C.1. Coin Stein Variational Gradient Descent +Let F(µ) = KL(µ|π), with ∇W2F(µ) = ∇ ln dµ +dπ. Let k : Rd × Rd → R denote a positive semi-definite kernel, and Hk +denote the associated reproducing kernel Hilbert space (RKHS). In addition, define the integral operator Kµ,k : L2(µ) → Hk +according to Kµ,kf(x) = +� +Rd k(x, y)f(y)µ(dy). +Following Liu & Wang (2016), suppose that we replace ∇W2F(µ) by Kµ,k∇W2F(µ), its image under the integral operator +Kµ,k. This essentially plays the role of the Wasserstein gradient in Hk. Using integration by parts, and recalling that +π ∝ e−U, one can show that Kµ,k∇W2F(µ) = Ex∼µ [k(·, x)∇U(x) − ∇2k(·, x)] (e.g., Duncan et al., 2019; Korba et al., +2020; Chewi et al., 2020). It follows, in particular, that +KµN +t ,k∇W2F(µN +t )(xi +t) = 1 +N +N +� +j=1 +� +k(xi +t, xj +t)∇U(xj +t) − ∇2k(xi +t, xj +t) +� +. +(54) +Substituting this expression into Algorithm 1, we arrive at a learning-rate free analogue of the SVGD algorithm (Liu & +Wang, 2016). This algorithm is summarised in Algorithm 2. +We note that this algorithm is not entirely tuning free, since we are still required to specify a bandwidth for the kernel +k : Rd × Rd → R. However, in practice, this parameter can be tuned automatically using the median rule (Liu & Wang, +2016). +Algorithm 2 Coin Stein Variational Gradient Descent +Input: initial measure µx +0 ∈ P2(Rd), initial particles x1 +0, . . . , xN +0 ∼ µx +0, initial wealth function w0 : Rd → R≥ε, constant +L. +for t = 1 to T do +for i = 1 to N do +Compute +xi +t = − +t−1 +� +s=1 +N +� +j=1 +[k(xi +s, xj +s)∇U(xj +s) − ∇2k(xi +s, xj +s)] +LNt +� +w0(xi +0) − +t−1 +� +s=1 +� 1 +NL +N +� +j=1 +[k(xi +s, xj +s)∇U(xj +s) − ∇2k(xi +s, xj +s)], xi +s +�� +. +(55) +Define µx,N +t += 1 +N +�N +i=1 δxi +t. +Output: µx,N +T +or 1 +T +�T +t=1 µx,N +t +. +C.2. Coin Laplacian Adjusted Wasserstein Gradient Descent +Let F(µ) = KL(µ|π), with ∇W2F(µ) = ∇ ln dµ +dπ. Following Chewi et al. (2020), suppose that we replace ∇W2F(µ) +by ∇Kπ,kL +dµ +dπ, the gradient of the image of dµ +dπ under the integral operator Kµ,kL. The kernel kL is chosen such that +Kπ,kL = −L−1 +π , where Lπ denotes the infinitesimal generator of the overdamped Langevin diffusion with stationary +distribution π. +In this case, we have that ∇Kπ,kL +dµ +dπ = Ex∼µ[∇1kL(·, x)], and thus +∇Kπ,kL +dµN +dπ (xi +t) = 1 +N +N +� +j=1 +∇1kL(xi +t, xj +t). +(56) +By using these gradients in Algorithm 1, we obtain a learning-rate free analogue of the LAWGD algorithm (Chewi et al., +2020). This algorithm is summarised in Algorithm 3. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +19 +Algorithm 3 Coin Laplacian Adjusted Wasserstein Gradient Descent +Input: initial measure µx +0 ∈ P2(Rd), initial particles x1 +0, . . . , xN +0 ∼ µx +0, initial wealth function w0 : Rd → R≥ε, constant +L. +for t = 1 to T do +for i = 1 to N do +Compute +xi +t = − +t−1 +� +s=1 +N +� +j=1 +∇1kL(xi +s, xj +s) +LNt +� +w0(xi +0) − +t−1 +� +s=1 +� +1 +NL +N +� +j=1 +∇1kL(xi +s, xj +s), xi +s +� � +. +(57) +Define µN +t = 1 +N +�N +i=1 δxi +t. +Output: µx,N +T +or 1 +T +�T +t=1 µx,N +t +. +C.3. Coin Kernel Stein Discrepancy Descent +Let F(µ) = +1 +2KSD2(µ|π), where KSD(µ|π) is the kernel Stein discrepancy, defined according to (Liu et al., 2016; +Chwialkowski et al., 2016; Gorham & Mackey, 2017) +KSD(µ|π) = +�� +Rd +� +Rd kπ(x, y)µ(dx)µ(dy), +(58) +and where kπ is the Stein kernel, defined in terms of the score s = ∇ log π, and a positive semi-definite kernel k, as +kπ(x, y) = sT (x)s(y)k(x, y) + sT (x)∇2k(x, y) + ∇1kT (x, y)s(y) + ∇·1∇2k(x, y) +(59) +In this case, given a discrete measure µN = 1 +N +�N +j=1 δxj, the loss function and its gradient are given by +F(µN) = +1 +N 2 +N +� +i,j=1 +kπ(xi, xj) , +∇xiF(µN +t ) = +1 +N 2 +N +� +j=1 +∇2kπ(xj +t, xi +t). +(60) +By substituting these gradients into Algorithm 1, we obtain a learning-rate free analogue of KSDD (Korba et al., 2021).4 +This algorithm is summarised in Algorithm 4. +Algorithm 4 Coin Kernel Stein Discrepancy Descent +Input: initial measure µx +0 ∈ P2(Rd), initial particles x1 +0, . . . , xN +0 ∼ µx +0, initial wealth function w0 : Rd → R≥ε, constant +L. +for t = 1 to T do +for i = 1 to N do +Compute +xi +t = − +t−1 +� +s=1 +N +� +j=1 +∇2kπ(xj +s, xi +s) +LN 2t +� +�w0(xi +0) − +t−1 +� +s=1 +� +1 +N 2L +N +� +j=1 +∇2kπ(xj +s, xi +s), xi +s +�� +� . +(61) +Define µx,N +t += 1 +N +�x,N +i=1 δxi +t. +Output: µx,N +T +or 1 +T +�T +t=1 µx,N +t +. +4In fact, Korba et al. (2021) also propose a learning-rate free version of KSDD based on the quasi-Newton L-BFGS algorithm (Liu & +Nocedal, 1989). Our method provides an alternative approach based on the ‘coin-betting’ paradigm. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +20 +D. Coin Sampling with Adaptive Gradient Bounds +In principle, in order to implement Algorithm 1, one requires knowledge of a constant L > 0 such that, for all u ∈ Rd, +||∇W2F(µx +t )(u)|| ≤ L for all t = 1, . . . , T. In practice, this constant may not be not known a priori. In this case, following +Orabona & Tommasi (2017), we can use a modified version of our algorithm in which the gradient bounds are adaptively +estimated. This algorithm is summarised in Algorithm 5. +D.1. Adaptive Coin Wasserstein Gradient Descent +Algorithm 5 Adaptive Coin Wasserstein Gradient Descent +Input: initial measure µx +1 ∈ P2(Rd), initial parameter x1 ∼ µx +1 or x1 ∈ Rd, functional F : P2(Rd) → (−∞, ∞]. +Initialise: for j = 1, . . . , d, L0,j = 0, G0,j = 0, R0,j = 0. +for t = 1 to T do +Compute the negative Wasserstein gradient: ct(x1) = −∇W2F(µx +t )(xt(x1)). +for j = 1 to d do +Update the maximum observed scale Lt,j = max(Lt−1,j, |ct,j(x1)|). +Update the sum of the absolute value of the gradients: Gt,j = Gt−1,j + |ct,j|. +Update the reward: Rt,j(x1) = max(Rt−1,j(x1) + ct,j(x1)(xt,j(x1) − x1,j), 0) +Update the parameter +xt+1,j(x1) = x1,j + +�t +s=1 ct,j(x1) +Lt,j(Gt,j + Lt,j)(Lt,j + nt,j(x1)). +(62) +Define µx +t+1 = (xt+1)#µx +1. +Output: µx +T . +D.2. Adaptive Coin Stein Variational Gradient Descent +We now provide the adaptive version of Coin SVGD (Algorithm 2). In the interest of brevity, we do not provide the adaptive +versions of Coin LAWGD (Algorithm 3) and Coin KSDD (Algorithm 4). However, these are easily obtained by substituting +the relevant gradients into the adaptive version of the Coin SVGD +Algorithm 6 Adaptive Coin Stein Variational Gradient Descent +Input: initial measure µx +1 ∈ P2(Rd); for i = 1, . . . , N, initial particles x1 +1, . . . , xN +1 +i.i.d. +∼ µx +1. +Initialise: for i = 1, . . . , N, j = 1, . . . , d, Li +0,j = 0, Gi +0,j = 0, Ri +0,j = 0. +for t = 1 to T do +for i = 1 to N do +Compute the negative gradient ci +t = − 1 +N +�N +j=1[k(xi +t, xj +t)∇U(xj +t) − ∇2k(xi +t, xj +t)]. +for j = 1 to d do +Update the maximum observed scale: Li +t,j = max(Li +t−1,j, |ci +t,j|) +Update the sum of the absolute value of the gradients: Gi +t,j = Gi +t−1,j + |ci +t,j| +Update the reward Ri +t,j = max(Ri +t−1 + ⟨ci +t,j, xi +t,j − xi +t,j⟩, 0) +Update the parameter +xi +t+1,j = xi +1,j + +�t +s=1 ci +t,j +Li +t,j(Gi +t + Li +t,j)(Li +t,j + Ri +t,j). +(63) +Define µN +t+1 = 1 +N +�N +i=1 δxi +t. +Output: µN +T . +Following Orabona & Tommasi (2017), when we use Algorithm 6 for the Bayesian neural network (see Section 4.4), the +update equation becomes +xi +t+1,j = xi +1,j + +�t +s=1 ci +t,j +Li +t,j max(Gi +t + Li +t,j, αLt,i)(Li +t,j + Ri +t,j). +(64) +where α > 0 is a positive constant which we set equal to 100. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +21 +E. Additional Experimental Results +E.1. SVGD vs Coin SVGD +We compare the performance of SVGD (Liu & Wang, 2016) and Coin SVGD (Algorithm 2) on the following two-dimensional +distributions. +Two-Dimensional Gaussian. The first example is an anisotropic bivariate Gaussian distribution, viz +p(x) = N(x|µ, Σ) +(65) +where µ = (−1, 1)⊤ and Σ−1 = +� +3 +−0.5 +−0.5 +1 +� +. +Mixture of Two Two-Dimensional Gaussians. The next example is a mixture of two bivariate Gaussian distributions, with +p(x) = α1N(x; µ1, Σ1) + α2N(x; µ2, Σ2), +(66) +where α1 = 0.5, µ1 = (−2, 2)⊤, and Σ1 = 1 +21; α2 = 0.5, µ2 = (2, −2)⊤, and Σ2 = 1 +21. +Donut Distribution. For the next example, we consider an annulus or ‘donut’ distribution, with density +p(x) ∝ exp(−(|x| − r0)2 +2σ2 +) +(67) +where r0 = 2.5 and σ2 = 0.5. +Rosenbrock Distribution. We next consider the so-called Rosenbrock or ‘banana’ distribution (Pagani et al., 2022), a +correlated two-dimensional distribution with density +p(x1, x2) ∝ exp +��x1 +a − µ1 +�2 ++ +� +ax2 + ab(x2 +1 + a2) − µ2 +�2� +, +with a = −1, b = 1, µ1 = 0, and µ2 = 1. This is a common example used to benchmark sampling algorithms (e.g., Haario +et al., 1999; Ma et al., 2015; Ye et al., 2020). +Squiggle Distribution. Our next example is a two-dimensional ‘squiggle’ distribution; see, e.g., Appendix E in Hartmann +et al. (2022). In this case, the target density is given by +p(x) ∝ exp +� +(x′ − µ)T Σ−1(x′ − µ) +� +(68) +where x′ +1 = x1, x′ +2 = x1 + sin(ωx1); and µ = (1, 1)⊤, Σ = +� +2 +0.25 +0.25 0.5 +� +, and ω = 2. +Funnel Distribution. Our final example is a two-dimensional ‘funnel’ distribution, with density +p(x1, x2) ∝ N(x1; µ1, σ2 +1)N(x2; µ2, exp(x1 +2 )) +(69) +where µ1 = 4, µ2 = 1, and σ2 +1 = 3. This example, in ten-dimensions, was first introduced in (Neal, 2003) to illustrate the +difficulty of sampling from some hierarchical models. +In Figure 7, we provide a more detailed comparison of the performance of SVGD and Coin SVGD, plotting the KSD for +both algorithms after 1000 iterations as a function of the learning rate. Following Gorham & Mackey (2017), we use the +inverse multi-quadratic (IMQ) kernel k(x, x′) = (c2 + ||x − x′||2 +2)β to compute the KSD, where c > 0 and β(−1, 0). We +truncate each plot at approximately the largest value of the step size such that SVGD is numerically stable. +In most cases, with an optimally tuned step size, SVGD achieves the best performance, attaining the lowest value of the +KSD. However, using a step size which is too small leads to very slow convergence, while using a step size which is too +large leads to non-convergence and, ultimately, numerical instability. It is worth emphasising that it is difficult to determine +a good step size, or to implement a line-search method, since SVGD does not minimise a simple function. On the other +hand, Coin SVGD achieves performance close to, or even better than, the performance of optimally-tuned SVGD, without +any need to tune a step size. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +22 +10 +2 +10 +1 +100 +Step Size +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +KSD +SVGD +Coin SVGD +(a) Bivariate Gaussian +10 +2 +10 +1 +100 +Step Size +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +KSD +SVGD +Coin SVGD +(b) Mixture of Bivariate Gaussians +10 +2 +10 +1 +100 +Step Size +0.25 +0.30 +0.35 +0.40 +0.45 +0.50 +0.55 +KSD +SVGD +Coin SVGD +(c) ‘Donut’ Distribution +10 +2 +10 +1 +100 +Step Size +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +KSD +SVGD +Coin SVGD +(d) Rosenbrock Distribution +10 +2 +10 +1 +100 +Step Size +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +KSD +SVGD +Coin SVGD +(e) ‘Squiggle’ Distribution +10 +2 +10 +1 +100 +Step Size +0.2 +0.3 +0.4 +0.5 +0.6 +KSD +SVGD +Coin SVGD +(f) ‘Funnel’ Distribution +Figure 7. A comparison between SVGD (Liu & Wang, 2016) and its learning-rate free analogue, Coin SVGD (Algorithm 2). We +plot the KSD of SVGD as a function of the step size, and the KSD of Coin SVGD, after T = 1000 iterations, for each of the +two-dimensional target distributions plotted in Figure 1. +E.2. LAWGD vs Coin LAWGD +We now compare the performance of LAWGD (Chewi et al., 2020) and Coin LAWGD (Algorithm 3). In our two examples, +we run the algorithm with N = 100 or N = 25 particles, and for T = 2500 iterations. Further details regarding +implementation of LAWGD can be found in Chewi et al. (2020). +One-Dimensional Gaussian. +We begin by considering a simple one-dimensional Gaussian, with density p(x) = +N(x; µ, σ2), where µ = 3 and σ2 = 1.5. +Mixture of Three One-Dimensional Gaussians. We also consider a mixture of three one-dimensional Gaussians, with +p(x) = +3 +� +i=1 +αiN(x|µi, σ2 +i ), +(70) +where α1 = 1 +3, µ1 = 6, σ2 +1 = 2; α2 = 1 +2, µ2 = −3, and σ2 +2 = 1; and α3 = 1 +6, µ3 = 2, and σ2 +3 = 1. +It is worth noting that, even for relatively simple one- and two-dimensional examples, LAWGD is challenging to implement +as it depends on spectral decomposition of a certain differential operator; see the discussion in Section 5 of Chewi et al. +(2020). As a result, despite its attractive theoretical properties, LAWGD has not yet been widely adopted by practitioners. +Nonetheless, we find it useful to include this comparison to demonstrate the flexibility of our coin-based methodology. +Indeed, similar to before, we see that Coin LAWGD converges to the target distribution for both of our test cases, and enjoys +a similar performance to the standard LAWGD algorithm (see Figure 8). +E.3. KSDD vs Coin KSDD +We next compare the performance of KSDD (Korba et al., 2021) and Coin KSDD (Algorithm 4). We use N = 20 particles; +and run both methods for T = 5000 iterations. Similar to Korba et al. (2021), we consider the following toy-examples. +Anistropic Two-Dimensional Gaussian. We first consider a single bivariate Gaussian, viz p(x) = N(x; µ, Σ), where +µ = (−3, 3)⊤ and Σ−1 = +� +0.2 +−0.05 +−0.05 +0.1 +� +. + +Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates +23 +(a) Univariate Gaussian +(b) Mixture of Three Univariate Gaussians +Figure 8. An illustrative comparison between LAWGD Chewi et al. (2020) and its learning-rate free analogue, Coin LAWGD +(Algorithm 3). We plot the samples generated by both methods for the two target distributions detailed in Section E.2. +Symmetric Mixture of Two Two-Dimensional Gaussians. In our second example, we consider a symmetrix mixture of +two, two-dimensional, isotropic Gaussians with the same variance: p(x) = 1 +2N(x; µ, σ21) + 1 +2N(x; −µ, σ21), where +µ = (6, 0)T and σ2 = 1. +In Figure 9, we plot the samples obtained using KSDD and Coin KSDD after 5000 iterations. Similar to before, the samples +generated by the coin sampling method, step-size free algorithm are very similar to those generated by the original algorithm. +In fact, even the dynamics of the two algorithms share many of the same properties. For example, the Coin KSDD particles +seem initially to be guided by the final repulsive term in the update, which determine their global arrangement. They are +then transported towards the mode(s), driven by the remaining score-based terms. This is in contrast to the Coin SVGD +particles, which are first driven by the score term, before being dispersed around the mode by the repulsive term. These +dynamics were first observed in Korba et al. (2021) for the standard SVGD and KSDD algorithms, and also to be present for +their step-size free analogues. +(a) Anisotropic Bivariate Gaussian +(b) Symmetric Mixture of Bivariate Gaussians +Figure 9. A comparison between KSDD (Korba et al., 2021) and its learning-rate free analogue, Coin KSDD (Algorithm 4). We +plot the samples generated by both methods for the two target distributions detailed in Section E.3. +Unsurprisingly, Coin KSDD also inherits some of the shortcomings of KSDD. Given a symmetric target, and a radial +kernel, it is known that any plane of symmetry is invariant under the KSD gradient flow (Korba et al., 2021, Lemma 11). +Thus, if KSDD is initialised close to a plane of symmetry, it can become stuck there indefinitely. In practice, this also +appears to holds true for Coin KSDD (see Figure 9). Korba et al. (2021) propose an annealing strategy can be used to +resolve this behaviour; see also Wenliang & Kanagawa (2021). One first runs KSDD to obtain samples from the target +πβ(x) ∝ exp(−βU(x)), where the inverse temperature β ∼ 0. One then runs the algorithm a second time, initialised at +these samples, on the true target π(x) ∝ exp(−U(x)). A similar strategy can also be used for Coin KSDD (see Figure 10). + +LAWGD +Coin LAWGDLAWGD +Coin LAWGDKsD Descent +Coin KSD DecentKsD Descent +Coin KSD DecentCoin Sampling: Gradient-Based Bayesian Inference without Learning Rates +24 +(a) β = 1 +(b) β = 0.02 +(c) β = 0.02 → 1 +Figure 10. A comparison between annealing KSDD (Korba et al., 2021) and annealing Coin KSDD (Algorithm 4). We plot the +samples generated by both methods using no annealing (β = 1), after the first step of the annealing method (β = 0.02), and after the full +annealing method (β = 0.02 → β = 1). +E.4. Bayesian Neural Network: Additional Numerical Results +Below we include additional results for the Bayesian neural network model. The experimental setting are all as described in +Section 4.4, +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +2 +3 +4 +5 +6 +7 +Test RMSE +SVGD +Coin SVGD +(a) Protein +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +0.65 +0.70 +0.75 +0.80 +0.85 +Test RMSE +SVGD +Coin SVGD +(b) Wine +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +2 +4 +6 +8 +10 +12 +14 +16 +Test RMSE +SVGD +Coin SVGD +(c) Yacht +10 +9 +10 +7 +10 +5 +10 +3 +10 +1 +Step Size +10 +12 +14 +16 +18 +20 +22 +24 +26 +Test RMSE +SVGD +Coin SVGD +(d) Year +Figure 11. Results for the Bayesian neural network. We plot the test RMSE for SVGD and Coin SVGD for several UCI benchmark +datasets. For each method, we use N = 20 particles and T = 1000 iterations. + +KsD Descent +Coin KSD DecentKSD Descent +Coin KSD DecentKsD Descent +Coin KSD Decent \ No newline at end of file diff --git a/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/load_file.txt b/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5435d826ccd4250be89a5be864e35bba540fc607 --- /dev/null +++ b/XtFIT4oBgHgl3EQfjCsN/content/tmp_files/load_file.txt @@ -0,0 +1,1685 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf,len=1684 +page_content='Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates Louis Sharrock 1 Christopher Nemeth 1 Abstract In recent years, particle-based variational infer- ence (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popular- ity as scalable methods for Bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Unfortunately, the properties of such methods in- variably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demon- strating comparable performance to other ParVI algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Introduction The task of sampling from complex, high-dimensional probability distributions is of fundamental importance to Bayesian inference (Robert & Casella, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Gelman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=', 2013), machine learning (Neal, 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Andrieu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=', 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Welling & Teh, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Wilson & Izmailov, 2020), molecular dynamics (Krauth, 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Leli`evre & Stoltz, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Leimkuh- ler & Matthews, 2016), and scientific computing (MacKay, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Liu, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' In this paper, we consider the canonical task of sampling from a probability distribution π(dx) on Rd with density π(x) with respect to the Lebesgue measure of the form1 π(x) := exp (−U(x)) Z (1) where U : Rd → R is a measurable, continuously dif- ferentiable function known as the potential, and Z = � Rd exp(−U(x))dx is an unknown normalising constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' 1Department of Mathematics, Lancaster University, UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XtFIT4oBgHgl3EQfjCsN/content/2301.11294v1.pdf'} +page_content=' Corre- spondence to: Louis Sharrock csample. +Batch-level high-quality: The proportion of high-quality +reasoning +samples +in +the +batch +is +high +denoted +as +Nsample h/Nb > cbacth, and the prediction accuracy of the +optimization is better than the previous one. Nsample h is the +number of high-quality reasoning samples in the batch. +Parameters estimated Kes +t +are updated as the training step t. +To ensure the continuity of the optimization, optimization on +the high-quality reasoning batch and that on the low-quality +one are weightedly integrated by β, where β equals 1 for high- +quality one and Nsample h/Nb for low-quality one. Parameters +estimated Kes +t +at the step t are generated based on parameters +optimized this time and parameters estimated at the previous +step t − 1 as follow: +Kes +t += β ∗ (1 − γ) ∗ Kt + (1 − β ∗ (1 − γ)) ∗ Kes +t−1, +(10) +where γ is the hyperparameter controlling the number of steps +for integrating. + +5 +E. Implementation +The proposed framework is implemented on PyTorch and +trained with 4 Tesla V100 GPUs. The models for the subtasks +Q → A and QA → R possess identical architecture with +their weights trained separately. The prediction for the subtask +Q → AR is the combination of the predictions for Q → A +and QA → R. In the stage of feature extraction for original +visual and linguistic data, each object in the given image is +extracted as a 512-dimensional vector by the method in [10] +with ResNet101 [22] as the backbone. Each word is embedded +as a 768-dimensional feature by a pre-trained BERT [23], +and sequential words as a whole sentence are further input +into a single-layer bidirectional LSTM model to obtain 512- +dimensional vectors for each word. The CNN networks used +for depth images have three convolutional layers, and a fully- +connected layer to generate 512-dimensional vectors. The vi- +sual features enhanced are also 512-dimensional. The dropout +rate is 0.3 in Bi-LSTM and 0.1 in Transformer. The parameters +of Transform-based model are trained by Noam [13] while the +remaining modules are trained by Adam [24] with the learning +rate initialized as 0.0002. α in depth-aware Transformer is set +as 0.6, and γ in PEMRC is set as 0.9998. csample and cbacth +are 0.55 and 0.6. The batch size is 96, and the model is trained +for 30 epochs with early stopping. +IV. EXPERIMENT +A. Dataset +Extensive experiments are carried out on the VCR bench- +mark dataset [7], which is composed of 290k four-way multi- +choice QA problems derived from 110k movie scenes. Differ- +ent from VQA dataset where the answer is usually a single +word, the answer and rationale in the VCR dataset is more +complicated and in the form of mixtures of visual and linguis- +tic words. The average lengths of the answers and rationales +are over 7.5 words and 16 words, respectively. Following the +data partition practice [7], the training set consists of 80,418 +images with 212,923 questions, the validation set is composed +of 9,929 images with 26,534 questions. +B. Evaluation Metric and Baseline +The evaluation metric is classification accuracy, which is +a ratio of correctly classified samples to all test samples. +The competing methods are divided into three categories: (1) +text-only baselines, including BERT [23], BERT (response +only) [23], ESIM+ELMO [25] and LSTM+ELMO [25], which +don’t utilize visual information and can be used to evaluate +the influence of visual context; (2) VQA baselines, including +RevisitedVQA [26], BottomUpTopDown [27], MLB [28] and +MUTAN [29], which are originally designed for VQA and +modified to perform VCR (compared with these methods, the +capability of the proposed framework to model the correlation +between the complex response and the question or image +can be evaluated); (3) VCR methods, including R2C [7], +CKRM [14], TAB-VCR [10], CCN [17], HGL [9], ECMR [8], +VC R-CNN [30], CL-VCR [31], MCC [11] and JAE [32]. +The brief descriptions of the competing VCR methods are +presented below. R2C adopts bilinear attention mechanism and +LSTM to associate image with text for reasoning. CKRM is +an attention-based model to transfere external knowledge into +the VCR task. TAB-VCR integrates attribute information into +visual features and assigns extra tags to image grounding for +the VCR task. CCN employs a connective cognition network +and reorganizes visual neuron connectivity to do VCR. HGL +operates heterogeneous graph learning based on the cross- +modal correlation between image and text. ECMR integrates +visual graph and linguistic graph for cross-modal reasoning. +VC R-CNN employs region-based CNN to perform causal +intervention for visual feature enhancement. CL-VCR adopts +a curriculum-based masking approach to training model more +robustly for VCR. MCC generates counterfactual samples and +uses a contrastive learning strategy to train VCR framework. +JAE presents a plug-and-play knowledge distillation enhanced +framework to do VCR. +C. Quantitative Result +The quantitative results achieved by the proposed PPTMCO +compared with several competing methods for the three sub- +tasks in VCR are given in Table I. With regard to these text- +only baselines, performances are bad without considering the +important visual information. These VQA baselines gain im- +provements compared with text-only baselines, but still cannot +achieve satisfactory results since the expressions in VCR are +more complicated. For the VCR methods, TAB-VCR [10], +ECMR [8], and MCC [11] adopting visual features integrating +attributes achieve better performances in general compared +with other baselines R2C [7], CKRM [14], CCN [17], HGL [9] +using plain visual features. Further considering exact 3D +positions via image depth, the proposed PPTMCO framework +obtains the best performance with 72.2% for the Q → A task, +73.8% for the QA → R task, 53.5% for the Q → AR task on +the validation set, respectively. In comparison to MCC [11] +where the framework is trained via counterfactual samples +and contrastive learning, the proposed PPTMCO adopts a +parameter estimation method guided by multi-level reasoning +confidence to optimize the framework. As a result, PPTMCO +gains the improvements of 0.5% for the Q → AR task on +the validation set over MCC. As for the VC R-CNN [30] +method using causal intervention, the CL-VCR [31] method +with robust training, and JAE [32] adopting knowledge distil- +lation, the proposed PPTMCO has superiority as well. All the +above results demonstrate the effectiveness of the proposed +PPTMCO. +D. Ablation Study +To evaluate the effectiveness of the visual feature enhanc- +ing (VFE), DT and PEMRC modules in the framework, several +models are designed to do ablation study as follows. +Base. A variant of the R2C model [7] replaces the backbone +with ResNet101, and uses plain Transformer to do contextu- +alization and reasoning instead of LSTM. +Base+visual +features +enhanced +with +2D +positions (VFE2D). A variant of the base model uses +the visual features enhanced by 2D positions obtained in the + +6 +Fig. 3. Instances of successful cases for the VCR task obtained by the proposed PPTMCO. The percentages in brackets are the probabilities predicted by +PPTMCO, and the choices filled in brown are ground-truths. To be distinguishable, < person 1 > means visual object, [person1] means linguistic entity. +The heatmaps for the ground-truth choices on the right indicate the final adjustment matrice for answer-image contextualization. +TABLE I +COMPARISON OF ACCURACY FOR THREE SUBTASKS IN VCR ACHIEVED +BY THE COMPETING METHODS ON THE VALIDATION SET OF VCR +DATASET. +Methods +Q → A +QA → R +Q → AR +BERT [23] +53.8 +64.1 +34.8 +BERT (response only) [23] +27.6 +26.3 +7.6 +ESIM+ELMO [25] +45.8 +55.0 +25.3 +LSTM+ELMO [25] +28.1 +28.7 +8.3 +RevisitedVQA [26] +39.4 +34.0 +13.5 +BottomUpTopDown [27] +42.8 +25.1 +10.7 +MLB [28] +45.5 +36.1 +17.0 +MUTAN [29] +44.4 +32.0 +14.6 +R2C [7] +63.8 +67.2 +43.1 +CKRM [14] +66.2 +68.5 +45.6 +TAB-VCR [10] +69.9 +72.2 +50.6 +CCN [17] +67.4 +70.6 +47.7 +HGL [9] +69.4 +70.6 +49.1 +ECMR [8] +70.7 +72.0 +51.1 +MCC [11] +71.7 +73.4 +52.9 +JAE [32] +70.5 +73.1 +51.8 +VC R-CNN [30] +67.4 +69.5 +- +CL-VCR [31] +69.9 +70.6 +- +PPTMCO +72.2 +73.8 +53.5 +RGB image, which is to evaluate the effect of 2D object +positions. +Base+VFE. A variant model of PPTMCO only adopts the +visual features enhanced by pseudo 3D positions and depth +image features. This model is utilized to evaluate the effect of +image depth. +Base+VFE+DT. A variant model of PPTMCO leverages +VFE and DT to evaluate the effectiveness of attention mech- +anism guided by depth difference. +Base+VFE+DT+PEMRC. The proposed PPTMCO model +incorporates VFE, DT and PEMRC. +The ablation study results for the three subtasks in VCR +are shown in Table II. As can be observed, Base+VFE2D +obtains the improvements of 0.4% for the Q → A task, 0.5% +for the QA → R task, and 0.6% for the Q → AR task +TABLE II +ABLATION STUDY ON THE VALIDATION SET FOR THREE SUBTASKS IN +VCR. +Models +Q → A +QA → R +Q → AR +Base +70.2 +71.6 +50.5 +Base+VFE2D +70.6 +72.1 +51.1 +Base+VFE +71.2 +72.6 +51.9 +Base+VFE+DT +71.7 +73.2 +52.7 +Base+VFE+DT+PEMRC (PPTMCO) +72.2 +73.8 +53.5 +on the validation set respectively, indicating the importance +of object positions for image understanding. With depth in- +formation considered, Base+VFE further gains improvements +since pseudo 3D positions are more exact. Compared with +Base+VFE, Base+VFE+DT adopting depth differences to +guide attention mechanism achieves better performances of +0.5%, 0.6% and 0.8% improvements for the three subtasks, +indicating that depth differences focus the model to pay more +attention to the objects in the related depth level. The proposed +PPTMCO utilizes PEMRC to optimize parameters and obtains +the best performance on the validation set. +E. Visualization and Analysis +Instances of successful cases obtained by the proposed +PPTMCO are shown in Fig. 3. As can be seen in Fig. 3(a), +correlation between irrelevant < +person 1 +> and < +pottedplant 1 > is weakened in the adjustment matrix guided +by depth differences. The answer and rational both capture the +depth level of < person 1 >, < person 2 >, < person 3 >, +< pottedplant 2 >. In Fig. 3(b), the answer and rational +both pay more attention attention to closer < chair 2 >, +< chair 3 >, < chair 4 > instead of < chair 1 > on the +basis of understanding the sentence. Therefore, the proposed +PPTMCO can properly focus on key cues. Since models for +Q → A and QA → R are trained respectively, elements + +Q->A stage +QA->R stage + + +Question: +- 2.0 + + 1.25 + +Where is [person 1] running to? + + +1.00 + + +Answer: + +0.75 +1.0 +(A) [person 1] is running to score. (0.09%) + +0.50 +(B) [person 1 is running to help [person 2] [person 3] with the plants. (99.78%) +[person 2] + 0.5 +[e uosed] +0.25 +(C) [person 1] runs away from someone on the first floor. (0.09%) +help +- 0. 0 +are +(D) [person 1] is trying to escape out of the corridor. (0.04%) +working +-0.25 +-0.5 +the +Rationale +the +garden +(A) When someone has a lot of potted plants spread out methodically it's usually +-0.50 +plants +1.0 +heir family. (14 +son 1] is facing [person 2] [person 3] while they try to cut the tree. +30.78% +(C) [person 1] [person 2] are working the garden. (49.94%) +[t's common for owners of plants in greenhouses to check on them constantly +(a) +Q->A stage +QA->R stage +Question: + +What can [person 2] do if she becomes too tired? + + 1.25 + 2.0 +pe +Son + 1.00 +Answer: +1.5 +(A) [person 2] can run through the gap in the fence. (0.98%) +0.75 +1.0 +Cchair3 +(B) [person 2] could look in [dining table 1]. (1.54%) +0.50 +Kchair 4 +(C) [person 2] can sit down in chairs like [chair 3] or [chair 4]. (66.45%) +0.5 +0.25 +(D) [person 4] can jump off of [chair 3]. (31.03%) +0.00 + 0.0 +both +0.25 +[chair 3] +Rationale: +empty +-0.5 +[chair 4] ] +and +-0.50 +(A) [chair 3] [chair 4l are both empty and nearby. (78.54%) +nearby +(B) People can sit in chairs. (8.88%) +-0.75 +-1.0 +(C) [person 2] is carrying [chair 4] has a strap on it meant to hang on a hook, [chair +I [chair 3l are also outside. (4.17%) +a +(q)7 +in adjustment matrice from words to objects appear similar, +which also demonstrate the stability of the depth difference +guidance. +V. CONCLUSION +Visual commonsense reasoning is a challenging task since +it is difficult to sufficiently understand the image and properly +associate it with linguistic data. In this paper, a framework +named PPTMCO is proposed to achieve more discriminative +visual features and use image depth differences to assist asso- +ciating between cross-modal data. Specifically, image depth is +introduced to represent pseudo 3D positions of objects along +with 2D coordinates in the image and further enhance visual +features. Depth-aware Transformer is proposed to do attention +mechanism with depth differences to guide from answer words +and objects to objects, where each word is tagged with pseudo +depth value according to related objects. Considering samples +of VCR varying from each other and difficulty to be fit, a +model parameter estimation method is further proposed to +weightedly integrate parameters optimized by mini-batches +based on multi-level reasoning confidence. The experiments +conducted on the benchmark VCR dataset demonstrate the +effectiveness of the proposed method. +REFERENCES +[1] H. Shi, H. Li, Q. Wu, and K. N. Ngan, “Query reconstruction network +for referring expression image segmentation,” IEEE Trans. Multimedia, +vol. 23, pp. 995–1007, Apr. 2020. +[2] J. Zhu and H. Wang, “Multi-scale conditional relationship graph network +for referring relationships in images,” IEEE Trans. Cogn. Dev. Syst., +vol. 14, no. 2, pp. 752–760, Jun. 2022. +[3] L. Yang, H. Wang, P. Tang, and Q. Li, “Captionnet: A tailor-made +recurrent neural network for generating image descriptions,” IEEE Trans. +Multimedia, vol. 23, pp. 835–845, Apr. 2020. +[4] H. Wang, P. Tang, Q. Li, and M. Cheng, “Emotion expression with fact +transfer for video description,” IEEE Trans. Multimedia, vol. 24, pp. +715–727, Feb. 2022. +[5] W. Guo, Y. Zhang, J. Yang, and X. Yuan, “Re-attention for visual +question answering,” IEEE Trans. Image Process., vol. 30, pp. 6730– +6743, Jul. 2021. +[6] H. Zhong, J. Chen, C. Shen, H. Zhang, J. Huang, and X.-S. Hua, “Self- +adaptive neural module transformer for visual question answering,” IEEE +Trans. Multimedia, vol. 23, pp. 1264–1273, May 2020. +[7] R. Zellers, Y. Bisk, A. Farhadi, and Y. Choi, “From recognition to +cognition: Visual commonsense reasoning,” in Proc. CVPR’19, Jun. +2019, pp. 6713–6724. +[8] X. Zhang, F. Zhang, and C. Xu, “Explicit cross-modal representation +learning for visual commonsense reasoning,” IEEE Trans. Multimedia, +vol. 24, pp. 2986–2997, 2022. +[9] W. Yu, J. Zhou, W. Yu, X. Liang, and N. Xiao, “Heterogeneous graph +learning for visual commonsense reasoning,” in Proc. NeurIPS’19, Dec. +2019, pp. 2769–2779. +[10] J. Lin, U. Jain, and A. G. Schwing, “Tab-vcr: Tags and attributes based +vcr baselines,” in Proc. NeurIPS’19, Dec. 2019, pp. 15 615–15 628. +[11] X. Zhang, F. Zhang, and C. Xu, “Multi-level counterfactual contrast for +visual commonsense reasoning,” in Proc. ACM MM’21, Oct. 2021, pp. +1793–1802. +[12] R. Ranftl, A. Bochkovskiy, and V. Koltun, “Vision transformers for dense +prediction,” in Proc. CVPR’21, Jun. 2021, pp. 12 179–12 188. +[13] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, +Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” in Proc. +NeurIPS’17, Dec. 2017, pp. 5998–6008. +[14] Z. Wen and Y. Peng, “Multi-level knowledge injecting for visual +commonsense reasoning,” IEEE Trans. Circuits Syst. Video Technol., +vol. 31, no. 3, pp. 1042–1054, May 2020. +[15] W. Su, X. Zhu, Y. Cao, B. Li, L. Lu, F. Wei, and J. Dai, “Vl-bert: Pre- +training of generic visual-linguistic representations,” in Proc. ICLR’20, +Apr. 2020. +[16] W. Li, C. Gao, G. Niu, X. Xiao, H. Liu, J. Liu, H. Wu, and W. Haifeng, +“Unimo: Towards unified-modal understanding and generation via cross- +modal contrastive learning,” in Proc. ACL’21, Aug. 2021, pp. 2592– +2607. +[17] A. Wu, L. Zhu, Y. Han, and Y. Yang, “Connective cognition network for +directional visual commonsense reasoning,” in Proc. NeurIPS’19, Dec. +2019, pp. 5669–5679. +[18] H. Zhang, H. Uchiyama, S. Ono, and H. Kawasaki, “Motslam: Mot- +assisted monocular dynamic slam using single-view depth estimation,” +in arXiv:2210.02038, Oct. 2022. +[19] Y. Cao, H. Zhang, Y. Li, C. Ren, and C. Lang, “Cman: Leaning global +structure correlation for monocular 3d object detection,” IEEE Trans. +Intell. Transp. Syst. (Early access), pp. 1–11, 2022. +[20] M. Erg¨ul and A. Alatan, “Depth is all you need: Single-stage weakly +supervised semantic segmentation from image-level supervision,” in +Proc. ICIP’22, Oct. 2022, pp. 4233–4237. +[21] A. Pilzer, S. Lathuili`ere, D. Xu, M. M. Puscas, E. Ricci, and N. Sebe, +“Progressive fusion for unsupervised binocular depth estimation using +cycled networks,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 42, +no. 10, pp. 2380–2395, Oct. 2020. +[22] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image +recognition,” in Proc. CVPR’16, Jun. 2016, pp. 770–778. +[23] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, “Bert: Pre-training +of deep bidirectional transformers for language understanding,” in Proc. +NAACL’19, Jun. 2019, pp. 4171–4186. +[24] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” +in Proc. ICLR’14, Apr. 2014. +[25] Q. Chen, X. Zhu, Z.-H. Ling, S. Wei, H. Jiang, and D. Inkpen, +“Enhanced lstm for natural language inference,” in Proc. ACL’17, Jul. +2017, pp. 1657–1668. +[26] A. Jabri, A. Joulin, and L. Van Der Maaten, “Revisiting visual question +answering baselines,” in Proc. ECCV’16, Oct. 2016, pp. 727–739. +[27] P. Anderson, X. He, C. Buehler, D. Teney, M. Johnson, S. Gould, and +L. Zhang, “Bottom-up and top-down attention for image captioning and +visual question answering,” in Proc. CVPR’18, Jun. 2018, pp. 6077– +6086. +[28] J.-H. Kim, K.-W. On, W. Lim, J. Kim, J.-W. Ha, and B.-T. Zhang, +“Hadamard product for low-rank bilinear pooling,” in Proc. ICLR’17, +Nov. 2017. +[29] H. Ben-Younes, R. Cadene, M. Cord, and N. Thome, “Mutan: Multi- +modal tucker fusion for visual question answering,” in Proc. CVPR’17, +Jun. 2017, pp. 2612–2620. +[30] T. Wang, J. Huang, H. Zhang, and Q. Sun, “Visual commonsense r-cnn,” +in Proc. CVPR’20, Jun. 2020, pp. 10 757–10 767. +[31] K. Ye and A. Kovashka, “A case study of the shortcut effects in visual +commonsense reasoning,” in Proc. AAAI’21, Feb. 2021, pp. 3181–3189. +[32] Z. Li, Y. Guo, K. Wang, Y. Wei, L. Nie, and M. Kankanhalli, “Joint +answering and explanation for visual commonsense reasoning,” in +arXiv:2202.12626, Feb. 2022. + diff --git a/Y9FQT4oBgHgl3EQfeTYb/content/tmp_files/load_file.txt b/Y9FQT4oBgHgl3EQfeTYb/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..63cdcc1ee7588b0c305b6e240a1402a835081e59 --- /dev/null +++ b/Y9FQT4oBgHgl3EQfeTYb/content/tmp_files/load_file.txt @@ -0,0 +1,712 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf,len=711 +page_content='1 Pseudo 3D Perception Transformer with Multi-level Confidence Optimization for Visual Commonsense Reasoning Jian Zhu, and Hanli Wang, Senior Member, IEEE, Abstract—A framework performing Visual Commonsense Rea- soning (VCR) needs to choose an answer and further provide a rationale justifying based on the given image and question, where the image contains all the facts for reasoning and requires to be sufficiently understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Previous methods use a detector applied on the image to obtain a set of visual objects without considering the exact positions of them in the scene, which is inadequate for properly understanding spatial and semantic relationships between objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In addition, VCR samples are quite diverse, and parameters of the framework tend to be trained suboptimally based on mini-batches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To address above challenges, pseudo 3D perception Transformer with multi-level confidence optimization named PPTMCO is proposed for VCR in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Specifically, image depth is introduced to represent pseudo 3-dimension (3D) positions of objects along with 2-dimension (2D) coordinates in the image and further enhance visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Then, considering that relationships between objects are influenced by depth, depth- aware Transformer is proposed to do attention mechanism guided by depth differences from answer words and objects to objects, where each word is tagged with pseudo depth value according to related objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To better optimize parameters of the frame- work, a model parameter estimation method is further proposed to weightedly integrate parameters optimized by mini-batches based on multi-level reasoning confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Experiments on the benchmark VCR dataset demonstrate the proposed framework performs better against the state-of-the-art approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Index Terms—Visual commonsense reasoning, pseudo 3D per- ception, transformer, multi-level confidence optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' INTRODUCTION In recently years, with the rapid growth of the available vision-and-language data volume, many challenging tasks have been studied to analyze these data such as referring expres- sions [1], [2], image and video captioning [3], [4], visual question answering (VQA) [5], [6] and visual commonsense reasoning (VCR) [7], [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' These tasks all require the cross- modal intelligence to not only recognize entities in data but also understand their intrinsic interactions in varying degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' For instance, referring expressions is to localize the entities described by the language in the image, where cross-modal associations are primarily considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' VCR is a reasoning task to choose an answer and further provide a rationale justifying based on the given image and question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In such a task, the Corresponding author: Hanli Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang are with the Department of Computer Science & Technology, Key Laboratory of Embedded System and Service Com- puting (Ministry of Education), Tongji University, Shanghai 200092, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' China, and with Frontiers Science Center for Intelligent Autonomous Systems, Shanghai 201210, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' China (e-mail: jianzhu@tongji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='cn, hanliwang@tongji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='cn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' cross-modal intelligence also need to model discriminative intra-modal associations for reasoning, and VCR is promising in many fields such as robot dialogue system, private virtual assistant and baby development assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To tackle the challenging VCR task, various approaches have been adopted to analyze the complicated and associated data in VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Many frameworks adopted multi-branch models to independently associate the cross-modal data, and fuse features obtained for reasoning later [7]–[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' For instance, Zeller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [7] used LSTM and attention mechanism to contextualize the answer with the image or the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [9] constructed heterogeneous graphs to model correlations between different domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [8] associated struc- tured syntactic triplets of different sentences with the visual graphs for reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In the VCR task, the image contains all the facts that can be leveraged to do reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, ex- tracting discriminative visual features and properly associating them with languages are crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [10] adopted an object detector integrating attributes such as colors, texture, size to enhance visual features for VCR, and some works following also used such an enhanced detector [8], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Examples of RGB images (left) and depth images (right) generated from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In depth images, the pixel appears from yellow to black as the distance becomes farther.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With the help of image depth, the framework can represent objects in a way closer to human’s visual perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In general, all methods mentioned above utilized various detectors to obtain a set of objects for further processing without considering the exact positions of objects in the scene, which are crucial to understanding spatial and semantic relationships between objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Intuitively, 2-dimension (2D) coordinates of objects obtained by an object detector can be used to represent positions of objects in the image, which is This work has been submitted to the IEEE for possible publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Copyright may be transferred without notice, after which this version may no longer be accessible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='13335v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='CV] 30 Jan 2023 hair4 (b) a (c) (p)2 still insufficient for correct representation nevertheless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1(a), ”person 4” is close to ”chair 1” with regard to the 2D coordinates in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' However, an object need typically a set of 3-dimension (3D) coordinates to completely represent the position in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Compared with the 2D coordinates in the image, there is an additional dimension measuring the distance from the object to the image plane in the 3D coordinates, which can be converted to image depth [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Recently, with the development of monocular depth estimation [12], image depth can be easily obtained from a monocular RGB image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Fig 1(b) is the depth image generated from Fig 1(a), which reflects that ”person 4” is actually far away from ”chair 1” with image depth considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In addition, it can be observed in Fig 1(c) and (d) that objects with similar depth values (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ”person 1” and ”person 3”) are more likely to have close relationships (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ”person 1” holds the hand of ”person 1”), especially in the foreground of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With image depth introduced, the model owns more characteristics of human’s visual perception since different distances can be distinguished and the visual field becomes smaller as the distance is shorter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, image depth which is usually ignored in image understanding can be of benefit to exactly describing objects and analyzing associations between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' VCR is a challenging reasoning task, where the image needs to be understood as precisely as possible to provide the reasoning rationale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Inspiring by analyzing the image in a way closer to human’s visual perception, pseudo 3D per- ception Transformer with multi-level confidence optimization named PPTMCO for VCR is proposed in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The framework uses a two-branch Transformer [13] architecture to independently associate the answer with the image or the question, and combine results of branches for further reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In the stage of image processing, visual features of objects detected are enhanced by pseudo 3D positions and features of depth image regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In the answer-image branch, depth-aware Transformer (DT) is proposed which uses depth differences to guide attention mechanism from words and objects to objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Words of each answers are also tagged with pseudo depth values according to related objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Since samples of VCR usually vary from each other and are difficulty to be fit, a model parameter estimation method guided by multi-level reasoning confidence (PSMRC) is further proposed to weightedly integrate parameters of models optimized by mini-batches to obtain better parameter values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In summary, the major contributions of this work are the following three-folds: (1) Image depth is firstly investigated in the cross-modal reasoning task by enhancing object fea- tures and guiding depth-aware attention in a way closer to human’s visual perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (2) A model parameter estimation method is proposed to relieve sub-optimization caused by di- verse samples via weightedly integrating parameters based on multi-level reasoning confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (3) The proposed framework achieves new state-of-the-art results on the VCR benchmark dataset, demonstrating the effectiveness of the approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' RELATED WORK A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Visual Commonsense Reasoning Visual commonsense reasoning (VCR) is a reasoning task to choose an answer and further provide a rationale justifying based on the given image and question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A main difficulty of VCR is how to sufficiently and properly represent visual cues from the image and associate them with linguistic data for reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Previous methods can be roughly divided into two categories: (1) explore models processing sequential data, (2) adopt graph-based networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' At the earliest, Zeller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [7] used LSTM with attention mechanism to contextualize sequential answer words with sequential question words or visual objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Later, Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [10] integrated attributions of objects such as color and texture to enhance visual features used in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [14] adopted an additional linguistic knowledge base to transfer commonsense knowledge to the LSTM model doing VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [15] used cross-modal sequential data consisting of visual objects and linguistic words from several cross-modal datasets to train BERT model, then fine-tuned the framework on the VCR dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [16] proposed a cross-modal contrastive learning method to learn better alignment of cross-modal data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With regard to graph representation and learning, several methods [8], [9], [17] were investigated on the VCR task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [9] built answer-vision and answer-question heterogeneous graphs for networks to do reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [17] developed visual neuron connectivity to build visual graph with linguistic data considered for graph convolutional networks to learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [8] constructed visual and linguistic graphs respectively, and then fused them for cross-modal reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' These methods all focused on visual features of objects and ignored their exact spatial representations and relationships, which also have influence on correctly understanding on visual interactive features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In this work, image depth is introduced into VCR, enhancing visual features with pseudo 3D position and depth image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Then, depth differences are used to guide the attention mechanism originally based on semantic similarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Depth Estimation Depth estimation from images is an important task in computer vision, which is widely used in simultaneous lo- calization and mapping (SLAM) [18], object detection [19] and semantic segmentation [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Depth estimation can be divided into binocular depth estimation [21] and monocular depth estimation [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Compared with the binocular camera system, the monocular camera system is more convenient and inexpensive to be deployed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, monocular depth estimation is easier to be applied to other tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [18] presented a dynamic visual SLAM system tracking both poses and bounding boxes of dynamic object, where dynamic features were fetched by monocular depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [19] encoded structure correlations from monocular depth data, and embeded them with appearance information learnt from RGB data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ergul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [20] proposed to fuse the 3D geometric structure of the scene into the segmentation based on depth maps estimated from one single image via a monocular depth estimation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' All works above used 3 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Illustration of the proposed PPTMCO architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The framework consists of three key parts: (1) visual features enhancing, (2) answer-image contextualization by depth-aware Transformer, and (3) parameter estimation by reasoning confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' depth images to assist pure visual task, and few efforts were devoted to more complicated cross-modal tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In this paper, depth images are investigated in the cross-modal VCR task, where visual data need to further interact with linguistic data to realize image understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' PROPOSED PPTMCO In this section, the overview of the proposed framework is firstly introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Then, visual features enhancing with image depth, depth-aware Transformer for answer-image association, and parameter estimation method guided by multi-level rea- soning confidence are described in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Overview The VCR task is to choose an answer and further provide a rationale justifying based on the given image and question, which consists of the following three subtasks: 1) Q → A: Given an image and a question, the model should choose the right option from four answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2) QA → R: Given an image, a question and the correct answer, the model should choose the right option from four rationales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3) Q → AR: Given an image and a question, the model should choose both the right answer and rationale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To do Q → AR, the frameworks need to both do Q → A and QA → R, which can be viewed as two four-way classification problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The results of Q → AR can be obtained by combining the results of Q → A and QA → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The architecture of the proposed PPTMCO framework is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The image regions, question and answer data are firstly fed into pre-trained networks to extract features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Then, original visual features are enhanced by image depth features along with pseudo 3D positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The framework utilizes plain Transformer and depth-aware Transformer to do answer-question and answer-image contextualization, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Finally, model parameters are estimated by weightedly integrating multiple sets of parameters based on multi-level reasoning confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Visual Feature Enhancing with Image Depth Given a question with Nq words Uq = {uq i }Nq i=1 or a answer with Na words Ua = {ua i }Na i=1, the linguistic features of the question Tq = {tq i }Nq i=1, tq i ∈ Rd or those of the answer Ta = {ta i }Na i=1, ta i ∈ Rd are obtained by a pre-trained BERT and a subsequent bidirectional LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Visual features are enhanced by pseudo 3D positions and depth image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Given No objects O = {oi}No i=1 in a RGB image I, the original visual features S = {si}No i=1, si ∈ Rd are extracted by a pre-trained CNN, where d is the feature dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The depth image ID is generated via the monocular depth estimation model [12] applied on the original RGB image I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Each object oi corresponds to a bounding box denoted as (xi, yi, wi, hi), where xi, yi represent the 2D coordinates of the box center and wi, hi represent the width and height of the box in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The depth image is aligned with the RGB image, and the bounding box can also be used to indicate the 2D position of the object in the depth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Since the object is typically in the center of the bounding box with a few irrelevant pixels on the edge, the pixel value zi at the position of box center (xi, yi) in the depth image is used as the depth coordinate of the object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Then, the pseudo 3D position feature is characterized by the box feature sbox i consisting of six elements as sbox i = [xi, yi, zi, wi, hi, wi ∗ hi], (1) where xi, yi, zi, wi, hi are all normalized in range [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To integrate depth information more accurately, a typical CNN is applied on the box region of the depth image to obtain the depth feature sdepth i ∈ Rd of the object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The enhanced Visual features enhancing Parameter estimation Reasoning Sample-level Batch-level CNN 17 ★ ★ ★ ★ Visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=" ★ : High quality ★ ★ + RGB image Low quality High quality MLP Low quality [x,y,w,h] monocular depth estimation', [z] Box features Reasoning CNN 11 networks : : 11 ↓ : 1 'Enhanced objecti i I Depth features : Prediction probability!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Step t optimization Step t parameters Step t-1 parametersi features Depth image Contextualization Answer encoder Answer-image Answer-question [person 2] can sit down BERT Depth-aware Transformer in chairs like [chair 3] or [chair 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' : Answer : Transformer + Question encoder What can [personll do Z BERT if she becomes too Vision tired?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Pseudo Object Depth Semantic : depth difference map attention map guidance depth Question guidance Question4 object feature se i ∈ Rd is jointly learnt from si, sbox i , sdepth i , which can be formulated as se i = fc(concat([si, sbox i , sdepth i ])), (2) where fc(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=') is a fully-connected layer, and concat is the concatenating operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The enhanced object feature with exact spatial information can more sufficiently represent the object, and provide spatial positional encoding for cross-modal Transformer in analogy with sequential positional encoding in plain Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Depth-aware Transformer After obtaining visual and linguistic features, the framework adopts Transformer-based models to associate them with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Plain Transformer model is used in the answer-question branch while depth-aware Transformer is proposed in the answer-image branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Given a sequence X = {xi}n i=1 for a plain Transformer layer, the attention mechanism can be formulated as A = Q · (K)T √ d , (3) where A ∈ Rn×n represents the attention weight matrix, and Qi, Ki are projections of xi using independent fully-connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In the answer-image branch, the sequence for depth- aware Transformer is composed of objects and answer words as {s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='sNo, t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='.tNa}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Depth-aware attention between objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The plain at- tention mechanism is mainly based on semantic similarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' However, two objects with similar visual appearances and quite different depth values may have discriminative semantic relationships with another object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As is assumed that objects with similar depth values are more likely to have close relationships, depth differences are used to guide the attention mechanism in depth-aware Transformer, following the princi- ple that the more similar the depth is, the more attention need be paid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With regard to objects i, j, depth difference can be calculated as ∆zij = |zi − zj| (4) where ∆zij ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To design the attention mechanism as the principle above, bij is proposed to adjust the semantic attention weights by ∆zij, which is formulated as bij = |Aij| ∗ (e−∆zij − α), (5) where adjust matrix bij grows from negative to positive in the scale of |Aij| as ∆zij declines, and α is the depth bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The depth-aware attention weight is calculated as follow: Adepth ij = Aij + bij (6) Depth-aware attention from words to objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The answer is a description related to objects in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' For an word in the answer, it is mainly associated with objects in a level of depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, the word implicitly corresponds to a depth level, which is reflected by a pseudo depth value given in depth-aware Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The pseudo depth ˜zi of the word i based on objects is calculated as follow: ˜zi = � softmax(Aij) ∗ zj (No < j ≤ No + Na) (7) Therefore, with regard to a word i and an object j, depth difference can also be obtained by ∆zij = |˜zi − zj|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (8) The depth-aware attention mechanism from words to objects can be integrated into the unified framework in a way similar as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (5) and (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Parameter Estimation Guided by Multi-level Reasoning Confidence After contextualizing answer words with image regions and question words, the vision-guidance answer word rep- resentation Tai ∈ RNa×d and the question-guidance answer word representation Taq ∈ RNa×d are selected for further reasoning, which are concatenated with the original answer word representation Ta to obtain the sequential reasoning feature T reason a ∈ RNa×3d as T reason a = concat([Ta, Tai, Taq]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (9) The sequential reasoning feature is required to be pooled as a vector for the classification network, which is a two-layer fully-connected network adopted in [7], [8], [10] as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The output is activated by softmax function to obtain the prediction probability for four choices P = [p1, p2, p3, p4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The framework is trained to optimize parameters on mini- batches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' For such a challenging reasoning task with diverse samples, an optimization is probable to lead to a sub-optimized direction for the barely satisfactory reasoning performance on the mini-batch, especially at a later stage of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, selectively using multiple sets of parameters to estimate parameters can relieve the stochastic optimization problem on a mini-batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Here, according to the sample-level and batch-level reason- ing confidence, an optimization is divided into high-quality and low-quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Given a batch with Nb samples, predictions on the batch can be denoted as {Pi}Nb i=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Sample-level high-quality: The sample is predicted cor- rectly with high-confidence denoted as max(Pi) > csample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Batch-level high-quality: The proportion of high-quality reasoning samples in the batch is high denoted as Nsample h/Nb > cbacth, and the prediction accuracy of the optimization is better than the previous one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Nsample h is the number of high-quality reasoning samples in the batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Parameters estimated Kes t are updated as the training step t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To ensure the continuity of the optimization, optimization on the high-quality reasoning batch and that on the low-quality one are weightedly integrated by β, where β equals 1 for high- quality one and Nsample h/Nb for low-quality one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Parameters estimated Kes t at the step t are generated based on parameters optimized this time and parameters estimated at the previous step t − 1 as follow: Kes t = β ∗ (1 − γ) ∗ Kt + (1 − β ∗ (1 − γ)) ∗ Kes t−1, (10) where γ is the hyperparameter controlling the number of steps for integrating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 5 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Implementation The proposed framework is implemented on PyTorch and trained with 4 Tesla V100 GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The models for the subtasks Q → A and QA → R possess identical architecture with their weights trained separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The prediction for the subtask Q → AR is the combination of the predictions for Q → A and QA → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In the stage of feature extraction for original visual and linguistic data, each object in the given image is extracted as a 512-dimensional vector by the method in [10] with ResNet101 [22] as the backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Each word is embedded as a 768-dimensional feature by a pre-trained BERT [23], and sequential words as a whole sentence are further input into a single-layer bidirectional LSTM model to obtain 512- dimensional vectors for each word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The CNN networks used for depth images have three convolutional layers, and a fully- connected layer to generate 512-dimensional vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The vi- sual features enhanced are also 512-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The dropout rate is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='3 in Bi-LSTM and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 in Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The parameters of Transform-based model are trained by Noam [13] while the remaining modules are trained by Adam [24] with the learning rate initialized as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' α in depth-aware Transformer is set as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6, and γ in PEMRC is set as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='9998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' csample and cbacth are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='55 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The batch size is 96, and the model is trained for 30 epochs with early stopping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' EXPERIMENT A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Dataset Extensive experiments are carried out on the VCR bench- mark dataset [7], which is composed of 290k four-way multi- choice QA problems derived from 110k movie scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Differ- ent from VQA dataset where the answer is usually a single word, the answer and rationale in the VCR dataset is more complicated and in the form of mixtures of visual and linguis- tic words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The average lengths of the answers and rationales are over 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 words and 16 words, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Following the data partition practice [7], the training set consists of 80,418 images with 212,923 questions, the validation set is composed of 9,929 images with 26,534 questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Evaluation Metric and Baseline The evaluation metric is classification accuracy, which is a ratio of correctly classified samples to all test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The competing methods are divided into three categories: (1) text-only baselines, including BERT [23], BERT (response only) [23], ESIM+ELMO [25] and LSTM+ELMO [25], which don’t utilize visual information and can be used to evaluate the influence of visual context;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (2) VQA baselines, including RevisitedVQA [26], BottomUpTopDown [27], MLB [28] and MUTAN [29], which are originally designed for VQA and modified to perform VCR (compared with these methods, the capability of the proposed framework to model the correlation between the complex response and the question or image can be evaluated);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (3) VCR methods, including R2C [7], CKRM [14], TAB-VCR [10], CCN [17], HGL [9], ECMR [8], VC R-CNN [30], CL-VCR [31], MCC [11] and JAE [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The brief descriptions of the competing VCR methods are presented below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' R2C adopts bilinear attention mechanism and LSTM to associate image with text for reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CKRM is an attention-based model to transfere external knowledge into the VCR task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' TAB-VCR integrates attribute information into visual features and assigns extra tags to image grounding for the VCR task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CCN employs a connective cognition network and reorganizes visual neuron connectivity to do VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' HGL operates heterogeneous graph learning based on the cross- modal correlation between image and text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ECMR integrates visual graph and linguistic graph for cross-modal reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' VC R-CNN employs region-based CNN to perform causal intervention for visual feature enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CL-VCR adopts a curriculum-based masking approach to training model more robustly for VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' MCC generates counterfactual samples and uses a contrastive learning strategy to train VCR framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' JAE presents a plug-and-play knowledge distillation enhanced framework to do VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Quantitative Result The quantitative results achieved by the proposed PPTMCO compared with several competing methods for the three sub- tasks in VCR are given in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With regard to these text- only baselines, performances are bad without considering the important visual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' These VQA baselines gain im- provements compared with text-only baselines, but still cannot achieve satisfactory results since the expressions in VCR are more complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' For the VCR methods, TAB-VCR [10], ECMR [8], and MCC [11] adopting visual features integrating attributes achieve better performances in general compared with other baselines R2C [7], CKRM [14], CCN [17], HGL [9] using plain visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Further considering exact 3D positions via image depth, the proposed PPTMCO framework obtains the best performance with 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2% for the Q → A task, 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8% for the QA → R task, 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5% for the Q → AR task on the validation set, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In comparison to MCC [11] where the framework is trained via counterfactual samples and contrastive learning, the proposed PPTMCO adopts a parameter estimation method guided by multi-level reasoning confidence to optimize the framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As a result, PPTMCO gains the improvements of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5% for the Q → AR task on the validation set over MCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As for the VC R-CNN [30] method using causal intervention, the CL-VCR [31] method with robust training, and JAE [32] adopting knowledge distil- lation, the proposed PPTMCO has superiority as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' All the above results demonstrate the effectiveness of the proposed PPTMCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ablation Study To evaluate the effectiveness of the visual feature enhanc- ing (VFE), DT and PEMRC modules in the framework, several models are designed to do ablation study as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A variant of the R2C model [7] replaces the backbone with ResNet101, and uses plain Transformer to do contextu- alization and reasoning instead of LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Base+visual features enhanced with 2D positions (VFE2D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A variant of the base model uses the visual features enhanced by 2D positions obtained in the 6 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Instances of successful cases for the VCR task obtained by the proposed PPTMCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The percentages in brackets are the probabilities predicted by PPTMCO, and the choices filled in brown are ground-truths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' To be distinguishable, < person 1 > means visual object, [person1] means linguistic entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The heatmaps for the ground-truth choices on the right indicate the final adjustment matrice for answer-image contextualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' TABLE I COMPARISON OF ACCURACY FOR THREE SUBTASKS IN VCR ACHIEVED BY THE COMPETING METHODS ON THE VALIDATION SET OF VCR DATASET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Methods Q → A QA → R Q → AR BERT [23] 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 BERT (response only) [23] 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='3 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 ESIM+ELMO [25] 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='3 LSTM+ELMO [25] 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='3 RevisitedVQA [26] 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 BottomUpTopDown [27] 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 MLB [28] 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 MUTAN [29] 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 R2C [7] 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 CKRM [14] 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 TAB-VCR [10] 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='9 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 CCN [17] 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 HGL [9] 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 ECMR [8] 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 MCC [11] 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='9 JAE [32] 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 VC R-CNN [30] 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 CL-VCR [31] 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='9 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 PPTMCO 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 RGB image, which is to evaluate the effect of 2D object positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Base+VFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A variant model of PPTMCO only adopts the visual features enhanced by pseudo 3D positions and depth image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' This model is utilized to evaluate the effect of image depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Base+VFE+DT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' A variant model of PPTMCO leverages VFE and DT to evaluate the effectiveness of attention mech- anism guided by depth difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Base+VFE+DT+PEMRC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The proposed PPTMCO model incorporates VFE, DT and PEMRC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The ablation study results for the three subtasks in VCR are shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As can be observed, Base+VFE2D obtains the improvements of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='4% for the Q → A task, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5% for the QA → R task, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6% for the Q → AR task TABLE II ABLATION STUDY ON THE VALIDATION SET FOR THREE SUBTASKS IN VCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Models Q → A QA → R Q → AR Base 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 Base+VFE2D 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='1 Base+VFE 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='9 Base+VFE+DT 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='7 Base+VFE+DT+PEMRC (PPTMCO) 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 on the validation set respectively, indicating the importance of object positions for image understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' With depth in- formation considered, Base+VFE further gains improvements since pseudo 3D positions are more exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Compared with Base+VFE, Base+VFE+DT adopting depth differences to guide attention mechanism achieves better performances of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5%, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='6% and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='8% improvements for the three subtasks, indicating that depth differences focus the model to pay more attention to the objects in the related depth level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The proposed PPTMCO utilizes PEMRC to optimize parameters and obtains the best performance on the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Visualization and Analysis Instances of successful cases obtained by the proposed PPTMCO are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' As can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3(a), correlation between irrelevant < person 1 > and < pottedplant 1 > is weakened in the adjustment matrix guided by depth differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The answer and rational both capture the depth level of < person 1 >, < person 2 >, < person 3 >, < pottedplant 2 >.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3(b), the answer and rational both pay more attention attention to closer < chair 2 >, < chair 3 >, < chair 4 > instead of < chair 1 > on the basis of understanding the sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Therefore, the proposed PPTMCO can properly focus on key cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Since models for Q → A and QA → R are trained respectively, elements Q->A stage QA->R stage Question: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 Where is [person 1] running to?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='00 Answer: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 (A) [person 1] is running to score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='09%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='50 (B) [person 1 is running to help [person 2] [person 3] with the plants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='78%) [person 2] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 [e uosed] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 (C) [person 1] runs away from someone on the first floor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='09%) help 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 0 are (D) [person 1] is trying to escape out of the corridor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='04%) working 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content="5 the Rationale the garden (A) When someone has a lot of potted plants spread out methodically it's usually 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='50 plants 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 heir family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (14 son 1] is facing [person 2] [person 3] while they try to cut the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='78% (C) [person 1] [person 2] are working the garden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content="94%) [t's common for owners of plants in greenhouses to check on them constantly (a) Q->A stage QA->R stage Question: What can [person 2] do if she becomes too tired?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 pe Son 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='00 Answer: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 (A) [person 2] can run through the gap in the fence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='98%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 Cchair3 (B) [person 2] could look in [dining table 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='54%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='50 Kchair 4 (C) [person 2] can sit down in chairs like [chair 3] or [chair 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='45%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 (D) [person 4] can jump off of [chair 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='03%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 both 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='25 [chair 3] Rationale: empty 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='5 [chair 4] ] and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='50 (A) [chair 3] [chair 4l are both empty and nearby.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='54%) nearby (B) People can sit in chairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='88%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='0 (C) [person 2] is carrying [chair 4] has a strap on it meant to hang on a hook, [chair I [chair 3l are also outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='17%) a (q)7 in adjustment matrice from words to objects appear similar, which also demonstrate the stability of the depth difference guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CONCLUSION Visual commonsense reasoning is a challenging task since it is difficult to sufficiently understand the image and properly associate it with linguistic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' In this paper, a framework named PPTMCO is proposed to achieve more discriminative visual features and use image depth differences to assist asso- ciating between cross-modal data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Specifically, image depth is introduced to represent pseudo 3D positions of objects along with 2D coordinates in the image and further enhance visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Depth-aware Transformer is proposed to do attention mechanism with depth differences to guide from answer words and objects to objects, where each word is tagged with pseudo depth value according to related objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Considering samples of VCR varying from each other and difficulty to be fit, a model parameter estimation method is further proposed to weightedly integrate parameters optimized by mini-batches based on multi-level reasoning confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' The experiments conducted on the benchmark VCR dataset demonstrate the effectiveness of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' REFERENCES [1] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Shi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wu, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ngan, “Query reconstruction network for referring expression image segmentation,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 995–1007, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang, “Multi-scale conditional relationship graph network for referring relationships in images,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 752–760, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Tang, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, “Captionnet: A tailor-made recurrent neural network for generating image descriptions,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 835–845, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Tang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cheng, “Emotion expression with fact transfer for video description,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 715–727, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yuan, “Re-attention for visual question answering,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Image Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 6730– 6743, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Shen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Huang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Hua, “Self- adaptive neural module transformer for visual question answering,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 23, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1264–1273, May 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zellers, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Bisk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Farhadi, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Choi, “From recognition to cognition: Visual commonsense reasoning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’19, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 6713–6724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [8] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Xu, “Explicit cross-modal representation learning for visual commonsense reasoning,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2986–2997, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Liang, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Xiao, “Heterogeneous graph learning for visual commonsense reasoning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' NeurIPS’19, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2769–2779.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lin, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Jain, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Schwing, “Tab-vcr: Tags and attributes based vcr baselines,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' NeurIPS’19, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 15 615–15 628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [11] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Xu, “Multi-level counterfactual contrast for visual commonsense reasoning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ACM MM’21, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1793–1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ranftl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Bochkovskiy, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Koltun, “Vision transformers for dense prediction,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’21, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 12 179–12 188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Gomez, Ł.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kaiser, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Polosukhin, “Attention is all you need,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' NeurIPS’17, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 5998–6008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [14] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wen and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Peng, “Multi-level knowledge injecting for visual commonsense reasoning,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Circuits Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Video Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1042–1054, May 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Su, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wei, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Dai, “Vl-bert: Pre- training of generic visual-linguistic representations,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ICLR’20, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [16] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Gao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Niu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Xiao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wu, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Haifeng, “Unimo: Towards unified-modal understanding and generation via cross- modal contrastive learning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ACL’21, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2592– 2607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Han, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Yang, “Connective cognition network for directional visual commonsense reasoning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' NeurIPS’19, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 5669–5679.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Uchiyama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ono, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kawasaki, “Motslam: Mot- assisted monocular dynamic slam using single-view depth estimation,” in arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='02038, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [19] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ren, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lang, “Cman: Leaning global structure correlation for monocular 3d object detection,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Transp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' (Early access), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1–11, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Erg¨ul and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Alatan, “Depth is all you need: Single-stage weakly supervised semantic segmentation from image-level supervision,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ICIP’22, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 4233–4237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Pilzer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lathuili`ere, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Xu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Puscas, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ricci, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Sebe, “Progressive fusion for unsupervised binocular depth estimation using cycled networks,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2380–2395, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Sun, “Deep residual learning for image recognition,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’16, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Devlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Toutanova, “Bert: Pre-training of deep bidirectional transformers for language understanding,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' NAACL’19, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 4171–4186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [24] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kingma and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ba, “Adam: A method for stochastic optimization,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ICLR’14, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [25] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ling, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wei, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Jiang, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Inkpen, “Enhanced lstm for natural language inference,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ACL’17, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 1657–1668.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Jabri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Joulin, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Van Der Maaten, “Revisiting visual question answering baselines,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ECCV’16, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 727–739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [27] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Anderson, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' He, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Buehler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Teney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Johnson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Gould, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, “Bottom-up and top-down attention for image captioning and visual question answering,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’18, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 6077– 6086.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' On, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Lim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ha, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, “Hadamard product for low-rank bilinear pooling,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' ICLR’17, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [29] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ben-Younes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cadene, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Cord, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Thome, “Mutan: Multi- modal tucker fusion for visual question answering,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’17, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2612–2620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [30] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Zhang, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Sun, “Visual commonsense r-cnn,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' CVPR’20, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 10 757–10 767.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [31] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Ye and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kovashka, “A case study of the shortcut effects in visual commonsense reasoning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' AAAI’21, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 3181–3189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' [32] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Guo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Wei, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Nie, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' Kankanhalli, “Joint answering and explanation for visual commonsense reasoning,” in arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content='12626, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Y9FQT4oBgHgl3EQfeTYb/content/2301.13335v1.pdf'} diff --git a/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/2301.01343v1.pdf.txt b/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/2301.01343v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..ccbd368ce45a50e8a6b0948ffdd52526eb3506ec --- /dev/null +++ b/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/2301.01343v1.pdf.txt @@ -0,0 +1,1700 @@ +Explainability and Robustness of Deep +Visual Classification Models +Jindong Gu +Munich 2022 +arXiv:2301.01343v1 [cs.CV] 3 Jan 2023 + +mAbstract +Deep learning has revolutionized AI and deep neural networks, in particular, have been +hugely successful in a wide range of applications. Deep neural network architectures with +different inductive biases have been proposed in different communities. In the computer vi- +sion community, Convolutional Neural Networks (CNNs), first proposed in the 1980’s, have +become the standard visual classification model. Recently, as alternatives to CNNs, Cap- +sule Networks (CapsNets) and Vision Transformers (ViTs) have been proposed. CapsNets, +which were inspired by the information processing of the human brain, are considered to +have more inductive bias than CNNs, whereas ViTs are considered to have less inductive +bias than CNNs. All three classification models have received great attention since they +can serve as backbones for various downstream tasks, e.g. object detection and semantic +segmentation. However, these models are far from being perfect. +As pointed out by the community, there are two weaknesses in standard Deep Neural +Networks (DNNs). One of the limitations of DNNs is the lack of explainability. Even +though they can achieve or surpass human expert performance in the image classification +task, the DNN-based decisions are difficult to understand. In many real-world applica- +tions, however, individual decisions need to be explained. The other limitation of DNNs +is adversarial vulnerability. Concretely, the small and imperceptible perturbations of in- +puts can mislead DNNs. The vulnerability of deep neural networks poses challenges to +current visual classification models. The potential threats thereof can lead to unaccept- +able consequences. Besides, studying model adversarial vulnerability can lead to a better +understanding of the underlying models. +Our research aims to address the two limitations of DNNs. Specifically, we focus on +deep visual classification models, especially the core building parts of each classification +model, e.g. dynamic routing in CapsNets and self-attention module in ViTs. +We argue that both the lack of explainability and adversarial vulnerability can be +attributed to the difference in the visual features used by visual recognition models and +the human visual system to recognize objects. Namely, the visual clues used by standard +CNNs are different from the ones used by our visual system. The differences make the +interpretation of classifications difficult. Similarly, the differences also leave attackers the +chance to manipulate decisions with quasi-imperceptible input perturbations. +We have analyzed if the brain-inspired Capsule Network (CapsNet) performs more ro- +bustly than the CNNs. Our investigation on CapsNet shows CapsNets with more inductive + +Abstract +3 +bias do not perform better than CNNs. The dynamic routing therein can even harm the +robustness, in contrast to the common belief. Compared to CNNs and CapsNets, Vision +Transformers (ViTs) are considered to have less inductive bias in their architecture. Given +the patch-wise input image representation of ViT, we dissect ViT with adversarial patch +attack methods. We find that vision transformers are more robust to naturally corrupted +patches than CNNs, whereas they are more vulnerable to adversarial patches. Specifically, +the attention module can effectively ignore naturally corrupted patches. However, when +attacked by an adversary, it can be easily fooled. +Overall, our work provides a detailed analysis of CNNs, CapsNet, and ViTs in terms of +explainability and robustness. The contribution of this thesis will facilitate the application +of existing popular deep visual classification models and inspires the development of more +intelligent classifiers in the future. + +Chapter 1 +Introduction +1.1 +Motivation +Artificial intelligence changes our daily lives in many perspectives. The recent advances of +artificial intelligence are mainly powered by Deep Learning method [1]. As a revolutionary +technique, Deep Learning methods are also embraced by other disciplines, e.g. bioscience +and astronomy. As a representative model in the framework of deep learning, deep neural +networks (DNNs) dominate the community due to their powerful expressiveness. However, +two limitations of deep neural networks prevent their wide application in safety-critical +domains, e.g. the medical domain and autonomous driving system. +One of the limitations of deep neural networks is their lack of explainability. Even +though the DNN-based intelligent system can achieve or surpass human expert perfor- +mance on some tasks, it is not clear how the system reaches its decisions. +For exam- +ple, Deep convolutional neural networks (DCNNs) achieve start-of-the-art performance on +many tasks, such as visual object recognition [2, 3, 4, 5]. However, since they lack trans- +parency, they are considered as ”black box” solutions. In real-world applications, however, +individual decisions need to be explained to gain the trust of the users. e.g., autonomous +driving systems should reassure passengers by giving explanations when braking the car +abruptly [6, 7]. Decisions made by deep models are also required to be verified in the med- +ical domain. Mistakes of unverified models could have an unexpected impact on humans +or lead to unfair decisions [8, 9, 10]. Besides, AI applications must comply with related +legislation, e.g., the right to explanation in GDPR of the European Union [11]. +The other limitation of deep neural networks is limited generalization robustness. When +deep neural networks are deployed in real-world applications, the input can deviate from + +2 +1. Introduction +Figure 1.1: The overview of deep visual classification model architectures. This figure is +based on the figures in [17, 3, 12] +the training data distribution. The inference on the input with overlapped patterns [12], +affine-transformed pattern [12, 13], and natural corruption [14] can result in unexpected +results. Besides the robustness to out-of-distribution data, the low robustness to artificial +perturbation also raises great concern in the community. Concretely, the small and im- +perceptible artificial perturbations of inputs can mislead DNN-based intelligent systems. +For example, given an image correctly classified by a deep convolutional neural network, +a hardly human-perceptible artificial perturbation can cause the convolutional neural net- +work to misclassify the image when added to it. The vulnerability of Deep Learning poses +challenges to current intelligent systems. The adversarial images on CNNs can pose po- +tential threats to security-sensitive CNN-based applications, e.g., face verification [15] and +autonomous driving [16]. The potential threats thereof can lead to unacceptable conse- +quences. Besides, the existence of adversarial images demonstrates that the object recogni- +tion process in CNNs is dramatically different from that in human brains. Hence, the study +of adversarial examples on deep neural networks can also lead to a better understanding +of the underlying object recognition models. +Since [18] proposed the AlexNet, deep neural networks have revolutionized the computer +vision community. In the image classification task, the classification model consists of two +parts, i.e., feature extractor and classifier. The modules that extract features from input +images are also adopted as feature extractor (dubbed backbone) in downstream tasks, +e.g., object detection [19, 20] and semantic segmentation [21, 22, 23]. The improvement +of the classification models often also benefits the downstream tasks due to the improved +backbone. In this thesis, we focus on deep visual classification models from the perspectives +of explainability and robustness. + +MLP +Head +Transformer Encoder +IIL,lI +001..0 + +Linear Projection of Flattened Patches +Wij = [8 × 16] +Vision Transformer +Convolutional Neural Network +Capsule Network +Inductive Bias +High +Low1.1 Motivation +3 +As one of the representatives of deep visual classification models, convolutional neural +networks have dominated the computer vision community in the last decade [18]. How- +ever, CNNs suffer from many limitations, e.g., only local information aggregation at lower +layers and the broken equivariance. +Recently, the community has been attempting to +propose new models to overcome the limitations. Two among them have received great +attention from the community. The one is Capsule Networks (CapsNet) which is inspired +by the information processing in the human brain [12]. Compared to CNNs, CapsNet is +more inductively-biased where the partial information processing in the human brain is +integrated into the model, e.g., the transformation process. The other is Vision Trans- +former(ViT) [17]. Given the success of Transformer in natural language processing (NLP), +the work [17] generalizes Transformer architectures to image classification task by rep- +resenting the input image as a sequence of image patches. +Compared to CNNs, ViTs +are less inductive-biased where information aggregation is also possible at lower layers. +Convolutional Neural Networks, Capsule Networks, and Vision Transformers raise great +attention in the community. Hence, in this work, we mainly focus on the three deep visual +classification models. +In the rest of this chapter, we first introduce background knowledge about CNNs, Cap- +sNets, and ViTs in Section 1.2. Then, in Section 1.3, we present a summary of the explain- +ability of deep visual classifications and describe our contributions to the explainability of +deep visual classification models. Last, in Section 1.4, we show the categorization of the +robustness of deep visual classifications and describe our contributions to the robustness +of deep visual classification models. +Contributions. In this dissertation, our contributions can be summarized from two +perspectives. From the perspective of explainability, we first present a novel method, called +CLRP, to explain CNN-based image classifications in Chapter 2. Then, in Chapter 3, we +present our interpretable capsule networks whose predictions can be explained with built-in +modules. Last, we show our understanding of ViT-based image classifications in Chapter 7. +From the perspective of robustness, our contributions mainly focus on the role the model +architecture plays in terms of both natural robustness and adversarial robustness. We +present our findings and improvements of Capsule Networks’ natural robustness to non- +additive perturbation in Chapters 4 and 5, and further propose our adversary Vote Attack +method to show the vulnerability of CapsNets in Chapter 6. Besides, we introduce our +understanding of the robustness of ViT-based classifications to patch-wise perturbations +in Chapter 7. + +4 +1. Introduction +1.2 +Background Knowledge +1.2.1 +Convolutional Neural Networks +To recognize the patterns of the images, many operations have been proposed, e.g., Scale- +Invariant Feature Transform (SIFT) [24], Histogram of Oriented Gradients(HOG) [25], and +Convolution. Especially, the convolutional operation dominates the community in the last +decade as an image feature extraction operation. +Formally, convolution is a mathematical operation on two functions that produces a +third function that expresses how the shape of one is modified by the other. In the domain +of computer vision, the discrete variant of convolution is adopted since the images are +saved as discrete signals. Concretely, given an image X ∈ R(C×H×W) and a convolution +kernel k ∈ R(C×P×Q), the feature map H ∈ R(H′×W ′) extracted by the convolution kernel +is computed as +H(i, j) = +C +� +c=1 +P +� +p=1 +Q +� +q=1 +X(c, i+p−1, j+q−1) k(c, p, q), +(1.1) +where (i, j) is the index of elements in the feature map H, C is the number of channels of +input images and (P, Q) are the size of the feature map. A single kernel corresponds to a +single feature map. Multiple kernels are often applied to extract multiple feature maps. +Besides, the pooling (subsampling) operation is applied to the feature maps extracted +by convolution operation to aggregate the visual information. In the pooling operation, +the mean operation or the max operation is often applied. The pooling operation with size +(s, s) can be expressed as +H′ +(i, j) = +P +max +p=1 H(i, j). +(1.2) +Convolution can be further applied to the pooled feature maps. The convolutional and +pooling operations are applied alternatively on the image to obtain the final feature maps. +The features HL +(i, j) extracted by a list of convolutional operations and pooling opera- +tions are taken as the final image representation. A single or multiple fully connected layers +(i.e. a MLP module) is used as classifier that maps the features into the ground-truth class. +Z = MLP(HL +(i, j)) +(1.3) +The output probabilities can be obtained by applying softmax function on the logits Z. +The predicted class is defined as argmax(Zi). + +1.2 Background Knowledge +5 +Figure 1.2: The overview of LeNet-5 architecture [26]. +The work [26] proposes Convolution Neural Network (CNN) in the end-to-end learning +framework to recognize hand-written digits. Therein, LeNet-5 is the classic instance of +convolution neural networks, which is visualized in Fig. 1.2. The proposed LeNet-5 starts +with two convolutional layers, and each is followed by a pooling layer. Then, a three-layer +MLP module maps the feature to the logits. +Figure 1.3: The overview of AlexNet architecture [18]. +Given the limited computational resource, the architecture and the corresponding train- +ing strategy proposed in [26] does not scale well to the large-scale dataset. With the advance +of the computational power, the work [18] proposes AlexNet, which achieves impressive +accuracy on ImageNet-1k dataset. AlexNet consists of five convolutional layers, some of +which are followed by max-pooling layers, and three fully-connected layers with a final 1000- +way softmax. In terms of model architecture, AlexNet is deeper and wider than LeNet-5. +From the perspective training strategy, to make AlexNet work well, the work [18] proposes +non-saturating neurons, i.e., Rectified Linear Units (ReLUs) to activate the neurons and + +C3: f. maps 16@10x10 +C1: feature maps +S4: f. maps 16@5x5 +INPUT +6@28x28 +32x32 +s2: f. maps +C5: layer +F6: layer +OUTPUT +6@14x14 +120 +84 +10 +Full connection +Gaussian connections +Convolutions +Subsampling +Convolutions +Subsampling +Full connection3 +3/ +3 +3 +3 +5 +3 +3 +2048 +dense +192 +192 +128 +2048 +48 +128 +55 +27. +13° +(13 +13 +5 +224 +3 + 5 +13 +13.2 +13 +dense +densée +[27 +w +114 +3 +1000 +155 +192 +192 +128 Max +2048 +2048 +224 +Max +Max +pooling +Stridel +128 +pooling +of 4 +pooling +3 +486 +1. Introduction +Figure 1.4: The overview of Residual block with skip connection [3]. +Figure 1.5: The overview of ResNet architecture [3]. +employs dropout method to regularize the training process. Especially, they propose a +GPU-specific implementation of GPU operation to make the training process feasible. +One intuitive way to improve AlexNet is to build deeper layers. However, the AlexNet +with deeper layers does not converge well during training due to the gradient vanishing +problem. Namely, the gradients become zeros or close to zeros when propagating from +the output layer to low layers. Due to the gradient vanishing problem, the parameter +update of low layers is challenging. To overcome the challenges, the work [3] proposes +skip-connection, which can propagate the gradients from deep layers to low layers directly +by skipping some intermediate layers. +The block with such a skip connection is called residual block. A popular residual block +is shown in Fig. 1.4. As an instance, the work [3] proposes ResNet which consists of a list +of residual blocks. When equipped with skip connections, ResNets with even more than +100 layers can converge well. ResNets still dominate the computer vision community. We +show the ResNet18 in Fig. 1.5 as an example where 18 layers are built into the ResNet to +extract features. + +x +weight layer +F(x) +I relu +x +weight layer +identity +F(x) +x +relu7x7 conv, 64, /2 +128./2 +3x3, pool, /2 +3x3 conv, 64 +.28 +3x3 conv, 64 +28 +9 +avg pool +Image +fc 1000 +conv. +conv. + conv. +con +3x3 conV, +coT +3x3 +3X3 +5x3 +5X3 +3x3 +3x3 +3X31.2 Background Knowledge +7 +Figure 1.6: The overview of CapsNet architectures. The CapsNet architecture consists of +four components, such as primary capsule extraction, voting, routing, and class-conditional +reconstruction. The primary capsule extraction module first maps the raw input features +to low-level capsules. The voting process transforms low-level capsules to make votes with +a transformation matrix. Then, the routing module identifies the weight of each vote and +computes the final high-level capsules. In the last part, the reconstruction subnetwork +reconstructs input images from capsules to regularize the learning process. +Convolutional Network Follow-Ups: +The CNN-based deep visual classifier has al- +ready surpassed human-level performance in the image classification task [27]. In the last +years, the architectures of convolutional neural networks have still been improved from +different perspectives. On the one hand, the more advanced architectures have been pro- +posed to further push the state-of-the-art performance [4, 5, 28]. On the other hand, the +efficiency of architecture has received great attention since real-world CNN-based appli- +cations often require less memory consumption and computational cost. The efficiency of +architecture has been addressed from different perspective, e.g., light-weight architecture +design [29, 30], architecture pruning [31, 32, 33, 34], and distilling knowledge from large +architectures to small architectures [35, 36, 37, 38]. More recently, many researchers focus +on neural architecture search where the architectures are searched automatically from a +predefined search space [39, 40, 41]. The found architecture can surpass the manually +designed ones. +1.2.2 +Capsule Networks +Inspired by the information process in the human brain, Hinton proposes Capsule Networks +(CapsNet) [12]. Different from CNNs, CapsNets represent a visual entity with a vector +instead of a single scale value, called Capsule. CapsNets [12] encode visual entities with + +Primary Capsules +Votes +Class-Conditional Reconstruction +Output +Capsules +Routing +M8 +1. Introduction +capsules. Each capsule is represented by an activity vector (e.g., the activation of a group +of neurons), and elements of each vector encode the properties of the corresponding entity. +The length of the activation vector indicates the confidence of the entity’s existence. The +output classes are represented as high-level capsules. +The most popular version of Capsule Networks is Dynamic Routing Capsule Networks +(DR-CaosNet). We introduce the architecture details of DR-CapsNet as follows. As shown +in Fig. 1.6, CapsNet starts with one (or more) convolutional layer(s) that convert the +raw pixel intensities X into low-level visual entities ui. +Concretely, CapsNet extracts +feature maps of shape (C′, H′, W ′) from input image X ∈ R(C×H×W) with two standard +convolutional layers where C′, H′, W ′ are the number of channels, the height, and the width +of the feature maps, respectively. The extracted feature maps are reformulated as primary +capsules (C′/Din, H′, W ′, Din) where Din is the dimensions of the primary capsules. There +are N = C′/Din∗H′∗W ′ primary capsules all together. Each capsule ui, a Din-dimensional +vector, consists of Din units across Din feature maps at the same location. For example, +the red bar marked with ui in Fig. 1.6 is a low-level capsule. +In the voting process, each primary capsule is transformed to make a vote with a +transformation matrix W ij ∈ R(Din×N∗Dout) in, where N is the number of output classes +and Dout is the dimensions of output capsules. The vote from the i-th low-level capsules +to the j-th high-level capsules is +ˆuj|i = W ijui. +(1.4) +Then, a routing module is applied to identify weight for each vote. Given all N votes +ˆuj|i of the L-th layer with N capsules, M high-level capsule sj of the (L + 1)-th layer with +M capsules, the routing process is +sj = +N +� +i +cij ˆuj|i +(1.5) +where cij is a coupling coefficient that models the degree with which ˆuj|i is able to predict +sj. The capsule sj is shrunk to a length in [0, 1) by a non-linear squashing function g(·), +which is defined as +vj = g(sj) = +∥sj∥2 +1 + ∥sj∥2 +sj +∥sj∥. +(1.6) +By doing the squashing operation, the length of the vector is mapped to [0, 1) that rep- +resents the confidence of the high-level entity’s existence. In DR-CapsNet, the high-level +capsules correspond to output classes, and its length means the output probability. + +1.2 Background Knowledge +9 +Note that the coupling coefficients {cij} in Equation 1.5 are computed by an iterative +routing procedure. They are updated so that high agreement (aij = vT +j ˆuj|i) corresponds +to a high value of cij. +cij = +exp(bij) +� +k exp(bik) +(1.7) +where initial logits bik are the log prior probabilities and updated with bik = bik + aij in +each routing iteration. The coupling coefficients between a i-th capsule of the L-th layer +and all capsules of the (L+1)-th layer sum to 1, i.e., �M +j=1 cij = 1. The steps in Equations +1.9, 1.5, 1.6, and 1.7 are repeated K times in the routing process, where sj and cij depend +on each other. +The length of the final output capsule vj corresponds to the output probability of +the j-th class. Different from CNNs where cross-entropy loss is often applied to compute +classification loss. In DR-CapsNet, the margin loss function is applied to compute the +classification loss +Lk =Tk max(0, m+ − ∥vk∥)2 ++ λ(1 − Tk) max(0, ∥vk∥ − m−)2 +(1.8) +where Tk = 1 if the object of the k-th class is present in the input. +As in [12], the +hyper-parameters are often empirically set as m+ = 0.9, m− = 0.1 and λ = 0.5. +A reconstruction sub-network reconstructs the input image from all N output capsules +with a masking mechanism. The ones corresponding to the non-ground-truth classes are +masked with zeros before being transferred to the reconstruction sub-network. Due to +the masking mechanism, only the capsule of the ground-truth class is visible for the re- +construction. Hence, the reconstruction process is called class-conditional reconstruction. +The reconstruction loss is computed as a regularization term in the loss function. +Capsule Network Follow-Ups: +Many routing mechanisms have been proposed to im- +prove the performance of CapsNet, such as Expectation-Maximization Routing [42], Self- +Routing [43], Variational Bayes Routing [44], Straight-Through Attentive Routing [45], and +Inverted Dot-Product Attention routing [46]. An alternative to the routing mechanism to +aggregate information is proposed in work [47] where they replace the dynamic routing +with a multi-head attention-based graph pooling approach. To reduce the parameters of +CapsNet, a matrix or a tensor is used to represent an entity instead of a vector [42, 48]. The +size of the learnable transformation matrix can also be reduced by the matrix/tensor repre- +sentations. Besides, the work [13] proposes to share a transformation matrix to reduce the + +10 +1. Introduction +Figure 1.7: +The overview of Vision Transformer Architectures. +The figure is taken +from [17]. +network parameters. Another way to improve CapsNet is to integrate advanced modules +of ConvNet into CapsNet, e.g., skip connections [3, 48] and dense connections [5, 49]. +1.2.3 +Vision Transformers +Transformers with self-attention-based architectures have become the model of choice in +natural language processing (NLP) [50]. Inspired by the success of Transformers in NLP +community, the work [17] proposes Vision Transformer(ViT) where they replace the convo- +lutions entirely with self-attention layers and achieve remarkable performance in the image +classification task. As a promising alternative to CNNs, Vision Transformer raises the +great attention of our community. +Different from CNNs, ViT represents an input image as a sequence of image patches. +Then, the list of self-attention modules are applied to the sequence of image patches se- +quentially. We now introduce the details of the primary Vision Transformer architecture +in [17]. As shown in Fig. 1.7, the input image X ∈ R(C×H×W) is split into image patches +{xi ∈ RP×P×C|i ∈ (1, 2, 3, ..., H/P × W/P)} where P is the patch size. The embedding +of each patch is extracted from the raw image patch with linear projection parameters +W 0 ∈ R(HW/P 2×Dp). Before the application of self-attention module, the position informa- + +Vision Transformer (ViT) +Class +Bird +MLP +Ball +Head +Car +Transformer Encoder +Patch + Position +Embedding +*Extra learnable +[class] embedding +Linear Projection of Flattened Patches1.2 Background Knowledge +11 +Figure 1.8: The overview of Transformer Encoder. +tion of image patches is also integrated into the patch embedding. The embedding of the +patch xi is described as +E0 +i = xi · W 0 + P Ei, +(1.9) +where P Ei is the position embedding of the image patch {xi, which encodes the patch +position information in the input images. The position embedding P Ei could be manually +designed or learnable. In ViT, the learnable version is adopted. +A learnable class-token embedding E0 +0 is added into the list of patch embeddings. The +class embedding in the last layer is taken as the image embedding for classification. We +now introduce the transformer encoder where the list of blocks is applied to transform +the input embeddings. As shown in Fig. 1.8, each block consists of two main modules, +namely, a multi-head self-attention module to model the inter-patch relationship and an +MLP module to project each patch respectively. +When the self-attention module with a single head in l + 1-th layer is applied to input +patches {El +i ∈ RDp|i ∈ (0, 1, 2, 3, ..., H/P ×W/P)} in the l-th layer, the output embedding +of the patch El +i is +Kl+1 +i += W l+1 +k +· El +i, +Ql+1 +i += W l+1 +q +· El +i, +V l+1 +i += W l+1 +v +· El +i, +Al+1 +i += Softmax(Ql+1 +i +· Kl+1 +0 +, +Ql+1 +i +· Kl+1 +1 +, +..., +Ql+1 +i +· Kl+1 +H/P×W/P+1, ), +El+1 +i += +H/P×W/P+1 +� +j=1 +Al+1 +ij +· V j. +(1.10) + +Transformer Encoder +- +Lx +MLP +4 +Norm +A +A +Multi-Head +Attention +K +Q +K +Q +K +Q +Norm +Embedded +Patches12 +1. Introduction +In this equation, the key, query, and value of patch embedding is computed first. The +attention of El+1 +i +to all patches in l-th layer is obtained with the query of i-th patch and +all keys. The output embedding El+1 +i +is the weighted sum of all values of patches. The +output embeddings of different heads are concatenated as the final embedding. Then, an +MLP module with two MLP layers is applied to project the final embedding of each patch +into a new feature space. The final embedding of the class-token patch is taken as the +image representation to classify the image. A linear classifier maps the features to output +space. +Vision Transformer Follow-Ups: +Since the ViT was proposed, many new vision trans- +former architectures have been proposed [51, 52, 53]. A hybrid architecture that consists +of both convolutional layers and self-attention blocks has also been explored [54, 55]. Be- +sides, the pure patch-based architecture without attention mechanism has also been pro- +posed [56]. By the time this thesis is written, the arm-race between ResNet and Vision +Transformers is still going on [57]. Recently, many researchers employ the Transformer +architecture as a uniform architecture that model both images and texts [58, 59]. + +1.3 Explanability of Deep Visual Classifications +13 +Approach +Description +Saliency Maps +Identifying the relevance of each input pixel to the out- +put class [60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, +72, 73, 74]. +Counterfactual Explanation +Identifies how the given input could change such that the +classifier would output a different specified class [75, 76]. +Explanatory Sentences +Generating natural language sentences that describe the +class-discriminative pixels [77, 78]. +Supporting Training Images +Identifying training images most responsible for a given +prediction [79]. +Built-in Explanation +Generating Explanations with built-in modules (in ex- +plainable classifier) for a given prediction [79]. +Disentangled Representations +Identifying the human-interpretable properties of the +recognized object in the input image [80, 12, 81, 82]. +Table 1.1: Summarization of different approaches for explaining image classifications. +1.3 +Explanability of Deep Visual Classifications +1.3.1 +Introduction +Deep Neural Networks (DNNs) have shown impressive performance in high-dimensional +input data. Especially, the performance of DNNs can even surpass human-level perfor- +mance in the image classification task. The traditional machine learning methods classify +images with hand-crafted images, while DNNs make predictions based on the features +learned automatically from data with an optimization algorithm. Hence, it is challenging +to understand the classification decisions made by DNNs. In recent years, many directions +have been explored to explain individual image classifications. We summarize and roughly +categorize them in Table 1.1. We introduce each approach as follows. +Saliency Maps, as intuitive explanations, have received great attention in the commu- +nity. The saliency map is a heat map, each element of which indicates the importance of +the pixel in the corresponding position. The saliency map is expected to have recognizable +patterns like the objects in the input image. The primary work [60] takes the vanilla gra- +dient of the loss with respect to the input as the saliency map. However, the gradients are +noisy and the pattern therein is barely recognizable. To improve the saliency map, many + +14 +1. Introduction +methods have been proposed [60, 83, 61, 62, 63, 64, 65, 66, 67, 84, 85]. The primary method +and the improved variants are model-aware, which leverage the parameters and the gradi- +ents of neural networks to compute saliency maps. Besides the model-aware methods, the +model-agnostic saliency methods are also preferred in many scenarios. For example, they +are able to explain any classifiers; the explanations produced from two or more different +types of models are comparable; an ensemble model can be explained without requiring +knowledge of model components. There are two types of model-agnostic saliency methods. +The one is to build an explanation generation model, e.g. a neural network with U-net +architecture [86, 68, 69]. The other is to approximate the local decision boundary of the +underlying model with an explainable model, e.g., linear classifier [70]. The explanation +generated from the explainable surrogate model can be used to explain individual decisions. +Counterfactual Explanation describes what changes to the situation would have resulted +in arriving at the alternative decision. In the case of image classification, Counterfactual +Explanation is the counterfactual image, which indicates that the output will become the +target class if the input image is replaced with the counterfactual image. The work [75] +creates a counterfactual image with a conditional generative model, which generates part +of the pre-defined image region conditional on the rest of the image. The desired property +of the generated image is to most change the classifier’s decision. +Another work [76] +formulates the generation of the counterfactual image as an image editing problem. Their +method performs well even in the fine-grained classifications. +Natural language, as a natural interface, has also been explored to explain the visual +classifications. The works [77, 78] build modules to generate natural language sentences to +explain the decisions where the sentences describe the class-discriminative features. The +explanatory sentences are different from the caption/description generated by multi-model +models. The contemporary vision-language models describe image content but fail to tell +class-discriminative features which justify visual predictions. +Another way to explain visual classifications is to identify the training points most +responsible for a given prediction. To trace a model’s prediction back to its training data, +the work [79] leverages influence functions, i.e., a classic technique from robust statistics. +Given a classification, they can be the most responsible training image that supports the +predictions. The created explanation can tell where the local decision boundary of the +model came from at a specific data point. +The approaches introduced above are post-hoc. Namely, the explanations are created +for off-shelf models without intervening in their training process. An alternative to post- + +1.3 Explanability of Deep Visual Classifications +15 +hoc explanation methods is to integrate dedicated modules into the model to be trained, +e.g. attention mechanism [47], explanation module [68] and prototype module [87]. In +the inference stage, the modules can be used to create explanations directly. The created +explanations are dubbed built-in explanations, which are more efficient and easy to create. +The image representations learned by DNNs are often distributed, which makes the +classification decision less explanation. It is difficult to interpretable the decision process +inside the model. One way to mitigate this problem is to constrain the model to learn +disentangled representations where each element of representation corresponds to a human- +understandable concept [80, 12, 81, 88, 82]. +In this subsection, we have introduced the popular methods applied to explain individ- +ual classification decisions. In the rest of this section, we present our contributions towards +understanding the classifications. Specifically, we briefly introduce our works on the topic +of explaining classification decisions made by Convolutional Networks, Capsule Networks, +and Vision Transformers. +1.3.2 +Explainability of Convolutional Neural Network-based Clas- +sification +A large number of saliency methods have been proposed to better understand individ- +ual decisions of deep convolutional neural networks. As one of the representatives, the +Layer-wise Relevance Propagation (LRP) approach is able to create pixel-wise explana- +tory saliency maps. LRP method has also been widely applied to many tasks in different +domains, e.g., in medical domain [89] and in NLP [90]. +The explanations generated by LRP are known to be pixel-wise and instance-specific. +However, the discriminativeness of the explanations has not been evaluated yet. Ideally, the +visualized objects in the explanation should correspond to the class that the class-specific +neuron represents. Namely, the explanations should be class-discriminative. +Our work [66] evaluates the discriminativeness of the explanations generated by LRP. +Concretely, we evaluate the explanations generated by LRP on the off-the-shelf models, +e.g., VGG16 [2] pre-trained on the ImageNet dataset [91]. The results are shown in Fig. +1.9. For each test image, we create four saliency maps as explanations. The first three ex- +planation maps are generated for top-3 predictions, respectively. The fourth one is created +for randomly chosen 10 classes from the top-100 predicted classes (which ensure that the +score to be propagated is positive). The white text in each explanation map indicates the + +16 +1. Introduction +Figure 1.9: The explanations generated by LRP on VGG16 Network. The images from +validation datasets of ImageNet are classified using the off-the-shelf models pre-trained on +the ImageNet. The classifications of the images are explained by the LRP approach. For +each image, we generate four explanations that correspond to the top-3 predicted classes +and a randomly chosen multiple-classes. The explanations are not class-discriminative. +class the output neuron represents and the corresponding classification probability. The +generated explanations are instance-specific, but not class-discriminative. In other words, +they are independent of class information. The explanations for different target classes, +even randomly chosen classes, are almost identical. +Based on LRP, our work [66] proposes Contrastive Layer-wise Relevance Propagation +(CLRP), which is capable of producing instance-specific, class-discriminative, pixel-wise +explanations. Before introducing our CLRP, we first discuss the conservative property +in the LRP. In a DNN, given the input X = {x1, x2, x3, · · · , xn}, the output Y += +{y1, y2, y3, · · · , ym}, the score Syj (activation value) of the neuron yj before softmax layer, +the LRP generate an explanation for the class yj by redistributing the score Syj layer- +wise back to the input space. +The assigned relevance values of the input neurons are +R = {r1, r2, r3, · · · , rn}. The conservative property is defined as follows: The generated +saliency map is conservative if the sum of assigned relevance values of the input is equal +to the score of the class-specific neuron, �n +i=1 ri = Syj. +The overview of the CLRP are shown in Fig. 1.10. We first describe the LRP as follows. +The j-th class-specific neuron yj is connected to input variables by the weights W of layers +between them. The neuron yj models a visual concept O. For an input example X, the +LRP maps the score Syj of the neuron back into the input space to get relevance vector +R = fLRP(X, W , Syj). In our contrastive LRP, we construct a dual virtual concept O, +which models the opposite visual concept to the concept O. For instance, the concept O + +alp: 0.5645 +ski: 0.4280 +mountain_tent:0.0046 +Random10classes +Shetland_sheepdog: 0.6152 +collie: 0.3844 +borzoi:0.0002 +Random10classes1.3 Explanability of Deep Visual Classifications +17 +Figure 1.10: The figure shows an overview of our CLRP. For each predicted class, the +approach generates a class-discriminative explanation by comparing two signals. The blue +line means the signal that the predicted class represents. +The red line models a dual +concept opposite to the predicted class. The final explanation is the difference between the +two saliency maps that the two signal generate. +models the zebra, and the constructed dual concept O models the non-zebra. One way +to model the O is to select all classes except for the target class representing O, i.e. the +dashed red lines in Fig. 1.10 are connected to all classes except for the target class zebra. +Next, the score Syj of target class is uniformly redistributted to other classes. Given the +same input example X, the LRP generates an explanation Rdual = fLRP(X, W , Syj) for +the dual concept. The Contrastive LRP is defined as follows: +RCLRP = max(0, (R − Rdual)) +(1.11) +where the function max(0, X) means replacing the negative elements of X with zeros. +The difference between the two saliency maps cancels the common parts. Without the +dominant common parts, the non-zero elements in RCLRP are the most relevant pixels. +Besides the qualitative evaluation, we also evaluate the explanations quantitatively with +a Pointing Game and an ablation study. Both qualitative and quantitative evaluations show +that the CLRP generates better explanations than the LRP. +1.3.3 +Explainability of Capsule Network-based Classification +Capsule Networks, as alternatives to Convolutional Neural Networks, have been proposed +to recognize objects from images. The current literature demonstrates many advantages +of CapsNets over CNNs. However, how to create explanations for individual classifications +of CapsNets has not been well explored. + +CNN +ebra +backward pass +CNN +forward pass +'Eléphant +CNN +backward pass18 +1. Introduction +Figure 1.11: The illustration of GraCapsNets: The extracted primary capsules are trans- +formed and modeled as multiple graphs. The pooling result on each graph (head) corre- +sponds to one vote. The votes on multiple graphs (heads) are averaged to generate the +final prediction. +The widely used saliency methods are mainly proposed for explaining CNN-based clas- +sifications; they create saliency map explanations by combining activation values and the +corresponding gradients, e.g., Grad-CAM. They combine activation values and the received +gradients in specific layers, e.g., deep convolutional layers. In CapsNets, instead of deep +convolutional layers, an iterative routing mechanism is applied to extract high-level visual +concepts. Hence, these saliency methods cannot be trivially applied to CapsNets. Besides, +the routing mechanism makes it more challenging to identify interpretable input features +relevant to a classification. +To overcome the lack of interpretability, we can either propose new post-hoc interpre- +tation methods for CapsNets or modify the model to have build-in explanations. In our +published work [47], we explore the latter. Specifically, we propose interpretable Graph +Capsule Networks (GraCapsNets), where we replace the routing part with a multi-head +attention-based Graph Pooling approach. Our GraCapsNet includes an attention-based +pooling module, with which individual classification explanations can be created effectively +and efficiently. +As introduced in Background Section, CapsNets start with convolutional layers that +convert the input pixel intensities X into primary capsules ui (i.e., low-level visual entities). +Each ui is transformed to vote for high-level capsules ˆuj|i with learned transformation +matrices. Then, a routing process is used to identify the coupling coefficients cij, which +describe how to weight votes from primary capsules. +Finally, a squashing function is +applied to the identified high-level capsules sj so that the lengths of them correspond to +the confidence of the class’s existence. + +Multi-head +Attention-based Graph Pooling +Capsules +uj +wi +Reconstruction +Capsules +Wi1.3 Explanability of Deep Visual Classifications +19 +Different routing mechanisms differ only in how to identify cij. Routing processes de- +scribe one way to aggregate information from primary capsules into high-level ones. In +our GraCapsNets, we implement the information aggregation by multi-head graph pooling +processes. In CapsNets, the primary capsules represent object parts, e.g., the eyes and +nose of a cat. In our GraCapsNets, we explicitly model the relationship between the pri- +mary capsules (i.e., part-part relationship) with graphs. Then, the followed graph pooling +operations pool relevant object parts from the graphs to make a classification vote. Since +the graph pooling operation reveals which input features are pooled as relevant ones, we +can easily create explanations to explain the classification decisions. +The overview of our GraCapsNets is illustrated in Fig. +1.11. +In GraCapsNet, the +primary capsules ui are transformed into a feature space. All transformed capsules u′ +i +are modeled as multiple graphs. Each graph corresponds to one head, the pooling result +on which corresponds to one vote. The votes on multiple heads are averaged as the final +prediction. +The transformed capsules u′ +i can be modeled as multiple graphs. A graph consists +of a set of nodes and a set of edges. As shown in Fig. 1.11, the primary capsules are +reshaped from L groups of feature maps. Each group consists of C feature maps of the +size K × K. Correspondingly, the transformed capsules u′ +i where i ∈ {1, 2, ...K2} form a +single graph with K2 nodes. Each node corresponds to one transformed capsule u′ +i, and +the activation vector of u′ +i is taken as features of the corresponding node. The graph edge +can be represented by an adjacency matrix, where different priors can be modeled. The +spatial relationship between primary capsules is modeled in our work. +Given node features Xl ∈ R(K2×Dout) and adjacency matrix A ∈ R(K2×K2) in the l-th +head of GraCapsNet. We first compute the attention of the head as Attl = softmax(AXlW) +where W ∈ RDout×M are learnable parameters. Dout is the dimension of the node features +and M is the number of output classes. The output is of the shape (K2 × M). In our +GraCapsNet for object recognition, Attl corresponds to the visual attention of the heads. +The graph pooling output Sl ∈ R(M×Dout) of the head is computed as Sl = (Attl)TXl. +The final predictions of GraCapsNets are based on all L heads with outputs Sl where +l ∈ {1, 2, ..., L}. The output capsules are V = squash( 1 +L +�L +l=1 Sl). +In our GraCapsNet, we can use visual attention as built-in explanation to explain the +predictions of GraCapsNets. The averaged attenion over l heads is +E = 1 +L +L +� +l=1 +Attl +(1.12) + +20 +1. Introduction +Figure 1.12: Adversarial Patch Attack or Natural Patch Corruption on Vision Transformer. +where Attl corresponds to the attention of the l-th head. The created explanations E are +of the shape (K2 × M). Given the predicted class, the K × K attention map indicates +which pixels of the input image support the prediction. +The explanations for individual classifications of GraCapsNets can be created in an +effective and efficient way. Surprisingly, without a routing mechanism, our GraCapsNets +can achieve better classification performance and better adversarial robustness, and still +keep other advantages of CapsNets, namely, disentangled representations and affine trans- +formation robustness. +1.3.4 +Explainability of Vision Transformer-based Classification +The recent advances in Vision Transformer (ViT) have demonstrated its impressive perfor- +mance in image classification [17, 51], which makes it a promising alternative to Convolu- +tional Neural Network (CNN). Unlike CNNs, ViT represents an input image as a sequence +of image patches. Then, a self-attention mechanism is applied to aggregate information +from all patches. The attention can be used to create saliency maps to explain ViT-based +classification decisions, e.g. with Rollout Attention method [92]. The patch-wise input +image representation in ViT makes the following question interesting: How does the at- +tention of ViT change when individual input image patches are perturbed with natural +corruptions or adversarial perturbations? For example, Fig. 1.12 illustrates the case where +a single patch of the input is perturbed or attacked. + +Vision Transformer (ViT) +Class +Bird +MLP +Ball +Head +Car +Transformer Encoder +Patch + Position +Embedding +* Extra learnable +[class] embedding +Linear Projection of Flattened Patches +Attack or Corrupt1.3 Explanability of Deep Visual Classifications +21 +(a) Clean Image +(b) with Naturally Corrupted Patch +(c) with Adversarial Patch +Figure 1.13: Images with patch-wise perturbations (top) and their corresponding atten- +tion maps (bottom). The attention mechanism in ViT can effectively ignore the naturally +corrupted patches to maintain a correct prediction, whereas it is forced to focus on the +adversarial patches to make a mistake. The images with corrupted patches are all cor- +rectly classified. The images with adversary patches in subfigure 1.13c are misclassified as +dragonfly, axolotl, and lampshade, respectively. +In our work [93], we study the robustness of vision transformers to patch-wise per- +turbations. Surprisingly, we find that vision transformers are more robust to naturally +corrupted patches than CNNs, whereas they are more vulnerable to adversarial patches. +Furthermore, we conduct extensive qualitative and quantitative experiments to understand +the classification under patch perturbations. +We have revealed that ViT’s stronger robustness to natural corrupted patches and +higher vulnerability against adversarial patches are both caused by the attention mecha- +nism. Specifically, the attention model can help improve the robustness of vision transform- +ers by effectively ignoring natural corrupted patches. However, when vision transformers +are attacked by an adversary, the attention mechanism can be easily fooled to focus more +on the adversarially perturbed patches and cause a mistake. +Digging down further, we find the reason behind this is that the self-attention mech- +anism of ViT can effectively ignore the natural patch corruption, while it’s also easy to +manipulate the self-attention mechanism to focus on an adversarial patch. This is well +supported by rollout attention visualization [92] on ViT. As shown in Fig. 1.13 (a), ViT +successfully attends to the class-relevant features on the clean image, i.e., the head of the +dog. When one or more patches are perturbed with natural corruptions, shown in Fig. 1.13 +(b), ViT can effectively ignore the corrupted patches and still focus on the main foreground +to make a correct prediction. In Fig. 1.13 (b), the attention weights on the positions of + +22 +1. Introduction +naturally corrupted patches are much smaller even when the patches appear in the fore- +ground. In contrast, when the patches are perturbed with adversarial perturbations by an +adversary, shown in Fig. 1.13 (c), ViT is successfully fooled to make a wrong prediction +because the attention of ViT is misled to focus on the adversarial patches instead. +In our work [93], we provide our understanding of the attention changes of ViT when +individual input image patches are perturbed with natural corruptions or adversarial per- +turbations. + +1.4 Robustness of Deep Visual Classification Models +23 +Natural +Robustness +Additive +Natural Corruption +Robustness to the noisy images that are added +with various noise [94, 14], such as, white noise, +blur, weather, and digital categories. +Non-Additive +Affine Transformation +Robustness to the images that are affine- +transformed from standard ones [95, 12, 13]. +Additive +Dense Attack +Robustness to the images where all pixels can +be changed under a certain constraint [96, 97]. +Adversarial +Robustness +Sparse Attack +Robustness to the images where only a few pix- +els of each image can be manipulated [98]. +Patch Attack +Robustness to the perturbed images where only +a single patch (a specific region) of each image +can be manipulated [99, 100]. +Non-Additive +Transformation +-Based Attack +Robustness to adversarial images that is cre- +ated by delicated affine transformations [101]. +Sementic Attack +Robustness to semantic adversarial images that +is created by image synthesis [102]. +Table 1.2: Categorization of Robustness in Image Classification Task. +1.4 +Robustness of Deep Visual Classification Models +1.4.1 +Introduction +In this thesis, we mainly consider two types of robustness, namely, natural robustness and +adversarial robustness. When an image is captured, different corruption can happen, e.g., +the existence of white noise, the effect of weather, the compression in the digitalization +process, and random affine transformation. The robustness to these images with natural +corruption is denoted as natural robust. Adversarial robustness describes the robustness +of models to adversarial images, which is created by an adversary. Both natural robustness +and adversarial robustness are critical in some safety-critical domains. We summarize and +categorize the robustness in Tab. 1.2. +Besides the type of attacks in Tab. 1.2, adversarial attacks can be categorized into +targeted and untargeted ones. The goal of targeted attacks is to mislead the model to a +specific target class, while the goal of untargeted ones is to fool the model to make wrong +predictions. +In terms of the availability of the target models, adversarial attacks can also be cat- +egorized into white-box and black-box attacks. The white-box attacks assume that the + +24 +1. Introduction +adversary has all access to target models including model parameters, model architectures, +and even defense methods. In contrast, in the setting of black-box attacks, the adversary +can only obtain the output of the target model. The black-box attacks have also received +great attention since it is realistic in real-world applications. +The implementation of white-box attacks is relatively cheap where they create adversar- +ial examples with the gradients of the self-defined objective function with respect to inputs. +However, the implementation of black-box attacks can be computationally expensive given +the limited available information. One way to created adversarial examples in a black-box +fashion is to leverage their transferability [103, 104, 105, 106, 107, 108, 109, 110, 111, 112, +113], namely, the adversarial examples created on one model can also fool another. The +adversary first trains a surrogate model on the same training data as the one used for the +target model and creates adversarial examples on the surrogate model to fool the target +model, which is called transfer-based black-box attack. However, the transfer-based black- +box attacks require access to the training data of the target model. To overcome the limi- +tation, the query-based black-box attacks have been proposed where the attacks are based +on the outputs obtained by querying the target models directly [114, 115, 116, 115, 117]. +In addition, based on the constraints on the adversarial images, the generated adver- +sarial perturbations can be quasi-imperceptible or unbounded. The popular metric of to +measure the distance between clean images and adversarial image is ℓp norm [98], such +as, ℓ1, ℓ2 and ℓ∞. However, the metric is not perfectly aligned with human perception. +The more advanced metric has also been explored in the community, e.g., Wasserstein +distance [118]. +Given the potential threats posed by adversarial attacks, many defense strategies have +been proposed to build adversarially robust models. One of the most effective defense +methods is adversarial training, which creates adversarial examples and adds them to the +training dataset in each training iteration. Besides, the pre-processing methods have been +explored to purify adversarial examples [119, 120, 121, 122, 123, 124, 125, 126, 127, 128, +129, 130, 131, 132, 133]. However, some of the defense strategies have broken again in later +publications [134]. Some defense methods provide certified robustness to break arm-race +between adversary and defense [135, 136, 137, 138, 139, 140, 141, 142, 143, 144]. Even +many methods have been published to address, the accuracy of the model under attacks is +still much lower than the accuracy on clean images, especially on the large dataset [145]. +In addition to building robust model, another way to address the threats is to detect +adversarial examples first [146, 147, 148, 149, 150, 151, 152]. + +1.4 Robustness of Deep Visual Classification Models +25 +In this subsection, we categorize the robustness of image classifications. Our contri- +butions of this thesis mainly focus on the role the model architecture plays in terms of +both natural robustness and adversarial robustness. In the rest of this section, we present +our contributions towards the robustness of image classification models, such as Capsule +Networks and Vision Transformers. +1.4.2 +Robustness of Capsule Network-based Classification +Human visual recognition is quite insensitive to affine transformations. For example, enti- +ties in an image, and a rotated version of the entities in the image, can both be recognized +by the human visual system, as long as the rotation is not too large. Convolutional Neural +Networks (CNNs), the currently leading approach to image analysis, achieve affine ro- +bustness by training on a large amount of data that contain different transformations of +target objects. Given limited training data, a common issue in many real-world tasks, the +robustness of CNNs to novel affine transformations is limited [12]. +With the goal of learning image features that are more aligned with human percep- +tion, Capsule Networks (CapsNets) have recently been proposed [12]. Our work [13] first +investigates the effectiveness of components that make CapsNets robust to input affine +transformations, with a focus on the routing algorithm. However, recent work [153] shows +that all routing algorithms proposed so far perform even worse than a uniform/random +routing procedure. +From both numerical analysis and empirical experiments, our investigation reveals that +the dynamic routing procedure contributes neither to the generalization ability nor to the +affine robustness of CapsNets. Therefore, it is infeasible to improve the affine robustness by +modifying the routing procedure. Instead, we investigate the limitations of the CapsNet +architectures and propose a simple solution. Namely, we propose to apply an identical +transformation function for all primary capsules and replace the routing with a simple +averaging procedure. +Besides the high affine transformation robustness, CapsNets also demonstrate other ad- +vantages, such as the ability to recognize overlapping digits and the semantic representation +compactness. In recent years, It has been suggested that CapsNets have the potential to +surpass the dominant convolutional networks in these aspects [12, 42, 48, 154]. However, +there lack of comprehensive comparisons to support this assumption, and even for some +reported improvements, there are no solid ablation studies to figure out which ones of the +components in CapsNets are, in fact, effective. + +26 +1. Introduction +In our work [155], we first carefully examine the major differences in design between the +capsule networks and the common convolutional networks adopted for image classification. +The difference can be summarized as a non-shared transformation module, a dynamic +routing layer to automatically group input capsules to produce output capsules, a squashing +function, a marginal classification loss, and a class-conditional reconstruction sub-network +with a reconstruction loss. +Unlike previous studies [12, 42] which usually take CapsNet as a whole to test its +robustness, our work [155] instead tries to study the effects of each of the above components +in their effectiveness on robustness. We consider the three different aspects, such as the +robustness to affine transformations, the ability to recognize overlapping digits, and the +semantic representation compactness. +Our investigations reveal that some widely believed benefits of Capsule networks could +be wrong: +1. The dynamic routing actually may harm the robustness to input affine transforma- +tion, in contrast to the common belief; +2. The high performance of CapsNets to recognize overlapping digits can be mainly +attributed to the extra modeling capacity brought by the transformation matrices. +3. Some components of CapsNets are indeed beneficial for learning semantic represen- +tations, e.g., the conditional reconstruction and the squashing function, but they are +mainly auxiliary components and can be applied beyond CapsNets. +In addition to these findings, we also enhance common ConvNets by the useful compo- +nents of CapsNet, and achieve greater robustness. Our investigation shows that Capsule +Network is not more robust than Convolutional Network. +1.4.3 +Robustness of Vision Transformer-based Classification +CapsNets with brain-inspired architectures have more inductive bias than CNNs. Different +from CapsNet, Vision Transformer (ViT) [17] has less architecture bias than CNNs. ViT +processes the input image as a sequence of image patches. Then, a self-attention mechanism +is applied to aggregate information from all patches. +Existing works have shown that +ViTs are more robust than CNNs when the whole input image is perturbed with natural +corruptions or adversarial perturbations [156, 157, 158]. Given the patch-based architecture +of ViT, our work studies the robustness of ViT to patch-based perturbation. + +1.4 Robustness of Deep Visual Classification Models +27 +Two typical types of perturbations are considered to compare the robustness between +ViTs and CNN (e.g., ResNets [3]). One is natural corruptions [14], which is to test models’ +robustness under distributional shift. The other is adversarial perturbations [159, 119], +which are created by an adversary to specifically fool a model to make a wrong prediction. +We reveal that ViT does not always perform more robustly than ResNet. When indi- +vidual image patches are naturally corrupted, ViT performs more robustly than ResNet. +However, when input image patch(s) are adversarially attacked, ViT shows a higher vul- +nerability. Digging down further, we find the reason behind this is that the self-attention +mechanism of ViT can effectively ignore the natural patch corruption, while it’s also easy +to manipulate the self-attention mechanism to focus on an adversarial patch. +Based on the patch-based architectural structure of vision transformers, we further +investigate the sensitivity of ViT against patch positions and patch alignment of adversarial +patches. First, we discover that ViT is insensitive to different patch positions, while ResNet +shows high vulnerability on the central area of input images and much less on corners. We +attribute this to the architecture bias of ResNet where pixels in the center can affect more +neurons than the ones in corners. In contrast, each patch within ViT can equally interact +with other patches regardless of its position. Further, we find that for ViT, the adversarial +perturbation designed to attack one particular position can successfully transfer to other +positions of the same image as long as they are aligned with input patches. In contrast, +the ones on ResNet hardly do. +To summarise, in our work [93], we compare ViT and CNNs in terms of the robustness +to natural patch corruptions or adversarial patch attacks. + +28 +1. Introduction + +Bibliography +[1] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. In nature, 2015. +[2] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large- +scale image recognition. In ICLR, 2014. +[3] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for +image recognition. In Proceedings of the IEEE International Conference on Computer +Vision, pages 770–778, 2016. +[4] Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wo- +jna. Rethinking the inception architecture for computer vision. In Proceedings of the +IEEE International Conference on Computer Vision, pages 2818–2826, 2016. +[5] Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger. +Densely connected convolutional networks. In Proceedings of the IEEE International +Conference on Computer Vision, pages 4700–4708, 2017. +[6] Jinkyu Kim and John F Canny. Interpretable learning for self-driving cars by visu- +alizing causal attention. In International Conference on Computer Vision (ICCV), +pages 2961–2969, 2017. +[7] Jinkyu Kim, Anna Rohrbach, Trevor Darrell, John Canny, Zeynep Akata, et al. +Textual explanations for self-driving vehicles. In ECCV, pages 577–593. Springer, +2018. +[8] Lydia T Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt. Delayed +impact of fair machine learning. In ICML, 2018. +[9] Tatsunori B Hashimoto, Megha Srivastava, Hongseok Namkoong, and Percy Liang. +Fairness without demographics in repeated loss minimization. In ICML, 2018. + +30 +BIBLIOGRAPHY +[10] Jindong Gu and Daniela Oelke. Understanding bias in machine learning. In arXiv +preprint arXiv:1909.01866, 2019. +[11] Andrew Selbst and Julia Powles. “meaningful information” and the right to expla- +nation. In Conference on Fairness, Accountability and Transparency, pages 48–48. +PMLR, 2018. +[12] Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton. Dynamic routing between +capsules. In Advances in neural information processing systems (NeurIPS), pages +3856–3866, 2017. +[13] Jindong Gu and Volker Tresp. Improving the robustness of capsule networks to image +affine transformations. In Proceedings of the IEEE/CVF Conference on Computer +Vision and Pattern Recognition (CVPR), pages 7285–7293, 2020. +[14] Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness +to common corruptions and perturbations. In International Conference on Learning +Representations (ICLR), 2019. +[15] Mahmood Sharif, Sruti Bhagavatula, Lujo Bauer, and Michael K Reiter. Accessorize +to a crime: Real and stealthy attacks on state-of-the-art face recognition. In Proceed- +ings of the 2016 acm sigsac conference on computer and communications security, +pages 1528–1540, 2016. +[16] Kevin Eykholt, Ivan Evtimov, Earlence Fernandes, Bo Li, Amir Rahmati, Chaowei +Xiao, Atul Prakash, Tadayoshi Kohno, and Dawn Song. Robust physical-world at- +tacks on deep learning visual classification. In Proceedings of the IEEE conference +on computer vision and pattern recognition, pages 1625–1634, 2018. +[17] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua +Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, +Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recog- +nition at scale. In arXiv:2010.11929, 2020. +[18] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with +deep convolutional neural networks. In Advances in neural information processing +systems, 2012. + +BIBLIOGRAPHY +31 +[19] Ross Girshick, Jeff Donahue, Trevor Darrell, and Jitendra Malik. Rich feature hier- +archies for accurate object detection and semantic segmentation. In CVPR, pages +580–587, 2014. +[20] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Girshick. Mask r-cnn. In +International Conference on Computer Vision (ICCV), pages 2961–2969, 2017. +[21] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks +for semantic segmentation. In Proceedings of the IEEE International Conference on +Computer Vision, pages 3431–3440, 2015. +[22] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyra- +mid scene parsing network. In CVPR, 2017. +[23] Liang-Chieh Chen, George Papandreou, Florian Schroff, and Hartwig Adam. Re- +thinking atrous convolution for semantic image segmentation. In arXiv:1706.05587, +2017. +[24] David G Lowe. Object recognition from local scale-invariant features. In Proceedings +of the seventh IEEE international conference on computer vision, volume 2, pages +1150–1157. Ieee, 1999. +[25] Navneet Dalal and Bill Triggs. Histograms of oriented gradients for human detection. +In 2005 IEEE computer society conference on computer vision and pattern recognition +(CVPR’05), volume 1, pages 886–893. Ieee, 2005. +[26] Yann LeCun, L´eon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based +learning applied to document recognition. In Proceedings of the IEEE, 1998. +[27] Asifullah Khan, Anabia Sohail, Umme Zahoora, and Aqsa Saeed Qureshi. A sur- +vey of the recent architectures of deep convolutional neural networks. In Artificial +intelligence review, 2020. +[28] Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen +Wei. Deformable convolutional networks. In Proceedings of the IEEE International +Conference on Computer Vision, pages 764–773, 2017. +[29] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, +Tobias Weyand, Marco Andreetto, and Hartwig Adam. +Mobilenets: +Efficient + +32 +BIBLIOGRAPHY +convolutional neural networks for mobile vision applications. +In arXiv preprint +arXiv:1704.04861, 2017. +[30] Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely +efficient convolutional neural network for mobile devices. In Proceedings of the IEEE +conference on computer vision and pattern recognition, pages 6848–6856, 2018. +[31] Yann LeCun, John S Denker, and Sara A Solla. Optimal brain damage. In NIPS, +pages 598–605, 1990. +[32] Babak Hassibi and David G Stork. Second order derivatives for network pruning: +Optimal brain surgeon. In NeurIPS, 1993. +[33] Song Han, Jeff Pool, John Tran, and William Dally. Learning both weights and +connections for efficient neural network. In NeurIPS, pages 1135–1143, 2015. +[34] Pavlo Molchanov, Stephen Tyree, Tero Karras, Timo Aila, and Jan Kautz. Pruning +convolutional neural networks for resource efficient inference. In ICLR, 2017. +[35] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural +network. In stat, volume 1050, page 9, 2015. +[36] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo +Gatta, and Yoshua Bengio. Fitnets: Hints for thin deep nets. In ICLR, 2015. +[37] Jindong Gu and Volker Tresp. Search for better students to learn distilled knowledge. +In arXiv preprint arXiv:2001.11612, 2020. +[38] Jindong Gu, Wei Liu, and Yonglong Tian. Simple distillation baselines for improving +small self-supervised models. In arXiv preprint arXiv:2106.11304, 2021. +[39] Barret Zoph and Quoc V. Le. Neural architecture search with reinforcement learning. +In ICLR, 2017. +[40] Hanxiao Liu, Karen Simonyan, Oriol Vinyals, Chrisantha Fernando, and Koray +Kavukcuoglu. Hierarchical representations for efficient architecture search. In ICLR, +2018. +[41] Hanxiao Liu, Karen Simonyan, and Yiming Yang. Darts: Differentiable architecture +search. In ICLR, 2019. + +BIBLIOGRAPHY +33 +[42] Geoffrey E Hinton, Sara Sabour, and Nicholas Frosst. +Matrix capsules with em +routing. In International conference on learning representations (ICLR), 2018. +[43] Taeyoung Hahn, Myeongjang Pyeon, and Gunhee Kim. Self-routing capsule net- +works. +In Advances in Neural Information Processing Systems (NeurIPS), pages +7658–7667, 2019. +[44] Fabio De Sousa Ribeiro, Georgios Leontidis, and Stefanos D Kollias. Capsule routing +via variational bayes. In AAAI, pages 3749–3756, 2019. +[45] Karim Ahmed and Lorenzo Torresani. Star-caps: Capsule networks with straight- +through attentive routing. In Advances in Neural Information Processing Systems, +2019. +[46] Yao-Hung Hubert Tsai, Nitish Srivastava, Hanlin Goh, and Ruslan Salakhutdinov. +Capsules with inverted dot-product attention routing. In International Conference +on Learning Representations (ICLR), 2020. +[47] Jindong Gu. Interpretable graph capsule networks for object recognition. In Pro- +ceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2020. +[48] Jathushan +Rajasegaran, +Vinoj +Jayasundara, +Sandaru +Jayasekara, +Hirunima +Jayasekara, Suranga Seneviratne, and Ranga Rodrigo. Deepcaps: Going deeper with +capsule networks. In The IEEE/CVF Conference on Computer Vision and Pattern +Recognition (CVPR), pages 10725–10733, 2019. +[49] Sai Samarth R Phaye, Apoorva Sikka, Abhinav Dhall, and Deepti R Bathula. Multi- +level dense capsule networks. In Asian Conference on Computer Vision, pages 577– +592. Springer, 2018. +[50] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N +Gomez, �Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances +in neural information processing systems, pages 5998–6008, 2017. +[51] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablay- +rolles, and Herv´e J´egou. Training data-efficient image transformers & distillation +through attention. In International Conference on Machine Learning, pages 10347– +10357. PMLR, 2021. + +34 +BIBLIOGRAPHY +[52] Kai Han, An Xiao, Enhua Wu, Jianyuan Guo, Chunjing Xu, and Yunhe Wang. +Transformer in transformer. In arXiv:2103.00112, 2021. +[53] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, +and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted +windows. In arXiv:2103.14030, 2021. +[54] Ben Graham, Alaaeldin El-Nouby, Hugo Touvron, Pierre Stock, Armand Joulin, +Herv´e J´egou, and Matthijs Douze. Levit: a vision transformer in convnet’s clothing +for faster inference. In arXiv:2104.01136, 2021. +[55] Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Doll´ar, and Ross Gir- +shick. Early convolutions help transformers see better. In arXiv:2106.14881, 2021. +[56] Ilya O Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, +Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszko- +reit, et al. Mlp-mixer: An all-mlp architecture for vision. In Advances in Neural +Information Processing Systems, volume 34, 2021. +[57] Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, +and Saining Xie. A convnet for the 2020s. In arXiv preprint arXiv:2201.03545, 2022. +[58] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sand- +hini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. +Learning transferable visual models from natural language supervision. In Interna- +tional Conference on Machine Learning, pages 8748–8763. PMLR, 2021. +[59] Wenhui Wang, Hangbo Bao, Li Dong, and Furu Wei. Vlmo: Unified vision-language +pre-training with mixture-of-modality-experts. In arXiv preprint arXiv:2111.02358, +2021. +[60] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional +networks: Visualising image classification models and saliency maps. In ICLR, 2013. +[61] Sebastian Bach, Alexander Binder, Gr´egoire Montavon, Frederick Klauschen, Klaus- +Robert M¨uller, and Wojciech Samek. On pixel-wise explanations for non-linear clas- +sifier decisions by layer-wise relevance propagation. In PloS one, 2015. + +BIBLIOGRAPHY +35 +[62] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedan- +tam, Devi Parikh, Dhruv Batra, et al. Grad-cam: Visual explanations from deep +networks via gradient-based localization. In International Conference on Computer +Vision (ICCV), pages 618–626, 2017. +[63] Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. +Learning important +features through propagating activation differences. In ICML-Volume 70, pages 3145– +3153. JMLR. org, 2017. +[64] Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep +networks. In ICML-Volume 70, pages 3319–3328. JMLR. org, 2017. +[65] Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda Vi´egas, and Martin Wattenberg. +Smoothgrad: removing noise by adding noise. In arXiv preprint arXiv:1706.03825, +2017. +[66] Jindong Gu, Yinchong Yang, and Volker Tresp. Understanding individual decisions +of cnns via contrastive backpropagation. In Asian Conference on Computer Vision, +2018. +[67] Suraj Srinivas and Fran¸cois Fleuret. Full-gradient representation for neural network +visualization. In Advances in Neural Information Processing Systems, pages 4126– +4135, 2019. +[68] Piotr Dabkowski and Yarin Gal. Real time image saliency for black box classifiers. +In Advances in Neural Information Processing Systems, pages 6967–6976, 2017. +[69] Patrick Schwab and Walter Karlen. Cxplain: Causal explanations for model inter- +pretation under uncertainty. In Advances in Neural Information Processing Systems, +pages 10220–10230, 2019. +[70] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Why should i trust you?: +Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD +international conference on knowledge discovery and data mining, pages 1135–1144. +ACM, 2016. +[71] Luisa M Zintgraf, Taco S Cohen, Tameem Adel, and Max Welling. Visualizing deep +neural network decisions: Prediction difference analysis. In ICLR, 2017. + +36 +BIBLIOGRAPHY +[72] Jindong Gu. Verification of classification decisions in convolutional neural networks, +2022. US Patent App. 17/294,746. +[73] Ruth C Fong and Andrea Vedaldi. +Interpretable explanations of black boxes by +meaningful perturbation. In Proceedings of the IEEE International Conference on +Computer Vision, pages 3429–3437, 2017. +[74] Jindong Gu and Volker Tresp. Contextual prediction difference analysis for explaining +individual image classifications. In arXiv preprint arXiv:1910.09086, 2019. +[75] Chun-Hao Chang, Elliot Creager, Anna Goldenberg, and David Duvenaud. Explain- +ing image classifiers by counterfactual generation. In ICLR, 2019. +[76] Yash Goyal, Ziyan Wu, Jan Ernst, Dhruv Batra, Devi Parikh, and Stefan Lee. Coun- +terfactual visual explanations. In ICML, 2019. +[77] Lisa Anne Hendricks, Zeynep Akata, Marcus Rohrbach, Jeff Donahue, Bernt Schiele, +and Trevor Darrell. +Generating visual explanations. +In European Conference on +Computer Vision (ECCV), pages 3–19. Springer, 2016. +[78] Lisa Anne Hendricks, Ronghang Hu, Trevor Darrell, and Zeynep Akata. Grounding +visual explanations. In European Conference on Computer Vision (ECCV), pages +269–286. Springer, 2018. +[79] Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence +functions. In Proceedings of the 34th International Conference on Machine Learning- +Volume 70, pages 1885–1894. JMLR. org, 2017. +[80] Mhd Hasan Sarhan, Abouzar Eslami, Nassir Navab, and Shadi Albarqouni. Learning +interpretable disentangled representations using adversarial vaes. In Domain Adap- +tation and Representation Transfer and Medical Image Learning with Less Labels and +Imperfect Data, pages 37–44. Springer, 2019. +[81] Dahuin Jung, Jonghyun Lee, Jihun Yi, and Sungroh Yoon. icaps: An interpretable +classifier via disentangled capsule networks. +In arXiv preprint arXiv:2008.08756, +2020. +[82] Xinqi Zhu, Chang Xu, and Dacheng Tao. Where and what? examining interpretable +disentangled representations. In Proceedings of the IEEE/CVF Conference on Com- +puter Vision and Pattern Recognition, pages 5861–5870, 2021. + +BIBLIOGRAPHY +37 +[83] Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. +Striving for simplicity: The all convolutional net. In ICLR, 2014. +[84] Jindong Gu and Volker Tresp. Saliency methods for explaining adversarial attacks. +In arXiv preprint arXiv:1908.08413, 2019. +[85] Jindong Gu and Volker Tresp. Semantics for global and local interpretation of deep +neural networks. In arXiv preprint arXiv:1910.09085, 2019. +[86] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional net- +works for biomedical image segmentation. In International Conference on Medical +image computing and computer-assisted intervention, pages 234–241. Springer, 2015. +[87] Chaofan Chen, Oscar Li, Daniel Tao, Alina Barnett, Cynthia Rudin, and Jonathan K +Su. +This looks like that: deep learning for interpretable image recognition. +In +Advances in neural information processing systems, volume 32, 2019. +[88] Jindong Gu and Volker Tresp. Neural network memorization dissection. In arXiv +preprint arXiv:1911.09537, 2019. +[89] Yinchong Yang, Volker Tresp, Marius Wunderle, and Peter A Fasching. Explaining +therapy predictions with layer-wise relevance propagation in neural networks. +In +2018 IEEE International Conference on Healthcare Informatics (ICHI), pages 152– +162. IEEE, 2018. +[90] Leila Arras, Gr´egoire Montavon, Klaus-Robert M¨uller, and Wojciech Samek. Ex- +plaining recurrent neural network predictions in sentiment analysis. In arXiv preprint +arXiv:1706.07206, 2017. +[91] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A +large-scale hierarchical image database. In 2009 IEEE conference on computer vision +and pattern recognition, pages 248–255. Ieee, 2009. +[92] Samira Abnar and Willem Zuidema. Quantifying attention flow in transformers. In +Annual Meeting of the Association for Computational Linguistics (ACL), 2020. +[93] Jindong Gu, Volker Tresp, and Yao Qin. Are vision transformers robust to patch +perturbations? In arXiv preprint arXiv:2111.10659, 2021. + +38 +BIBLIOGRAPHY +[94] Jungkyu Lee, Taeryun Won, Tae Kwan Lee, Hyemin Lee, Geonmo Gu, and Kiho +Hong. Compounding the performance improvements of assembled techniques in a +convolutional neural network. In arXiv preprint arXiv:2001.06268, 2020. +[95] Simyung Chang, John Yang, SeongUk Park, and Nojun Kwak. Broadcasting con- +volutional network for visual relational reasoning. In Proceedings of the European +Conference on Computer Vision (ECCV), pages 754–769, 2018. +[96] IJ Goodfellow, J Shlens, and C Szegedy. +Explaining and harnessing adversarial +examples. In ICLR, 2014. +[97] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and +Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In +arXiv preprint arXiv:1706.06083, 2017. +[98] Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, +and Ananthram Swami. The limitations of deep learning in adversarial settings. In +2016 IEEE European symposium on security and privacy (EuroS&P), pages 372–387. +IEEE, 2016. +[99] Tom B Brown, Dandelion Man´e, Aurko Roy, Mart´ın Abadi, and Justin Gilmer. +Adversarial patch. In arXiv preprint arXiv:1712.09665, 2017. +[100] Danny Karmon, Daniel Zoran, and Yoav Goldberg. Lavan: Localized and visible +adversarial noise. In International Conference on Machine Learning, pages 2507– +2515. PMLR, 2018. +[101] Chaowei Xiao, Jun-Yan Zhu, Bo Li, Warren He, Mingyan Liu, and Dawn Song. +Spatially transformed adversarial examples. +In arXiv preprint arXiv:1801.02612, +2018. +[102] Hossein Hosseini and Radha Poovendran. Semantic adversarial examples. In Proceed- +ings of the IEEE Conference on Computer Vision and Pattern Recognition Work- +shops, pages 1614–1619, 2018. +[103] Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable +adversarial examples and black-box attacks. In arXiv preprint arXiv:1611.02770, +2016. + +BIBLIOGRAPHY +39 +[104] Cihang Xie, Zhishuai Zhang, Yuyin Zhou, Song Bai, Jianyu Wang, Zhou Ren, and +Alan L Yuille. Improving transferability of adversarial examples with input diversity. +In CVPR, 2019. +[105] Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu. Evading defenses to transferable +adversarial examples by translation-invariant attacks. In CVPR, 2019. +[106] Junhua Zou, Zhisong Pan, Junyang Qiu, Xin Liu, Ting Rui, and Wei Li. Improv- +ing the transferability of adversarial examples with resized-diverse-inputs, diversity- +ensemble and region fitting. In ECCV, 2020. +[107] Yiwen Guo, Qizhang Li, and Hao Chen. Backpropagating linearly improves trans- +ferability of adversarial examples. In NeurIPS, 2020. +[108] Dongxian Wu, Yisen Wang, Shu-Tao Xia, James Bailey, and Xingjun Ma. +Skip +connections matter: On the transferability of adversarial examples generated with +resnets. In ICLR, 2020. +[109] Qian Huang, Isay Katsman, Horace He, Zeqi Gu, Serge Belongie, and Ser-Nam Lim. +Enhancing adversarial example transferability with an intermediate level attack. In +International Conference on Computer Vision (ICCV), 2019. +[110] Nathan Inkawhich, Kevin J Liang, Binghui Wang, Matthew Inkawhich, Lawrence +Carin, and Yiran Chen. Perturbing across the feature hierarchy to improve standard +and strict blackbox attack transferability. In NeurIPS, 2020. +[111] Yingwei Li, Song Bai, Yuyin Zhou, Cihang Xie, Zhishuai Zhang, and Alan Yuille. +Learning transferable adversarial examples via ghost networks. In AAAI, 2020. +[112] Xin Wang, Jie Ren, Shuyun Lin, Xiangming Zhu, Yisen Wang, and Quanshi Zhang. +A unified approach to interpreting and boosting adversarial transferability. In ICLR, +2021. +[113] Jindong Gu, Hengshuang Zhao, Volker Tresp, and Philip Torr. Adversarial examples +on segmentation models can be easy to transfer. In arXiv preprint arXiv:2111.11368, +2021. +[114] Pin-Yu Chen, Huan Zhang, Yash Sharma, Jinfeng Yi, and Cho-Jui Hsieh. +Zoo: +Zeroth order optimization based black-box attacks to deep neural networks without + +40 +BIBLIOGRAPHY +training substitute models. In Proceedings of the 10th ACM workshop on artificial +intelligence and security, 2017. +[115] Minhao Cheng, Thong Le, Pin-Yu Chen, Jinfeng Yi, Huan Zhang, and Cho-Jui +Hsieh. Query-efficient hard-label black-box attack: An optimization-based approach. +In arXiv preprint arXiv:1807.04457, 2018. +[116] Arjun Nitin Bhagoji, Warren He, Bo Li, and Dawn Song. Practical black-box attacks +on deep neural networks using efficient query mechanisms. In ECCV, 2018. +[117] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. +Square attack: a query-efficient black-box adversarial attack via random search. In +ECCV, 2020. +[118] Eric Wong, Frank Schmidt, and Zico Kolter. Wasserstein adversarial examples via +projected sinkhorn iterations. +In International Conference on Machine Learning, +pages 6808–6817. PMLR, 2019. +[119] Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harness- +ing adversarial examples. In arXiv preprint arXiv:1412.6572, 2014. +[120] Florian Tram`er, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and +Patrick McDaniel. Ensemble adversarial training: Attacks and defenses. In arXiv +preprint arXiv:1705.07204, 2017. +[121] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural +networks. In 2017 ieee symposium on security and privacy (sp), pages 39–57. IEEE, +2017. +[122] Ali Shafahi, Mahyar Najibi, Amin Ghiasi, Zheng Xu, John Dickerson, Christoph +Studer, Larry S Davis, Gavin Taylor, and Tom Goldstein. Adversarial training for +free! In arXiv preprint arXiv:1904.12843, 2019. +[123] Dinghuai Zhang, Tianyuan Zhang, Yiping Lu, Zhanxing Zhu, and Bin Dong. You +only propagate once: Accelerating adversarial training via maximal principle. In +NeurIPS, 2019. +[124] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and +Michael Jordan. Theoretically principled trade-off between robustness and accuracy. +In International Conference on Machine Learning, pages 7472–7482. PMLR, 2019. + +BIBLIOGRAPHY +41 +[125] Maksym Andriushchenko and Nicolas Flammarion. Understanding and improving +fast adversarial training. In arXiv preprint arXiv:2007.02617, 2020. +[126] Hoki Kim, Woojin Lee, and Jaewook Lee. Understanding catastrophic overfitting in +single-step adversarial training. In arXiv preprint arXiv:2010.01799, 2020. +[127] Eric Wong, Leslie Rice, and J Zico Kolter. +Fast is better than free: Revisiting +adversarial training. In arXiv preprint arXiv:2001.03994, 2020. +[128] Leslie Rice, Eric Wong, and Zico Kolter. Overfitting in adversarially robust deep +learning. +In International Conference on Machine Learning, pages 8093–8104. +PMLR, 2020. +[129] BS Vivek and R Venkatesh Babu. +Single-step adversarial training with dropout +scheduling. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recog- +nition (CVPR), pages 947–956. IEEE, 2020. +[130] Saehyung Lee, Hyungyu Lee, and Sungroh Yoon. Adversarial vertex mixup: To- +ward better adversarially robust generalization. In Proceedings of the IEEE/CVF +Conference on Computer Vision and Pattern Recognition, pages 272–281, 2020. +[131] Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan +Gu. On the convergence and robustness of adversarial training. In arXiv preprint +arXiv:2112.08304, 2021. +[132] Gaurang Sriramanan, Sravanti Addepalli, Arya Baburaj, et al. Towards efficient and +effective adversarial training. In Advances in Neural Information Processing Systems, +volume 34, 2021. +[133] Boxi Wu, Heng Pan, Li Shen, Jindong Gu, Shuai Zhao, Zhifeng Li, Deng Cai, Xiaofei +He, and Wei Liu. +Attacking adversarial attacks as a defense. +In arXiv preprint +arXiv:2106.04938, 2021. +[134] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false +sense of security: Circumventing defenses to adversarial examples. In International +conference on machine learning, pages 274–283. PMLR, 2018. +[135] Aditi Raghunathan, Jacob Steinhardt, and Percy Liang. Certified defenses against +adversarial examples. In arXiv preprint arXiv:1801.09344, 2018. + +42 +BIBLIOGRAPHY +[136] Jinyuan Jia, Xiaoyu Cao, Binghui Wang, and Neil Zhenqiang Gong. Certified robust- +ness for top-k predictions against adversarial perturbations via randomized smooth- +ing. In arXiv preprint arXiv:1912.09899, 2019. +[137] Jeremy Cohen, Elan Rosenfeld, and Zico Kolter. Certified adversarial robustness +via randomized smoothing. In International Conference on Machine Learning, pages +1310–1320. PMLR, 2019. +[138] Bai Li, Changyou Chen, Wenlin Wang, and Lawrence Carin. Certified adversarial +robustness with additive noise. In Advances in neural information processing systems, +volume 32, 2019. +[139] Hadi Salman, Greg Yang, Huan Zhang, Cho-Jui Hsieh, and Pengchuan Zhang. A +convex relaxation barrier to tight robustness verification of neural networks. +In +Advances in Neural Information Processing Systems, volume 32, 2019. +[140] Hadi Salman, Jerry Li, Ilya Razenshteyn, Pengchuan Zhang, Huan Zhang, Sebastien +Bubeck, and Greg Yang. Provably robust deep learning via adversarially trained +smoothed classifiers. In Advances in Neural Information Processing Systems, vol- +ume 32, 2019. +[141] Jeet Mohapatra, Ching-Yun Ko, Tsui-Wei Weng, Pin-Yu Chen, Sijia Liu, and Luca +Daniel. Higher-order certification for randomized smoothing. In Advances in Neural +Information Processing Systems, volume 33, pages 4501–4511, 2020. +[142] Hadi Salman, Mingjie Sun, Greg Yang, Ashish Kapoor, and J Zico Kolter. Denoised +smoothing: A provable defense for pretrained classifiers. +In Advances in Neural +Information Processing Systems, volume 33, pages 21945–21957, 2020. +[143] Jindong Gu, Hengshuang Zhao, Volker Tresp, and Philip HS Torr. +Segpgd: An +effective and efficient adversarial attack for evaluating and boosting segmentation +robustness. In European Conference on Computer Vision, pages 308–325. Springer, +2022. +[144] Boxi Wu, Jindong Gu, Zhifeng Li, Deng Cai, Xiaofei He, and Wei Liu. Towards +efficient adversarial training on vision transformers. +In European Conference on +Computer Vision, pages 307–325. Springer, 2022. + +BIBLIOGRAPHY +43 +[145] Cihang Xie, Yuxin Wu, Laurens van der Maaten, Alan L Yuille, and Kaiming He. Fea- +ture denoising for improving adversarial robustness. In Proceedings of the IEEE/CVF +Conference on Computer Vision and Pattern Recognition, pages 501–509, 2019. +[146] Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial +examples in deep neural networks. In arXiv preprint arXiv:1704.01155, 2017. +[147] Reuben Feinman, Ryan R Curtin, Saurabh Shintre, and Andrew B Gardner. Detect- +ing adversarial samples from artifacts. In arXiv preprint arXiv:1703.00410, 2017. +[148] Tianyu Pang, Chao Du, Yinpeng Dong, and Jun Zhu. Towards robust detection +of adversarial examples. +In Advances in Neural Information Processing Systems, +volume 31, 2018. +[149] Kimin Lee, Kibok Lee, Honglak Lee, and Jinwoo Shin. A simple unified framework +for detecting out-of-distribution samples and adversarial attacks. In Advances in +neural information processing systems, volume 31, 2018. +[150] Zhihao Zheng and Pengyu Hong. Robust detection of adversarial attacks by modeling +the intrinsic properties of deep neural networks. In Advances in Neural Information +Processing Systems, volume 31, 2018. +[151] Kevin Roth, Yannic Kilcher, and Thomas Hofmann. The odds are odd: A statistical +test for detecting adversarial examples. +In International Conference on Machine +Learning, pages 5498–5507. PMLR, 2019. +[152] Gilad Cohen, Guillermo Sapiro, and Raja Giryes. +Detecting adversarial samples +using influence functions and nearest neighbors. In Proceedings of the IEEE/CVF +conference on computer vision and pattern recognition, pages 14453–14462, 2020. +[153] Inyoung Paik, Taeyeong Kwak, and Injung Kim. Capsule networks need an improved +routing algorithm. In Asian Conference on Machine Learning, pages 489–502. PMLR, +2019. +[154] Jindong Gu, Baoyuan Wu, and Volker Tresp. Effective and efficient vote attack on +capsule networks. In International Conference on Learning Representations (ICLR), +2021. + +44 +BIBLIOGRAPHY +[155] Jindong Gu, Volker Tresp, and Han Hu. Capsule network is not more robust than +convolutional network. In Proceedings of the IEEE/CVF Conference on Computer +Vision and Pattern Recognition, pages 14309–14317, 2021. +[156] Srinadh Bhojanapalli, Ayan Chakrabarti, Daniel Glasner, Daliang Li, Thomas Un- +terthiner, and Andreas Veit. Understanding robustness of transformers for image +classification. In arXiv:2103.14586, 2021. +[157] Rulin Shao, Zhouxing Shi, Jinfeng Yi, Pin-Yu Chen, and Cho-Jui Hsieh. On the +adversarial robustness of visual transformers. In arXiv:2103.15670, 2021. +[158] Sayak Paul and Pin-Yu Chen. +Vision transformers are robust learners. +In +arXiv:2105.07581, 2021. +[159] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, +Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. In ICLR, +2013. + diff --git a/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/load_file.txt b/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..3fa0e24ce2659ff19cab01e4a3569d9290029aa5 --- /dev/null +++ b/YtAzT4oBgHgl3EQfY_wz/content/tmp_files/load_file.txt @@ -0,0 +1,1264 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf,len=1263 +page_content='Explainability and Robustness of Deep Visual Classification Models Jindong Gu Munich 2022 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='01343v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='CV] 3 Jan 2023 mAbstract Deep learning has revolutionized AI and deep neural networks, in particular, have been hugely successful in a wide range of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deep neural network architectures with different inductive biases have been proposed in different communities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the computer vi- sion community, Convolutional Neural Networks (CNNs), first proposed in the 1980’s, have become the standard visual classification model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Recently, as alternatives to CNNs, Cap- sule Networks (CapsNets) and Vision Transformers (ViTs) have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' CapsNets, which were inspired by the information processing of the human brain, are considered to have more inductive bias than CNNs, whereas ViTs are considered to have less inductive bias than CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' All three classification models have received great attention since they can serve as backbones for various downstream tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' object detection and semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, these models are far from being perfect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As pointed out by the community, there are two weaknesses in standard Deep Neural Networks (DNNs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One of the limitations of DNNs is the lack of explainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Even though they can achieve or surpass human expert performance in the image classification task, the DNN-based decisions are difficult to understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In many real-world applica- tions, however, individual decisions need to be explained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The other limitation of DNNs is adversarial vulnerability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Concretely, the small and imperceptible perturbations of in- puts can mislead DNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The vulnerability of deep neural networks poses challenges to current visual classification models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The potential threats thereof can lead to unaccept- able consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, studying model adversarial vulnerability can lead to a better understanding of the underlying models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our research aims to address the two limitations of DNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Specifically, we focus on deep visual classification models, especially the core building parts of each classification model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' dynamic routing in CapsNets and self-attention module in ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We argue that both the lack of explainability and adversarial vulnerability can be attributed to the difference in the visual features used by visual recognition models and the human visual system to recognize objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Namely, the visual clues used by standard CNNs are different from the ones used by our visual system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The differences make the interpretation of classifications difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Similarly, the differences also leave attackers the chance to manipulate decisions with quasi-imperceptible input perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We have analyzed if the brain-inspired Capsule Network (CapsNet) performs more ro- bustly than the CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our investigation on CapsNet shows CapsNets with more inductive Abstract 3 bias do not perform better than CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The dynamic routing therein can even harm the robustness, in contrast to the common belief.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Compared to CNNs and CapsNets, Vision Transformers (ViTs) are considered to have less inductive bias in their architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the patch-wise input image representation of ViT, we dissect ViT with adversarial patch attack methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We find that vision transformers are more robust to naturally corrupted patches than CNNs, whereas they are more vulnerable to adversarial patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Specifically, the attention module can effectively ignore naturally corrupted patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, when attacked by an adversary, it can be easily fooled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Overall, our work provides a detailed analysis of CNNs, CapsNet, and ViTs in terms of explainability and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The contribution of this thesis will facilitate the application of existing popular deep visual classification models and inspires the development of more intelligent classifiers in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Chapter 1 Introduction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 Motivation Artificial intelligence changes our daily lives in many perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The recent advances of artificial intelligence are mainly powered by Deep Learning method [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As a revolutionary technique, Deep Learning methods are also embraced by other disciplines, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' bioscience and astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As a representative model in the framework of deep learning, deep neural networks (DNNs) dominate the community due to their powerful expressiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, two limitations of deep neural networks prevent their wide application in safety-critical domains, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' the medical domain and autonomous driving system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One of the limitations of deep neural networks is their lack of explainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Even though the DNN-based intelligent system can achieve or surpass human expert perfor- mance on some tasks, it is not clear how the system reaches its decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For exam- ple, Deep convolutional neural networks (DCNNs) achieve start-of-the-art performance on many tasks, such as visual object recognition [2, 3, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, since they lack trans- parency, they are considered as ”black box” solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In real-world applications, however, individual decisions need to be explained to gain the trust of the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', autonomous driving systems should reassure passengers by giving explanations when braking the car abruptly [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Decisions made by deep models are also required to be verified in the med- ical domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Mistakes of unverified models could have an unexpected impact on humans or lead to unfair decisions [8, 9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, AI applications must comply with related legislation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the right to explanation in GDPR of the European Union [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The other limitation of deep neural networks is limited generalization robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When deep neural networks are deployed in real-world applications, the input can deviate from 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1: The overview of deep visual classification model architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' This figure is based on the figures in [17, 3, 12] the training data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The inference on the input with overlapped patterns [12], affine-transformed pattern [12, 13], and natural corruption [14] can result in unexpected results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides the robustness to out-of-distribution data, the low robustness to artificial perturbation also raises great concern in the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Concretely, the small and im- perceptible artificial perturbations of inputs can mislead DNN-based intelligent systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For example, given an image correctly classified by a deep convolutional neural network, a hardly human-perceptible artificial perturbation can cause the convolutional neural net- work to misclassify the image when added to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The vulnerability of Deep Learning poses challenges to current intelligent systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The adversarial images on CNNs can pose po- tential threats to security-sensitive CNN-based applications, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', face verification [15] and autonomous driving [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The potential threats thereof can lead to unacceptable conse- quences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, the existence of adversarial images demonstrates that the object recogni- tion process in CNNs is dramatically different from that in human brains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hence, the study of adversarial examples on deep neural networks can also lead to a better understanding of the underlying object recognition models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Since [18] proposed the AlexNet, deep neural networks have revolutionized the computer vision community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the image classification task, the classification model consists of two parts, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', feature extractor and classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The modules that extract features from input images are also adopted as feature extractor (dubbed backbone) in downstream tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', object detection [19, 20] and semantic segmentation [21, 22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The improvement of the classification models often also benefits the downstream tasks due to the improved backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In this thesis, we focus on deep visual classification models from the perspectives of explainability and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' MLP Head Transformer Encoder IIL,lI 001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='.0 Linear Projection of Flattened Patches Wij = [8 × 16] Vision Transformer Convolutional Neural Network Capsule Network Inductive Bias High Low1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 Motivation 3 As one of the representatives of deep visual classification models, convolutional neural networks have dominated the computer vision community in the last decade [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' How- ever, CNNs suffer from many limitations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', only local information aggregation at lower layers and the broken equivariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Recently, the community has been attempting to propose new models to overcome the limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Two among them have received great attention from the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The one is Capsule Networks (CapsNet) which is inspired by the information processing in the human brain [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Compared to CNNs, CapsNet is more inductively-biased where the partial information processing in the human brain is integrated into the model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the transformation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The other is Vision Trans- former(ViT) [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the success of Transformer in natural language processing (NLP), the work [17] generalizes Transformer architectures to image classification task by rep- resenting the input image as a sequence of image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Compared to CNNs, ViTs are less inductive-biased where information aggregation is also possible at lower layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Convolutional Neural Networks, Capsule Networks, and Vision Transformers raise great attention in the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hence, in this work, we mainly focus on the three deep visual classification models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the rest of this chapter, we first introduce background knowledge about CNNs, Cap- sNets, and ViTs in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3, we present a summary of the explain- ability of deep visual classifications and describe our contributions to the explainability of deep visual classification models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Last, in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4, we show the categorization of the robustness of deep visual classifications and describe our contributions to the robustness of deep visual classification models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In this dissertation, our contributions can be summarized from two perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' From the perspective of explainability, we first present a novel method, called CLRP, to explain CNN-based image classifications in Chapter 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, in Chapter 3, we present our interpretable capsule networks whose predictions can be explained with built-in modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Last, we show our understanding of ViT-based image classifications in Chapter 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' From the perspective of robustness, our contributions mainly focus on the role the model architecture plays in terms of both natural robustness and adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We present our findings and improvements of Capsule Networks’ natural robustness to non- additive perturbation in Chapters 4 and 5, and further propose our adversary Vote Attack method to show the vulnerability of CapsNets in Chapter 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, we introduce our understanding of the robustness of ViT-based classifications to patch-wise perturbations in Chapter 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Background Knowledge 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 Convolutional Neural Networks To recognize the patterns of the images, many operations have been proposed, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', Scale- Invariant Feature Transform (SIFT) [24], Histogram of Oriented Gradients(HOG) [25], and Convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Especially, the convolutional operation dominates the community in the last decade as an image feature extraction operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Formally, convolution is a mathematical operation on two functions that produces a third function that expresses how the shape of one is modified by the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the domain of computer vision, the discrete variant of convolution is adopted since the images are saved as discrete signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Concretely, given an image X ∈ R(C×H×W) and a convolution kernel k ∈ R(C×P×Q), the feature map H ∈ R(H′×W ′) extracted by the convolution kernel is computed as H(i, j) = C � c=1 P � p=1 Q � q=1 X(c, i+p−1, j+q−1) k(c, p, q), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1) where (i, j) is the index of elements in the feature map H, C is the number of channels of input images and (P, Q) are the size of the feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A single kernel corresponds to a single feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Multiple kernels are often applied to extract multiple feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, the pooling (subsampling) operation is applied to the feature maps extracted by convolution operation to aggregate the visual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the pooling operation, the mean operation or the max operation is often applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The pooling operation with size (s, s) can be expressed as H′ (i, j) = P max p=1 H(i, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2) Convolution can be further applied to the pooled feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The convolutional and pooling operations are applied alternatively on the image to obtain the final feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The features HL (i, j) extracted by a list of convolutional operations and pooling opera- tions are taken as the final image representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A single or multiple fully connected layers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' a MLP module) is used as classifier that maps the features into the ground-truth class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Z = MLP(HL (i, j)) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3) The output probabilities can be obtained by applying softmax function on the logits Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The predicted class is defined as argmax(Zi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Background Knowledge 5 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2: The overview of LeNet-5 architecture [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The work [26] proposes Convolution Neural Network (CNN) in the end-to-end learning framework to recognize hand-written digits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Therein, LeNet-5 is the classic instance of convolution neural networks, which is visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The proposed LeNet-5 starts with two convolutional layers, and each is followed by a pooling layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, a three-layer MLP module maps the feature to the logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3: The overview of AlexNet architecture [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the limited computational resource, the architecture and the corresponding train- ing strategy proposed in [26] does not scale well to the large-scale dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' With the advance of the computational power, the work [18] proposes AlexNet, which achieves impressive accuracy on ImageNet-1k dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' AlexNet consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000- way softmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In terms of model architecture, AlexNet is deeper and wider than LeNet-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' From the perspective training strategy, to make AlexNet work well, the work [18] proposes non-saturating neurons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', Rectified Linear Units (ReLUs) to activate the neurons and C3: f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' maps 16@10x10 C1: feature maps S4: f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' maps 16@5x5 INPUT 6@28x28 32x32 s2: f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' maps C5: layer F6: layer OUTPUT 6@14x14 120 84 10 Full connection Gaussian connections Convolutions Subsampling Convolutions Subsampling Full connection3 3/ 3 3 3 5 3 3 2048 dense 192 192 128 2048 48 128 55 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 13° (13 13 5 224 3 5 13 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 13 dense densée [27 w 114 3 1000 155 192 192 128 Max 2048 2048 224 Max Max pooling Stridel 128 pooling of 4 pooling 3 486 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4: The overview of Residual block with skip connection [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5: The overview of ResNet architecture [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' employs dropout method to regularize the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Especially, they propose a GPU-specific implementation of GPU operation to make the training process feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One intuitive way to improve AlexNet is to build deeper layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the AlexNet with deeper layers does not converge well during training due to the gradient vanishing problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Namely, the gradients become zeros or close to zeros when propagating from the output layer to low layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Due to the gradient vanishing problem, the parameter update of low layers is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To overcome the challenges, the work [3] proposes skip-connection, which can propagate the gradients from deep layers to low layers directly by skipping some intermediate layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The block with such a skip connection is called residual block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A popular residual block is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As an instance, the work [3] proposes ResNet which consists of a list of residual blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When equipped with skip connections, ResNets with even more than 100 layers can converge well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' ResNets still dominate the computer vision community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We show the ResNet18 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5 as an example where 18 layers are built into the ResNet to extract features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' x weight layer F(x) I relu x weight layer identity F(x) +x relu7x7 conv, 64, /2 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='/2 3x3, pool, /2 3x3 conv, 64 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='28 3x3 conv, 64 28 9 avg pool Image fc 1000 conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' con 3x3 conV, coT 3x3 3X3 5x3 5X3 3x3 3x3 3X31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Background Knowledge 7 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6: The overview of CapsNet architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The CapsNet architecture consists of four components, such as primary capsule extraction, voting, routing, and class-conditional reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The primary capsule extraction module first maps the raw input features to low-level capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The voting process transforms low-level capsules to make votes with a transformation matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, the routing module identifies the weight of each vote and computes the final high-level capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the last part, the reconstruction subnetwork reconstructs input images from capsules to regularize the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Convolutional Network Follow-Ups: The CNN-based deep visual classifier has al- ready surpassed human-level performance in the image classification task [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the last years, the architectures of convolutional neural networks have still been improved from different perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' On the one hand, the more advanced architectures have been pro- posed to further push the state-of-the-art performance [4, 5, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' On the other hand, the efficiency of architecture has received great attention since real-world CNN-based appli- cations often require less memory consumption and computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The efficiency of architecture has been addressed from different perspective, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', light-weight architecture design [29, 30], architecture pruning [31, 32, 33, 34], and distilling knowledge from large architectures to small architectures [35, 36, 37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' More recently, many researchers focus on neural architecture search where the architectures are searched automatically from a predefined search space [39, 40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The found architecture can surpass the manually designed ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Capsule Networks Inspired by the information process in the human brain, Hinton proposes Capsule Networks (CapsNet) [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Different from CNNs, CapsNets represent a visual entity with a vector instead of a single scale value, called Capsule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' CapsNets [12] encode visual entities with Primary Capsules Votes Class-Conditional Reconstruction Output Capsules Routing M8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each capsule is represented by an activity vector (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the activation of a group of neurons), and elements of each vector encode the properties of the corresponding entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The length of the activation vector indicates the confidence of the entity’s existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The output classes are represented as high-level capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The most popular version of Capsule Networks is Dynamic Routing Capsule Networks (DR-CaosNet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We introduce the architecture details of DR-CapsNet as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6, CapsNet starts with one (or more) convolutional layer(s) that convert the raw pixel intensities X into low-level visual entities ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Concretely, CapsNet extracts feature maps of shape (C′, H′, W ′) from input image X ∈ R(C×H×W) with two standard convolutional layers where C′, H′, W ′ are the number of channels, the height, and the width of the feature maps, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The extracted feature maps are reformulated as primary capsules (C′/Din, H′, W ′, Din) where Din is the dimensions of the primary capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' There are N = C′/Din∗H′∗W ′ primary capsules all together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each capsule ui, a Din-dimensional vector, consists of Din units across Din feature maps at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For example, the red bar marked with ui in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6 is a low-level capsule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the voting process, each primary capsule is transformed to make a vote with a transformation matrix W ij ∈ R(Din×N∗Dout) in, where N is the number of output classes and Dout is the dimensions of output capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The vote from the i-th low-level capsules to the j-th high-level capsules is ˆuj|i = W ijui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4) Then, a routing module is applied to identify weight for each vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given all N votes ˆuj|i of the L-th layer with N capsules, M high-level capsule sj of the (L + 1)-th layer with M capsules, the routing process is sj = N � i cij ˆuj|i (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5) where cij is a coupling coefficient that models the degree with which ˆuj|i is able to predict sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The capsule sj is shrunk to a length in [0, 1) by a non-linear squashing function g(·), which is defined as vj = g(sj) = ∥sj∥2 1 + ∥sj∥2 sj ∥sj∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6) By doing the squashing operation, the length of the vector is mapped to [0, 1) that rep- resents the confidence of the high-level entity’s existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In DR-CapsNet, the high-level capsules correspond to output classes, and its length means the output probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Background Knowledge 9 Note that the coupling coefficients {cij} in Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5 are computed by an iterative routing procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' They are updated so that high agreement (aij = vT j ˆuj|i) corresponds to a high value of cij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' cij = exp(bij) � k exp(bik) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='7) where initial logits bik are the log prior probabilities and updated with bik = bik + aij in each routing iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The coupling coefficients between a i-th capsule of the L-th layer and all capsules of the (L+1)-th layer sum to 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', �M j=1 cij = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The steps in Equations 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='7 are repeated K times in the routing process, where sj and cij depend on each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The length of the final output capsule vj corresponds to the output probability of the j-th class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Different from CNNs where cross-entropy loss is often applied to compute classification loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In DR-CapsNet, the margin loss function is applied to compute the classification loss Lk =Tk max(0, m+ − ∥vk∥)2 + λ(1 − Tk) max(0, ∥vk∥ − m−)2 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='8) where Tk = 1 if the object of the k-th class is present in the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As in [12], the hyper-parameters are often empirically set as m+ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='9, m− = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 and λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A reconstruction sub-network reconstructs the input image from all N output capsules with a masking mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The ones corresponding to the non-ground-truth classes are masked with zeros before being transferred to the reconstruction sub-network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Due to the masking mechanism, only the capsule of the ground-truth class is visible for the re- construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hence, the reconstruction process is called class-conditional reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The reconstruction loss is computed as a regularization term in the loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Capsule Network Follow-Ups: Many routing mechanisms have been proposed to im- prove the performance of CapsNet, such as Expectation-Maximization Routing [42], Self- Routing [43], Variational Bayes Routing [44], Straight-Through Attentive Routing [45], and Inverted Dot-Product Attention routing [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' An alternative to the routing mechanism to aggregate information is proposed in work [47] where they replace the dynamic routing with a multi-head attention-based graph pooling approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To reduce the parameters of CapsNet, a matrix or a tensor is used to represent an entity instead of a vector [42, 48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The size of the learnable transformation matrix can also be reduced by the matrix/tensor repre- sentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, the work [13] proposes to share a transformation matrix to reduce the 10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='7: The overview of Vision Transformer Architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The figure is taken from [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' network parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Another way to improve CapsNet is to integrate advanced modules of ConvNet into CapsNet, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', skip connections [3, 48] and dense connections [5, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Vision Transformers Transformers with self-attention-based architectures have become the model of choice in natural language processing (NLP) [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Inspired by the success of Transformers in NLP community, the work [17] proposes Vision Transformer(ViT) where they replace the convo- lutions entirely with self-attention layers and achieve remarkable performance in the image classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As a promising alternative to CNNs, Vision Transformer raises the great attention of our community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Different from CNNs, ViT represents an input image as a sequence of image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, the list of self-attention modules are applied to the sequence of image patches se- quentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We now introduce the details of the primary Vision Transformer architecture in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='7, the input image X ∈ R(C×H×W) is split into image patches {xi ∈ RP×P×C|i ∈ (1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', H/P × W/P)} where P is the patch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The embedding of each patch is extracted from the raw image patch with linear projection parameters W 0 ∈ R(HW/P 2×Dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Before the application of self-attention module, the position informa- Vision Transformer (ViT) Class Bird MLP Ball Head Car Transformer Encoder Patch + Position Embedding Extra learnable [class] embedding Linear Projection of Flattened Patches1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Background Knowledge 11 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='8: The overview of Transformer Encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' tion of image patches is also integrated into the patch embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The embedding of the patch xi is described as E0 i = xi · W 0 + P Ei, (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='9) where P Ei is the position embedding of the image patch {xi, which encodes the patch position information in the input images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The position embedding P Ei could be manually designed or learnable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ViT, the learnable version is adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A learnable class-token embedding E0 0 is added into the list of patch embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The class embedding in the last layer is taken as the image embedding for classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We now introduce the transformer encoder where the list of blocks is applied to transform the input embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='8, each block consists of two main modules, namely, a multi-head self-attention module to model the inter-patch relationship and an MLP module to project each patch respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When the self-attention module with a single head in l + 1-th layer is applied to input patches {El i ∈ RDp|i ∈ (0, 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', H/P ×W/P)} in the l-th layer, the output embedding of the patch El i is Kl+1 i = W l+1 k El i, Ql+1 i = W l+1 q El i, V l+1 i = W l+1 v El i, Al+1 i = Softmax(Ql+1 i Kl+1 0 , Ql+1 i Kl+1 1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', Ql+1 i Kl+1 H/P×W/P+1, ), El+1 i = H/P×W/P+1 � j=1 Al+1 ij V j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='10) Transformer Encoder Lx MLP 4 Norm A A Multi-Head Attention K Q K Q K Q Norm Embedded Patches12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction In this equation, the key, query, and value of patch embedding is computed first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The attention of El+1 i to all patches in l-th layer is obtained with the query of i-th patch and all keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The output embedding El+1 i is the weighted sum of all values of patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The output embeddings of different heads are concatenated as the final embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, an MLP module with two MLP layers is applied to project the final embedding of each patch into a new feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The final embedding of the class-token patch is taken as the image representation to classify the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A linear classifier maps the features to output space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Vision Transformer Follow-Ups: Since the ViT was proposed, many new vision trans- former architectures have been proposed [51, 52, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A hybrid architecture that consists of both convolutional layers and self-attention blocks has also been explored [54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Be- sides, the pure patch-based architecture without attention mechanism has also been pro- posed [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' By the time this thesis is written, the arm-race between ResNet and Vision Transformers is still going on [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Recently, many researchers employ the Transformer architecture as a uniform architecture that model both images and texts [58, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 13 Approach Description Saliency Maps Identifying the relevance of each input pixel to the out- put class [60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Counterfactual Explanation Identifies how the given input could change such that the classifier would output a different specified class [75, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Explanatory Sentences Generating natural language sentences that describe the class-discriminative pixels [77, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Supporting Training Images Identifying training images most responsible for a given prediction [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Built-in Explanation Generating Explanations with built-in modules (in ex- plainable classifier) for a given prediction [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Disentangled Representations Identifying the human-interpretable properties of the recognized object in the input image [80, 12, 81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1: Summarization of different approaches for explaining image classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 Introduction Deep Neural Networks (DNNs) have shown impressive performance in high-dimensional input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Especially, the performance of DNNs can even surpass human-level perfor- mance in the image classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The traditional machine learning methods classify images with hand-crafted images, while DNNs make predictions based on the features learned automatically from data with an optimization algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hence, it is challenging to understand the classification decisions made by DNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In recent years, many directions have been explored to explain individual image classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We summarize and roughly categorize them in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We introduce each approach as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Saliency Maps, as intuitive explanations, have received great attention in the commu- nity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The saliency map is a heat map, each element of which indicates the importance of the pixel in the corresponding position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The saliency map is expected to have recognizable patterns like the objects in the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The primary work [60] takes the vanilla gra- dient of the loss with respect to the input as the saliency map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the gradients are noisy and the pattern therein is barely recognizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To improve the saliency map, many 14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction methods have been proposed [60, 83, 61, 62, 63, 64, 65, 66, 67, 84, 85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The primary method and the improved variants are model-aware, which leverage the parameters and the gradi- ents of neural networks to compute saliency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides the model-aware methods, the model-agnostic saliency methods are also preferred in many scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For example, they are able to explain any classifiers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' the explanations produced from two or more different types of models are comparable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' an ensemble model can be explained without requiring knowledge of model components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' There are two types of model-agnostic saliency methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The one is to build an explanation generation model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' a neural network with U-net architecture [86, 68, 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The other is to approximate the local decision boundary of the underlying model with an explainable model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', linear classifier [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanation generated from the explainable surrogate model can be used to explain individual decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Counterfactual Explanation describes what changes to the situation would have resulted in arriving at the alternative decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the case of image classification, Counterfactual Explanation is the counterfactual image, which indicates that the output will become the target class if the input image is replaced with the counterfactual image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The work [75] creates a counterfactual image with a conditional generative model, which generates part of the pre-defined image region conditional on the rest of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The desired property of the generated image is to most change the classifier’s decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Another work [76] formulates the generation of the counterfactual image as an image editing problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Their method performs well even in the fine-grained classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Natural language, as a natural interface, has also been explored to explain the visual classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The works [77, 78] build modules to generate natural language sentences to explain the decisions where the sentences describe the class-discriminative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanatory sentences are different from the caption/description generated by multi-model models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The contemporary vision-language models describe image content but fail to tell class-discriminative features which justify visual predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Another way to explain visual classifications is to identify the training points most responsible for a given prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To trace a model’s prediction back to its training data, the work [79] leverages influence functions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', a classic technique from robust statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given a classification, they can be the most responsible training image that supports the predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The created explanation can tell where the local decision boundary of the model came from at a specific data point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The approaches introduced above are post-hoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Namely, the explanations are created for off-shelf models without intervening in their training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' An alternative to post- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 15 hoc explanation methods is to integrate dedicated modules into the model to be trained, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' attention mechanism [47], explanation module [68] and prototype module [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the inference stage, the modules can be used to create explanations directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The created explanations are dubbed built-in explanations, which are more efficient and easy to create.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The image representations learned by DNNs are often distributed, which makes the classification decision less explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' It is difficult to interpretable the decision process inside the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One way to mitigate this problem is to constrain the model to learn disentangled representations where each element of representation corresponds to a human- understandable concept [80, 12, 81, 88, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In this subsection, we have introduced the popular methods applied to explain individ- ual classification decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the rest of this section, we present our contributions towards understanding the classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Specifically, we briefly introduce our works on the topic of explaining classification decisions made by Convolutional Networks, Capsule Networks, and Vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Explainability of Convolutional Neural Network-based Clas- sification A large number of saliency methods have been proposed to better understand individ- ual decisions of deep convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As one of the representatives, the Layer-wise Relevance Propagation (LRP) approach is able to create pixel-wise explana- tory saliency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' LRP method has also been widely applied to many tasks in different domains, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', in medical domain [89] and in NLP [90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanations generated by LRP are known to be pixel-wise and instance-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the discriminativeness of the explanations has not been evaluated yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ideally, the visualized objects in the explanation should correspond to the class that the class-specific neuron represents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Namely, the explanations should be class-discriminative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our work [66] evaluates the discriminativeness of the explanations generated by LRP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Concretely, we evaluate the explanations generated by LRP on the off-the-shelf models, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', VGG16 [2] pre-trained on the ImageNet dataset [91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For each test image, we create four saliency maps as explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The first three ex- planation maps are generated for top-3 predictions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The fourth one is created for randomly chosen 10 classes from the top-100 predicted classes (which ensure that the score to be propagated is positive).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The white text in each explanation map indicates the 16 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='9: The explanations generated by LRP on VGG16 Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The images from validation datasets of ImageNet are classified using the off-the-shelf models pre-trained on the ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The classifications of the images are explained by the LRP approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For each image, we generate four explanations that correspond to the top-3 predicted classes and a randomly chosen multiple-classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanations are not class-discriminative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' class the output neuron represents and the corresponding classification probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The generated explanations are instance-specific, but not class-discriminative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In other words, they are independent of class information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanations for different target classes, even randomly chosen classes, are almost identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Based on LRP, our work [66] proposes Contrastive Layer-wise Relevance Propagation (CLRP), which is capable of producing instance-specific, class-discriminative, pixel-wise explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Before introducing our CLRP, we first discuss the conservative property in the LRP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In a DNN, given the input X = {x1, x2, x3, · · · , xn}, the output Y = {y1, y2, y3, · · · , ym}, the score Syj (activation value) of the neuron yj before softmax layer, the LRP generate an explanation for the class yj by redistributing the score Syj layer- wise back to the input space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The assigned relevance values of the input neurons are R = {r1, r2, r3, · · · , rn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The conservative property is defined as follows: The generated saliency map is conservative if the sum of assigned relevance values of the input is equal to the score of the class-specific neuron, �n i=1 ri = Syj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The overview of the CLRP are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We first describe the LRP as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The j-th class-specific neuron yj is connected to input variables by the weights W of layers between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The neuron yj models a visual concept O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For an input example X, the LRP maps the score Syj of the neuron back into the input space to get relevance vector R = fLRP(X, W , Syj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our contrastive LRP, we construct a dual virtual concept O, which models the opposite visual concept to the concept O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For instance, the concept O alp: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='5645 ski: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4280 mountain_tent:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='0046 Random10classes Shetland_sheepdog: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6152 collie: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3844 borzoi:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='0002 Random10classes1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 17 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='10: The figure shows an overview of our CLRP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For each predicted class, the approach generates a class-discriminative explanation by comparing two signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The blue line means the signal that the predicted class represents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The red line models a dual concept opposite to the predicted class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The final explanation is the difference between the two saliency maps that the two signal generate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' models the zebra, and the constructed dual concept O models the non-zebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One way to model the O is to select all classes except for the target class representing O, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' the dashed red lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='10 are connected to all classes except for the target class zebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Next, the score Syj of target class is uniformly redistributted to other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the same input example X, the LRP generates an explanation Rdual = fLRP(X, W , Syj) for the dual concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The Contrastive LRP is defined as follows: RCLRP = max(0, (R − Rdual)) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11) where the function max(0, X) means replacing the negative elements of X with zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The difference between the two saliency maps cancels the common parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Without the dominant common parts, the non-zero elements in RCLRP are the most relevant pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides the qualitative evaluation, we also evaluate the explanations quantitatively with a Pointing Game and an ablation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Both qualitative and quantitative evaluations show that the CLRP generates better explanations than the LRP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explainability of Capsule Network-based Classification Capsule Networks, as alternatives to Convolutional Neural Networks, have been proposed to recognize objects from images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The current literature demonstrates many advantages of CapsNets over CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, how to create explanations for individual classifications of CapsNets has not been well explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=" CNN ebra backward pass CNN forward pass 'Eléphant CNN backward pass18 1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11: The illustration of GraCapsNets: The extracted primary capsules are trans- formed and modeled as multiple graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The pooling result on each graph (head) corre- sponds to one vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The votes on multiple graphs (heads) are averaged to generate the final prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The widely used saliency methods are mainly proposed for explaining CNN-based clas- sifications;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' they create saliency map explanations by combining activation values and the corresponding gradients, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', Grad-CAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' They combine activation values and the received gradients in specific layers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', deep convolutional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CapsNets, instead of deep convolutional layers, an iterative routing mechanism is applied to extract high-level visual concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hence, these saliency methods cannot be trivially applied to CapsNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, the routing mechanism makes it more challenging to identify interpretable input features relevant to a classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To overcome the lack of interpretability, we can either propose new post-hoc interpre- tation methods for CapsNets or modify the model to have build-in explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our published work [47], we explore the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Specifically, we propose interpretable Graph Capsule Networks (GraCapsNets), where we replace the routing part with a multi-head attention-based Graph Pooling approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our GraCapsNet includes an attention-based pooling module, with which individual classification explanations can be created effectively and efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As introduced in Background Section, CapsNets start with convolutional layers that convert the input pixel intensities X into primary capsules ui (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', low-level visual entities).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each ui is transformed to vote for high-level capsules ˆuj|i with learned transformation matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, a routing process is used to identify the coupling coefficients cij, which describe how to weight votes from primary capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Finally, a squashing function is applied to the identified high-level capsules sj so that the lengths of them correspond to the confidence of the class’s existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Multi-head Attention-based Graph Pooling Capsules uj wi Reconstruction Capsules Wi1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 19 Different routing mechanisms differ only in how to identify cij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Routing processes de- scribe one way to aggregate information from primary capsules into high-level ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our GraCapsNets, we implement the information aggregation by multi-head graph pooling processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CapsNets, the primary capsules represent object parts, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the eyes and nose of a cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our GraCapsNets, we explicitly model the relationship between the pri- mary capsules (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', part-part relationship) with graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, the followed graph pooling operations pool relevant object parts from the graphs to make a classification vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Since the graph pooling operation reveals which input features are pooled as relevant ones, we can easily create explanations to explain the classification decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The overview of our GraCapsNets is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In GraCapsNet, the primary capsules ui are transformed into a feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' All transformed capsules u′ i are modeled as multiple graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each graph corresponds to one head, the pooling result on which corresponds to one vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The votes on multiple heads are averaged as the final prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The transformed capsules u′ i can be modeled as multiple graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A graph consists of a set of nodes and a set of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11, the primary capsules are reshaped from L groups of feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each group consists of C feature maps of the size K × K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Correspondingly, the transformed capsules u′ i where i ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='K2} form a single graph with K2 nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Each node corresponds to one transformed capsule u′ i, and the activation vector of u′ i is taken as features of the corresponding node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The graph edge can be represented by an adjacency matrix, where different priors can be modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The spatial relationship between primary capsules is modeled in our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given node features Xl ∈ R(K2×Dout) and adjacency matrix A ∈ R(K2×K2) in the l-th head of GraCapsNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We first compute the attention of the head as Attl = softmax(AXlW) where W ∈ RDout×M are learnable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Dout is the dimension of the node features and M is the number of output classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The output is of the shape (K2 × M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our GraCapsNet for object recognition, Attl corresponds to the visual attention of the heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The graph pooling output Sl ∈ R(M×Dout) of the head is computed as Sl = (Attl)TXl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The final predictions of GraCapsNets are based on all L heads with outputs Sl where l ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', L}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The output capsules are V = squash( 1 L �L l=1 Sl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our GraCapsNet, we can use visual attention as built-in explanation to explain the predictions of GraCapsNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The averaged attenion over l heads is E = 1 L L � l=1 Attl (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='12) 20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='12: Adversarial Patch Attack or Natural Patch Corruption on Vision Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' where Attl corresponds to the attention of the l-th head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The created explanations E are of the shape (K2 × M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the predicted class, the K × K attention map indicates which pixels of the input image support the prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The explanations for individual classifications of GraCapsNets can be created in an effective and efficient way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Surprisingly, without a routing mechanism, our GraCapsNets can achieve better classification performance and better adversarial robustness, and still keep other advantages of CapsNets, namely, disentangled representations and affine trans- formation robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4 Explainability of Vision Transformer-based Classification The recent advances in Vision Transformer (ViT) have demonstrated its impressive perfor- mance in image classification [17, 51], which makes it a promising alternative to Convolu- tional Neural Network (CNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Unlike CNNs, ViT represents an input image as a sequence of image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, a self-attention mechanism is applied to aggregate information from all patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The attention can be used to create saliency maps to explain ViT-based classification decisions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' with Rollout Attention method [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The patch-wise input image representation in ViT makes the following question interesting: How does the at- tention of ViT change when individual input image patches are perturbed with natural corruptions or adversarial perturbations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For example, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='12 illustrates the case where a single patch of the input is perturbed or attacked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Vision Transformer (ViT) Class Bird MLP Ball Head Car Transformer Encoder Patch + Position Embedding Extra learnable [class] embedding Linear Projection of Flattened Patches Attack or Corrupt1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Explanability of Deep Visual Classifications 21 (a) Clean Image (b) with Naturally Corrupted Patch (c) with Adversarial Patch Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13: Images with patch-wise perturbations (top) and their corresponding atten- tion maps (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The attention mechanism in ViT can effectively ignore the naturally corrupted patches to maintain a correct prediction, whereas it is forced to focus on the adversarial patches to make a mistake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The images with corrupted patches are all cor- rectly classified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The images with adversary patches in subfigure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13c are misclassified as dragonfly, axolotl, and lampshade, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our work [93], we study the robustness of vision transformers to patch-wise per- turbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Surprisingly, we find that vision transformers are more robust to naturally corrupted patches than CNNs, whereas they are more vulnerable to adversarial patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Furthermore, we conduct extensive qualitative and quantitative experiments to understand the classification under patch perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We have revealed that ViT’s stronger robustness to natural corrupted patches and higher vulnerability against adversarial patches are both caused by the attention mecha- nism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Specifically, the attention model can help improve the robustness of vision transform- ers by effectively ignoring natural corrupted patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, when vision transformers are attacked by an adversary, the attention mechanism can be easily fooled to focus more on the adversarially perturbed patches and cause a mistake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Digging down further, we find the reason behind this is that the self-attention mech- anism of ViT can effectively ignore the natural patch corruption, while it’s also easy to manipulate the self-attention mechanism to focus on an adversarial patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' This is well supported by rollout attention visualization [92] on ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13 (a), ViT successfully attends to the class-relevant features on the clean image, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the head of the dog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When one or more patches are perturbed with natural corruptions, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13 (b), ViT can effectively ignore the corrupted patches and still focus on the main foreground to make a correct prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13 (b), the attention weights on the positions of 22 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction naturally corrupted patches are much smaller even when the patches appear in the fore- ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In contrast, when the patches are perturbed with adversarial perturbations by an adversary, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='13 (c), ViT is successfully fooled to make a wrong prediction because the attention of ViT is misled to focus on the adversarial patches instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In our work [93], we provide our understanding of the attention changes of ViT when individual input image patches are perturbed with natural corruptions or adversarial per- turbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4 Robustness of Deep Visual Classification Models 23 Natural Robustness Additive Natural Corruption Robustness to the noisy images that are added with various noise [94, 14], such as, white noise, blur, weather, and digital categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Non-Additive Affine Transformation Robustness to the images that are affine- transformed from standard ones [95, 12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Additive Dense Attack Robustness to the images where all pixels can be changed under a certain constraint [96, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial Robustness Sparse Attack Robustness to the images where only a few pix- els of each image can be manipulated [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Patch Attack Robustness to the perturbed images where only a single patch (a specific region) of each image can be manipulated [99, 100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Non-Additive Transformation Based Attack Robustness to adversarial images that is cre- ated by delicated affine transformations [101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Sementic Attack Robustness to semantic adversarial images that is created by image synthesis [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2: Categorization of Robustness in Image Classification Task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4 Robustness of Deep Visual Classification Models 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='1 Introduction In this thesis, we mainly consider two types of robustness, namely, natural robustness and adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When an image is captured, different corruption can happen, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the existence of white noise, the effect of weather, the compression in the digitalization process, and random affine transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The robustness to these images with natural corruption is denoted as natural robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial robustness describes the robustness of models to adversarial images, which is created by an adversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Both natural robustness and adversarial robustness are critical in some safety-critical domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We summarize and categorize the robustness in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides the type of attacks in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2, adversarial attacks can be categorized into targeted and untargeted ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The goal of targeted attacks is to mislead the model to a specific target class, while the goal of untargeted ones is to fool the model to make wrong predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In terms of the availability of the target models, adversarial attacks can also be cat- egorized into white-box and black-box attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The white-box attacks assume that the 24 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction adversary has all access to target models including model parameters, model architectures, and even defense methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In contrast, in the setting of black-box attacks, the adversary can only obtain the output of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The black-box attacks have also received great attention since it is realistic in real-world applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The implementation of white-box attacks is relatively cheap where they create adversar- ial examples with the gradients of the self-defined objective function with respect to inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the implementation of black-box attacks can be computationally expensive given the limited available information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One way to created adversarial examples in a black-box fashion is to leverage their transferability [103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113], namely, the adversarial examples created on one model can also fool another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The adversary first trains a surrogate model on the same training data as the one used for the target model and creates adversarial examples on the surrogate model to fool the target model, which is called transfer-based black-box attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the transfer-based black- box attacks require access to the training data of the target model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To overcome the limi- tation, the query-based black-box attacks have been proposed where the attacks are based on the outputs obtained by querying the target models directly [114, 115, 116, 115, 117].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In addition, based on the constraints on the adversarial images, the generated adver- sarial perturbations can be quasi-imperceptible or unbounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The popular metric of to measure the distance between clean images and adversarial image is ℓp norm [98], such as, ℓ1, ℓ2 and ℓ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, the metric is not perfectly aligned with human perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The more advanced metric has also been explored in the community, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', Wasserstein distance [118].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the potential threats posed by adversarial attacks, many defense strategies have been proposed to build adversarially robust models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One of the most effective defense methods is adversarial training, which creates adversarial examples and adds them to the training dataset in each training iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides, the pre-processing methods have been explored to purify adversarial examples [119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, some of the defense strategies have broken again in later publications [134].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Some defense methods provide certified robustness to break arm-race between adversary and defense [135, 136, 137, 138, 139, 140, 141, 142, 143, 144].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Even many methods have been published to address, the accuracy of the model under attacks is still much lower than the accuracy on clean images, especially on the large dataset [145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In addition to building robust model, another way to address the threats is to detect adversarial examples first [146, 147, 148, 149, 150, 151, 152].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4 Robustness of Deep Visual Classification Models 25 In this subsection, we categorize the robustness of image classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our contri- butions of this thesis mainly focus on the role the model architecture plays in terms of both natural robustness and adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In the rest of this section, we present our contributions towards the robustness of image classification models, such as Capsule Networks and Vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='2 Robustness of Capsule Network-based Classification Human visual recognition is quite insensitive to affine transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' For example, enti- ties in an image, and a rotated version of the entities in the image, can both be recognized by the human visual system, as long as the rotation is not too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Convolutional Neural Networks (CNNs), the currently leading approach to image analysis, achieve affine ro- bustness by training on a large amount of data that contain different transformations of target objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given limited training data, a common issue in many real-world tasks, the robustness of CNNs to novel affine transformations is limited [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' With the goal of learning image features that are more aligned with human percep- tion, Capsule Networks (CapsNets) have recently been proposed [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our work [13] first investigates the effectiveness of components that make CapsNets robust to input affine transformations, with a focus on the routing algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, recent work [153] shows that all routing algorithms proposed so far perform even worse than a uniform/random routing procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' From both numerical analysis and empirical experiments, our investigation reveals that the dynamic routing procedure contributes neither to the generalization ability nor to the affine robustness of CapsNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Therefore, it is infeasible to improve the affine robustness by modifying the routing procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Instead, we investigate the limitations of the CapsNet architectures and propose a simple solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Namely, we propose to apply an identical transformation function for all primary capsules and replace the routing with a simple averaging procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Besides the high affine transformation robustness, CapsNets also demonstrate other ad- vantages, such as the ability to recognize overlapping digits and the semantic representation compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In recent years, It has been suggested that CapsNets have the potential to surpass the dominant convolutional networks in these aspects [12, 42, 48, 154].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, there lack of comprehensive comparisons to support this assumption, and even for some reported improvements, there are no solid ablation studies to figure out which ones of the components in CapsNets are, in fact, effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 26 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction In our work [155], we first carefully examine the major differences in design between the capsule networks and the common convolutional networks adopted for image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The difference can be summarized as a non-shared transformation module, a dynamic routing layer to automatically group input capsules to produce output capsules, a squashing function, a marginal classification loss, and a class-conditional reconstruction sub-network with a reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Unlike previous studies [12, 42] which usually take CapsNet as a whole to test its robustness, our work [155] instead tries to study the effects of each of the above components in their effectiveness on robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We consider the three different aspects, such as the robustness to affine transformations, the ability to recognize overlapping digits, and the semantic representation compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our investigations reveal that some widely believed benefits of Capsule networks could be wrong: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The dynamic routing actually may harm the robustness to input affine transforma- tion, in contrast to the common belief;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The high performance of CapsNets to recognize overlapping digits can be mainly attributed to the extra modeling capacity brought by the transformation matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Some components of CapsNets are indeed beneficial for learning semantic represen- tations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', the conditional reconstruction and the squashing function, but they are mainly auxiliary components and can be applied beyond CapsNets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In addition to these findings, we also enhance common ConvNets by the useful compo- nents of CapsNet, and achieve greater robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Our investigation shows that Capsule Network is not more robust than Convolutional Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='3 Robustness of Vision Transformer-based Classification CapsNets with brain-inspired architectures have more inductive bias than CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Different from CapsNet, Vision Transformer (ViT) [17] has less architecture bias than CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' ViT processes the input image as a sequence of image patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Then, a self-attention mechanism is applied to aggregate information from all patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Existing works have shown that ViTs are more robust than CNNs when the whole input image is perturbed with natural corruptions or adversarial perturbations [156, 157, 158].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Given the patch-based architecture of ViT, our work studies the robustness of ViT to patch-based perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='4 Robustness of Deep Visual Classification Models 27 Two typical types of perturbations are considered to compare the robustness between ViTs and CNN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=', ResNets [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' One is natural corruptions [14], which is to test models’ robustness under distributional shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The other is adversarial perturbations [159, 119], which are created by an adversary to specifically fool a model to make a wrong prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We reveal that ViT does not always perform more robustly than ResNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' When indi- vidual image patches are naturally corrupted, ViT performs more robustly than ResNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' However, when input image patch(s) are adversarially attacked, ViT shows a higher vul- nerability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Digging down further, we find the reason behind this is that the self-attention mechanism of ViT can effectively ignore the natural patch corruption, while it’s also easy to manipulate the self-attention mechanism to focus on an adversarial patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Based on the patch-based architectural structure of vision transformers, we further investigate the sensitivity of ViT against patch positions and patch alignment of adversarial patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' First, we discover that ViT is insensitive to different patch positions, while ResNet shows high vulnerability on the central area of input images and much less on corners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' We attribute this to the architecture bias of ResNet where pixels in the center can affect more neurons than the ones in corners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In contrast, each patch within ViT can equally interact with other patches regardless of its position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Further, we find that for ViT, the adversarial perturbation designed to attack one particular position can successfully transfer to other positions of the same image as long as they are aligned with input patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In contrast, the ones on ResNet hardly do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' To summarise, in our work [93], we compare ViT and CNNs in terms of the robustness to natural patch corruptions or adversarial patch attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 28 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Introduction Bibliography [1] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In nature, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [2] Karen Simonyan and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Very deep convolutional networks for large- scale image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [3] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [4] Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wo- jna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Rethinking the inception architecture for computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 2818–2826, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [5] Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Densely connected convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 4700–4708, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [6] Jinkyu Kim and John F Canny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Interpretable learning for self-driving cars by visu- alizing causal attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Computer Vision (ICCV), pages 2961–2969, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [7] Jinkyu Kim, Anna Rohrbach, Trevor Darrell, John Canny, Zeynep Akata, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Textual explanations for self-driving vehicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ECCV, pages 577–593.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [8] Lydia T Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Delayed impact of fair machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICML, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [9] Tatsunori B Hashimoto, Megha Srivastava, Hongseok Namkoong, and Percy Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Fairness without demographics in repeated loss minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICML, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 30 BIBLIOGRAPHY [10] Jindong Gu and Daniela Oelke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding bias in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='01866, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [11] Andrew Selbst and Julia Powles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' “meaningful information” and the right to expla- nation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Conference on Fairness, Accountability and Transparency, pages 48–48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [12] Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Dynamic routing between capsules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems (NeurIPS), pages 3856–3866, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [13] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Improving the robustness of capsule networks to image affine transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 7285–7293, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [14] Dan Hendrycks and Thomas Dietterich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Benchmarking neural network robustness to common corruptions and perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [15] Mahmood Sharif, Sruti Bhagavatula, Lujo Bauer, and Michael K Reiter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Accessorize to a crime: Real and stealthy attacks on state-of-the-art face recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceed- ings of the 2016 acm sigsac conference on computer and communications security, pages 1528–1540, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [16] Kevin Eykholt, Ivan Evtimov, Earlence Fernandes, Bo Li, Amir Rahmati, Chaowei Xiao, Atul Prakash, Tadayoshi Kohno, and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Robust physical-world at- tacks on deep learning visual classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1625–1634, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [17] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' An image is worth 16x16 words: Transformers for image recog- nition at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11929, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [18] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Imagenet classification with deep convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 31 [19] Ross Girshick, Jeff Donahue, Trevor Darrell, and Jitendra Malik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Rich feature hier- archies for accurate object detection and semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CVPR, pages 580–587, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [20] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Mask r-cnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Computer Vision (ICCV), pages 2961–2969, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [21] Jonathan Long, Evan Shelhamer, and Trevor Darrell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Fully convolutional networks for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 3431–3440, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [22] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Pyra- mid scene parsing network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CVPR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [23] Liang-Chieh Chen, George Papandreou, Florian Schroff, and Hartwig Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Re- thinking atrous convolution for semantic image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='05587, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [24] David G Lowe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Object recognition from local scale-invariant features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the seventh IEEE international conference on computer vision, volume 2, pages 1150–1157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ieee, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [25] Navneet Dalal and Bill Triggs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Histograms of oriented gradients for human detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), volume 1, pages 886–893.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ieee, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [26] Yann LeCun, L´eon Bottou, Yoshua Bengio, and Patrick Haffner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Gradient-based learning applied to document recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [27] Asifullah Khan, Anabia Sohail, Umme Zahoora, and Aqsa Saeed Qureshi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A sur- vey of the recent architectures of deep convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Artificial intelligence review, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [28] Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deformable convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 764–773, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [29] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Mobilenets: Efficient 32 BIBLIOGRAPHY convolutional neural networks for mobile vision applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='04861, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [30] Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Shufflenet: An extremely efficient convolutional neural network for mobile devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6848–6856, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [31] Yann LeCun, John S Denker, and Sara A Solla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Optimal brain damage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NIPS, pages 598–605, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [32] Babak Hassibi and David G Stork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Second order derivatives for network pruning: Optimal brain surgeon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NeurIPS, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [33] Song Han, Jeff Pool, John Tran, and William Dally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Learning both weights and connections for efficient neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NeurIPS, pages 1135–1143, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [34] Pavlo Molchanov, Stephen Tyree, Tero Karras, Timo Aila, and Jan Kautz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Pruning convolutional neural networks for resource efficient inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [35] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Distilling the knowledge in a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In stat, volume 1050, page 9, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [36] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Fitnets: Hints for thin deep nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [37] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Search for better students to learn distilled knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11612, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [38] Jindong Gu, Wei Liu, and Yonglong Tian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Simple distillation baselines for improving small self-supervised models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11304, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [39] Barret Zoph and Quoc V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Neural architecture search with reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [40] Hanxiao Liu, Karen Simonyan, Oriol Vinyals, Chrisantha Fernando, and Koray Kavukcuoglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Hierarchical representations for efficient architecture search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [41] Hanxiao Liu, Karen Simonyan, and Yiming Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Darts: Differentiable architecture search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 33 [42] Geoffrey E Hinton, Sara Sabour, and Nicholas Frosst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Matrix capsules with em routing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International conference on learning representations (ICLR), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [43] Taeyoung Hahn, Myeongjang Pyeon, and Gunhee Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Self-routing capsule net- works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), pages 7658–7667, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [44] Fabio De Sousa Ribeiro, Georgios Leontidis, and Stefanos D Kollias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Capsule routing via variational bayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In AAAI, pages 3749–3756, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [45] Karim Ahmed and Lorenzo Torresani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Star-caps: Capsule networks with straight- through attentive routing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [46] Yao-Hung Hubert Tsai, Nitish Srivastava, Hanlin Goh, and Ruslan Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Capsules with inverted dot-product attention routing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [47] Jindong Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Interpretable graph capsule networks for object recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Pro- ceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [48] Jathushan Rajasegaran, Vinoj Jayasundara, Sandaru Jayasekara, Hirunima Jayasekara, Suranga Seneviratne, and Ranga Rodrigo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deepcaps: Going deeper with capsule networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10725–10733, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [49] Sai Samarth R Phaye, Apoorva Sikka, Abhinav Dhall, and Deepti R Bathula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Multi- level dense capsule networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Asian Conference on Computer Vision, pages 577– 592.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [50] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, �Lukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems, pages 5998–6008, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [51] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablay- rolles, and Herv´e J´egou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Training data-efficient image transformers & distillation through attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 10347– 10357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 34 BIBLIOGRAPHY [52] Kai Han, An Xiao, Enhua Wu, Jianyuan Guo, Chunjing Xu, and Yunhe Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Transformer in transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='00112, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [53] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Swin transformer: Hierarchical vision transformer using shifted windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='14030, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [54] Ben Graham, Alaaeldin El-Nouby, Hugo Touvron, Pierre Stock, Armand Joulin, Herv´e J´egou, and Matthijs Douze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Levit: a vision transformer in convnet’s clothing for faster inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='01136, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [55] Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Doll´ar, and Ross Gir- shick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Early convolutions help transformers see better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='14881, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [56] Ilya O Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszko- reit, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Mlp-mixer: An all-mlp architecture for vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 34, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [57] Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A convnet for the 2020s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='03545, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [58] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sand- hini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Learning transferable visual models from natural language supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Interna- tional Conference on Machine Learning, pages 8748–8763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [59] Wenhui Wang, Hangbo Bao, Li Dong, and Furu Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Vlmo: Unified vision-language pre-training with mixture-of-modality-experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='02358, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [60] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Deep inside convolutional networks: Visualising image classification models and saliency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [61] Sebastian Bach, Alexander Binder, Gr´egoire Montavon, Frederick Klauschen, Klaus- Robert M¨uller, and Wojciech Samek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' On pixel-wise explanations for non-linear clas- sifier decisions by layer-wise relevance propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In PloS one, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 35 [62] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedan- tam, Devi Parikh, Dhruv Batra, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Grad-cam: Visual explanations from deep networks via gradient-based localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Computer Vision (ICCV), pages 618–626, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [63] Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Learning important features through propagating activation differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICML-Volume 70, pages 3145– 3153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' JMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' org, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [64] Mukund Sundararajan, Ankur Taly, and Qiqi Yan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Axiomatic attribution for deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICML-Volume 70, pages 3319–3328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' JMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' org, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [65] Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda Vi´egas, and Martin Wattenberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Smoothgrad: removing noise by adding noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='03825, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [66] Jindong Gu, Yinchong Yang, and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding individual decisions of cnns via contrastive backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Asian Conference on Computer Vision, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [67] Suraj Srinivas and Fran¸cois Fleuret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Full-gradient representation for neural network visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 4126– 4135, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [68] Piotr Dabkowski and Yarin Gal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Real time image saliency for black box classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 6967–6976, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [69] Patrick Schwab and Walter Karlen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Cxplain: Causal explanations for model inter- pretation under uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, pages 10220–10230, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [70] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Why should i trust you?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' : Explaining the predictions of any classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pages 1135–1144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' ACM, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [71] Luisa M Zintgraf, Taco S Cohen, Tameem Adel, and Max Welling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Visualizing deep neural network decisions: Prediction difference analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 36 BIBLIOGRAPHY [72] Jindong Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Verification of classification decisions in convolutional neural networks, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' US Patent App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 17/294,746.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [73] Ruth C Fong and Andrea Vedaldi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Interpretable explanations of black boxes by meaningful perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Computer Vision, pages 3429–3437, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [74] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Contextual prediction difference analysis for explaining individual image classifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09086, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [75] Chun-Hao Chang, Elliot Creager, Anna Goldenberg, and David Duvenaud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Explain- ing image classifiers by counterfactual generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [76] Yash Goyal, Ziyan Wu, Jan Ernst, Dhruv Batra, Devi Parikh, and Stefan Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Coun- terfactual visual explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICML, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [77] Lisa Anne Hendricks, Zeynep Akata, Marcus Rohrbach, Jeff Donahue, Bernt Schiele, and Trevor Darrell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Generating visual explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In European Conference on Computer Vision (ECCV), pages 3–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [78] Lisa Anne Hendricks, Ronghang Hu, Trevor Darrell, and Zeynep Akata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Grounding visual explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In European Conference on Computer Vision (ECCV), pages 269–286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [79] Pang Wei Koh and Percy Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding black-box predictions via influence functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the 34th International Conference on Machine Learning- Volume 70, pages 1885–1894.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' JMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' org, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [80] Mhd Hasan Sarhan, Abouzar Eslami, Nassir Navab, and Shadi Albarqouni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Learning interpretable disentangled representations using adversarial vaes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Domain Adap- tation and Representation Transfer and Medical Image Learning with Less Labels and Imperfect Data, pages 37–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [81] Dahuin Jung, Jonghyun Lee, Jihun Yi, and Sungroh Yoon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' icaps: An interpretable classifier via disentangled capsule networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='08756, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [82] Xinqi Zhu, Chang Xu, and Dacheng Tao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Where and what?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' examining interpretable disentangled representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition, pages 5861–5870, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 37 [83] Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Striving for simplicity: The all convolutional net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [84] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Saliency methods for explaining adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='08413, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [85] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Semantics for global and local interpretation of deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09085, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [86] Olaf Ronneberger, Philipp Fischer, and Thomas Brox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' U-net: Convolutional net- works for biomedical image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Medical image computing and computer-assisted intervention, pages 234–241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [87] Chaofan Chen, Oscar Li, Daniel Tao, Alina Barnett, Cynthia Rudin, and Jonathan K Su.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' This looks like that: deep learning for interpretable image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems, volume 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [88] Jindong Gu and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Neural network memorization dissection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09537, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [89] Yinchong Yang, Volker Tresp, Marius Wunderle, and Peter A Fasching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Explaining therapy predictions with layer-wise relevance propagation in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2018 IEEE International Conference on Healthcare Informatics (ICHI), pages 152– 162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [90] Leila Arras, Gr´egoire Montavon, Klaus-Robert M¨uller, and Wojciech Samek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ex- plaining recurrent neural network predictions in sentiment analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='07206, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [91] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Imagenet: A large-scale hierarchical image database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ieee, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [92] Samira Abnar and Willem Zuidema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Quantifying attention flow in transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Annual Meeting of the Association for Computational Linguistics (ACL), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [93] Jindong Gu, Volker Tresp, and Yao Qin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Are vision transformers robust to patch perturbations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='10659, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 38 BIBLIOGRAPHY [94] Jungkyu Lee, Taeryun Won, Tae Kwan Lee, Hyemin Lee, Geonmo Gu, and Kiho Hong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Compounding the performance improvements of assembled techniques in a convolutional neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='06268, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [95] Simyung Chang, John Yang, SeongUk Park, and Nojun Kwak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Broadcasting con- volutional network for visual relational reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the European Conference on Computer Vision (ECCV), pages 754–769, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [96] IJ Goodfellow, J Shlens, and C Szegedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Explaining and harnessing adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [97] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Towards deep learning models resistant to adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='06083, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [98] Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, and Ananthram Swami.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The limitations of deep learning in adversarial settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2016 IEEE European symposium on security and privacy (EuroS&P), pages 372–387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' IEEE, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [99] Tom B Brown, Dandelion Man´e, Aurko Roy, Mart´ın Abadi, and Justin Gilmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09665, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [100] Danny Karmon, Daniel Zoran, and Yoav Goldberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Lavan: Localized and visible adversarial noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 2507– 2515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [101] Chaowei Xiao, Jun-Yan Zhu, Bo Li, Warren He, Mingyan Liu, and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Spatially transformed adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='02612, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [102] Hossein Hosseini and Radha Poovendran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Semantic adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceed- ings of the IEEE Conference on Computer Vision and Pattern Recognition Work- shops, pages 1614–1619, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [103] Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Delving into transferable adversarial examples and black-box attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='02770, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 39 [104] Cihang Xie, Zhishuai Zhang, Yuyin Zhou, Song Bai, Jianyu Wang, Zhou Ren, and Alan L Yuille.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Improving transferability of adversarial examples with input diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CVPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [105] Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Evading defenses to transferable adversarial examples by translation-invariant attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In CVPR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [106] Junhua Zou, Zhisong Pan, Junyang Qiu, Xin Liu, Ting Rui, and Wei Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Improv- ing the transferability of adversarial examples with resized-diverse-inputs, diversity- ensemble and region fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [107] Yiwen Guo, Qizhang Li, and Hao Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Backpropagating linearly improves trans- ferability of adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [108] Dongxian Wu, Yisen Wang, Shu-Tao Xia, James Bailey, and Xingjun Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Skip connections matter: On the transferability of adversarial examples generated with resnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [109] Qian Huang, Isay Katsman, Horace He, Zeqi Gu, Serge Belongie, and Ser-Nam Lim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Enhancing adversarial example transferability with an intermediate level attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Computer Vision (ICCV), 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [110] Nathan Inkawhich, Kevin J Liang, Binghui Wang, Matthew Inkawhich, Lawrence Carin, and Yiran Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Perturbing across the feature hierarchy to improve standard and strict blackbox attack transferability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [111] Yingwei Li, Song Bai, Yuyin Zhou, Cihang Xie, Zhishuai Zhang, and Alan Yuille.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Learning transferable adversarial examples via ghost networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In AAAI, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [112] Xin Wang, Jie Ren, Shuyun Lin, Xiangming Zhu, Yisen Wang, and Quanshi Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A unified approach to interpreting and boosting adversarial transferability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [113] Jindong Gu, Hengshuang Zhao, Volker Tresp, and Philip Torr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial examples on segmentation models can be easy to transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='11368, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [114] Pin-Yu Chen, Huan Zhang, Yash Sharma, Jinfeng Yi, and Cho-Jui Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Zoo: Zeroth order optimization based black-box attacks to deep neural networks without 40 BIBLIOGRAPHY training substitute models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the 10th ACM workshop on artificial intelligence and security, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [115] Minhao Cheng, Thong Le, Pin-Yu Chen, Jinfeng Yi, Huan Zhang, and Cho-Jui Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Query-efficient hard-label black-box attack: An optimization-based approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='04457, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [116] Arjun Nitin Bhagoji, Warren He, Bo Li, and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Practical black-box attacks on deep neural networks using efficient query mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ECCV, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [117] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Square attack: a query-efficient black-box adversarial attack via random search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [118] Eric Wong, Frank Schmidt, and Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Wasserstein adversarial examples via projected sinkhorn iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 6808–6817.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [119] Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Explaining and harness- ing adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='6572, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [120] Florian Tram`er, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick McDaniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Ensemble adversarial training: Attacks and defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='07204, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [121] Nicholas Carlini and David Wagner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Towards evaluating the robustness of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2017 ieee symposium on security and privacy (sp), pages 39–57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' IEEE, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [122] Ali Shafahi, Mahyar Najibi, Amin Ghiasi, Zheng Xu, John Dickerson, Christoph Studer, Larry S Davis, Gavin Taylor, and Tom Goldstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial training for free!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='12843, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [123] Dinghuai Zhang, Tianyuan Zhang, Yiping Lu, Zhanxing Zhu, and Bin Dong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' You only propagate once: Accelerating adversarial training via maximal principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In NeurIPS, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [124] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Theoretically principled trade-off between robustness and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 7472–7482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 41 [125] Maksym Andriushchenko and Nicolas Flammarion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding and improving fast adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='02617, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [126] Hoki Kim, Woojin Lee, and Jaewook Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding catastrophic overfitting in single-step adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='01799, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [127] Eric Wong, Leslie Rice, and J Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Fast is better than free: Revisiting adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='03994, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [128] Leslie Rice, Eric Wong, and Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Overfitting in adversarially robust deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 8093–8104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [129] BS Vivek and R Venkatesh Babu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Single-step adversarial training with dropout scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recog- nition (CVPR), pages 947–956.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [130] Saehyung Lee, Hyungyu Lee, and Sungroh Yoon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Adversarial vertex mixup: To- ward better adversarially robust generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 272–281, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [131] Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' On the convergence and robustness of adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='08304, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [132] Gaurang Sriramanan, Sravanti Addepalli, Arya Baburaj, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Towards efficient and effective adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 34, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [133] Boxi Wu, Heng Pan, Li Shen, Jindong Gu, Shuai Zhao, Zhifeng Li, Deng Cai, Xiaofei He, and Wei Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Attacking adversarial attacks as a defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='04938, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [134] Anish Athalye, Nicholas Carlini, and David Wagner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International conference on machine learning, pages 274–283.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [135] Aditi Raghunathan, Jacob Steinhardt, and Percy Liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Certified defenses against adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09344, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 42 BIBLIOGRAPHY [136] Jinyuan Jia, Xiaoyu Cao, Binghui Wang, and Neil Zhenqiang Gong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Certified robust- ness for top-k predictions against adversarial perturbations via randomized smooth- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='09899, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [137] Jeremy Cohen, Elan Rosenfeld, and Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Certified adversarial robustness via randomized smoothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 1310–1320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [138] Bai Li, Changyou Chen, Wenlin Wang, and Lawrence Carin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Certified adversarial robustness with additive noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems, volume 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [139] Hadi Salman, Greg Yang, Huan Zhang, Cho-Jui Hsieh, and Pengchuan Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A convex relaxation barrier to tight robustness verification of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [140] Hadi Salman, Jerry Li, Ilya Razenshteyn, Pengchuan Zhang, Huan Zhang, Sebastien Bubeck, and Greg Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Provably robust deep learning via adversarially trained smoothed classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, vol- ume 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [141] Jeet Mohapatra, Ching-Yun Ko, Tsui-Wei Weng, Pin-Yu Chen, Sijia Liu, and Luca Daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Higher-order certification for randomized smoothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 33, pages 4501–4511, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [142] Hadi Salman, Mingjie Sun, Greg Yang, Ashish Kapoor, and J Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Denoised smoothing: A provable defense for pretrained classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 33, pages 21945–21957, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [143] Jindong Gu, Hengshuang Zhao, Volker Tresp, and Philip HS Torr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Segpgd: An effective and efficient adversarial attack for evaluating and boosting segmentation robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In European Conference on Computer Vision, pages 308–325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [144] Boxi Wu, Jindong Gu, Zhifeng Li, Deng Cai, Xiaofei He, and Wei Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Towards efficient adversarial training on vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In European Conference on Computer Vision, pages 307–325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' BIBLIOGRAPHY 43 [145] Cihang Xie, Yuxin Wu, Laurens van der Maaten, Alan L Yuille, and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Fea- ture denoising for improving adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 501–509, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [146] Weilin Xu, David Evans, and Yanjun Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Feature squeezing: Detecting adversarial examples in deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='01155, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [147] Reuben Feinman, Ryan R Curtin, Saurabh Shintre, and Andrew B Gardner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Detect- ing adversarial samples from artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv preprint arXiv:1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='00410, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [148] Tianyu Pang, Chao Du, Yinpeng Dong, and Jun Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Towards robust detection of adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [149] Kimin Lee, Kibok Lee, Honglak Lee, and Jinwoo Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' A simple unified framework for detecting out-of-distribution samples and adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in neural information processing systems, volume 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [150] Zhihao Zheng and Pengyu Hong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Robust detection of adversarial attacks by modeling the intrinsic properties of deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, volume 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [151] Kevin Roth, Yannic Kilcher, and Thomas Hofmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' The odds are odd: A statistical test for detecting adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Machine Learning, pages 5498–5507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [152] Gilad Cohen, Guillermo Sapiro, and Raja Giryes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Detecting adversarial samples using influence functions and nearest neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 14453–14462, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [153] Inyoung Paik, Taeyeong Kwak, and Injung Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Capsule networks need an improved routing algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Asian Conference on Machine Learning, pages 489–502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [154] Jindong Gu, Baoyuan Wu, and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Effective and efficient vote attack on capsule networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In International Conference on Learning Representations (ICLR), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' 44 BIBLIOGRAPHY [155] Jindong Gu, Volker Tresp, and Han Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Capsule network is not more robust than convolutional network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14309–14317, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [156] Srinadh Bhojanapalli, Ayan Chakrabarti, Daniel Glasner, Daliang Li, Thomas Un- terthiner, and Andreas Veit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Understanding robustness of transformers for image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='14586, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [157] Rulin Shao, Zhouxing Shi, Jinfeng Yi, Pin-Yu Chen, and Cho-Jui Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' On the adversarial robustness of visual transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='15670, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [158] Sayak Paul and Pin-Yu Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Vision transformers are robust learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content='07581, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' [159] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' Intriguing properties of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} +page_content=' In ICLR, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtAzT4oBgHgl3EQfY_wz/content/2301.01343v1.pdf'} diff --git a/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/2301.11298v1.pdf.txt b/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/2301.11298v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..6caea0eb018fe74e3df5de1c83594d546b40e6bc --- /dev/null +++ b/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/2301.11298v1.pdf.txt @@ -0,0 +1,1160 @@ +Investigating the impact of the molecular +charge-exchange rate on detached SOLPS-ITER +simulations +K. Verhaegh1,∗, A. C. Williams2,∗, D. Moulton1, B. Lipschultz2, +B. P. Duval3, O. F´evrier3, A. Fil1, J. Harrison1, N. Osborne4, H. +Reimerdes3, C. Theiler3, the TCV team∗∗ and the EuroFusion +MST1 team∗∗∗ +1 Culham Centre for Fusion Energy, Culham, United Kingdom +2 York Plasma Institute, University of York, United Kingdom +3 Swiss Plasma Centre, ´Ecole Polytechnique F´e´erale de Lausanne, Lausanne, +Switzerland +4 University of Liverpool, Liverpool, United Kingdom +∗ These authors contributed equally +∗∗ See author list of ”H. Reimerdes, et al. 2022 Nucl. Fusion 62 042018” +∗∗∗ See author list of ”B. Labit et al 2019 Nucl. Fusion 59 086020” +Abstract. +Divertor detachment requires plasma-neutral interactions that dissipate momentum +& power and reduces ion target fluxes simultaneously. Plasma-molecular interactions +generate molecular ions which react with the plasma and contribute to detachment +through molecular activated recombination (MAR), reducing the ion target flux, and +molecular activated dissociation (MAD), both of which create excited atoms. Hydrogenic +emission from these atoms have been detected experimentally in detached TCV, JET +and MAST-U deuterium plasmas. The TCV findings, however, were in disagreement +with SOLPS-ITER simulations for deuterium indicating a molecular ion density (D+ +2 ) +that was insufficient to lead to significant hydrogenic emission. This was attributed to +inaccuracies in the molecular charge exchange rate (D2 + D+ → D+ +2 + D), which seems +to be particularly underestimated in deuterium (obtained by rescaling the hydrogen +rates by their isotope mass). +In this work, we have performed new SOLPS-ITER simulations with the default +rate setup and a modified rate setup where ion isotope mass rescaling was disabled. +This increased the D+ +2 content by > ×100. By disabling ion isotope mass rescaling: +1) the total ion sinks are more than doubled due to the inclusion of MAR; 2) an ion +target flux roll-over occurs; 3) the total Dα emission in the divertor increases during +deep detachment by ∼ ×4; 4) the neutral atom density in the divertor is doubled due +to MAD; 5) total hydrogenic power loss is enhanced through MAD. These differences +result in a greatly improved agreement between the experiment and the simulations +in terms of spectroscopic measurements, ion source/sink inferences and measured ion +target fluxes. +Keywords: Tokamak divertor; Molecules; plasma; SOLPS-ITER; Detachment; TCV +tokamak; Eirene +arXiv:2301.11298v1 [physics.plasm-ph] 26 Jan 2023 + +Impact of mol. CX in SOLPS-ITER +2 +1. Introduction +Power exhaust is an important challenge in the realisation of fusion power plants as the +tolerable heat flux engineering limits to the vessel walls may otherwise be greatly exceeded. +Large heat flux reduction requires plasma detachment which is triggered when relatively +low temperatures (Te <∼ 5 eV) are obtained; these can be achieved by increasing the core +density and/or inducing impurity radiation by extrinsic impurity seeding. Detachment +is a state where plasma-atom and molecule interactions result in simultaneous power, +particle and momentum dissipation; which is experimentally recognised by a reduction +of the ion target flux. Although the incoming flux can mostly be considered atomic, the +recycling of the ions from the wall can have a strong molecular component. Therefore, +the relevant collisional processes include atomic processes, such as electron-impact +excitation (EIE power loss), electron-impact ionisation (ion source) and electron-ion +recombination (EIR ion sink); as well as molecular processes. Interactions between the +plasma and the molecules can lead to momentum and energy transfer from the plasma +to the molecules exciting molecules rovibronically (i.e. rotationally, vibrationally and +electronically). Vibrational excitation (ν) increases the probability of creating molecular +ions, in particular H+ +2 (through molecular charge exchange H2(ν) + H+ → H+ +2 + H) +and H− (through e− + H2(ν) → H− +2 → H− + H). These ions can then undergo further +interactions with the plasma, leading to Molecular Activated Recombination (MAR) [1] +and Molecular Activated Dissociation (MAD) [1]; that result in excited atoms and, thus, +radiative losses. +Recent experimental investigations have used spectroscopy and filtered camera +imaging on TCV [2, 3, 4, 5, 6, 7, 8, 9, 10], MAST-Upgrade [11] and JET [12, 13, 14] that +register significant Balmer line emission after the break-up of molecular ions. For TCV +[6, 7], it was shown that MAR from molecular ions is a dominant contributor to the +reduction of the ion target flux in contradiction with SOLPS-ITER simulations [6, 15] +that did not show a roll-over of the ion target flux [15, 16, 17, 18]. Additionally, the D+ +2 +density in the simulations was negligible during detachment, leading to negligible MAR +and a much lower simulated Dα emission [6]. That disagreement was likely caused by +an underestimated molecular charge exchange rate when the hydrogen rates are isotope +mass rescaled to deuterium [7], leading to orders of magnitude underestimations in the +D+ +2 content in detached conditions (sections 2.1 and 4.3). More recent studies, however, +indicate the difference between the molecular charge exchange rate for hydrogen and +deuterium should be much smaller and may be even (< 5% at 1-3 eV) [19, 20]. +To illustrate the impact upon SOLPS-ITER simulations, ”post-processing” of the +predicted results in a non self-consistent manner after convergence were performed +[7]. Using the simulated D2 densities, the D+ +2 density was modelled based upon the +D+ +2 /D2 ratio from [20]. +This post-processing lead to a better agreement with the +experimental data: 1) the MAR ion sink became significant; 2) if this MAR ion source is +subtracted from the ion target flux, an ion target flux roll-over would have occurred; 3) +D+ +2 interactions added significant Balmer line emission. However, these effects appeared + +Impact of mol. CX in SOLPS-ITER +3 +’overestimated’ after post-processing. +When integrally simulated, modifying the D+ +2 content leads to modifications in the +plasma solution (i.e. ne, Te, ...) itself, that cannot be accounted for in post-processing. +Hence, in this work, we present a comparison between self-consistent SOLPS-ITER +simulations for TCV (same as those used in [15, 16]) which use: 1) the default SOLPS- +ITER rate setup that employs ion isotope rescaling to the molecular charge exchange +rate; 2) a modified rate setup where the ion isotope mass rescaling of the molecular +charge exchange rate is disabled, see figure 2. For simplicity, we refer to this as the +’default’ and the ’modified’ setup. +We observe that including these rates self consistently leads to an ion target flux +roll-over, induced by strong MAR ion sinks, and an increase in the Dα emission - all +three in agreement with experiment. Additionally, we find that the neutral content in +the divertor is more than doubled through MAD, significantly elevating the hydrogenic +plasma power loss channel. +The aim of this work is to show that molecular charge exchange can impact +detachment significantly in SOLPS-ITER simulations (in agreement with the experiment) +and to motivate the necessity of investigating the reaction rate set in more detail. Since +re-deriving and using new molecular charge exchange rates is outside of the scope of this +work, we have chosen to do this by disabling the ion isotope mass rescaling for modelling +simplicity. The motivation for this (section 2.1) is that there are various inaccuracies in +the molecular charge exchange rates employed by SOLPS-ITER at temperatures below +2 eV. Although, there is a physics reason for ion isotope mass rescaling (section 2.1), it +exacerbates the various rate problems at temperatures below 4 eV (for D) and below +6 eV (for T), respectively. Disabling ion isotope mass rescaling is not advisable as a +new SOLPS-ITER default and improved rate data needs to be implemented in Eirene +(section 4.3). +2. Simulation setup and theory +The simulation set-up follows the previously published work by Alex Fil [15, 16] ‡. In +the simulation, the upstream density is scanned by a fuelling puff, similarly to [15, 16]. +Photon opacity, neutral-neutral collisions and drifts are not included; currents are +included. [7] calculated that photon opacity is expected to play a negligible role in +the simulated cases. Chemical sputtering of carbon is included as a fixed fraction of +the ion target flux, estimated by matching the magnitude of carbon emission signals +in the divertor to experiments [15, 3]. The power input in the simulation was matched +to the experiment by assuming a 1:1 in:out symmetry and by defining PSOL as the +Ohmic power minus core + SOL (above X-point) radiative losses (equivalent to [3]); thus +accounting for any carbon radiation that may occur from main chamber erosion directly. +An illustration of the plasma grid, Eirene grid and vessel geometry used is shown in figure +1. The original simulations performed were interpretive simulations of TCV tokamak +‡ For providence, this was re-run with a newer SOLPS-ITER version (version 3.0.7) + +Impact of mol. CX in SOLPS-ITER +4 +DSS +D2 LP +Separatrix +Eirene grid +B2.5 (fluid) grid +Outer div. +Figure 1. A visualisation of the TCV vessel geometry, fluid grid (red), Eirene grid +(black/grey), spectroscopic (DSS) lines of sight (green), outer divertor fluid grid cells +(blue shading), separatrix fluid grid cells (cyan), D2 fuelling location (cyan) and +Langmuir probe (LP) location (magenta). +[21, 22], discharge # 52065, which is a single null L-mode unbaffled [23, 24] density ramp +discharge that has been extensively reported in literature [3, 7, 5, 9, 25, 26]. +The simulations are set-up to run with kinetic neutrals (e.g. Eirene) using the +default Eirene rate setup. The rates used by Eirene are derived for a hydrogen plasma +(for simplicity, as isotope resolved data is often not available), whereas a deuterium +plasma is simulated. Rates (σv) that involve interactions with ions, depend on the +kinetic velocity of the ions. Since the velocity, at the same ion temperature is lower for +heavier particles, ion isotope mass rescaling to < σv > (Ti) is applied by default [27]. +This assumes that there is no isotope difference between the rates in velocity space (e.g. +no chemical isotopical differences) - evidence for this, depending on the reaction, can be +sparse. + +Impact of mol. CX in SOLPS-ITER +5 +2.1. Molecular charge exchange rates +It has been hypothesised [7] that the D+ +2 content may be severely underestimated in +SOLPS-ITER simulations in detachment relevant regimes. Eirene uses the effective +molecular charge exchange rate tabulated in ’AMJUEL’ [28] by polynomial fit +coefficients. Such effective rates average the reaction rate for molecular charge exchange +< σv >CX,H2(ν) per vibrational state (ν) over the vibrational distribution of the molecules +fν - equation 1. +fν is modelled based on the local plasma parameters assuming that transport can be +neglected and mostly depends on electron impact collisions with the molecules, changing +the vibrational distribution [32] depending on the electron temperature Te: fν(Te, ...). +The < σv >CX,H2(ν) rate is obtained from the σCX,H2(ν) and depends on the relative +velocity between H+ and H2. Assuming H2 is near stationary, the < σv >CX,H2(ν) rate +is only a function of ion temperature. Hence, the effective reaction rate is sensitive to +both the ion and the electron temperatures - equation 1. The effective rate fit coefficient +tables used by Eirene only have a temperature sensitivity, under the assumption that +T = Te = Ti. +< σv >CX,H2,eff= +� +ν +fν(Te, ...) < σv >H2(ν) (Ti) +(1) +σCX,H2(ν=0) is obtained from Janev, 1987 [29] based on measurements in the 1970s by +Holliday, et al. [30]. These cross-sections for the vibrational ground state are then scaled +to higher vibrational levels using an analytic equation (Aν(ν)) from Greenland, 2001 [31]: +< σv >CX,H2(ν) (T) = Aν(ν) < σv >CX,H2(0) (T). Although < σv >CX,H2(0) (T) decays +strongly for T < 2 eV (and thus for < σv >CX,H2(ν) (T) = Aν(ν) < σv >CX,H2(0) (T), +this does not occur for newer vibrationally resolved calculations of < σv >CX,H2(ν) [56] at +H2(ν ≥ 4), which contribute most to < σv >CX,H2,eff. The simplified Greenland scaling +cannot account for this, leading to order-of-magnitude underestimates of the default +< σv >CX,H2(ν) Eirene rates in detachment relevant conditions. +For deuterium and tritium, the velocity of the ion interacting with the molecule +at same ion temperature is reduced by the isotope mass. Assuming that the σCX,H2(ν) +cross-sections are the same for all hydrogen isotopes, the vibrationally resolved rates +can be ’ion isotope mass rescaled’ from hydrogen to deuterium: < σv >CX,D2(ν) (Ti) =< +σv >CX,H2(ν) (Ti/2) [27, 33]. However, since Eirene only knows about the effective rate +(for a vibrationally unresolved setup), the total effective rate is ion isotope mass rescaled, +inadvertently also rescaling the electron temperature dependency of the vibrational +distribution incorrectly (equation 2). +< σv >CX,D2,eff,Eirene (T) =< σv >CX,H2,eff (T/2) += +� +ν +fν(T/2, ...) < σv >CX,H2(ν) (T/2, ...) +< σv >CX,D2,eff,correct (T) = +� +ν +fν(T, ...) < σv >CX,H2(ν) (T/2, ...) +(2) + +Impact of mol. CX in SOLPS-ITER +6 +Since < σv >CX,H2,eff (T) decreases with decreasing T §, this rescaling greatly +reduces the effective molecular charge exchange rate in detachment relevant conditions +for deuterium (a factor ∼ 100) and tritium. This is shown in figure 2, where the D+ +2 /D2 +ratios obtained from SOLPS-ITER simulations with and without isotope mass rescaling +as well as the theoretically expected D+ +2 /D2 ratio based on a no-transport model (e.g. +balancing the D+ +2 creation/destruction rates) are compared. It is these conditions in +where the molecular density greatly increases for decreasing temperatures [34, 6, 11]. +In contrast, using a more accurate analysis of the molecular charge exchange rate +[19] for T = 1, 2, 3 eV shows a negligible (∼ 5 %) isotope dependency ∥. In this, three +issues discussed above were resolved: 1) < σv >ν rates were obtained from [56], using +full vibrationally resolved simulations, rather than applying the simplified Greenland +rescaling; 2) rates specifically derived for H and D were utilised, accounting for chemical +isotope differences; 3) the lower velocity of the heavier hydrogen isotopes was correctly +accounted for only in < σv >ν (Ti, ...) and not in the vibrational distribution (fν(Te, ...). +The ratios obtained with these rates (figure 2), for both H+ +2 /H2 and D+ +2 /D2, are in closer +agreement to the AMJUEL effective H+ +2 /H2 ratio; motivating our choice for disabling +ion isotope mass rescaling in the ’modified’ setup. +. +3. Simulation results +The obtained outer target ion target fluxes, together with the total outer divertor ion +source (atomic ionisation and molecular activated ionisation arising from D2 and D+ +2 ), +ion sinks (electron-ion recombination and molecular activated recombination arising +from D+ +2 ) and net ion flow into the divertor is shown in figure 3 during a core density +ramp, together with the experimentally measured ion target particle flux (assuming a 15 +% uncertainty [36, 37]) for # 52065. The upstream density was measured combining +Thomson scattering measurements with the equilibrium reconstruction of the separatrix +and assuming a spatial uncertainty of ±2.2 cm (e.g. the Thomson resolution), resulting +in an upstream density uncertainty of ±0.5 × 1019m−3 before the ion target flux roll-over +and ±1.5 × 1019m−3 afterwards. We will now compare the ’default’ and ’modified’ (e.g. +ion isotope mass rescaling for molecular charge exchange disabled) setups. +In both the ’default’ and ’modified’ setups, we observe a movement of the divertor +ionisation source towards the X-point as the upstream density is increased, reducing +the total outer divertor integrated ion source, whilst electron-ion recombination remains +negligible, in agreement with experimental observations [3]. As the ionisation moves +upstream, the ion flux from upstream of the divertor towards the outer target is increased, +replenishing the loss of divertor ionisation, in agreement with measurements by a +reciprocating divertor probe array [?], as well as upstream spectroscopic measurements +§ The fν(Te, ...) used for the derivation of the effective rates in Eirene is not fully documented +∥ However, this is based on a simplified Boltzmann relation for fν, which is different from fν(Te, ...) +used for deriving the effective rates in Eirene. + +Impact of mol. CX in SOLPS-ITER +7 +10 0 +10 1 +Te (eV) +10 -4 +10 -3 +10 -2 +10 -1 +D2 ++ / D 2 ratio +Default rates +Isotope mass rescaling ++ ++ +D + D -> D + D disabled +2 +2 +Prediction (from rates - lines) +D mol. CX rate [Janev, 2018, et al.] +H mol. CX rate [Janev, 2018, et al.] +2 +Default rates +Isotope mass rescaling ++ ++ +D + D -> D + D disabled +2 +SOLPS-ITER result (symbols) +Figure 2. The D+ +2 /D2 ratio obtained from SOLPS simulations (symbols), over the +entire simulation domain, as function of the electron temperature for both the default +SOLPS-ITER set-up as well as the set-up where mass rescaling is disabled for molecular +charge exchange. The expected D+ +2 /D2 ratio with and without isotope mass rescaling +of the molecular charge exchange rate are also shown, modelled as the sum of the +creation rates of D+ +2 (from D2) divided by the sum of the destruction rates of D+ +2 . +Additional H+ +2 /H2 and D+ +2 /D2 ratios are shown (’H, D mol CX rate [Janev, et al. +2018]’) using the molecular charge-exchange rate from [19] in combination with reaction +rates from [28, 35] for the remaining reactions. +[5]. In the ’default’ setup, this prevents the roll-over of the ion target flux as the upstream +density is increased. This is in contrast to the experiment, where a clear roll-over is +observed as indicated in figure 3 [26, 25, 2, 3, 15]. The absence of an ion target flux +roll-over in plasma-edge simulations, even though other detachment markers are clearly +obtained in the simulations (movement of the ionisation source; appearance of Te ∼ 1 +eV temperatures; volumetric momentum losses; ...), is a general observation for TCV +density ramp SOLPS-ITER simulations [17, 18, 38, 15, 16]. +For the ’modified’ setup, the obtained particle balance is similar to the default +SOLPS-ITER setup in the attached phase. This is unsurprising, as molecular charge +exchange only becomes an important source of D+ +2 at detachment-relevant temperatures +of 1-3 eV, before which the D+ +2 creation is dominated by D2 ionisation and the isotope +ion mass rescaling of molecular charge exchange has a negligible impact on the D+ +2 /D2 +ratio. However, as the core density increases and detachment relevant temperatures +are achieved, a clear increase of MAR ion sinks, together with a roll-over of the ion +target flux is now observed; in contrast to the cases which used the default reaction rates. + +Impact of mol. CX in SOLPS-ITER +8 +19 +-3 +Upstream density (10 m ) +0 +5 +10 +15 +21 + 10 Particles / s +Default rates +2 +3 +4 +5 +6 +2 +3 +4 +5 +6 +Modified rates +Ion target flux +Ion source +Upstream ion flow +MAR ion sink +EIR ion sink +Measured ion +target flux +19 +-3 +Upstream density (10 m ) +a) +Figure 3. Obtained particle balance in terms of integrated outer divertor ion target +flux; total outer divertor integrated ion sources/sinks are shown, together with the +net ion flow from outside the divertor region towards the outer divertor target. The +measured ion target flux is shown in grey, together with estimated uncertainty margins +in the upstream density before/after roll-over and an assumed ±15% uncertainty in +the ion target flux. The characteristic upstream density uncertainty is ±0.5 × 1019m−3 +before the ion target flux roll-over and ±1.5 × 1019m−3 afterwards a) the default +SOLPS-ITER simulation setup; b) a SOLPS-ITER simulation setup where ion isotope +mass rescaling for molecular charge exchange was disabled. +This is attributed to the additional ion sinks obtained from MAR (D2 + D+ → D+ +2 + D +followed by e− + D+ +2 → D + D), which leads to a reduction of the ion target flux. +We find that in both cases, the contribution of MAI to the total ion source is minor: +throughout the density scan it starts at 16-18 % dropping to 5-10 % of the total ion +source during detachment for both SOLPS-ITER rate setups. The total ionisation source +however, at the same upstream density, is smaller for the ’modified’ setup after detachment +- e.g. after MAR and Dα emission arising from plasma-molecular interactions starts to +become important. The ionisation front is further removed from the target, after the +detachment onset, for the ’modified’ setup with lower target temperatures: more ’deeply +detached’ scenarios (in terms of ionisation front displacement, and target temperature) +are obtained. This is likely related to the additional ion sinks and hydrogenic power +losses associated with Molecular Activated Dissociation (MAD), explained in section 3.2. +There may be processes, other than molecular charge exchange, that may result in +discrepancies between experiment and simulations. For instance, it was hypothesised +in [39] that enhanced erosion of carbon from the main chamber wall through enhanced +perpendicular transport at higher densities may result in additional impurities that +strengthen detachment on TCV. However, investigating this is outside of the scope of + +Impact of mol. CX in SOLPS-ITER +9 +this work and requires additional diagnostics, such as filtered imaging of the main plasma +to diagnose carbon erosion [10], which should be addressed in the future. +3.1. Comparison of SOLPS-ITER results to ion source & sink measurements +The simulated discharge, # 52065, was repeated several times to perform a detailed +spectroscopic characterisation (# 56567 and repeats) ¶. This facilitated a detailed +spectroscopic characterisation of the ion sources and sinks in the lower divertor +[2, 3, 4, 5, 6, 7] and separating the measured Dα emission into its various emission +contributions [5, 6, 7]. That result is shown in figure 4, together with the obtained +simulation results where the ion sources/sinks have been integrated over the spectroscopic +lines of sight. +This previously reported experimental analysis [5, 6, 7] indicates 1) +significant ion sinks through MAR, dominating over EIR ion sinks; 2) a strong increase of +Dα due to emission from excited atoms after plasma-molecular interactions. Both these +aspects absent in the ’default’ setup simulations, but are present and in quantitative +agreement with the experiment in the ’modified’ setup, greatly improving the agreement +between experiment and simulation. +3.2. The impact of molecular charge exchange on neutral atom content and hydrogenic +power losses +Disabling the ion isotope mass rescaling for the molecular charge exchange reaction +not only has a strong impact on the divertor particle balance and hydrogenic emission +processes, but also on the neutral atomic content. The total neutral D atom content +(excluding molecules) in the outer divertor is increased by more than a factor of two for +identical upstream densities with the ’modified’ compared to the ’default’ setup (figure 5 +a), at the deepest detached phases. Even when the neutral atom content between the +two simulation setups is compared as a function of the target temperature, the neutral +atom content is enhanced by more than 50 % for the modified rate setup (not shown). +However, since the electron density decays in the modified rate setup, the total nuclei +content (e.g. total amount of D particles considering ions, atoms and molecules) remains +similar (within 5 %) for both simulation setups as function of upstream density. +This increase in neutral atom content can be explained by the additional neutral +atoms created through MAR & MAD by the modified rate. The strength of volumetric +processes generating neutral atoms (e.g. +EIR, MAR, MAD and electron-impact +dissociation) is compared between the default and modified rates in figure 5 c) and d). +This shows that the volumetric creation of neutral atoms is significantly enhanced in the +modified rate setup, where the neutral atom creation continuously increases as one goes +into deeper detached regimes, due to MAR & MAD. MAR & MAD provide additional +dissociation processes that are significant below 5 eV, by which time the electron-impact +dissociation cross-sections are strongly reduced, but the molecular content is strongly +¶ It should be noted that the ion target flux roll-over is less clear in # 56567 than # 52065 as significantly +lower core densities were obtained before the plasma disrupted. + +Impact of mol. CX in SOLPS-ITER +10 +19 +-3 +Upstream density (10 m ) +D +D +[total] +[total] +[atomic contribution] +2 +3 +4 +5 +6 +19 +-3 +Upstream density (10 m ) +19 +-3 +Upstream density (10 m ) +2 +3 +4 +5 +6 +19 +-3 +Upstream density (10 m ) +Experiment +SOLPS-ITER default rates +SOLPS-ITER modified rates +D +D +a) +b) +b) +c) +d) +e) +f) +Figure 4. Obtained particle balance (top figure) in terms of integrated outer divertor +ion target flux; and the ion sources/sinks obtained in view of the DSS diagnostic. +Measured total Dα emission (bottom figure) in the outer divertor, captured in between +the DSS lines of sight, and its inferred contribution arising from electron-impact +excitation and EIR (e.g. ’atomic’ interactions) and from plasma-molecular interactions. +These results are shown simulations where ion isotope mass rescaling was disabled for +molecular charge exchange, which are compared against the experimental observations +of outer the ion target flux (Langmuir probes), the total Dα emission and spectroscopic +inferences of the divertor ion source, ion sinks (MAR & EIR) as well as the separation +of Dα in atomic (e.g. +EIE & EIR) and ’molecular’ (associated with D2, D+ +2 & +D− +2 → D− + D components). +increased [34, 11]. Therefore, MAR & MAD can be stronger neutral atom creation +processes than electron-impact dissociation & EIR, particularly in detached regimes. +Using a synthetic diagnostic pressure gauge (’baratron’) setup [18, 39, 40], the +divertor neutral pressure has been calculated and compared against the experiment +(not shown). We find that the divertor neutral pressure starts to bifurcate between the +modified rates and the default rates at the detachment onset. At the deepest levels of +detachment, the divertor neutral pressure is increased by up to 50 % when the modified +rates are used (at the same upstream density). Experimentally, a strong increase in the +divertor neutral pressure is observed after detachment, with divertor pressures of up to 0.6 +Pa at the deepest levels of detachment ( upstream density of ne = 4.5[3.4−6]×1019m−3). +This agrees with the ’modified’ setup simulations, but only at the deepest levels of +detachment (0.6 [0.47 - 0.74] Pa). +. +Analogous to power losses due to ionisation, there are potential (plasma) energy +losses associated with molecular dissociation. The additional dissociation mechanisms ++ The divertor pressure obtained during the attached phase is overestimated (by a factor ∼ 4) in the +code for both the modified and default rate setup, in agreement with previous TCV results [18]. The +origin of this discrepancy is unknown and is inconsistent with the agreement of the Balmer line emission +and the inferred ionisation sources between the experiment and the simulation [3]. + +Impact of mol. CX in SOLPS-ITER +11 +0 +10 +20 +30 +Power loss (kW) +Hydrogenic power loss outer divertor +0 +1 +2 +3 +22 +D creation (10 part. / s) +D creation rate outer divertor +Default rates + 2 + 3 + 4 + 5 + 6 +19 +-3 +Upstream density (10 m ) +0 +5 +10 +15 +17 +Neutral atoms (10 ) +# neutral D atoms outer divertor +Total ++ +MAD (D ) +2 ++ +Ionisation & MAI (D & D ) +2 +2 +Dissociation (D ) +2 +Default rates +Modified rates + 2 + 3 + 4 + 5 + 6 +19 +-3 +Upstream density (10 m ) +Default rates +Modified rates +D creation rate outer divertor +Modified rates +MAR & EIR < 1 kW +(power sources/ +sinks cancel) +MAR +EIR +a) +b) +c) +d) +Figure 5. The impact of increased MAD, due to the modified reaction rates, on +hydrogen atom content and hydrogenic power losses. a) Evolution of the total neutral +atom content (excluding molecules) as function of upstream density for the default and +modified rates. b) Evolution of hydrogenic power loss processes for the default and +modified rates, including: ionisation power loss (sum of radiative power loss due to +excitation collisions preceding ionisation and the potential energy, ϵ = 13.6 eV, spent +on ionisation); power losses associated with electron-impact dissociation and associated +with MAD. The net power loss associated with MAR & EIR has been estimated to be +below 1 kW. c) and d) Volumetric neutral atom creation source, integrated over the +outer divertor, from MAR, MAD, EIR and electron-impact dissociation for c) default +rate setup; d) the modified rate setup. + +Impact of mol. CX in SOLPS-ITER +12 +through MAD after the detachment onset result in a significant increase in the total +effective hydrogenic (plasma) power losses (figure 5 b). The hydrogenic power losses +associated with plasma-molecular interactions are due to the dissociative energy losses +to the plasma channel since the radiative losses and potential energy gains from MAR +roughly cancel [7]. ∗ Although the total hydrogenic power loss at the same upstream +density is only 20 % higher for the modified rate at the same upstream density, the total +hydrogenic power loss can be 60 % higher for the modified rate setup for similar levels +of detachment (e.g. similar Tt and similar ionisation front positions). +4. Implications, relevance and accuracy of our findings and future pathways +Increasing the D+ +2 content through the ’modified’ rate setup in our work results in: 1) +increased neutral atom sources through MAD and associated hydrogenic power losses; +2) significantly enhanced hydrogenic atomic line emission from excited atoms after +plasma-molecular interactions; and 3) additional ion sinks through MAR, resulting in +the ion target flux roll-over. Such interactions start becoming significant at detachment +onset with a spatial preference towards the target side of the ionisation region where the +molecular density builds up. The TCV simulations, consistent with TCV [5, 6, 7, 10] and +MAST-U [11] experimental results, indicate that plasma-molecular chemistry involving +molecular charge exchange generating D+ +2 and associated MAD neutral atom sources, +MAR ion sinks and atomic hydrogen emission: 1) starts to occur from the detachment +onset on-wards as the ionisation and electron-impact dissociation regions detach from +the target; 2) increase in magnitude as higher molecular densities are obtained below the +ionisation region when Te drops below 3 eV [34]. Neutral baffling may play a strong role +in this point 2), which was brought forward as an explanation for why plasma-molecular +effects plays a much more significant role in the MAST Upgrade Super-X divertor than +the TCV open divertor (experiments from 2016 before baffles were present) [11]. +4.1. Could molecular ions play a role in reactors during detachment? +An important question is whether such interactions are also relevant for reactors. +Answering that question requires further investigation, including further studies on +the applicable molecular charge exchange as well as applying those to a range of reactor +conditions, which is outside the scope of this work. Although there are large uncertainties +regarding the molecular charge exchange rates, the molecular vibrational distribution +(that determines these effective rates to a large extent) and their applicability to reactors, +signatures of the impact of molecular ions on the hydrogen emission are being observed +in JET with the ITER-like wall [12, 13, 14] during deep detachment. +∗ The dissociation cost itself is a power loss only from the plasma channel: this potential energy can +be released back to the target as hydrogen atoms re-associate into molecules. Therefore, this may not +result in target heat load reductions, unless the distance between the dissociating area and the target is +significant such that the higher energy atom population has room to dissipate radially. + +Impact of mol. CX in SOLPS-ITER +13 +The ion isotope mass rescaling has been applied correctly (e.g. +using < +σv >CX,D2,eff,correct as opposed to < σv >CX,D2,eff,Eirene - equation 2) for a limited +set of SOLPS-ITER simulations in [20]. Although MAR was a significant ion sink with +the new rates, it lead to a reduction of EIR as the electron density in the simulation +was reduced: the target profiles obtained by the SOLPS-ITER simulations were similar. +This was hypothesised to be associated with increased power limitation of the ionisation +source due to energy losses associated with MAR and MAD [20] ♯. +However, for molecular ions to potentially play a role in reactors, the two conditions +at the start of section 4 must be satisfied. This implies that molecular ions likely +could play a stronger role in reactor scenarios that feature divertor designs & operation +where the ionisation region is sufficiently detached from the target, with Te dropping +to 1-3 eV below the ionisation region, to have a significant MAR rate. Although this +may be feasible in current designs of reactor-class devices with conventional divertors, +such as ITER and (potentially) DEMO, this may be more achievable in alternative +divertor concept designs [41, 42, 43] and, potentially, X-point radiator designs [44, 45, 46]. +Existing plasma-edge simulations of reactors could be post-processed to assess, in a +simple way, whether molecular charge exchange can play a role in reactors [5, 6, 7]. This +allows estimating whether a modified rate could impact hydrogen emission, MAR ion +sinks and MAD neutral atom sources significantly in a non-self consistent way. This can +only be used to map out whether molecular ions could potentially play a strong role in a +simulation, self-consistent simulations are then required to investigate the precise impact +of molecular ions. +The impact of transport and plasma-wall interactions on the vibrational distribution +(section 4.4) can be different in reactors than in devices like TCV and MAST-U. +Differences in power and density result in a shortening of the mean free path in reactors, +making transport of vibrationally excited molecules less likely (although it can still +be significant in the low temperature region below the ionisation front). Differences +in wall material (metal for reactors, carbon for TCV and MAST-U) can impact the +initial vibrational distribution of the molecules coming off the wall [39]; as well as the +reflection of atoms from the wall (in contrast to the adsorption of atoms to the wall, +after which re-association occurs and molecules are released back into the plasma), which +may relatively reduce the molecular density. +4.1.1. Simplified MAR rate modelling +One argument as to why plasma-molecular +interactions may play a relatively weaker role for reactors is that reactors will operate +at significantly higher electron densities (ne ∼ 1021m−3). Since the EIR source scales +∝ n2−3 +e +for Te < 1.5 eV, it would be expected that the relative role of EIR increases +for reactor-relevant conditions at low temperatures; potentially reducing the relative +impact of MAR as a neutral atom source and hydrogen ion sink. To investigate this +♯ The underlying vibrationally resolved cross-sections used in the Eirene rates are likely underestimated +at low temperatures, as shown in section 4.3, which can result in a significant under-prediction of +molecular charge exchange even if ion isotope mass rescaling is applied correctly. + +Impact of mol. CX in SOLPS-ITER +14 +EIR +Ionisation +Dissociation +MAR +MAD +Ionisation +EIR +MAR +MAD +Dissociation +19 +-3 +MAST-U scaling; n = 10 + m +e +19 +-3 +TCV (unbaffled) scaling; n=7.10 + m +e +19 +-3 +MAST-U scaling; n = 10 + m +e +Te (eV) +1 +10 +0.1 +2 +∫ Reaction rate / n +e +L +2 +∫ Reaction rate / n +e +L +-19 +10 +-18 +10 +-17 +10 +-16 +10 +-19 +10 +-18 +10 +-17 +10 +-16 +10 +21 +-3 +TCV (unbaffled) scaling; n=10 +m +e +21 +-3 +MAST-U scaling; n = 10 +m +e +Te (eV) +1 +10 +0.1 +EIR +Ionisation +Dissociation +MAR +MAD +Ionisation +EIR +MAR +MAD +Dissociation +Figure 6. Comparison of the expected chordally integrated reaction rate scalings as +function of Te for the TCV (c, d) [15] (unbaffled) and MAST Upgrade Super-X (a, b) +[47] divertor, based on SOLPS-ITER scalings [11] at a characteristic density (a,c) and +extrapolated scalings to a reactor-relevant density (ne = 1021m−3) (b,d). +further, we have obtained scalings from previous SOLPS-ITER simulations of both +MAST Upgrade [47] and TCV [15] (open divertor - without baffles) for the evolution +of the spectroscopic line-of-sight integrated neutral atom and neutral molecular density +relative to the electron density as function of Te [11] using all of the divertor spectroscopic +lines of sight for both TCV and MAST-U. Using a simplified model for the rates [11], +together with the D+ +2 /D2 ratios with the ’modified’ rate setup (figure 2), the evolution +of the various atomic and molecular rates can be calculated as function of Te for a fixed +ne. That result is shown in figure 6 using the characteristic TCV & MAST-U electron +densities (ne = 7 × 1019m−3 and ne = 1019m3, respectively) as well as reactor-relevant +ne = 1021m−3 extrapolations. +The evolution of the reaction rates (figure 6) indeed indicates that, when the +SOLPS-ITER scalings for TCV are used, EIR becomes more important than MAR at +reactor-relevant densities. However, MAD † still remains important between ∼ 0.7 and +† Note that a single MAR/MAD reaction can result in the creation of 3-2 neutral atoms; whereas EIR +only results in 1 neutral atom. + +Impact of mol. CX in SOLPS-ITER +15 +∼ 3 eV for the TCV SOLPS-ITER scalings. Therefore, even at reactor-relevant densities, +MAD could be a dominant neutral generation rate - even when scalings for an open +divertor are extrapolated. Strikingly, when the MAST Upgrade derived SOLPS-ITER +scalings are used, we find that MAR+MAD can be dominant between 0.5 and 4 eV for +reactor-relevant densities. The difference between this result and that from the unbaffled +TCV scaling is associated with the higher molecular content in MAST-U, likely due to +its tight baffling. This shows that indeed, if one can have a significantly high molecular +density below the ionisation region, MAR can remain important despite EIR being +strongly elevated at reactor-relevant densities. +Using effective Eirene rates without ion isotope mass rescaling, the simplified model +results in figure 6 predict that plasma-molecular interactions involving molecular ions +are negligible at very low temperatures (Te ≪ 0.5 eV), in contrast with results from +MAST Upgrade experiments in the Super-X divertor, where such interactions are still +experimentally inferred at Te ≪ 0.5 eV [11]. This mismatch is likely caused by the +underestimated charge exchange cross-sections at low temperatures in Eirene (sections +2.1 & 4.3). +One important caveat to this approach is that the applied scalings derived from +SOLPS-ITER are different in reactor-relevant conditions. As such, the above result +should be seen as additional motivation as to why molecular ions leading to MAR & +MAD could be important for reactors and thus require further study in reactor relevant +regimes. It should not be interpreted as a prediction that they will be important for +reactors. +4.2. Impact on diagnostic design, analysis and real-time detachment control strategies +MAR & MAD not only have an impact on the divertor physics, but also result in a +significant content of excited hydrogen atoms and thus hydrogen Balmer line emission +as was shown in literature [48, 14, 13, 12, 5, 7, 6, 11] and is indicated by the increase +in Dα emission during detachment as shown in figure 3. Since that strong increase +in Dα emission is not captured by the ’default’ setup, this causes strong concerns on +the synthetic deuterium (and tritium) atomic emission diagnostic signals predicted +from plasma-edge modelling. This has implications on diagnostic design, analysis of +spectroscopic diagnostics as well as real-time control strategies that use spectroscopic +signals as a real-time sensor. +Synthetic diagnostic signals of hydrogen emission are used to test spectroscopic +analysis techniques [49, 10, 4, 7] and design diagnostics [50]. For example, synthetic +diagnostics have shown that unexpectedly high stray light emission from hydrogen, +deuterium and tritium Balmer-α emission can be a concern for diagnostic interpretation +in ITER [50]. Plasma-molecular chemistry with molecular ions could, if present, greatly +enhance the divertor hydrogenic emission beyond that predicted in the simulations (and +the Dα emission would be even further enhanced by photon opacity); which could grossly +misinform studies relying on synthetic diagnostic data. + +Impact of mol. CX in SOLPS-ITER +16 +Plasma-molecular effects result in a significantly enhanced population of the hydrogen +atom n = 3 state, which may have implications for the treatment of photon opacity to +the Lyman series in simulations [51, 52] as well as the diagnosis of photon opacity [7]. +Accounting for molecular ions in the analysis of hydrogen atomic line emission required +the creation of novel analysis techniques [14, 13, 6], which need to be further expanded +to include photon opacity effects. +Real-time detachment control strategies are required in reactors and spectrally +filtered imaging [53, 54] as well as line-of-sight passive spectroscopy of hydrogen atomic +emission [55] are important detachment sensor candidates. The complexity of including +molecular ions in the interpretation of the atomic hydrogenic emission as well as the +occurrence of photon opacity can complicate the usage of hydrogen atomic emission for +such purposes and using complementary or alternative methods such as monitoring the +molecular Fulcher band intensity may be required [11]. Plasma-edge simulations with +an improved plasma-molecular interaction set as well as photon opacity are required to +investigate this further. +4.3. Inaccuracies of the molecular charge exchange rate employed by Eirene +Increasing the molecular charge exchange rate during detachment through modified +rates is a first step in 1) explaining the discrepancy observed between the experiment +and SOLPS-ITER simulation results for TCV in terms of MAR, hydrogen emission +and the ion target flux; 2) the investigation of the importance of molecular ions during +detachment. This work aims to motivate that a rigorous revision and re-derivation of +the various molecular rates in plasma-edge codes is required and below we will discuss +the three inaccuracies of the molecular charge exchange rate used by Eirene, introduced +in section 2.1, in more detail. +First, we investigate the inaccuracies of the vibrationally resolved molecular charge +exchange cross-sections and their impact. As explained in section 2.1, the cross-sections +are underestimated at low temperatures for higher vibrational levels as a simplified +equation [31] is used to rescale the measured cross-sections from the vibrational ground +state [29, 30] to higher vibrational levels (refered to as ’Janev 1987 / Holliday 1971 / +Greenland 2001’). This is in strong contrast to more recent, fully vibrationally resolved, +calculations of the molecular charge exchange cross-sections [56, 57, 58, 59], referred to +as ’Ichihara 2000’ [56]. The underestimate of the effective rates at low temperatures are +exacerbated by ion isotope mass rescaling for deuterium (equation 2) and even more so +for tritium. +The impact of this on the effective molecular charge exchange rate is investigated in +figure 7, where the effective molecular charge exchange rate is calculated as function of +Ti using a fixed vibrational distribution (obtained from [60] assuming Te = 1 − 3 eV) for +both vibrationally resolved molecular charge exchange cross-sections ‡. This shows that, +‡ A fixed EH2 can introduce uncertainties since higher molecular energies can elevate the effective +cross-sections at low ion temperatures significantly. Nevertheless, this would not alter the conclusions of + +Impact of mol. CX in SOLPS-ITER +17 +< v>eff +T (eV) +i +1 +0.1 +5 +-3 +[m ] +Janev 1987 +/ Holliday 1971 +Ichihara 2000 +-10 +10 +-12 +10 +-14 +10 +Hydrogen +Deuterium +(T /2) +i +/ Greenland 2001 +Figure 7. Comparison of the effective molecular charge exchange rate, as function of +the ion temperature, using the vibrationally resolved molecular charge exchange rates +from Holliday 1971, Janev 1987, Greenland 2001 (red) [28, 29, 30, 31] and from Ichihara +2000 [56] (blue). The effective rate is calculated using equation 1. The vibrational +distribution is obtained from [60], which has been averaged over Te = 1 − 3 eV. Static +molecules (EH2 = 0.1 eV) has been assumed. Purely hydrogenic rates have been used +and ion isotope mass rescaling (Ti/2) has been applied to the dotted cases. +although the ion isotope mass rescaling is correctly applied to only the ion temperature +dependency, the effective cross-section greatly decays at low temperature for ’Janev 1987 +/ Holliday 1971 / Greenland 2001’ for D. Contrastingly, the effective rates derived using +the ’Ichihara 2000’ cross-sections are similar for H and D, in agreement with [19], and +are both in reasonable agreement with the ’Janev 1987 / Holliday 1971 / Greenland +2001’ effective rate for H Te = 1 − 3 eV. +Secondly, as explained through equations 1 and 2 in section 2.1, both the ion and +temperature dependencies are inadvertently rescaled when ion isotope mass rescaling +is applied by Eirene to effective rates. This results in inaccuracies not only because it +results in an incorrectly applied ion isotope mass rescaling to the electron temperature +dependency of the vibrational distribution model; but also because the ion temperature +can be different from the electron temperature. Resolving this may require modifications +to Eirene to support different electron and ion temperature dependencies. Using a +vibrationally resolved simulation setup (see section 4.4) would also ensure that ion mass +rescaling is applied correctly. +Thirdly, as mentioned in section 2.1, it is assumed that the cross-sections (in velocity +space) are the same for all isotopes. This is not true, however, as there are chemical +differences resulting in different cross-sections for each isotope [56, 19]. The chemical +isotope differences have a particularly strong impact on the rates resulting in D−. +SOLPS-ITER does not account for H− by default. In [20] it was argued that such +figure 7. + +Impact of mol. CX in SOLPS-ITER +18 +interactions can play an important role as they also result in MAR; that argument was +based on applying the correct ion isotope mass re-scaling under the assumption that the +cross-sections for creating H− is the same as for D− and T −. However, the D− and T − +creation cross-sections are strongly reduced compared to the H− ones due to chemical +isotopical differences in the various rates, which has been measured experimentally +[61]. Such measurements, however, occur at very low vibrational levels. The isotope +differences are expected to reduce at higher vibrational levels, which drive most of +the molecular ion generation [19]. As such, a more detailed analysis in [19] indicates +a 30 % reduction in the effective D− creation rate compared to H−. However, that +percentage, as well as the H− generation rate, will be even more sensitive to molecules +that are highly vibrationally excited (H2(ν ≥ 5)). This may imply that it is necessary, +in some conditions, to include interactions with H− and its isotopes in plasma-edge +modelling. There are experimental indications from the TCV tokamak on the presence of +D− during deep detached conditions, based on the inferred ratio between the ’molecular’ +contribution to Dβ and Dα [7]. +4.4. Uncertainties in the vibrational distribution of molecular hydrogen +Molecular charge exchange is highly sensitive to the vibrational distribution of the +molecule at the time of the reaction (fν). The modelling of fν has large uncertainties, +which can be broadly divided in two categories: 1) inaccuracies in the rates and reactions +used in the vibrational distribution modelling; 2) inaccuracies introduced by a lack of +transport. +The first category includes inaccuracies in reaction rates used as well as missing +reaction processes, including 1) the omission of H− creation; 2) re-distribution of +vibrationally excited states through electronic excitation [62, 60]; 3) omitting electron- +impact collisions that alter the vibrational state of a molecule by more than > ±1 [60]. +Including the latter two in the vibrational modelling can alter the vibrational distribution +considerably [60]. +The mean-free-path of vibrationally excited molecules can be sufficiently long for +transport to be significant, particularly below the dissociation region. Including such +transport requires vibrationally resolved simulations [63, 64, 65, 39]. The vibrational +distribution can vary strongly spatially and transport allows including such effects and +their propagation throughout the rest of the divertor. Plasma-wall interactions [39] can +alter the initial vibrational distribution of molecules coming off the wall, depending on +the precise interaction with the wall and the wall material [66, 67]. +Although vibrationally resolved simulations have been performed in the past for +Asdex-Upgrade [63, 64] and for TCV [66, 39], they may not have included all the relevant +processes (e.g. inaccuracies in the rates & reactions of vibrationally excited molecules +[60]) and would have employed the default Eirene cross-sections that are likely strongly +underestimated at high vibrational levels (section 4.3). Therefore, molecular charge +exchange in detached conditions was, likely, still significantly underestimated in these + +Impact of mol. CX in SOLPS-ITER +19 +simulations. Further investigation of the vibrational distribution of the molecules, through +both modelling and experiment to modelling comparisons, is required in conditions where +plasma chemistry with molecular ions may be important. +5. Conclusions +Recent experimental results on TCV, MAST-Upgrade and JET have indicated that +plasma-molecular chemistry, resulting in molecular ions (particularly D+ +2 ) that react +with the plasma, result in excited atoms that can contribute to the hydrogen Balmer line +emission significantly. Such interactions result in Molecular Activated Recombination +(MAR), which can impact divertor particle balance significantly during detachment. +Initial comparisons between SOLPS-ITER simulations and experiments on TCV had +shown that such interactions do not occur significantly in the simulations. +It was +hypothesised that this is related to the isotope mass rescaling employed by Eirene +to the effective hydrogenic molecular charge exchange rate, resulting in ∼ 100 times +lower D+ +2 densities in detachment-relevant regimes compared to H+ +2 , whereas more +detailed investigations in literature indicate differences between hydrogen and deuterium +molecular charge exchange rates of a few percent. +This has motivated our work to compare SOLPS-ITER simulation results with the +default rate setup and with a modified rate setup in which ion isotope mass rescaling has +been disabled for molecular charge exchange. We observe that disabling isotope mass +rescaling for molecular charge exchange has a strong impact on the solution obtained +after the detachment onset and provides a closer match to the experiment. The neutral +atom content in the lower divertor is greatly enhanced in the modified rate setup by +up to 100 %, due to Molecular Activated Dissociation (MAD) and MAR, which has +significant associated hydrogenic (plasma) power losses. +6. Acknowledgements +Discussions with Detlev Reiter are kindly acknowledged and were very helpful. This +work has received support from EPSRC Grants EP/T012250/1 and EP/N023846/1. +This work has been supported in part by the Swiss National Science Foundation and has +been carried out within the framework of the EUROfusion Consortium, funded by the +European Union via the Euratom Research and Training Programme (Grant Agreement +No 101052200 — EUROfusion; as well as No 633053 (2014-2018 & 2019-2020)). Views +and opinions expressed are however those of the author(s) only and do not necessarily +reflect those of the European Union or the European Commission. Neither the European +Union nor the European Commission can be held responsible for them. +7. References +[1] Krasheninnikov S, Pigarov A Y, Knoll D, LaBombard B, Lipschultz B, Sigmar D, Soboleva T, +Terry J and Wising F 1997 Physics of Plasmas 4 1638–1646 ISSN 1070-664X + +Impact of mol. CX in SOLPS-ITER +20 +[2] Verhaegh K, Lipschultz B, Duval B P, Harrison R, Reimerdes H, Theiler C, Labit B, Maurizio R, +Marini C, Nespoli F, Sheikh U, Tsui C K, Vianello N, Vijvers W A J and Team T T E M 2017 +Nuclear Materials and Energy 12 1112–1117 ISSN 2352-1791 +[3] Verhaegh K, Lipschultz B, Duval B, F´evrier O, Fil A, Theiler C, Wensing M, Bowman C, Gahle D, +Harrison J et al. 2019 Nuclear Fusion 59 +[4] Verhaegh K, Lipschultz B, Duval B, Fil A, Wensing M, Bowman C and Gahle D 2019 Plasma Phys. +Control. Fusion 61 +[5] Verhaegh K, Lipschultz B, Bowman C, Duval B P, Fantz U, Fil A, Harrison J R, Moulton D, +Myatra O, W¨underlich D, Federici F, Gahle D S, Perek A, Wensing M and and 2021 Plasma +Physics and Controlled Fusion 63 035018 +[6] Verhaegh K, Lipschultz B, Harrison J R, Duval B P, Bowman C, Fil A, Gahle D S, Moulton D, +Myatra O, Perek A, Theiler C and Wensing M 2021 Nuclear Materials and Energy 26 100922 +[7] Verhaegh K, Lipschultz B, Harrison J, Duval B, Fil A, Wensing M, Bowman C, Gahle D, Kukushkin +A, Moulton D, Perek A, Pshenov A, Federici F, F´evrier O, Myatra O, Smolders A, Theiler +C, the TCV Team and the EUROfusion MST1 Team 2021 Nuclear Fusion 61 106014 URL +https://doi.org/10.1088/1741-4326/ac1dc5 +[8] Perek A, Vijvers W A J, Andrebe Y, Classen I G J, Duval B P, Galperti C, Harrison J R, Linehan +B L, Ravensbergen T, Verhaegh K and de Baar M R 2019 Review of Scientific Instruments 90 +123514 +[9] Perek A, Linehan B, Wensing M, Verhaegh K, Classen I, Duval B, F´evrier O, Reimerdes H, Theiler +C, Wijkamp T and de Baar M 2021 Nuclear Materials and Energy 26 100858 ISSN 2352-1791 +[10] Perek A, Wensing M, Verhaegh K, Linehan B, Reimerdes H, Bowman C, van Berkel M, +Classen I, Duval B, F´evrier O, Koenders J, Ravensbergen T, Theiler C, de Baar M, the +EUROfusion MST1 Team and the TCV Team 2022 Nuclear Fusion 62 096012 URL https: +//doi.org/10.1088/1741-4326/ac7813 +[11] Verhaegh K, Lipschultz B, Harrison J, Osborne N, Williams A, Ryan P, Clark J, Federici F, Kool +B, Wijkamp T et al. 2022 arXiv preprint arXiv:2204.02118 +[12] Lomanowski B, Groth M, Coffey I H, Karhunen J, Maggi C F, Meigs A, Menmuir S and O’Mullane +M 2020 Plasma Physics and Controlled Fusion 62 +[13] Karhunen J, Holm A, Lomanowski B, Solokha V, Aleiferis S, Carvalho P, Groth M, Lawson K, +Meigs A, Shaw A et al. 2022 Plasma Physics and Controlled Fusion 64 075001 +[14] Karhunen J, Holm A, Aleiferis S, Carvalho P, Groth M, Lawson K, Lomanowski B, Meigs A, +Shaw A and Solokha V 2022 Nuclear Materials and Energy 101314 ISSN 2352-1791 URL +https://www.sciencedirect.com/science/article/pii/S2352179122001958 +[15] Fil A M D, Dudson B D, Lipschultz B, Moulton D, Verhaegh K H A, Fevrier O and Wensing M +2017 Contributions to plasma physics 58 ISSN 0863-1042 +[16] Fil A, Lipschultz B, Moulton D, Dudson B D, F´evrier O, Myatra O, Theiler C, Verhaegh K, +Wensing M and and 2020 Plasma Physics and Controlled Fusion 62 035008 +[17] Wensing M, Duval B, Fevrier O, Fil A, Galassi D, Havlickova E, Perek A, Reimerdes H, Theiler C, +Verhaegh K and Wischmeier M 2019 Plasma Phys. Control. Fusion 61 +[18] Wensing M, Loizu J, Reimerdes H, Duval B, Wischmeier M and the TCV team 2020 Nuclear +Fusion 60 054005 +[19] Janev R K and Reiter D 2018 Isotope effects in molecule assisted recombination and +dissociation in divertor plasmas J¨ulich report - juel 4411 Forschungszentrum J¨ulich GmbH +J¨ulich englisch URL https://juser.fz-juelich.de/record/850290/files/J%C3%BCl_4411_ +Reiter.pdf?version=1 +[20] Kukushkin A S, Krasheninnikov S I, Pshenov A A and Reiter D 2017 Nuclear Materials and Energy +12 984–988 ISSN 2352-1791 +[21] Coda S, Agostini M, Albanese R, Alberti S, Alessi E, Allan S, Allcock J, Ambrosino R, Anand H, +Andr`ebe Y, Arnichand H, Auriemma F, Ayllon-Guerola J, Bagnato F, Ball J, Baquero-Ruiz M, +Beletskii A, Bernert M, Bin W, Blanchard P et al. 2019 Nuclear Fusion 59 112023 + +Impact of mol. CX in SOLPS-ITER +21 +[22] Reimerdes H and et al 2022 Nuclear Fusion 62 042018 URL https://dx.doi.org/10.1088/ +1741-4326/ac369b +[23] Reimerdes H, Duval B, Elaian H, Fasoli A, F´evrier O, Theiler C, Bagnato F, Baquero-Ruiz M, +Blanchard P, Brida D et al. 2021 Nuclear Fusion 61 024002 +[24] Raj H, Theiler C, Thornton A, F´evrier O, Gorno S, Bagnato F, Blanchard P, Colandrea C, +de Oliveira H, Duval B P et al. 2022 Nuclear Fusion +[25] Harrison J R, Vijvers W A J, Theiler C, Duval B P, Elmore S, Labit B, Lipschultz B, van Limpt +S H M, Lisgo S W, Tsui C K, Reimerdes H, Sheikh U, Verhaegh K H A and Wischmeier M 2017 +Nuclear Materials and Energy 12 1071–1076 ISSN 23521791 +[26] Reimerdes H, Duval B P, Harrison J R, Labit B, Lipschultz B, Lunt T, Theiler C, Tsui C K, +Verhaegh K, Vijvers W A J, Boedo J A, Calabro G, Crisanti F, Innocente P, Maurizio R, Pericoli +V, Sheikh U, Spolare M, Vianello N, the T C V t and the E M S T t 2017 Nuclear Fusion 57 +126007 ISSN 0029-5515 URL http://stacks.iop.org/0029-5515/57/i=12/a=126007 +[27] Kotov V and Reiter D 2009 Plasma physics and controlled fusion 51 115002 ISSN 0741-3335 +[28] Reiter D 2000 The data file AMJUEL: Additional atomic and molecular data for EIRENE Tech. +rep. Forschungszentrum J¨ulich GmbH URL http://www.eirene.de/html/amjuel.html +[29] Janev R K, Langer W D, Douglass Jr E et al. 1987 Elementary processes in hydrogen-helium +plasmas: cross sections and reaction rate coefficients (Springer Science & Business Media) +[30] Holliday M G, Muckerman J T and Friedman L 1971 The Journal of Chemical Physics 54 1058–1072 +[31] Greenland P T 2001 The crmol manual: collisional-radiative models for molecular hydrogen +in plasmas J¨ulich report juel-3858 Forschungszentrum J¨ulich GmbH URL https://juser. +fz-juelich.de/record/24992/files/J%C3%BCl_3858_Greenland.pdf?version=1 +[32] Sawada K and Fujimoto T 1995 Journal of applied physics 78 2913–2924 +[33] Kotov V and Reiter D 2012 Plasma Physics and Controlled Fusion 54 082003 ISSN 0741-3335 +URL http://stacks.iop.org/0741-3335/54/i=8/a=082003 +[34] Stangeby P C 2018 Plasma Physics and Controlled Fusion 60 044022 ISSN 0741-3335 +[35] Reiter D et al. 2008 The eirene code user manual Report Forschungszentrum J¨ulich GmbH URL +http://www.eirene.de/manuals/eirene.pdf +[36] F´evrier O, Theiler C, Oliveira H D, Labit B, Fedorczak N and Baillod A 2018 Review of Scientific +Instruments 89 053502 +[37] De Oliveira H, Marmillod P, Theiler C, Chavan R, F´evrier O, Labit B, Lavanchy P, Marl´etaz B +and Pitts R A 2019 Review of Scientific Instruments 90 083502 +[38] Smolders A, Wensing M, Carli S, Oliveira H D, Dekeyser W, Duval B P, F´evrier O, Gahle D, +Martinelli L, Reimerdes H, Theiler C, Verhaegh K and the TCV team 2020 Plasma Physics and +Controlled Fusion 62 125006 +[39] Wischmeier M 2005 Simulating divertor detachment in the TCV and JET tokamaks Thesis EPFL +[40] Verhaegh K 2018 Spectroscopic Investigations of detachment on TCV Thesis University of York +URL http://etheses.whiterose.ac.uk/22523/ +[41] Militello F, Aho-Mantila L, Ambrosino R, Body T, Bufferand H, Calabro G, Ciraolo G, Coster D, +Di Gironimo G, Fanelli P et al. 2021 Nuclear Materials and Energy 26 100908 ISSN 2352-1791 +[42] Kuang A Q, Ballinger S, Brunner D, Canik J, Creely A J, Gray T, Greenwald M, Hughes J W, +Irby J, LaBombard B and et al 2020 Journal of Plasma Physics 86 865860505 +[43] Wigram M, LaBombard B, Umansky M, Kuang A, Golfinopoulos T, Terry J, Brunner D, Rensink +M, Ridgers C and Whyte D 2019 Nuclear Fusion 59 106052 URL https://doi.org/10.1088/ +1741-4326/ab394f +[44] Bernert M, Janky F, Sieglin B, Kallenbach A, Lipschultz B, Reimold F, Wischmeier M, Cavedon +M, David P, Dunne M et al. 2020 Nuclear Fusion 61 024001 +[45] Pan O, Bernert M, Lunt T, Cavedon M, Kurzan B, Wiesen S, Wischmeier M and Stroth U 2022 +Nuclear Fusion +[46] Stroth U, Bernert M, Brida D, Cavedon M, Dux R, Huett E, Lunt T, Pan O, Wischmeier M et al. +2022 Nuclear Fusion 62 076008 + +Impact of mol. CX in SOLPS-ITER +22 +[47] Myatra O 2021 Numerical modelling of detached plasmas in the MAST Upgrade super-X divertor +Ph.D. thesis University of York URL https://etheses.whiterose.ac.uk/29934/1/OMyatra_ +thesis.pdf +[48] Hollmann E M, Brezinsek S, Brooks N H, Groth M, McLean A G, Pigarov A Y and Rudakov D L +2006 Plasma Physics and Controlled Fusion 48 1165 ISSN 0741-3335 +[49] Bowman C, Harrison J R, Lipschultz B, Orchard S, Gibson K J, Carr M, Verhaegh K and Myatra +O 2020 Plasma Physics and Controlled Fusion 62 045014 +[50] Kukushkin A, Neverov V, Alekseev A, Lisgo S and Kukushkin A 2016 Fusion Science and Technology +69 628–642 +[51] Pshenov A, Kukushkin A, Marenkov E and Krasheninnikov S 2019 Nuclear Fusion 59 106025 URL +https://dx.doi.org/10.1088/1741-4326/ab3144 +[52] Pshenov A, Kukushkin A, Gorbunov A and Marenkov E 2023 Nuclear Materials and Energy +34 101342 ISSN 2352-1791 URL https://www.sciencedirect.com/science/article/pii/ +S235217912200223X +[53] Ravensbergen T, van Berkel M, Perek A, Galperti C, Duval B, F´evrier O, van Kampen R, Felici F, +Lammers J, Theiler C et al. 2021 Nature communications 12 1–9 +[54] Ravensbergen T, van Berkel M, Silburn S A, Harrison J R, Perek A, Verhaegh K, Vijvers W A J, +Theiler C, Kirk A and de Baar M 2020 Nuclear Fusion URL https://doi.org/10.1088% +2F1741-4326%2Fab8183 +[55] Biel W, Albanese R, Ambrosino R, Ariola M, Berkel M, Bolshakova I, Brunner K, Cavazzana R, +Cecconello M, Conroy S et al. 2019 Fusion engineering and design 146 465–472 +[56] Ichihara A, Iwamoto O and Janev R K 2000 Journal of Physics B: Atomic, Molecular and Optical +Physics 33 4747–4758 +[57] Laporta V, Agnello R, Fubiani G, Furno I, Hill C, Reiter D and Taccogna F 2021 Plasma Physics +and Controlled Fusion +[58] Krsti´c P S and Janev R K 2003 Phys. Rev. A 67(2) 022708 URL https://link.aps.org/doi/10. +1103/PhysRevA.67.022708 +[59] Roncero O, Andrianarijaona V, Aguado A and Sanz-Sanz C 2022 Molecular Physics 120 e1948125 +(Preprint https://doi.org/10.1080/00268976.2021.1948125) URL https://doi.org/10. +1080/00268976.2021.1948125 +[60] Holm A, W¨underlich D, Groth M and B¨orner P 2022 Contributions to Plasma Physics n/a +e202100189 +[61] Krishnakumar E, Denifl S, ˇCadeˇz I, Markelj S and Mason N J 2011 Phys. Rev. Lett. 106(24) 243201 +[62] Chandra R, Holm A and Groth M 2023 Nuclear Materials and Energy 34 101360 ISSN 2352-1791 +URL https://www.sciencedirect.com/science/article/pii/S2352179122002411 +[63] Fantz U, Reiter D, Heger B and Coster D 2001 Journal of Nuclear Materials 290 367–373 ISSN +0022-3115 +[64] Fantz U 2002 Contributions to Plasma Physics 42 675–684 ISSN 0863-1042 +[65] Fantz U and W¨underlich D 2006 New Journal of Physics 8 301–301 +[66] Wischmeier M, Pitts R A, Alfier A, Andrebe Y, Behn R, Coster D, Horacek J, Nielsen P, Pasqualotto +R, Reiter D and Zabolotsky A 2004 Contributions to Plasma Physics 44 268–273 ISSN 0863-1042 +[67] Eenshuistra P J, Bonnie J H M, Los J and Hopman H J 1988 Phys. Rev. Lett. 60(4) 341–344 URL +https://link.aps.org/doi/10.1103/PhysRevLett.60.341 + diff --git a/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/load_file.txt b/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2cdb9e883e23d0103eb5aca28d1f4c36d11783a7 --- /dev/null +++ b/YtFIT4oBgHgl3EQfjyu7/content/tmp_files/load_file.txt @@ -0,0 +1,739 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf,len=738 +page_content='Investigating the impact of the molecular charge-exchange rate on detached SOLPS-ITER simulations K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh1,∗, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Williams2,∗, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton1, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz2, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval3, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier3, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fil1, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison1, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Osborne4, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes3, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler3, the TCV team∗∗ and the EuroFusion MST1 team∗∗∗ 1 Culham Centre for Fusion Energy, Culham, United Kingdom 2 York Plasma Institute, University of York, United Kingdom 3 Swiss Plasma Centre, ´Ecole Polytechnique F´e´erale de Lausanne, Lausanne, Switzerland 4 University of Liverpool, Liverpool, United Kingdom ∗ These authors contributed equally ∗∗ See author list of ”H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2022 Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fusion 62 042018” ∗∗∗ See author list of ”B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Labit et al 2019 Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fusion 59 086020” Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Divertor detachment requires plasma-neutral interactions that dissipate momentum & power and reduces ion target fluxes simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Plasma-molecular interactions generate molecular ions which react with the plasma and contribute to detachment through molecular activated recombination (MAR), reducing the ion target flux, and molecular activated dissociation (MAD), both of which create excited atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Hydrogenic emission from these atoms have been detected experimentally in detached TCV, JET and MAST-U deuterium plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The TCV findings, however, were in disagreement with SOLPS-ITER simulations for deuterium indicating a molecular ion density (D+ 2 ) that was insufficient to lead to significant hydrogenic emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This was attributed to inaccuracies in the molecular charge exchange rate (D2 + D+ → D+ 2 + D), which seems to be particularly underestimated in deuterium (obtained by rescaling the hydrogen rates by their isotope mass).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In this work, we have performed new SOLPS-ITER simulations with the default rate setup and a modified rate setup where ion isotope mass rescaling was disabled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This increased the D+ 2 content by > ×100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' By disabling ion isotope mass rescaling: 1) the total ion sinks are more than doubled due to the inclusion of MAR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) an ion target flux roll-over occurs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3) the total Dα emission in the divertor increases during deep detachment by ∼ ×4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4) the neutral atom density in the divertor is doubled due to MAD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 5) total hydrogenic power loss is enhanced through MAD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' These differences result in a greatly improved agreement between the experiment and the simulations in terms of spectroscopic measurements, ion source/sink inferences and measured ion target fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Keywords: Tokamak divertor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Molecules;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' plasma;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' SOLPS-ITER;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Detachment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' TCV tokamak;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Eirene arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='11298v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='plasm-ph] 26 Jan 2023 Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Introduction Power exhaust is an important challenge in the realisation of fusion power plants as the tolerable heat flux engineering limits to the vessel walls may otherwise be greatly exceeded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Large heat flux reduction requires plasma detachment which is triggered when relatively low temperatures (Te <∼ 5 eV) are obtained;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' these can be achieved by increasing the core density and/or inducing impurity radiation by extrinsic impurity seeding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Detachment is a state where plasma-atom and molecule interactions result in simultaneous power, particle and momentum dissipation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' which is experimentally recognised by a reduction of the ion target flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although the incoming flux can mostly be considered atomic, the recycling of the ions from the wall can have a strong molecular component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Therefore, the relevant collisional processes include atomic processes, such as electron-impact excitation (EIE power loss), electron-impact ionisation (ion source) and electron-ion recombination (EIR ion sink);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' as well as molecular processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Interactions between the plasma and the molecules can lead to momentum and energy transfer from the plasma to the molecules exciting molecules rovibronically (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' rotationally, vibrationally and electronically).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Vibrational excitation (ν) increases the probability of creating molecular ions, in particular H+ 2 (through molecular charge exchange H2(ν) + H+ → H+ 2 + H) and H− (through e− + H2(ν) → H− 2 → H− + H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' These ions can then undergo further interactions with the plasma, leading to Molecular Activated Recombination (MAR) [1] and Molecular Activated Dissociation (MAD) [1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' that result in excited atoms and, thus, radiative losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Recent experimental investigations have used spectroscopy and filtered camera imaging on TCV [2, 3, 4, 5, 6, 7, 8, 9, 10], MAST-Upgrade [11] and JET [12, 13, 14] that register significant Balmer line emission after the break-up of molecular ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For TCV [6, 7], it was shown that MAR from molecular ions is a dominant contributor to the reduction of the ion target flux in contradiction with SOLPS-ITER simulations [6, 15] that did not show a roll-over of the ion target flux [15, 16, 17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Additionally, the D+ 2 density in the simulations was negligible during detachment, leading to negligible MAR and a much lower simulated Dα emission [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' That disagreement was likely caused by an underestimated molecular charge exchange rate when the hydrogen rates are isotope mass rescaled to deuterium [7], leading to orders of magnitude underestimations in the D+ 2 content in detached conditions (sections 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' More recent studies, however, indicate the difference between the molecular charge exchange rate for hydrogen and deuterium should be much smaller and may be even (< 5% at 1-3 eV) [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' To illustrate the impact upon SOLPS-ITER simulations, ”post-processing” of the predicted results in a non self-consistent manner after convergence were performed [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Using the simulated D2 densities, the D+ 2 density was modelled based upon the D+ 2 /D2 ratio from [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This post-processing lead to a better agreement with the experimental data: 1) the MAR ion sink became significant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) if this MAR ion source is subtracted from the ion target flux, an ion target flux roll-over would have occurred;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3) D+ 2 interactions added significant Balmer line emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, these effects appeared Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 3 ’overestimated’ after post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' When integrally simulated, modifying the D+ 2 content leads to modifications in the plasma solution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ne, Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') itself, that cannot be accounted for in post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Hence, in this work, we present a comparison between self-consistent SOLPS-ITER simulations for TCV (same as those used in [15, 16]) which use: 1) the default SOLPS- ITER rate setup that employs ion isotope rescaling to the molecular charge exchange rate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) a modified rate setup where the ion isotope mass rescaling of the molecular charge exchange rate is disabled, see figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For simplicity, we refer to this as the ’default’ and the ’modified’ setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' We observe that including these rates self consistently leads to an ion target flux roll-over, induced by strong MAR ion sinks, and an increase in the Dα emission - all three in agreement with experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Additionally, we find that the neutral content in the divertor is more than doubled through MAD, significantly elevating the hydrogenic plasma power loss channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The aim of this work is to show that molecular charge exchange can impact detachment significantly in SOLPS-ITER simulations (in agreement with the experiment) and to motivate the necessity of investigating the reaction rate set in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Since re-deriving and using new molecular charge exchange rates is outside of the scope of this work, we have chosen to do this by disabling the ion isotope mass rescaling for modelling simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The motivation for this (section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1) is that there are various inaccuracies in the molecular charge exchange rates employed by SOLPS-ITER at temperatures below 2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although, there is a physics reason for ion isotope mass rescaling (section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1), it exacerbates the various rate problems at temperatures below 4 eV (for D) and below 6 eV (for T), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Disabling ion isotope mass rescaling is not advisable as a new SOLPS-ITER default and improved rate data needs to be implemented in Eirene (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Simulation setup and theory The simulation set-up follows the previously published work by Alex Fil [15, 16] ‡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In the simulation, the upstream density is scanned by a fuelling puff, similarly to [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Photon opacity, neutral-neutral collisions and drifts are not included;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' currents are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' [7] calculated that photon opacity is expected to play a negligible role in the simulated cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Chemical sputtering of carbon is included as a fixed fraction of the ion target flux, estimated by matching the magnitude of carbon emission signals in the divertor to experiments [15, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The power input in the simulation was matched to the experiment by assuming a 1:1 in:out symmetry and by defining PSOL as the Ohmic power minus core + SOL (above X-point) radiative losses (equivalent to [3]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' thus accounting for any carbon radiation that may occur from main chamber erosion directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' An illustration of the plasma grid, Eirene grid and vessel geometry used is shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The original simulations performed were interpretive simulations of TCV tokamak ‡ For providence, this was re-run with a newer SOLPS-ITER version (version 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='7) Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 4 DSS D2 LP Separatrix Eirene grid B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 (fluid) grid Outer div.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' A visualisation of the TCV vessel geometry, fluid grid (red), Eirene grid (black/grey), spectroscopic (DSS) lines of sight (green), outer divertor fluid grid cells (blue shading), separatrix fluid grid cells (cyan), D2 fuelling location (cyan) and Langmuir probe (LP) location (magenta).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' [21, 22], discharge # 52065, which is a single null L-mode unbaffled [23, 24] density ramp discharge that has been extensively reported in literature [3, 7, 5, 9, 25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The simulations are set-up to run with kinetic neutrals (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Eirene) using the default Eirene rate setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The rates used by Eirene are derived for a hydrogen plasma (for simplicity, as isotope resolved data is often not available), whereas a deuterium plasma is simulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Rates (σv) that involve interactions with ions, depend on the kinetic velocity of the ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Since the velocity, at the same ion temperature is lower for heavier particles, ion isotope mass rescaling to < σv > (Ti) is applied by default [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This assumes that there is no isotope difference between the rates in velocity space (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' no chemical isotopical differences) - evidence for this, depending on the reaction, can be sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Molecular charge exchange rates It has been hypothesised [7] that the D+ 2 content may be severely underestimated in SOLPS-ITER simulations in detachment relevant regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Eirene uses the effective molecular charge exchange rate tabulated in ’AMJUEL’ [28] by polynomial fit coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Such effective rates average the reaction rate for molecular charge exchange < σv >CX,H2(ν) per vibrational state (ν) over the vibrational distribution of the molecules fν - equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' fν is modelled based on the local plasma parameters assuming that transport can be neglected and mostly depends on electron impact collisions with the molecules, changing the vibrational distribution [32] depending on the electron temperature Te: fν(Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The < σv >CX,H2(ν) rate is obtained from the σCX,H2(ν) and depends on the relative velocity between H+ and H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Assuming H2 is near stationary, the < σv >CX,H2(ν) rate is only a function of ion temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Hence, the effective reaction rate is sensitive to both the ion and the electron temperatures - equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The effective rate fit coefficient tables used by Eirene only have a temperature sensitivity, under the assumption that T = Te = Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' < σv >CX,H2,eff= � ν fν(Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') < σv >H2(ν) (Ti) (1) σCX,H2(ν=0) is obtained from Janev, 1987 [29] based on measurements in the 1970s by Holliday, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' These cross-sections for the vibrational ground state are then scaled to higher vibrational levels using an analytic equation (Aν(ν)) from Greenland, 2001 [31]: < σv >CX,H2(ν) (T) = Aν(ν) < σv >CX,H2(0) (T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although < σv >CX,H2(0) (T) decays strongly for T < 2 eV (and thus for < σv >CX,H2(ν) (T) = Aν(ν) < σv >CX,H2(0) (T), this does not occur for newer vibrationally resolved calculations of < σv >CX,H2(ν) [56] at H2(ν ≥ 4), which contribute most to < σv >CX,H2,eff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The simplified Greenland scaling cannot account for this, leading to order-of-magnitude underestimates of the default < σv >CX,H2(ν) Eirene rates in detachment relevant conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For deuterium and tritium, the velocity of the ion interacting with the molecule at same ion temperature is reduced by the isotope mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Assuming that the σCX,H2(ν) cross-sections are the same for all hydrogen isotopes, the vibrationally resolved rates can be ’ion isotope mass rescaled’ from hydrogen to deuterium: < σv >CX,D2(ν) (Ti) =< σv >CX,H2(ν) (Ti/2) [27, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, since Eirene only knows about the effective rate (for a vibrationally unresolved setup), the total effective rate is ion isotope mass rescaled, inadvertently also rescaling the electron temperature dependency of the vibrational distribution incorrectly (equation 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' < σv >CX,D2,eff,Eirene (T) =< σv >CX,H2,eff (T/2) = � ν fν(T/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') < σv >CX,H2(ν) (T/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') < σv >CX,D2,eff,correct (T) = � ν fν(T, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') < σv >CX,H2(ν) (T/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') (2) Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 6 Since < σv >CX,H2,eff (T) decreases with decreasing T §, this rescaling greatly reduces the effective molecular charge exchange rate in detachment relevant conditions for deuterium (a factor ∼ 100) and tritium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is shown in figure 2, where the D+ 2 /D2 ratios obtained from SOLPS-ITER simulations with and without isotope mass rescaling as well as the theoretically expected D+ 2 /D2 ratio based on a no-transport model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' balancing the D+ 2 creation/destruction rates) are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' It is these conditions in where the molecular density greatly increases for decreasing temperatures [34, 6, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In contrast, using a more accurate analysis of the molecular charge exchange rate [19] for T = 1, 2, 3 eV shows a negligible (∼ 5 %) isotope dependency ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In this, three issues discussed above were resolved: 1) < σv >ν rates were obtained from [56], using full vibrationally resolved simulations, rather than applying the simplified Greenland rescaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) rates specifically derived for H and D were utilised, accounting for chemical isotope differences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3) the lower velocity of the heavier hydrogen isotopes was correctly accounted for only in < σv >ν (Ti, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') and not in the vibrational distribution (fν(Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The ratios obtained with these rates (figure 2), for both H+ 2 /H2 and D+ 2 /D2, are in closer agreement to the AMJUEL effective H+ 2 /H2 ratio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' motivating our choice for disabling ion isotope mass rescaling in the ’modified’ setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Simulation results The obtained outer target ion target fluxes, together with the total outer divertor ion source (atomic ionisation and molecular activated ionisation arising from D2 and D+ 2 ), ion sinks (electron-ion recombination and molecular activated recombination arising from D+ 2 ) and net ion flow into the divertor is shown in figure 3 during a core density ramp, together with the experimentally measured ion target particle flux (assuming a 15 % uncertainty [36, 37]) for # 52065.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The upstream density was measured combining Thomson scattering measurements with the equilibrium reconstruction of the separatrix and assuming a spatial uncertainty of ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2 cm (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' the Thomson resolution), resulting in an upstream density uncertainty of ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 × 1019m−3 before the ion target flux roll-over and ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 × 1019m−3 afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' We will now compare the ’default’ and ’modified’ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ion isotope mass rescaling for molecular charge exchange disabled) setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In both the ’default’ and ’modified’ setups, we observe a movement of the divertor ionisation source towards the X-point as the upstream density is increased, reducing the total outer divertor integrated ion source, whilst electron-ion recombination remains negligible, in agreement with experimental observations [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' As the ionisation moves upstream, the ion flux from upstream of the divertor towards the outer target is increased, replenishing the loss of divertor ionisation, in agreement with measurements by a reciprocating divertor probe array [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ], as well as upstream spectroscopic measurements § The fν(Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') used for the derivation of the effective rates in Eirene is not fully documented ∥ However, this is based on a simplified Boltzmann relation for fν, which is different from fν(Te, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=') used for deriving the effective rates in Eirene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 7 10 0 10 1 Te (eV) 10 -4 10 -3 10 -2 10 -1 D2 + / D 2 ratio Default rates Isotope mass rescaling + + D + D -> D + D disabled 2 2 Prediction (from rates - lines) D mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX rate [Janev, 2018, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='] H mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX rate [Janev, 2018, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='] 2 Default rates Isotope mass rescaling + + D + D -> D + D disabled 2 SOLPS-ITER result (symbols) Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The D+ 2 /D2 ratio obtained from SOLPS simulations (symbols), over the entire simulation domain, as function of the electron temperature for both the default SOLPS-ITER set-up as well as the set-up where mass rescaling is disabled for molecular charge exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The expected D+ 2 /D2 ratio with and without isotope mass rescaling of the molecular charge exchange rate are also shown, modelled as the sum of the creation rates of D+ 2 (from D2) divided by the sum of the destruction rates of D+ 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Additional H+ 2 /H2 and D+ 2 /D2 ratios are shown (’H, D mol CX rate [Janev, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2018]’) using the molecular charge-exchange rate from [19] in combination with reaction rates from [28, 35] for the remaining reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In the ’default’ setup, this prevents the roll-over of the ion target flux as the upstream density is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is in contrast to the experiment, where a clear roll-over is observed as indicated in figure 3 [26, 25, 2, 3, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The absence of an ion target flux roll-over in plasma-edge simulations, even though other detachment markers are clearly obtained in the simulations (movement of the ionisation source;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' appearance of Te ∼ 1 eV temperatures;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' volumetric momentum losses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='), is a general observation for TCV density ramp SOLPS-ITER simulations [17, 18, 38, 15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For the ’modified’ setup, the obtained particle balance is similar to the default SOLPS-ITER setup in the attached phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is unsurprising, as molecular charge exchange only becomes an important source of D+ 2 at detachment-relevant temperatures of 1-3 eV, before which the D+ 2 creation is dominated by D2 ionisation and the isotope ion mass rescaling of molecular charge exchange has a negligible impact on the D+ 2 /D2 ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, as the core density increases and detachment relevant temperatures are achieved, a clear increase of MAR ion sinks, together with a roll-over of the ion target flux is now observed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' in contrast to the cases which used the default reaction rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 8 19 3 Upstream density (10 m ) 0 5 10 15 21 10 Particles / s Default rates 2 3 4 5 6 2 3 4 5 6 Modified rates Ion target flux Ion source Upstream ion flow MAR ion sink EIR ion sink Measured ion target flux 19 3 Upstream density (10 m ) a) Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Obtained particle balance in terms of integrated outer divertor ion target flux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' total outer divertor integrated ion sources/sinks are shown, together with the net ion flow from outside the divertor region towards the outer divertor target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The measured ion target flux is shown in grey, together with estimated uncertainty margins in the upstream density before/after roll-over and an assumed ±15% uncertainty in the ion target flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The characteristic upstream density uncertainty is ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 × 1019m−3 before the ion target flux roll-over and ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 × 1019m−3 afterwards a) the default SOLPS-ITER simulation setup;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' b) a SOLPS-ITER simulation setup where ion isotope mass rescaling for molecular charge exchange was disabled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is attributed to the additional ion sinks obtained from MAR (D2 + D+ → D+ 2 + D followed by e− + D+ 2 → D + D), which leads to a reduction of the ion target flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' We find that in both cases, the contribution of MAI to the total ion source is minor: throughout the density scan it starts at 16-18 % dropping to 5-10 % of the total ion source during detachment for both SOLPS-ITER rate setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The total ionisation source however, at the same upstream density, is smaller for the ’modified’ setup after detachment e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' after MAR and Dα emission arising from plasma-molecular interactions starts to become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The ionisation front is further removed from the target, after the detachment onset, for the ’modified’ setup with lower target temperatures: more ’deeply detached’ scenarios (in terms of ionisation front displacement, and target temperature) are obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is likely related to the additional ion sinks and hydrogenic power losses associated with Molecular Activated Dissociation (MAD), explained in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' There may be processes, other than molecular charge exchange, that may result in discrepancies between experiment and simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For instance, it was hypothesised in [39] that enhanced erosion of carbon from the main chamber wall through enhanced perpendicular transport at higher densities may result in additional impurities that strengthen detachment on TCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, investigating this is outside of the scope of Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 9 this work and requires additional diagnostics, such as filtered imaging of the main plasma to diagnose carbon erosion [10], which should be addressed in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Comparison of SOLPS-ITER results to ion source & sink measurements The simulated discharge, # 52065, was repeated several times to perform a detailed spectroscopic characterisation (# 56567 and repeats) ¶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This facilitated a detailed spectroscopic characterisation of the ion sources and sinks in the lower divertor [2, 3, 4, 5, 6, 7] and separating the measured Dα emission into its various emission contributions [5, 6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' That result is shown in figure 4, together with the obtained simulation results where the ion sources/sinks have been integrated over the spectroscopic lines of sight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This previously reported experimental analysis [5, 6, 7] indicates 1) significant ion sinks through MAR, dominating over EIR ion sinks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) a strong increase of Dα due to emission from excited atoms after plasma-molecular interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Both these aspects absent in the ’default’ setup simulations, but are present and in quantitative agreement with the experiment in the ’modified’ setup, greatly improving the agreement between experiment and simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The impact of molecular charge exchange on neutral atom content and hydrogenic power losses Disabling the ion isotope mass rescaling for the molecular charge exchange reaction not only has a strong impact on the divertor particle balance and hydrogenic emission processes, but also on the neutral atomic content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The total neutral D atom content (excluding molecules) in the outer divertor is increased by more than a factor of two for identical upstream densities with the ’modified’ compared to the ’default’ setup (figure 5 a), at the deepest detached phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Even when the neutral atom content between the two simulation setups is compared as a function of the target temperature, the neutral atom content is enhanced by more than 50 % for the modified rate setup (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, since the electron density decays in the modified rate setup, the total nuclei content (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' total amount of D particles considering ions, atoms and molecules) remains similar (within 5 %) for both simulation setups as function of upstream density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This increase in neutral atom content can be explained by the additional neutral atoms created through MAR & MAD by the modified rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The strength of volumetric processes generating neutral atoms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' EIR, MAR, MAD and electron-impact dissociation) is compared between the default and modified rates in figure 5 c) and d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This shows that the volumetric creation of neutral atoms is significantly enhanced in the modified rate setup, where the neutral atom creation continuously increases as one goes into deeper detached regimes, due to MAR & MAD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' MAR & MAD provide additional dissociation processes that are significant below 5 eV, by which time the electron-impact dissociation cross-sections are strongly reduced, but the molecular content is strongly ¶ It should be noted that the ion target flux roll-over is less clear in # 56567 than # 52065 as significantly lower core densities were obtained before the plasma disrupted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 10 19 3 Upstream density (10 m ) D D [total] [total] [atomic contribution] 2 3 4 5 6 19 3 Upstream density (10 m ) 19 3 Upstream density (10 m ) 2 3 4 5 6 19 3 Upstream density (10 m ) Experiment SOLPS-ITER default rates SOLPS-ITER modified rates D D a) b) b) c) d) e) f) Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Obtained particle balance (top figure) in terms of integrated outer divertor ion target flux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' and the ion sources/sinks obtained in view of the DSS diagnostic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Measured total Dα emission (bottom figure) in the outer divertor, captured in between the DSS lines of sight, and its inferred contribution arising from electron-impact excitation and EIR (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ’atomic’ interactions) and from plasma-molecular interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' These results are shown simulations where ion isotope mass rescaling was disabled for molecular charge exchange, which are compared against the experimental observations of outer the ion target flux (Langmuir probes), the total Dα emission and spectroscopic inferences of the divertor ion source, ion sinks (MAR & EIR) as well as the separation of Dα in atomic (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' EIE & EIR) and ’molecular’ (associated with D2, D+ 2 & D− 2 → D− + D components).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' increased [34, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Therefore, MAR & MAD can be stronger neutral atom creation processes than electron-impact dissociation & EIR, particularly in detached regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Using a synthetic diagnostic pressure gauge (’baratron’) setup [18, 39, 40], the divertor neutral pressure has been calculated and compared against the experiment (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' We find that the divertor neutral pressure starts to bifurcate between the modified rates and the default rates at the detachment onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' At the deepest levels of detachment, the divertor neutral pressure is increased by up to 50 % when the modified rates are used (at the same upstream density).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Experimentally, a strong increase in the divertor neutral pressure is observed after detachment, with divertor pressures of up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='6 Pa at the deepest levels of detachment ( upstream density of ne = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5[3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='4−6]×1019m−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This agrees with the ’modified’ setup simulations, but only at the deepest levels of detachment (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='6 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='47 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='74] Pa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Analogous to power losses due to ionisation, there are potential (plasma) energy losses associated with molecular dissociation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The additional dissociation mechanisms + The divertor pressure obtained during the attached phase is overestimated (by a factor ∼ 4) in the code for both the modified and default rate setup, in agreement with previous TCV results [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The origin of this discrepancy is unknown and is inconsistent with the agreement of the Balmer line emission and the inferred ionisation sources between the experiment and the simulation [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 11 0 10 20 30 Power loss (kW) Hydrogenic power loss outer divertor 0 1 2 3 22 D creation (10 part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' / s) D creation rate outer divertor Default rates 2 3 4 5 6 19 3 Upstream density (10 m ) 0 5 10 15 17 Neutral atoms (10 ) # neutral D atoms outer divertor Total + MAD (D ) 2 + Ionisation & MAI (D & D ) 2 2 Dissociation (D ) 2 Default rates Modified rates 2 3 4 5 6 19 3 Upstream density (10 m ) Default rates Modified rates D creation rate outer divertor Modified rates MAR & EIR < 1 kW (power sources/ sinks cancel) MAR EIR a) b) c) d) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The impact of increased MAD, due to the modified reaction rates, on hydrogen atom content and hydrogenic power losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' a) Evolution of the total neutral atom content (excluding molecules) as function of upstream density for the default and modified rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' b) Evolution of hydrogenic power loss processes for the default and modified rates, including: ionisation power loss (sum of radiative power loss due to excitation collisions preceding ionisation and the potential energy, ϵ = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='6 eV, spent on ionisation);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' power losses associated with electron-impact dissociation and associated with MAD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The net power loss associated with MAR & EIR has been estimated to be below 1 kW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' c) and d) Volumetric neutral atom creation source, integrated over the outer divertor, from MAR, MAD, EIR and electron-impact dissociation for c) default rate setup;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' d) the modified rate setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 12 through MAD after the detachment onset result in a significant increase in the total effective hydrogenic (plasma) power losses (figure 5 b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The hydrogenic power losses associated with plasma-molecular interactions are due to the dissociative energy losses to the plasma channel since the radiative losses and potential energy gains from MAR roughly cancel [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ∗ Although the total hydrogenic power loss at the same upstream density is only 20 % higher for the modified rate at the same upstream density, the total hydrogenic power loss can be 60 % higher for the modified rate setup for similar levels of detachment (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' similar Tt and similar ionisation front positions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Implications, relevance and accuracy of our findings and future pathways Increasing the D+ 2 content through the ’modified’ rate setup in our work results in: 1) increased neutral atom sources through MAD and associated hydrogenic power losses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) significantly enhanced hydrogenic atomic line emission from excited atoms after plasma-molecular interactions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' and 3) additional ion sinks through MAR, resulting in the ion target flux roll-over.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Such interactions start becoming significant at detachment onset with a spatial preference towards the target side of the ionisation region where the molecular density builds up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The TCV simulations, consistent with TCV [5, 6, 7, 10] and MAST-U [11] experimental results, indicate that plasma-molecular chemistry involving molecular charge exchange generating D+ 2 and associated MAD neutral atom sources, MAR ion sinks and atomic hydrogen emission: 1) starts to occur from the detachment onset on-wards as the ionisation and electron-impact dissociation regions detach from the target;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) increase in magnitude as higher molecular densities are obtained below the ionisation region when Te drops below 3 eV [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Neutral baffling may play a strong role in this point 2), which was brought forward as an explanation for why plasma-molecular effects plays a much more significant role in the MAST Upgrade Super-X divertor than the TCV open divertor (experiments from 2016 before baffles were present) [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Could molecular ions play a role in reactors during detachment?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' An important question is whether such interactions are also relevant for reactors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Answering that question requires further investigation, including further studies on the applicable molecular charge exchange as well as applying those to a range of reactor conditions, which is outside the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although there are large uncertainties regarding the molecular charge exchange rates, the molecular vibrational distribution (that determines these effective rates to a large extent) and their applicability to reactors, signatures of the impact of molecular ions on the hydrogen emission are being observed in JET with the ITER-like wall [12, 13, 14] during deep detachment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' ∗ The dissociation cost itself is a power loss only from the plasma channel: this potential energy can be released back to the target as hydrogen atoms re-associate into molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Therefore, this may not result in target heat load reductions, unless the distance between the dissociating area and the target is significant such that the higher energy atom population has room to dissipate radially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 13 The ion isotope mass rescaling has been applied correctly (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' using < σv >CX,D2,eff,correct as opposed to < σv >CX,D2,eff,Eirene - equation 2) for a limited set of SOLPS-ITER simulations in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although MAR was a significant ion sink with the new rates, it lead to a reduction of EIR as the electron density in the simulation was reduced: the target profiles obtained by the SOLPS-ITER simulations were similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This was hypothesised to be associated with increased power limitation of the ionisation source due to energy losses associated with MAR and MAD [20] ♯.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, for molecular ions to potentially play a role in reactors, the two conditions at the start of section 4 must be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This implies that molecular ions likely could play a stronger role in reactor scenarios that feature divertor designs & operation where the ionisation region is sufficiently detached from the target, with Te dropping to 1-3 eV below the ionisation region, to have a significant MAR rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although this may be feasible in current designs of reactor-class devices with conventional divertors, such as ITER and (potentially) DEMO, this may be more achievable in alternative divertor concept designs [41, 42, 43] and, potentially, X-point radiator designs [44, 45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Existing plasma-edge simulations of reactors could be post-processed to assess, in a simple way, whether molecular charge exchange can play a role in reactors [5, 6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This allows estimating whether a modified rate could impact hydrogen emission, MAR ion sinks and MAD neutral atom sources significantly in a non-self consistent way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This can only be used to map out whether molecular ions could potentially play a strong role in a simulation, self-consistent simulations are then required to investigate the precise impact of molecular ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The impact of transport and plasma-wall interactions on the vibrational distribution (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='4) can be different in reactors than in devices like TCV and MAST-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Differences in power and density result in a shortening of the mean free path in reactors, making transport of vibrationally excited molecules less likely (although it can still be significant in the low temperature region below the ionisation front).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Differences in wall material (metal for reactors, carbon for TCV and MAST-U) can impact the initial vibrational distribution of the molecules coming off the wall [39];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' as well as the reflection of atoms from the wall (in contrast to the adsorption of atoms to the wall, after which re-association occurs and molecules are released back into the plasma), which may relatively reduce the molecular density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Simplified MAR rate modelling One argument as to why plasma-molecular interactions may play a relatively weaker role for reactors is that reactors will operate at significantly higher electron densities (ne ∼ 1021m−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Since the EIR source scales ∝ n2−3 e for Te < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 eV, it would be expected that the relative role of EIR increases for reactor-relevant conditions at low temperatures;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' potentially reducing the relative impact of MAR as a neutral atom source and hydrogen ion sink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' To investigate this ♯ The underlying vibrationally resolved cross-sections used in the Eirene rates are likely underestimated at low temperatures, as shown in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3, which can result in a significant under-prediction of molecular charge exchange even if ion isotope mass rescaling is applied correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 14 EIR Ionisation Dissociation MAR MAD Ionisation EIR MAR MAD Dissociation 19 3 MAST-U scaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' n = 10 m e 19 3 TCV (unbaffled) scaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' n=7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='10 m e 19 3 MAST-U scaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' n = 10 m e Te (eV) 1 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 2 ∫ Reaction rate / n e L 2 ∫ Reaction rate / n e L 19 10 18 10 17 10 16 10 19 10 18 10 17 10 16 10 21 3 TCV (unbaffled) scaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' n=10 m e 21 3 MAST-U scaling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' n = 10 m e Te (eV) 1 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 EIR Ionisation Dissociation MAR MAD Ionisation EIR MAR MAD Dissociation Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Comparison of the expected chordally integrated reaction rate scalings as function of Te for the TCV (c, d) [15] (unbaffled) and MAST Upgrade Super-X (a, b) [47] divertor, based on SOLPS-ITER scalings [11] at a characteristic density (a,c) and extrapolated scalings to a reactor-relevant density (ne = 1021m−3) (b,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' further, we have obtained scalings from previous SOLPS-ITER simulations of both MAST Upgrade [47] and TCV [15] (open divertor - without baffles) for the evolution of the spectroscopic line-of-sight integrated neutral atom and neutral molecular density relative to the electron density as function of Te [11] using all of the divertor spectroscopic lines of sight for both TCV and MAST-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Using a simplified model for the rates [11], together with the D+ 2 /D2 ratios with the ’modified’ rate setup (figure 2), the evolution of the various atomic and molecular rates can be calculated as function of Te for a fixed ne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' That result is shown in figure 6 using the characteristic TCV & MAST-U electron densities (ne = 7 × 1019m−3 and ne = 1019m3, respectively) as well as reactor-relevant ne = 1021m−3 extrapolations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The evolution of the reaction rates (figure 6) indeed indicates that, when the SOLPS-ITER scalings for TCV are used, EIR becomes more important than MAR at reactor-relevant densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, MAD † still remains important between ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='7 and † Note that a single MAR/MAD reaction can result in the creation of 3-2 neutral atoms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' whereas EIR only results in 1 neutral atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 15 ∼ 3 eV for the TCV SOLPS-ITER scalings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Therefore, even at reactor-relevant densities, MAD could be a dominant neutral generation rate - even when scalings for an open divertor are extrapolated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Strikingly, when the MAST Upgrade derived SOLPS-ITER scalings are used, we find that MAR+MAD can be dominant between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 and 4 eV for reactor-relevant densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The difference between this result and that from the unbaffled TCV scaling is associated with the higher molecular content in MAST-U, likely due to its tight baffling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This shows that indeed, if one can have a significantly high molecular density below the ionisation region, MAR can remain important despite EIR being strongly elevated at reactor-relevant densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Using effective Eirene rates without ion isotope mass rescaling, the simplified model results in figure 6 predict that plasma-molecular interactions involving molecular ions are negligible at very low temperatures (Te ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 eV), in contrast with results from MAST Upgrade experiments in the Super-X divertor, where such interactions are still experimentally inferred at Te ≪ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='5 eV [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This mismatch is likely caused by the underestimated charge exchange cross-sections at low temperatures in Eirene (sections 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 & 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' One important caveat to this approach is that the applied scalings derived from SOLPS-ITER are different in reactor-relevant conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' As such, the above result should be seen as additional motivation as to why molecular ions leading to MAR & MAD could be important for reactors and thus require further study in reactor relevant regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' It should not be interpreted as a prediction that they will be important for reactors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact on diagnostic design, analysis and real-time detachment control strategies MAR & MAD not only have an impact on the divertor physics, but also result in a significant content of excited hydrogen atoms and thus hydrogen Balmer line emission as was shown in literature [48, 14, 13, 12, 5, 7, 6, 11] and is indicated by the increase in Dα emission during detachment as shown in figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Since that strong increase in Dα emission is not captured by the ’default’ setup, this causes strong concerns on the synthetic deuterium (and tritium) atomic emission diagnostic signals predicted from plasma-edge modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This has implications on diagnostic design, analysis of spectroscopic diagnostics as well as real-time control strategies that use spectroscopic signals as a real-time sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Synthetic diagnostic signals of hydrogen emission are used to test spectroscopic analysis techniques [49, 10, 4, 7] and design diagnostics [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' For example, synthetic diagnostics have shown that unexpectedly high stray light emission from hydrogen, deuterium and tritium Balmer-α emission can be a concern for diagnostic interpretation in ITER [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Plasma-molecular chemistry with molecular ions could, if present, greatly enhance the divertor hydrogenic emission beyond that predicted in the simulations (and the Dα emission would be even further enhanced by photon opacity);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' which could grossly misinform studies relying on synthetic diagnostic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 16 Plasma-molecular effects result in a significantly enhanced population of the hydrogen atom n = 3 state, which may have implications for the treatment of photon opacity to the Lyman series in simulations [51, 52] as well as the diagnosis of photon opacity [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Accounting for molecular ions in the analysis of hydrogen atomic line emission required the creation of novel analysis techniques [14, 13, 6], which need to be further expanded to include photon opacity effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Real-time detachment control strategies are required in reactors and spectrally filtered imaging [53, 54] as well as line-of-sight passive spectroscopy of hydrogen atomic emission [55] are important detachment sensor candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The complexity of including molecular ions in the interpretation of the atomic hydrogenic emission as well as the occurrence of photon opacity can complicate the usage of hydrogen atomic emission for such purposes and using complementary or alternative methods such as monitoring the molecular Fulcher band intensity may be required [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Plasma-edge simulations with an improved plasma-molecular interaction set as well as photon opacity are required to investigate this further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Inaccuracies of the molecular charge exchange rate employed by Eirene Increasing the molecular charge exchange rate during detachment through modified rates is a first step in 1) explaining the discrepancy observed between the experiment and SOLPS-ITER simulation results for TCV in terms of MAR, hydrogen emission and the ion target flux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) the investigation of the importance of molecular ions during detachment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This work aims to motivate that a rigorous revision and re-derivation of the various molecular rates in plasma-edge codes is required and below we will discuss the three inaccuracies of the molecular charge exchange rate used by Eirene, introduced in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1, in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' First, we investigate the inaccuracies of the vibrationally resolved molecular charge exchange cross-sections and their impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' As explained in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1, the cross-sections are underestimated at low temperatures for higher vibrational levels as a simplified equation [31] is used to rescale the measured cross-sections from the vibrational ground state [29, 30] to higher vibrational levels (refered to as ’Janev 1987 / Holliday 1971 / Greenland 2001’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is in strong contrast to more recent, fully vibrationally resolved, calculations of the molecular charge exchange cross-sections [56, 57, 58, 59], referred to as ’Ichihara 2000’ [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The underestimate of the effective rates at low temperatures are exacerbated by ion isotope mass rescaling for deuterium (equation 2) and even more so for tritium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The impact of this on the effective molecular charge exchange rate is investigated in figure 7, where the effective molecular charge exchange rate is calculated as function of Ti using a fixed vibrational distribution (obtained from [60] assuming Te = 1 − 3 eV) for both vibrationally resolved molecular charge exchange cross-sections ‡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This shows that, ‡ A fixed EH2 can introduce uncertainties since higher molecular energies can elevate the effective cross-sections at low ion temperatures significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Nevertheless, this would not alter the conclusions of Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 17 < v>eff T (eV) i 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 5 3 [m ] Janev 1987 / Holliday 1971 Ichihara 2000 10 10 12 10 14 10 Hydrogen Deuterium (T /2) i / Greenland 2001 Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Comparison of the effective molecular charge exchange rate, as function of the ion temperature, using the vibrationally resolved molecular charge exchange rates from Holliday 1971, Janev 1987, Greenland 2001 (red) [28, 29, 30, 31] and from Ichihara 2000 [56] (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The effective rate is calculated using equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The vibrational distribution is obtained from [60], which has been averaged over Te = 1 − 3 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Static molecules (EH2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1 eV) has been assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Purely hydrogenic rates have been used and ion isotope mass rescaling (Ti/2) has been applied to the dotted cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' although the ion isotope mass rescaling is correctly applied to only the ion temperature dependency, the effective cross-section greatly decays at low temperature for ’Janev 1987 / Holliday 1971 / Greenland 2001’ for D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Contrastingly, the effective rates derived using the ’Ichihara 2000’ cross-sections are similar for H and D, in agreement with [19], and are both in reasonable agreement with the ’Janev 1987 / Holliday 1971 / Greenland 2001’ effective rate for H Te = 1 − 3 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Secondly, as explained through equations 1 and 2 in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1, both the ion and temperature dependencies are inadvertently rescaled when ion isotope mass rescaling is applied by Eirene to effective rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This results in inaccuracies not only because it results in an incorrectly applied ion isotope mass rescaling to the electron temperature dependency of the vibrational distribution model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' but also because the ion temperature can be different from the electron temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Resolving this may require modifications to Eirene to support different electron and ion temperature dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Using a vibrationally resolved simulation setup (see section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='4) would also ensure that ion mass rescaling is applied correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Thirdly, as mentioned in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1, it is assumed that the cross-sections (in velocity space) are the same for all isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This is not true, however, as there are chemical differences resulting in different cross-sections for each isotope [56, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The chemical isotope differences have a particularly strong impact on the rates resulting in D−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' SOLPS-ITER does not account for H− by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' In [20] it was argued that such figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 18 interactions can play an important role as they also result in MAR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' that argument was based on applying the correct ion isotope mass re-scaling under the assumption that the cross-sections for creating H− is the same as for D− and T −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, the D− and T − creation cross-sections are strongly reduced compared to the H− ones due to chemical isotopical differences in the various rates, which has been measured experimentally [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Such measurements, however, occur at very low vibrational levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The isotope differences are expected to reduce at higher vibrational levels, which drive most of the molecular ion generation [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' As such, a more detailed analysis in [19] indicates a 30 % reduction in the effective D− creation rate compared to H−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' However, that percentage, as well as the H− generation rate, will be even more sensitive to molecules that are highly vibrationally excited (H2(ν ≥ 5)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This may imply that it is necessary, in some conditions, to include interactions with H− and its isotopes in plasma-edge modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' There are experimental indications from the TCV tokamak on the presence of D− during deep detached conditions, based on the inferred ratio between the ’molecular’ contribution to Dβ and Dα [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Uncertainties in the vibrational distribution of molecular hydrogen Molecular charge exchange is highly sensitive to the vibrational distribution of the molecule at the time of the reaction (fν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The modelling of fν has large uncertainties, which can be broadly divided in two categories: 1) inaccuracies in the rates and reactions used in the vibrational distribution modelling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) inaccuracies introduced by a lack of transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The first category includes inaccuracies in reaction rates used as well as missing reaction processes, including 1) the omission of H− creation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2) re-distribution of vibrationally excited states through electronic excitation [62, 60];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 3) omitting electron- impact collisions that alter the vibrational state of a molecule by more than > ±1 [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Including the latter two in the vibrational modelling can alter the vibrational distribution considerably [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The mean-free-path of vibrationally excited molecules can be sufficiently long for transport to be significant, particularly below the dissociation region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Including such transport requires vibrationally resolved simulations [63, 64, 65, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The vibrational distribution can vary strongly spatially and transport allows including such effects and their propagation throughout the rest of the divertor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Plasma-wall interactions [39] can alter the initial vibrational distribution of molecules coming off the wall, depending on the precise interaction with the wall and the wall material [66, 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Although vibrationally resolved simulations have been performed in the past for Asdex-Upgrade [63, 64] and for TCV [66, 39], they may not have included all the relevant processes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' inaccuracies in the rates & reactions of vibrationally excited molecules [60]) and would have employed the default Eirene cross-sections that are likely strongly underestimated at high vibrational levels (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Therefore, molecular charge exchange in detached conditions was, likely, still significantly underestimated in these Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 19 simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Further investigation of the vibrational distribution of the molecules, through both modelling and experiment to modelling comparisons, is required in conditions where plasma chemistry with molecular ions may be important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Conclusions Recent experimental results on TCV, MAST-Upgrade and JET have indicated that plasma-molecular chemistry, resulting in molecular ions (particularly D+ 2 ) that react with the plasma, result in excited atoms that can contribute to the hydrogen Balmer line emission significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Such interactions result in Molecular Activated Recombination (MAR), which can impact divertor particle balance significantly during detachment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Initial comparisons between SOLPS-ITER simulations and experiments on TCV had shown that such interactions do not occur significantly in the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' It was hypothesised that this is related to the isotope mass rescaling employed by Eirene to the effective hydrogenic molecular charge exchange rate, resulting in ∼ 100 times lower D+ 2 densities in detachment-relevant regimes compared to H+ 2 , whereas more detailed investigations in literature indicate differences between hydrogen and deuterium molecular charge exchange rates of a few percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This has motivated our work to compare SOLPS-ITER simulation results with the default rate setup and with a modified rate setup in which ion isotope mass rescaling has been disabled for molecular charge exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' We observe that disabling isotope mass rescaling for molecular charge exchange has a strong impact on the solution obtained after the detachment onset and provides a closer match to the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' The neutral atom content in the lower divertor is greatly enhanced in the modified rate setup by up to 100 %, due to Molecular Activated Dissociation (MAD) and MAR, which has significant associated hydrogenic (plasma) power losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Acknowledgements Discussions with Detlev Reiter are kindly acknowledged and were very helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This work has received support from EPSRC Grants EP/T012250/1 and EP/N023846/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' This work has been supported in part by the Swiss National Science Foundation and has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' as well as No 633053 (2014-2018 & 2019-2020)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Neither the European Union nor the European Commission can be held responsible for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' References [1] Krasheninnikov S, Pigarov A Y, Knoll D, LaBombard B, Lipschultz B, Sigmar D, Soboleva T, Terry J and Wising F 1997 Physics of Plasmas 4 1638–1646 ISSN 1070-664X Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 20 [2] Verhaegh K, Lipschultz B, Duval B P, Harrison R, Reimerdes H, Theiler C, Labit B, Maurizio R, Marini C, Nespoli F, Sheikh U, Tsui C K, Vianello N, Vijvers W A J and Team T T E M 2017 Nuclear Materials and Energy 12 1112–1117 ISSN 2352-1791 [3] Verhaegh K, Lipschultz B, Duval B, F´evrier O, Fil A, Theiler C, Wensing M, Bowman C, Gahle D, Harrison J et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2019 Nuclear Fusion 59 [4] Verhaegh K, Lipschultz B, Duval B, Fil A, Wensing M, Bowman C and Gahle D 2019 Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fusion 61 [5] Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Bowman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fantz U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fil A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Myatra O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' W¨underlich D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Federici F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Gahle D S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M and and 2021 Plasma Physics and Controlled Fusion 63 035018 [6] Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Bowman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fil A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Gahle D S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Myatra O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C and Wensing M 2021 Nuclear Materials and Energy 26 100922 [7] Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fil A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Bowman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Gahle D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Kukushkin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Pshenov A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Federici F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Myatra O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Smolders A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' the TCV Team and the EUROfusion MST1 Team 2021 Nuclear Fusion 61 106014 URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088/1741-4326/ac1dc5 [8] Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Vijvers W A J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Andrebe Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Classen I G J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Galperti C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Linehan B L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Ravensbergen T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K and de Baar M R 2019 Review of Scientific Instruments 90 123514 [9] Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Linehan B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Classen I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wijkamp T and de Baar M 2021 Nuclear Materials and Energy 26 100858 ISSN 2352-1791 [10] Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Linehan B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Bowman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' van Berkel M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Classen I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Koenders J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Ravensbergen T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' de Baar M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' the EUROfusion MST1 Team and the TCV Team 2022 Nuclear Fusion 62 096012 URL https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088/1741-4326/ac7813 [11] Verhaegh K, Lipschultz B, Harrison J, Osborne N, Williams A, Ryan P, Clark J, Federici F, Kool B, Wijkamp T et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2022 arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='02118 [12] Lomanowski B, Groth M, Coffey I H, Karhunen J, Maggi C F, Meigs A, Menmuir S and O’Mullane M 2020 Plasma Physics and Controlled Fusion 62 [13] Karhunen J, Holm A, Lomanowski B, Solokha V, Aleiferis S, Carvalho P, Groth M, Lawson K, Meigs A, Shaw A et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2022 Plasma Physics and Controlled Fusion 64 075001 [14] Karhunen J, Holm A, Aleiferis S, Carvalho P, Groth M, Lawson K, Lomanowski B, Meigs A, Shaw A and Solokha V 2022 Nuclear Materials and Energy 101314 ISSN 2352-1791 URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='com/science/article/pii/S2352179122001958 [15] Fil A M D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Dudson B D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K H A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fevrier O and Wensing M 2017 Contributions to plasma physics 58 ISSN 0863-1042 [16] Fil A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Moulton D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Dudson B D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Myatra O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M and and 2020 Plasma Physics and Controlled Fusion 62 035008 [17] Wensing M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fevrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fil A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Galassi D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Havlickova E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Perek A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K and Wischmeier M 2019 Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fusion 61 [18] Wensing M, Loizu J, Reimerdes H, Duval B, Wischmeier M and the TCV team 2020 Nuclear Fusion 60 054005 [19] Janev R K and Reiter D 2018 Isotope effects in molecule assisted recombination and dissociation in divertor plasmas J¨ulich report - juel 4411 Forschungszentrum J¨ulich GmbH J¨ulich englisch URL https://juser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='fz-juelich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='de/record/850290/files/J%C3%BCl_4411_ Reiter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='pdf?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='version=1 [20] Kukushkin A S, Krasheninnikov S I, Pshenov A A and Reiter D 2017 Nuclear Materials and Energy 12 984–988 ISSN 2352-1791 [21] Coda S, Agostini M, Albanese R, Alberti S, Alessi E, Allan S, Allcock J, Ambrosino R, Anand H, Andr`ebe Y, Arnichand H, Auriemma F, Ayllon-Guerola J, Bagnato F, Ball J, Baquero-Ruiz M, Beletskii A, Bernert M, Bin W, Blanchard P et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2019 Nuclear Fusion 59 112023 Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 21 [22] Reimerdes H and et al 2022 Nuclear Fusion 62 042018 URL https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088/ 1741-4326/ac369b [23] Reimerdes H, Duval B, Elaian H, Fasoli A, F´evrier O, Theiler C, Bagnato F, Baquero-Ruiz M, Blanchard P, Brida D et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2021 Nuclear Fusion 61 024002 [24] Raj H, Theiler C, Thornton A, F´evrier O, Gorno S, Bagnato F, Blanchard P, Colandrea C, de Oliveira H, Duval B P et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2022 Nuclear Fusion [25] Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Vijvers W A J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Elmore S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Labit B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' van Limpt S H M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lisgo S W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Tsui C K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Sheikh U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K H A and Wischmeier M 2017 Nuclear Materials and Energy 12 1071–1076 ISSN 23521791 [26] Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Labit B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lunt T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Tsui C K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Vijvers W A J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Boedo J A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Calabro G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Crisanti F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Innocente P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Maurizio R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Pericoli V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Sheikh U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Spolare M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Vianello N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' the T C V t and the E M S T t 2017 Nuclear Fusion 57 126007 ISSN 0029-5515 URL http://stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/0029-5515/57/i=12/a=126007 [27] Kotov V and Reiter D 2009 Plasma physics and controlled fusion 51 115002 ISSN 0741-3335 [28] Reiter D 2000 The data file AMJUEL: Additional atomic and molecular data for EIRENE Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Forschungszentrum J¨ulich GmbH URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='eirene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='de/html/amjuel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='html [29] Janev R K, Langer W D, Douglass Jr E et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 1987 Elementary processes in hydrogen-helium plasmas: cross sections and reaction rate coefficients (Springer Science & Business Media) [30] Holliday M G, Muckerman J T and Friedman L 1971 The Journal of Chemical Physics 54 1058–1072 [31] Greenland P T 2001 The crmol manual: collisional-radiative models for molecular hydrogen in plasmas J¨ulich report juel-3858 Forschungszentrum J¨ulich GmbH URL https://juser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' fz-juelich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='de/record/24992/files/J%C3%BCl_3858_Greenland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='pdf?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='version=1 [32] Sawada K and Fujimoto T 1995 Journal of applied physics 78 2913–2924 [33] Kotov V and Reiter D 2012 Plasma Physics and Controlled Fusion 54 082003 ISSN 0741-3335 URL http://stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/0741-3335/54/i=8/a=082003 [34] Stangeby P C 2018 Plasma Physics and Controlled Fusion 60 044022 ISSN 0741-3335 [35] Reiter D et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2008 The eirene code user manual Report Forschungszentrum J¨ulich GmbH URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='eirene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='de/manuals/eirene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='pdf [36] F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Oliveira H D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Labit B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Fedorczak N and Baillod A 2018 Review of Scientific Instruments 89 053502 [37] De Oliveira H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Marmillod P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Chavan R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Labit B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lavanchy P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Marl´etaz B and Pitts R A 2019 Review of Scientific Instruments 90 083502 [38] Smolders A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Wensing M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Carli S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Oliveira H D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Dekeyser W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Duval B P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' F´evrier O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Gahle D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Martinelli L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reimerdes H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Theiler C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K and the TCV team 2020 Plasma Physics and Controlled Fusion 62 125006 [39] Wischmeier M 2005 Simulating divertor detachment in the TCV and JET tokamaks Thesis EPFL [40] Verhaegh K 2018 Spectroscopic Investigations of detachment on TCV Thesis University of York URL http://etheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='whiterose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='uk/22523/ [41] Militello F, Aho-Mantila L, Ambrosino R, Body T, Bufferand H, Calabro G, Ciraolo G, Coster D, Di Gironimo G, Fanelli P et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2021 Nuclear Materials and Energy 26 100908 ISSN 2352-1791 [42] Kuang A Q, Ballinger S, Brunner D, Canik J, Creely A J, Gray T, Greenwald M, Hughes J W, Irby J, LaBombard B and et al 2020 Journal of Plasma Physics 86 865860505 [43] Wigram M, LaBombard B, Umansky M, Kuang A, Golfinopoulos T, Terry J, Brunner D, Rensink M, Ridgers C and Whyte D 2019 Nuclear Fusion 59 106052 URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088/ 1741-4326/ab394f [44] Bernert M, Janky F, Sieglin B, Kallenbach A, Lipschultz B, Reimold F, Wischmeier M, Cavedon M, David P, Dunne M et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2020 Nuclear Fusion 61 024001 [45] Pan O, Bernert M, Lunt T, Cavedon M, Kurzan B, Wiesen S, Wischmeier M and Stroth U 2022 Nuclear Fusion [46] Stroth U, Bernert M, Brida D, Cavedon M, Dux R, Huett E, Lunt T, Pan O, Wischmeier M et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2022 Nuclear Fusion 62 076008 Impact of mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' CX in SOLPS-ITER 22 [47] Myatra O 2021 Numerical modelling of detached plasmas in the MAST Upgrade super-X divertor Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' thesis University of York URL https://etheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='whiterose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='uk/29934/1/OMyatra_ thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='pdf [48] Hollmann E M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Brezinsek S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Brooks N H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Groth M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' McLean A G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Pigarov A Y and Rudakov D L 2006 Plasma Physics and Controlled Fusion 48 1165 ISSN 0741-3335 [49] Bowman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Harrison J R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lipschultz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Orchard S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Gibson K J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Carr M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Verhaegh K and Myatra O 2020 Plasma Physics and Controlled Fusion 62 045014 [50] Kukushkin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Neverov V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Alekseev A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lisgo S and Kukushkin A 2016 Fusion Science and Technology 69 628–642 [51] Pshenov A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Kukushkin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Marenkov E and Krasheninnikov S 2019 Nuclear Fusion 59 106025 URL https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088/1741-4326/ab3144 [52] Pshenov A, Kukushkin A, Gorbunov A and Marenkov E 2023 Nuclear Materials and Energy 34 101342 ISSN 2352-1791 URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='com/science/article/pii/ S235217912200223X [53] Ravensbergen T, van Berkel M, Perek A, Galperti C, Duval B, F´evrier O, van Kampen R, Felici F, Lammers J, Theiler C et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2021 Nature communications 12 1–9 [54] Ravensbergen T, van Berkel M, Silburn S A, Harrison J R, Perek A, Verhaegh K, Vijvers W A J, Theiler C, Kirk A and de Baar M 2020 Nuclear Fusion URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1088% 2F1741-4326%2Fab8183 [55] Biel W, Albanese R, Ambrosino R, Ariola M, Berkel M, Bolshakova I, Brunner K, Cavazzana R, Cecconello M, Conroy S et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 2019 Fusion engineering and design 146 465–472 [56] Ichihara A, Iwamoto O and Janev R K 2000 Journal of Physics B: Atomic, Molecular and Optical Physics 33 4747–4758 [57] Laporta V, Agnello R, Fubiani G, Furno I, Hill C, Reiter D and Taccogna F 2021 Plasma Physics and Controlled Fusion [58] Krsti´c P S and Janev R K 2003 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' A 67(2) 022708 URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='022708 [59] Roncero O, Andrianarijaona V, Aguado A and Sanz-Sanz C 2022 Molecular Physics 120 e1948125 (Preprint https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1080/00268976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1948125) URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 1080/00268976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1948125 [60] Holm A, W¨underlich D, Groth M and B¨orner P 2022 Contributions to Plasma Physics n/a e202100189 [61] Krishnakumar E, Denifl S, ˇCadeˇz I, Markelj S and Mason N J 2011 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 106(24) 243201 [62] Chandra R, Holm A and Groth M 2023 Nuclear Materials and Energy 34 101360 ISSN 2352-1791 URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='com/science/article/pii/S2352179122002411 [63] Fantz U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reiter D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Heger B and Coster D 2001 Journal of Nuclear Materials 290 367–373 ISSN 0022-3115 [64] Fantz U 2002 Contributions to Plasma Physics 42 675–684 ISSN 0863-1042 [65] Fantz U and W¨underlich D 2006 New Journal of Physics 8 301–301 [66] Wischmeier M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Pitts R A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Alfier A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Andrebe Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Behn R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Coster D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Horacek J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Nielsen P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Pasqualotto R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Reiter D and Zabolotsky A 2004 Contributions to Plasma Physics 44 268–273 ISSN 0863-1042 [67] Eenshuistra P J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Bonnie J H M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Los J and Hopman H J 1988 Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content=' 60(4) 341–344 URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} +page_content='341' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtFIT4oBgHgl3EQfjyu7/content/2301.11298v1.pdf'} diff --git a/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/2301.04089v1.pdf.txt b/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/2301.04089v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..c0bf0beac8effb02c0ee85c6f78c632930097152 --- /dev/null +++ b/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/2301.04089v1.pdf.txt @@ -0,0 +1,1520 @@ +An ultra-stable three-dimensional photophoretic trap in air +facilitated by a single multimode fiber +Souvik Sil,1 Anita Pahi,1 Aman Anil Punse,1 and Ayan Banerjee1, ∗ +1Department of Physical Sciences, IISER-Kolkata, Mohanpur 741246, India +(Dated: January 11, 2023) +Abstract +Photophoretic forces - which are of thermal origin - have defined an alternative route of optical +trapping of absorbing microparticles in air. Here, we show that a single multi-mode fiber facilitates +significantly more robust optical traps compared to a pure Gaussian beam emanating from a single +mode fiber for the trapping and manipulation of absorbing particles using photophoretic forces. +We carefully study the dependency of trapping on speckle patterns generated from different modes +from a multimode fiber, and experimentally observe that maximum trapping force can be obtained +when the mean speckle size is comparable to the diameter of a trapped particle. We explain this +observation by numerical simulations carried out to calculate the photophoretic force, and also +determine stable trapping conditions from force balance equations. Interestingly, we also observe +large oscillations of the trapped particle along the z-direction for multimode beams, which may be +demonstrative of an effective restoring force for photophoretic trapping even in the axial direction. +Our work may presage a new route for exciting applications on optical trapping and spectroscopy +with photophoretic forces due to the inherent ease-of-use, portability, and flexibility of single muti- +mode fiber based optical traps. +∗ ayan@iiserkol.ac.in +1 +arXiv:2301.04089v1 [physics.optics] 10 Jan 2023 + +I. +INTRODUCTION +Photophoretic forces - that arise due to the inhomogeneous heating of an absorbing +particle in a gaseous medium by a intense light (such as a laser beam) - have introduced a new +paradigm in optical trapping and manipulation of absorbing particles as demonstrated by a +series of experiments[1–3]. The photophoretic force[4] - which is also responsible for giant +planet formation[5] - can be categorized into two types of forces, F∆T and F∆α, where the +former arises from an inhomogeneous temperature distribution across an absorbing particle’s +surface due to laser heating of that particle, and is directed from the hotter side to the colder +side of the particle, while the later results from a difference in the accommodation coefficient +of the particle, and measures the efficiency of heat exchange between the heated particle and +ambient molecules of the medium[4]. Though it is clear that the magnitude of photophoretic +forces depends on the intensity of light, it needs to be pondered whether the magnitude only +depends on intensity or the gradient of intensity - especially if one uses structured light. In +our earlier works[6–8], we showed that particles are confined in at least one dimension due +to the photophoretic forces balancing the gravitational force, while in the other dimension, +there exists a restoring force possibly generated due to the complex motion of the particle +in the light field. Thus, due to the force balance, particles of a certain mass can be trapped +with the appropriate intensity of the trapping light[9], with higher and lower intensities +leading to particles escaping the trap[7, 9]. But in the presence of a structured intensity +profile, i.e., adjacent patterns of light and dark regions - there could be opposite forces on a +particle as it traverses the intensity profile. This would result in a complex restoring force +on the particle even in the direction of gravity, and not merely a force balance - leading to +a more efficient trap and a definite dependence of the trapping efficiency on the intensity +profile of the trapping beam. The challenge, however, is to create such light beams having +a complex intensity profile. +Several experimental configurations have been developed to achieve such intensity profiles. +These include counter-propagating vortex beams[2], doughnut-like vortex beam shapes cre- +ated by two hollow beams overlapping in the trapping volume[3],optical lattices[10], tapered +rings[11], dark-hollow[12] and optical hollow-cone beams[13, 14], etc. Moreover, to increase +flexibility, holographic beam shaping has been utilized to form optical bottle beams, either +by a Moire´technique employing spatial light modulators[15], or by creating discrete trapping +2 + +sites[16], that lead to a vanishing intensity region surrounded by light in all three dimen- +sions. Further, such structured light fields can be created using a speckle pattern[17], that +can be generated in various ways, such as the scattering of laser light from a rough surface or +transverse mode-mixing in a multi-mode fiber. For example, Shvedov et al. demonstrated +that a volume speckle field generated by a coherent laser beam and diffuser can be used +to confine a massive numbers of carbon particles in air using photophoretic forces[18, 19]. +However, the optical configurations to achieve such structured profiles are quite complex +and have very small alignment tolerance. Recently, speckle optical tweezers (ST) have been +developed where a speckle pattern, generated using a multi-mode fiber, has been used for +performing collective optical manipulation of high-refractive-index particles[20], and even +controlled manipulation of high and low refractive index micro-particles and nano-particle +loaded vesicles[21]. Besides, opto-thermoelectric speckle tweezers have been developed very +recently where an optical speckle field was fed into a thermal speckle field through in- +teraction with plasmonic substrates, thus converting the high-intensity speckle grains into +corresponding thermal speckle grains[22]. +The speckle optical tweezers described above have predominantly been employed in liquid +media and demonstrate trapping in two dimensions. In this paper, however, we report for +the first time the use of a multi-mode fiber to create a photophoretic trap in air for trapping +and manipulating mesoscopic absorbing particles in all three dimensions. It is important to +note that speckle patterns generated from a multi-mode fiber have advantages of uniform +speckle distribution, easy alignment, high optical transmission efficiency, and high flexibility. +Besides, optical fiber traps provide substantial benefits over conventional microscope-based +optical tweezers and are more advantageous than free-space photophoretic traps - the main +advantages being large working distance and ease of alignment, which finally results in +significantly increased convenience in trapping. In addition, we observe that a multi-mode +beam profile exerts a radial trapping force that is about eight times stronger than that +by a single-mode (Gaussian) beam profile. We also attain large manipulation velocities of +around 5 mm/s, both axially and radially, for the trapped particles using the multi-mode +beam profile. Note that this velocity is presently limited by our experimental capabilities, +and can possibly reach even higher values. We also determine the dependence of the trapping +force on the nature of the speckle pattern, and show that the maximum trapping force is +exerted when the average speckle size is similar to that of the particles. We perform an +3 + +analysis using the multiphysics tool COMSOL to explain our experimental observations. +Further, we also attempt to explain the origin of the large trapping force exerted by the +speckle pattern compared to that by a Gaussian beam profile from a simple model based +on a balance of all the forces that a trapped particle experiences. Our model predicts axial +trajectories of the trapped particles with the different beam profiles which we compare with +those measured in our experiments, and achieve reasonable agreement. +II. +MATERIALS AND METHODS +Earlier, we demonstrated through a series of experiments that an absorbing particle could +be trapped employing photophoretic forces, generated by a fundamental Gaussian beam in +free space [6, 8], or through a single-mode fiber[9]. In these experiments, it was clear that +in our experimental configuration, the particles are confined in the axial direction due to +the photophoretic ∆T force, while in the radial direction, a restoring force appears to be +generated by the helical motion of the particle caused by the transverse photophoretic body +force (F∆α), which applies a torque on particles due to its interaction with gravity[8, 23]. As +a result of this, the particle trajectories are found to be radially shifted off-axis with respect +to the trapping beam center[6], with the trap stiffness being linearly proportional to the +laser power or intensity[6, 8]. Thus, it is apparent that any beam profile which has a large +transverse extent resulting in a high off-axis intensity, would increase the trapping efficiency. +This is indeed the case - as we showed experimentally - where the trapping efficiency due to +a beam profile that was the superposition of a fundamental Gaussian and the first-excited +state (Hermite-Gaussian mode) generated by a quasi-single mode optical fiber, was higher +by around 80% compared to just the fundamental Gaussian mode[7]. Extrapolating from +this observation, we considered coupling the trapping laser using a multi-mode fiber for our +experiments. This was due to the fact that a multi-mode fiber has a higher mode volume +than a single-mode one, giving even higher off-axis intensity compared to that we achieved +in our previous experiments, and our intuition was that this would increase the trapping +efficiency even further. Thus, in the first set of results we report, we quantify the trapping +efficiency for input laser mode profiles generated by a multi-mode, and a single-mode fiber. +We determine the radial trapping force by the well-known viscous drag method[6], and also +measure the threshold laser power for trapping. +4 + +In the experiments, we use a graded-index multi-mode optical fiber (Thorlabs GIF625) +with core diameter 62 µm, around ten times higher mode volume compared to a single- +mode fiber with a core diameter of 6 µm. The total number of guided modes (N) for a +typical graded-index fiber can be defined as N = +q +2(q+2)V 2[24], where q is the exponent of +the power-law profile which has a value of 2 for typical graded-index multi-mode fibers, and +V [= K0aNA] is the waveguide parameter - signifying, the number of linearly polarized (LP) +modes propagating through the fiber for a given wavelength, where K0 (= 2π +λ ) is free space +propagation constant, a is the core radius, and NA is the numerical aperture of the fiber[24]. +By putting the value of K0 where λ = 671nm, a(= 31.5µm) and NA(= 0.275), the value +of V becomes 80 - signifying that the multi-mode fiber can support around 1200 LP modes. +Thus, due to the superposition of all those LP modes, a completely random distribution of +electric fields, which are typical termed as a speckle pattern - appears at the output of the +fiber, which is shown in Fig. 11(a). +FIG. 1. (a) Typical speckle pattern of Multimode fiber; (b) & (c) 1-D plot profile of Gaussian and +Multimode beam profiles, respectively +The line plot of Gaussian and multi-mode beam profile for the same beam size are shown +in Fig. 11 (b) and (c) respectively, in which the raw data (black line) of Fig. 11 b) is +fitted with a standard Gaussian function (gray line). But for the multi-mode case, we can +approximate the 1-D profile with a top hat function as shown in the blue line of Fig. 11 c) - +demonstrating the increased transverse extent, as well as higher off-axis intensity compared +to the Gaussian beam profile. Our expectation was that this would increase the trapping +efficiency for the multi-mode beam profile. +We now describe the experiment towards measuring trapping efficiency for both beam +profiles, keeping all other trapping parameters (i.e., laser power, beam size, etc.) invariant. +A schematic of the experimental setup is shown in Fig. 2 where we use a 671 nm laser source +5 + +RawData +Intensity (Arb. Unit) +100 +b) +Intensity (Arb. Unit) +140- +c) +RawData +Fitted with Gaussian +0 +120 +100 +80 +80 +70 +60 +40- +20- +50 +0 +3400 +3500 +3600 +3700 +3800 +3900 +500 +1000 +1500 +2000 +2500 +x (pixel) +x (pixel)of maximum power 300 mW as a trapping beam for trapping printer toner particles that have +very high absorptivity at our operating wavelength. Then, we couple the laser beam into +a multi-mode fiber using the mirrors M1, M2, and the fiber coupler (FC) [see Fig. 2] after +passing through an optical isolator (for preventing feedback from the fiber which destabilizes +laser output) and a combination of a half-wave plate (HWP) and a polarizing beamsplitter +(BS) [see Fig. 2] for changing the laser power in a controlled manner. The output beam from +the fiber is then collimated and focused into the sample chamber via a home-built mount +which contains an aspheric lens (AL) for collimation and a 25 mm plano-convex lens (CL1) +for focusing [see bottom right inset of Fig. 2]. This mount is then attached to a motorized +translation stage TS, so that when the stage is translated, so is the trapping beam within +the sample chamber. This is what employ for the drag force measurement. +FIG. 2. Schematic of the experiment. A: aperture; AL: Aspheric lens; C: Camera; CCD: Charge +coupled device CL: Convex lens; F: Filter; FC: Fiber Coupler; HWP: Half wave plate; I: isolator; +M: Mirror; MMF: Multimode fiber; MO: 10x objective; PBS: Polarizing beam splitter; SC: Sample +chamber; TL: Trapping Laser; TP: Trapped particle; WLS: White light source +The trapped particles are imaged along in the x and y directions for determining the +size and mass of the particle. For imaging, we use a white light source (WLS) which is +collimated by CL2 and passes through the sample chamber and trapped particle with the +6 + +F +CL3 +C1 +M5 +CCD2 +M1 +M01 +TL +X +40 um +HWP +M02 +C2 +M3 +PBS +F +CCD1 +SC +SCH +A +WLS +CL2 +CL1 +AL +M4 +M2 +FC +MMFhelp of mirrors M1 and M2. After that, the trapped particles are imaged on camera CCD1 +in the x-direction using a 10x collection objective MO2, and a notch-filter F to block the +trapping beam. In the y-direction, the particles are imaged on a Sony fast video camera C1 +(1000 FPS) with the help of a 3-f imaging system, which is composed of a 10x objective lens +(MO1), the lens CL3, and the lens placed inside the camera C1, where MO1 is used for the +collection and another filter F is used to cut off the light at 671 nm. This 3-f imaging system +provides a high contrast zoomed-in image of the trapped particles - a representative image +of which is shown in the top right inset of Fig. 2. In addition, another video camera, C2, +is used to determine the axial position of a trapped particle in the z-direction by taking an +image of the trapped particle along with a measuring scale affixed to the sample chamber, +and imaging the motion of the trapped particle in order to measure the radial velocity. A +representative zoomed-in image of the sample chamber with two particles trapped taken +using C2 is shown in the top-left inset of Fig. 2. +III. +RESULTS AND DISCUSSIONS +A. +Comparison of Trapping force for Single and Multi-mode fiber +We keep the laser power at 70 mW throughout the experiments and trap 20 particles using +both the multi-mode and single-mode fiber, and make a comparison of the trap parameters +for radial trapping between them. The results are shown in Table I, with the number in +parenthesis-denoting 1 σ errors in the mean. First, we determine the average particle size (a) +using the methodology described in Ref[8], where we observe that the average particle size +for both beam profiles is almost the same [see table I]. Then we determine radial trapping +force by the viscous drag method, where we accelerate the stage TS with an acceleration of +0.1 mm/s2 and thereby reach a maximum velocity of 5 mm/s along radially - so that the +trapped particle also translates radially with the same acceleration. Hence, the drag force +experienced by the particle increases till when it overcomes the trapping force, at which time +the particle leaves the trap. We record the particle movement using our camera CCD1 while +moving the stage, and perform a frame-by-frame analysis to measure the distance traversed +by the particle before it leaves the trap. We use the ImageJ software and correspondingly +measure the velocity of the particle (ve) at the point of escape from Newton’s equations +7 + +of motion. Thus, the escape velocity (ve) achieved by the particle in the single-mode fiber +trap is measured to be 0.33 (6) mm/s, while that in the multi-mode fiber trap is 2.53 (16) +mm/s [see Table I]. We are then able to calculate the radial trapping force Ftrap by using +the equation F = 6πηave for both trap systems, assuming the particle to be spherical, +where η is the viscosity of the air, and a is the trapped particle radius. The trapping force +measurements come out to be 1.01 (17) mm/s and 7.87 (51) mm/s for single-mode and +multi-mode fiber trap, respectively [see Table I]. Thus, from the results, it is clear that the +trapping force in the case of a multi-mode fiber trap is around eight times higher compared +to that by a single-mode fiber trap. +TABLE I. Comparison of trap parameters for Multimode and Gaussian beams +Trap parameters +Multi-mode (1) Single-mode (2) Ratio (1)/(2) +Average particle size (µm) +8.96 (0.30) +8.15 (0.33) +1.10 (0.08) +Average ve (mm/s) +2.53 (0.16) +0.33 (0.06) +7.67 (1.95) +Average Ftrap (pN) +7.87 (0.51) +1.01 (0.17) +7.79 (1.87) +Average threshold power (mW) +10(2) +47(2) +0.2 (0.05) +Next, we measure the threshold power for trapping where we trap a particle at a moderate +laser power and then reduce the laser power. While lowering, the trapped particle moves +closer to the focus, where the intensity is high enough to provide enough photophoretic force +to balance gravity. But, if we keep lowering the laser power, a point comes where the laser +intensity is no longer able to generate a photophoretic force that can balance the particle’s +weight - thus, the laser power at which the particle leaves the trap is called the threshold +power. The result is shown in Table I, where we observe that the threshold power is around +47 (2) mW for single-mode trap and 10 (2) mW for Multi-mode trap. This signifies that +the multi-mode beam profile can be trap particles at around 4.7 times % less power than +the Gaussian beam, which indicates the multi-mode trap is about 4.7 times more stable +than the single-mode trap. Hence, it is clear from our measurements that a multi-mode +trapping beam is considerably more effective in trapping absorbing particles compared to a +fundamental Gaussian beam. +8 + +B. +Trapping force for different modes of Multi-mode beam profile +However, while performing the experiment for measuring the trapping force using the +drag force method, we observe that the escape velocity of the trapped particle changes when +we modify the speckle pattern, which signifies that not only the transverse extent and off- +axis intensity would affect the trap efficiency, but also the speckle presents in the pattern. +Thus, we systematically generate three different speckle patterns at the output of the multi- +mode fiber by changing the coupling angle of the fiber coupler - so that different modes are +excited inside the fiber, and their interference creates different types of final mode or speckle +pattern at the output of the fiber. Three modes, which are hereafter referred to as Mode 1, +Mode 2, and Mode 3, are shown in Fig. 3 (a), (b) and (c), respectively. +FIG. 3. Speckle patterns created from Multimode fiber; a) Mode 1, b) Mode 2 c) Mode 3 +In the experiment, we trap around 15 particles for each mode, and take the images of +each by the cameras CCD1 (x-axis), C1 (y-axis), and C2 (axial position) [see Fig. 2]. We +introduce another camera, CCD2, for monitoring speckle patterns for further analysis. Here, +we also use the viscous drag method (discussed earlier) for radial trapping force measurement +by measuring the radial escape velocity of a particle trapped using each mode. The average +escape velocity (ve) and the corresponding average radial trapping force (Ftrap) are shown +in Table II for different modes, with the number in parenthesis-denoting 1 σ errors in the +mean as before. +Note that, while doing the experiment we keep the laser power beam +size invariant for each mode, and for determining the Ftrap, we consider an experimentally +measured average particle radius of 8.01(10) µm and viscosity of air η = 1.96×10−5 kg/(ms) +From Table II, it is clear that the Mode 1 pattern provides 41% and 27% higher trapping +force compared to Mode 2 and Mode 3, respectively. +Also, Mode 3 provides gives 20% +higher trapping force than Mode 2. Thus, we can conclude that the speckle distribution and +9 + +b) +a +c)TABLE II. Radial trapping force for all three mode +Mode name Average vescape (mm/s) Average Ftrap (pN) +Mode 1 +2.64 (14) +7.81 (45) +Mode 2 +1.54 (12) +4.57 (34) +Mode 3 +1.93 (12) +5.70 (35) +size definitely affect the efficiency of photophoretic trapping. To obtain a more quantitative +understanding of this observation, we further measure the average speckle size for all three +modes and determine the average intensity per speckle by counting the number of bright +spots present in each mode pattern. We describe this in the next section. +C. +Numerical Simulation and Analysis +1. +Speckle Size Measurement +We know that speckle is a random distribution of light field - consisting of a multitude of +dark and bright spots resulting from destructive and constructive interference[17]. There are +different speckle parameters such as mean speckle size, contrast, intensity and polarization +etc[25]. But here, we only consider the mean speckle size, defined as the average size of bright +or dark spots present in the pattern[17]. Thus, in order to find out the mean speckle size, we +need to measure the Wiener spectrum of the pattern, which is the average intensities of all +possible spatial frequency components of the pattern[17]. This can be done by calculating +the normalized autocovariance function of the intensity speckle pattern obtained in the +observation or image plane (x,y). Further, this function can be considered as the normalized +autocorrelation function of the intensity, which has a zero base, and its width provides a good +measurement of the average width of a speckle[25, 26]. The methodology for finding out the +speckle size is discussed in the Appendix Section 1. Thus, we determine the normalized auto- +correlation intensity distribution (CI(i, j)) of any given pattern image using the algorithm +described by Eq. 5 in the Appendix. +However, for representation, the speckle pattern of Mode 1, and the corresponding nor- +malized auto-correlation function CI(i, j) of that pattern are shown in Fig 4 (a) and (b), +respectively. Now, the mean speckle size is defined as a value where the horizontal (X) or +10 + +FIG. 4. (a) Speckle pattern image of mode 1; (b) Normalized auto-correlation intensity distribution +CI(i, j) profile of the image (a); c) & (d) Horizontal profile CI(i, 0) and Vertical profile CI(0, j) of +normalized auto-correlation function CI(i, j) (b), respectively +vertical (Y) profile of normalized auto-correlation of intensity function CI(i, j) decays to 1/e +[26]. So, CI(i, 0) and CI(0, j) give the horizontal (X) and vertical (Y) profile of CI(i, j), +which are shown in Fig. 4 (c) and (d), respectively. Then, we obtain the widths dx and +dy, where CI(0, dy) = CI(0, dy) = 1/e, for the horizontal (x) and vertical (y) directions, +respectively [see Fig. 4 (c) and (d)]. +We observe experimentally that on increasing the size of the beam, the speckle size also +increases correspondingly. +Hence, if we consider the ratio between the speckle size and +beam waist size at a particular plane of the respective pattern, the ratio should be invariant +irrespective of the beam size, which implies that we can exactly determine the speckle size +at any transverse plane along the laser propagation direction, if we know the beam size in +that plane. We now describe the methodology of determining this ratio. Fig. 4 (a) depicts +the speckle image of Mode 1 of dimension (1540 × 1864) (pixel)2 - implying the total length +along the horizontal direction (Lx) and vertical direction (Ly), are 1864 and 1540 pixel, +respectively [see Fig. 4 (c) and (d)]. Next, we find the width dx and dy both horizontally +and vertically to be 114 and 126 pixel, respectively, so the ratio along both the horizontal +and vertical direction becomes Rx = dx/Lx and Ry = dy/Ly, and finally take the average +(R) between Rx and Ry. This algorithm is applied for the other two modes (Mode 2 and +Mode 3). The speckle size along both x− and y−axes, and the average speckle size for all +three modes are shown in Table III. +Thus, using these ratios, we can find out the exact speckle size at the trapping region +of the respective modes from a knowledge of the beam size at that region. However, the +particles are trapped at a different position axially for each mode, so first we find out the +11 + +b) +c) +d) +200 +a +200 +0.34 +(A.U) +(A.U) + axis (pixel) +0.8 +0.8 +(pixel) +400 +400 +0.335 +600 +600 +0.6 +Amplitude +0.6 +0.33 +Amplitude +dx +dy +axis +800 +800 +0.4 +0.4 +0.325 +1000 +1000 + 1200 +1200 +0.32 +0.2 +0.2 +1400 +1400 +0.315 +05 +05 +500 +1000 +1500 +500 +1000 +1500 +0 +500 +1000 +1500 +2000 +0 +500 +1000 +1500 +X axis (pixel) +X axis (pixel) +Distance (pixel) +Distance (pixel)TABLE III. Speckle size ratio for all three modes +Mode name Horizontal (X) speckle Vertical (Y) speckle Average speckle +size ratio (Rx) +size ratio (Ry) +size ratio (R) +Mode 1 +0.061 +0.082 +0.071 +Mode 2 +0.226 +0.184 +0.205 +Mode 3 +0.026 +0.029 +0.027 +exact z position of the trapped particles by analyzing the camera images of C2 [see Fig. 2]. +The mean z positions of the trapped particles for each mode are shown in the first column +of Table IV. Next, we find out the beam sizes at those z positions by measuring the beam +radii using the well-known knife-edge technique[27], which are shown in the second column +of Table IV. Then, we find out the speckle size at the respective z positions by multiplying +the mean beam size (Table IV second column) with the respective average speckle size ratio +(R) [Table III] of each mode which are shown in the third column of Table IV. Finally, +we determine the trapped particles’ size and mass from their images, taken using cameras +CCD1 and C1 [see Fig. 2] using the methodology given in Ref. [8], and find out the average +trapped particle diameter for each mode which we display in the last column of Table IV. +This shows that the average diameter of trapped particles is almost the same for each mode. +TABLE IV. Mean speckle size and particle diameter for all three modes +Mode name Mean z position Mean Beam size Mean speckle size Mean particle diameter +(mm) +(µm) +(µm) +(µm) +Mode 1 +2.0 (0.1) +235.97 (10.78) +16.75 (0.77) +16.02 (1.32) +Mode 2 +1.80 (0.16) +218.17 (15.54) +44.72 (3.19) +14.76 (0.86) +Mode 3 +1.90 (0.09) +220.49 (10.01) +5.95 (0.27) +14.10 (0.64) +Thus, we generate three modes pattern with different speckle sizes, which are 16.75 (0.77) +µm, 44.72 (3.19) µm, 5.95 (0.27) µm for Mode 1, Mode 2 and Mode 3, respectively. The +radial trapping force is different for different modes, but interestingly for Mode 1, we get +maximum trapping force where the mean speckle size and particle diameter are almost the +same (see Table II). Thus, we may reasonably conclude that the trapping efficiency is better +when the particle dimension and speckle size are comparable. Besides, we also observe that +12 + +for both bigger and smaller speckle sizes compared to the particle size, the trapping force +decreases. We attempt to understand this more elaborately in the next section. +2. +Average Intensity per speckle: +We make use of the fact that the photophoretic forces depends on laser intensity[7, 23], +so that the average intensity per speckle will serve as a crucial parameter for controlling the +trapping force. We therefore proceed to estimate the average intensity per speckle for each +mode by counting the total number of bright spots present in the pattern, and determining +their average intensity. This can be considered as an average intensity per speckle (⟨Ispeckle⟩), +which notation we use hereafter. We first describe the methodology for counting the total +number of bright spots present in each speckle pattern. +Thus, we consider an rgb speckle image of any mode, say Mode 1, which is shown in +Fig. 5 (a). We then split the image into three channels (red, blue, and green) using the +ImageJ software, and work with the green channel image as it has good contrast, as shown +in Fig. 5(b). We proceed to performing the threshold of that green channel image, i.e. the +binary image as shown in Fig. 5(c). Note that we adjust the threshold value in such a way +that, the bright spots in the green channel image [Fig. 5(b)] are converted into complimentary +dark spots in the threshold image [Fig. 5(c)]. After that, we locate these dark spots with a +curve using the software (‘Analyze Particles’ tool) by setting up the appropriate size ranges +in pixels based on the speckle size. Finally, we use the software to count the total number +of dark spots in the bounded region - which gives us a count of the high intensity speckles +present in the pattern. +FIG. 5. (a) Speckle image for Mode 1; (b) Green channel image of a); (c) After doing threshold of +the image b); (d) Locate and count the Bright spot present in the pattern. +For Mode 1 Mode 2 and Mode 3 [Fig.3 (b) and (c)], we obtain numbers of 35, 10, and 308, +13 + +bright spots respectively [see Table V, second row]. Note that these number of bright spots +should be invariant for any beam size, which we experimentally verify. Understandably, +there also exists an inverse relationship between the speckle size and the number of bright +spots present in the speckle pattern. On another note, the particles are trapped at different +locations, which implies different beam sizes and speckle size as well for the respective modes +[see Table IV first, second and third column]. Thus, we find out the mean speckle size which +are depicted in the first row of Table V. The laser power (P) is kept constant throughout +the experiment for each mode. Hence, the laser power per speckle (p) for each mode should +be p = P +N . Then we find out ⟨Ispeckle⟩ = p +A where A is the area of the average speckle size of +the respective mode. The p and ⟨Ispeckle⟩ values for each mode are shown in Table V. +TABLE V. Number of bright speckle and average intensity per speckle for the three +modes +Mode name +Mode 1 +Mode 2 +Mode 3 +Average speckle size (µm) +16.75 (0.77) 44.72 (3.19) 5.95 (0.27) +Total number of bright speckle (N) +35 +10 +308 +Laser Power/speckle (p) (mW) +2.0 +7.0 +0.23 +Laser Intensity/speckle (µW/µm2) +7.13 (0.65) +3.50 (0.51) 6.50 (0.60) +Effective Intensity for Gaussian ⟨Ieff⟩ (µW/µm2) +1.62 +As shown in the Table V, average intensity per speckle is maximum for Mode 1 with +⟨Ispeckle⟩ = 7.13(0.65) µW/µm2 followed by Mode 3, which is 6.50 (0.60) µW/µm2, with +Mode 2 being the lowest at 3.50 (0.51) µW/µm2. Importantly, we observe a similar trend +for the radial trapping force as shown in Table II, where the radial trapping force is maximum +for Mode 1, followed by Mode 3 and Mode 2. Again, for the Gaussian beam, we determine +the effective intensity, which is the actual intensity perceived by the particle. Note that the +particle is smaller than the beam waist size, and thus does not perceive the entire beam +intensity. +This effective intensity is then given by an average of the intensity values of +different non-overlapping sections of the beam where the particles of average diameter 16 +µm can be trapped[9]. Besides, we observe from experiments that for the Gaussian beam, +the average beam size where the particles are trapped is 200 µm. Thus, for the 200 µm +beam diameter, ⟨Ieff⟩ becomes 1.62 µW/µm2. Note that, since Mode 1 gives the maximum +14 + +trapping force experimentally, we use this mode to compare with the Gaussian beam. In +our experiments, we compare the trapping force for both Multi-mode and Gaussian beam +profiles by trapping the particles at the same beam size. So, the average intensity per speckle +(⟨Ispeckle⟩) for 200 µm beam size is 9.92 µW/µm2. Hence, the experimentally measured force +enhancement factor of eight also compares well with our numerical estimation of six. +3. +COMSOL simulation to determine temperature distribution across a trapped spherical par- +ticle due to laser heating +We now numerically estimate the values of the photophoretic forces and radiation pres- +sure force experienced by the particle. Hence, we employ the analytical formula for pho- +tophoretic ∆T and ∆α forces acting on a spherical particle provided by Rohatschek in his +semi-empirical model of photophoretic forces [23], which we have described in detail in the +Appendix (Section II). Note that the quantitative analysis of photophoretic forces acting +on a particle is quite complex, as many factors are involved with this force - such as pres- +sure, different parameters of light (beam profile, intensity, wavelength of the laser, etc.), and +most importantly, particle properties (i.e., particle size, morphology, thermal conductivity, +absorptivity, etc.)[4]. Thus, only semi empirical estimates of the forces are available from +the literature. However, the photophoretic forces significantly depend on the temperature +distribution across the particle’s surface. Hence, we perform a COMSOL simulation to find +out the temperature distribution across a particle due to laser heating. We use the ’Heat +transfer in solid (time-dependent) model’ and assume a spherical particle of radius 8 µm +again, as our experiments revealed this to be the average radius of the trapped particles. +Further, we choose the incident heat flux (H) as H = χ < I >, where χ is the absorptivity +of the particle, and < I > is the average laser intensity which can be ⟨Ispeckle⟩ for a multi- +mode and ⟨Ieff⟩ for a Gaussian beam. Note that this heat flux is considered as a spatially +distributed heat source on the particle surface - introduced at the lower hemisphere [see +Fig. 6(a) and (b)]. +Now, according to our earlier estimation of the speckle size, it is clear that for Mode 1 +(16.75 µm), the speckle diameter is comparable to our particle diameter (16 µm), while both +for Mode 2 and the Gaussian beam, the speckle (44.72 µm) and waist diameter (∼ 200 µm), +respectively, are much bigger than the particle diameter. Therefore, in these cases, we fill +15 + +up the lower hemisphere of the particle by the laser beam - to replicate which, we set the +heat flux (H) over the entire region of the lower hemisphere of the particle as shown in +Fig. 6(a). The situation is more complex for Mode 3. Here, the average speckle size is +FIG. 6. +Schematic for providing heat flux (H) to the lower surface of the particle (a) for Mode +1, Mode 2 of the multi-mode fiber, and the Gaussian beam, (b) for mode 3. (c) Temperature +distribution across the particle surface due to the laser intensity corresponding to the Mode 1 of +the multi-mode beam profile; (d) Iso-surface of the temperature of the particle for input Gaussian +beam. +5.95 µm, so that the lower hemisphere experiences alternate bright and dark regions of the +trapping light, both radially and axially. Thus, to simulate this situation in the model, we +create two partitions on the lower hemisphere of the particle - one at -5 µm, and the other +at -2 µm from the bottom of the lower hemisphere [refer to the -8 µm position in Fig. 6(b)]. +Hence, we obtain three domains, of which the lowest one is of diameter 6 µm, so that we +set this as ‘Heat flux 1’ where H = χ ∗ ⟨Ispeckle⟩Mode 3. Next, we have the middle region, +once more of diameter 6 µm, which we set ‘as Heat flux 2’. Note that here the intensity is +virtually zero (since we assume a volume speckle field, where the bright and dark speckles are +distributed uniformly in all three dimensions) , as the particle encounters a dark region here +16 + +b) +a) +5 +5 +um +0 +μm +0 +-5 +-5 +Heat Flux 1 +Z +Z +0 +0 +ly-x +-5 +0 +5 +um +V +-5 +0 +um +μm +um +Heat Flux +Heat Flux 2 +Heat Flux 1 +Time=1sSurface:Temperature(K) +D +Time=1s +lsosurface:Temperature(K) +D +d) +c) +304.42 +335 +303.98 +303.54 +330 +303.09 +302.65 +325 +5 +302.21 +301.77 +320 +301.32 +μm +0 +um +315 +300.88 +300.44 +310 +299.99 +-5 +-5 +299.55 +0 +305 +z +μm +299.11 +5 +μm +0 +5 +-5 +0 +-5 +298.66 +300 +μm +从m +298.22[see Fig. 6(b)]. Finally, for the uppermost region of 4 µm diameter at the lower hemisphere, +we again set ‘Heat flux 1’ [see Fig. 6(b)]. Moreover, as the particle blocks the beam, we do +not provide any heat flux at the upper hemisphere and set the ambient temperature of the +particle at 298 K. The thermal conductivity, density, and specific heat of the printer toner +particle we trap are provided as user-defined values. +With this arrangement for multi-mode and Gaussian beams, we carry out our simulations. +The temperature distribution across the particle surface are noted down for all particular +simulations. A representative temperature distribution across the particle surface for Mode +1 of the multi-mode profile is shown in Fig. +6(c). +Note that we calculate the ∆Ts - +which determines both the ∆T and ∆α forces - by calculating the temperature difference +between two hemispheres, and for that, we take very thin iso-surface temperature shells of +both upper and lower hemispheres of the particle and correspondingly measure the average +values of the lower hemisphere (T1) and upper hemisphere (T2) which is shown in Fig. 6 +(d). The difference between T1 and T2 gives the ∆Ts value, while we approximate the Ts by +taking the average between T1 and T2 without going into too much complexity. The results +for T1, T2, ∆Ts and Ts for all speckle patterns of the multi-mode fibre are depicted in Table +VI +TABLE VI. Temperature difference across the particle surface for all beam profiles +Beam Profile +T1 (K) +T2 (K) +∆Ts +Ts +At lower hemisphere At upper hemisphere (T1 - T2) (K) +(K) +Mode 1 +325.31 (2.49) +307.01 (0.82) +18.30 (1.67) 316.16 (1.66) +Mode 2 +311.41 (1.93) +302.42 (0.63) +8.99 (1.31) +306.92 (1.28) +Mode 3 +313.91 (1.46) +303.14 (0.47) +10.77 (0.99) 308.53 (0.96) +As the heat flux (H) is proportional to the laser intensity for the same particle, we +obtain higher temperature difference at higher intensity, resulting in a maximum ∆Ts value +for Mode 1 - by a factor of about 2.1 and 1.7 over Mode 2 and Mode 3, respectively. However, +while the average intensity per speckle ⟨Ispeckle⟩ for Mode 2 is 46% less compared to Mode +3, the ∆Ts value is only 17% less. This occurs since for Mode 3, some regions of the lower +hemisphere of the particle interacts with the dark regions of the optical mode, which lowers +the average temperature of that region, and thereby decreases the temperature difference +17 + +between the two hemispheres. The results for T1, T2, ∆Ts and Ts for the Gaussian beam +and Mode 1 of multi-mode beam for the same beam size of 200 µm are shown in Table VII +. We see from the table that the ∆Ts value for Mode 1 of the multi-mode profile is around +six times higher compared to the Gaussian beam (generated from single-mode fiber), which +is similar to the numerical estimation of intensities for both the beam profiles. +TABLE VII. Temperature difference across the particle surface for mode 1 of multi- +mode and Gaussian beam +Beam Profile +T1 (K) +T2 (K) +∆Ts +Ts +At lower hemisphere At upper hemisphere (T1 - T2) (K) +(K) +Gaussian +304.20 +300.04 +4.15 +302.12 +Mode 1 +335.99 +310.54 +25.46 +323.26 +4. +Calculation of total force acting on a spherical particle +We now consider a force balance on the particle, by considering the effects of the pho- +tophoretic ∆T force, radiation pressure force FRP and buoyancy force FB - that always +point along the laser propagation direction (vertically upward in our configuration) - and +the gravity FG, that points away from the laser (vertically downwards in our configuration) +- as shown in Fig. 7. Further, there also exists the photophoretic ∆α force, which is a +body-fixed force, and so is directed from higher α to lower α as depicted by the green arrow +in Fig. 7. All the estimated forces acting on the particle for all modes of the multi-mode +fiber and the Gaussian beam are summarized in Table VIII. +First, we calculate the photophoretic ∆T force by plugging in the ∆Ts values [see the +fourth column of Table VI] into the Eq. 4, +F = D p∗ +p a∆Ts +(1) +where, D denotes a constant, determined entirely by the state of the gas and p∗ is the +characteristic pressure that depends on particle radius a, p is the atmospheric pressure and +∆Ts is the temperature difference across the particle surface [For more details see Appendix +Section 2]. The values of F∆Ts for all modes of the multi-mode fiber are shown in the second +column of Table VIII. Next, we calculate the radiation pressure force using the formula +18 + +FIG. 7. +Illustration of all the forces acting on a spherical particle +FRP = πa2 I +c(1 + R), where R is the reflectivity of the particle. For absorbing particles, this +should be almost negligible, but we choose R = 0.1 as an upper limit. For intensity I, we +take the average intensity per speckle (⟨Ispeckle⟩) for all modes from the multi-mode fiber, +and the effective intensity (⟨Ieff⟩) for the Gaussian beam [see Table V], which are shown in +the third column of Table VIII. Then, we calculate the gravitational force of the particle, and +since we consider the particles to be spherical, FG = 4 +3πa3ρ = 30.88 pN, where a is the radius +( ∼ 8µm), and ρ is the density of the particle. The buoyancy force, FB = ρairgV = 0.038 +pN, is negligible compared to the FG, where ρair is the density of air, g is the gravitational +constant, and V is the volume of the particle. Finally, we calculate the photophoretic ∆α +force using the Eq. 5 as depicted below (discussed in detail in Appendix), +F∆α = φ ∗ B1 = 3 +4D +1 +� +p +p∗ + p∗ +p +�a(Ts − Ti)∆α +(2) +The F∆α values are shown in the sixth column of Table VIII, where Ti is 298 K and the Ts +values are taken from the last column of Table VI. Note that it is impossible to know the +exact distribution of accommodation coefficient α value over the particle surface, so that +based on the literature [23], we assume the α1 and α2 of the particle as 0.9 and 0.8 - giving ∆α +value to be 0.85. Now, while we know that F∆α dominates over F∆T at atmospheric pressure, +in our case it is the F∆T values which dominate over F∆α, as the thermal conductivity of +the particles we use is minimal, (0.072 W/(m.K), which creates a substantial temperature +difference across the particle surface. +Similarly, we calculate all the forces acting on the particle for both the Gaussian beam +and mode 1 of multi-mode beam with the same beam size, which are shown in Table IX. For +19 + +FAT + FRP + FB ↑FAαL +Fμα +α2 +b +F△αT +α1 +α1 >α2 +FG +Incident +Laser BeamTABLE VIII. Calculation of all forces acting on the particle +Beam Profile +F∆Ts (pN) +FRP (pN) FG (pN) FB (pN) F∆α (pN) Ftrap (pN) +Mode 1 +130.10 (11.87) 4.56 (0.42) +30.88 +0.038 +9.68 (0.94) 7.81 (0.45) +Mode 2 +63.91 (9.28) +2.24 (0.32) +30.88 +0.038 +4.75 (0.68) 4.57 (0.34) +Mode 3 +76.57 (7.04) +4.16 (0.38) +30.88 +0.038 +5.61 (0.51) 5.70 (0.36) +the calculation of the photophoretic forces, we take the values of ∆Ts and Ts values from +Table VII. +TABLE IX. Calculation of all forces acting on the particle +Beam Profile F∆Ts (pN) FRP (pN) FG (pN) FB (pN) F∆α (pN) Ftrap (pN) +Gaussian +29.52 +1.38 +30.88 +0.038 +2.20 +1.01 +Mode 1 +181.01 +6.95 +30.88 +0.038 +13.46 +7.79 +Since the F∆α force is responsible for radial trapping (as we have mentioned earlier), the +experimentally measured Ftrap values (shown in the last column of Table VIII and IX) can +be compared with the F∆α values, obtained numerically. It is clear from Table VIII and IX +that we achieve good agreement between these values. It is also important to note that in +the experiments, we measure only the radial component of the F∆α force, which is not the +case in the numerical estimation - so that it is reasonable to expect that the experimentally +measured values would be lower than that estimated by the simulations. This is indeed what +we obtain, as is clear from Table VIII and IX. Note that, for Mode 3, we obtain a lower +numerical value than the experimental one, as the size of bright and dark spots present in the +pattern is lower than the trapped particle size, which might affect the numerical estimation +of the number of spots illuminating the particle. +Now, in our system, a particle is confined in a position axially when the gravitational force +(FG) balances the other three forces, F∆T, FRP and FB) [see Fig. 7], though F∆T dominates +the others. It can be observed from Table VIII and IX that in general, for the multi-mode +beam profile, the total upward force (FU = F∆T +FRP +FB) is significantly larger compared +to the gravity FG, as a result of which particles should shoot upwards in the propagation +direction, and should thus not be confined. However, we do observe very strong and stable +trapping in our experiments with the multi-mode fiber with the same beam parameters used +20 + +in the simulation. We now attempt to explain this discrepancy using a simple model. +In order to simulate the multi-mode profile consisting of alternate bright and dark regions, +we assume a beam structure in which these regions are stacked one after another axially, as +shown in the Fig.9. For simplicity, we assume that the particle experiences bright and dark +spots in sequence, which may be the case if there is a small angle between the beam axis +and the trajectory of the particles. Further, when we perform the experiments to compare +the trapping forces for the multi-mode and single-mode cases, the experimentally measured +particle location data shows that the average beam waist diameter where the particles are +trapped for the multi-mode profile is around 200 µm. Thus, in the simulation, we start +from this position, i.e., assume z = 0 µm here (depicted as a dotted line in Fig. 8), and +correspondingly measure average intensity per speckle (⟨Ispeckle⟩). Once again, we consider +the speckle size for the beam profile corresponding to Mode 1, since this is the mode we +choose for the experiments to compare performance. Now, using our earlier estimation of +all forces acting on the particle, we define a resultant force (FRE), which is [see Fig. 8]: +FRE = FU − FG +(3) +where FU = F∆T + FRP + FB. It is clear that FU >> FG, so that a particle experiences a +force axially and moves with a resultant acceleration ar = Fre +m − g, where m is the particle +mass and g is the gravitational constant. +Here, we assume that initial velocity (u) at the starting point is zero (i.e., at z = 0 µm), +and then determine the velocity v1 when the particle moves 8µm (h) using Newton’s motion +laws, viz. v = √u2 + 2arh, which gives v1 = 25.8 µ m/s [see Fig. 8]. After the particle +traverses 8 µm from the initial position axially, we recalculate all the forces (we ignore +the viscous drag by the air for simplicity), and determine FRE using Eq.6, followed by the +resultant acceleration ar of the particle at the new axial position. Since, FRE >> 1, the +particle continues to move in the upward direction with an estimated velocity v2 = 36.4 µm/s +[see Fig. 8]. After this, however, the particle is at z = 16 µm, and arrives in a dark region +of the beam, where the photophoretic ∆T and FRP forces are almost zero. So, the resultant +acceleration ar of the particle would be −g, but due to the initial large acceleration of the +particle - it continues to move in the upward direction by another 8 µm - albeit with a +reduced velocity v3 = 34.2 µm/s. Interestingly, at this position (i.e., at z = 24 µm, the +upper surface of the particle interacts with the bright region of the beam, while the lower +21 + +FIG. 8. Model for particle oscillation along the z direction while being confined. +region samples a dark region. As a result, the F∆T force and FR force are reversed, and +directed towards gravity. Hence, the particle falls under gravity almost immediately, and +back into a bright speckle again [see Fig. 8]. Thus, the particle undergoes a stable oscillation +in the axial direction, and remains confined in the photophoretic trap, even with the laser +intensity generating a photophoretic force higher than the gravitational force corresponding +to the weight of the particle. +FIG. 9. (a) X-Z plot of a trapped particle’s trajectory using multimode fiber of Mode 1 profile (b) +Corresponding velocity plot of that trajectory along the z direction. +A crucial issue now is to verify whether the mechanism we suggest for trapping from our +22 + + z = 64 μm + z = 48 μm +↑ + z = 40 μm +Z axis +- z=32 μm +个 +- z = 24 μm +Dark +V3 = 34.2 +um/s +_ z = 16 μm +V2 = 36.4 μm/s +- Z = 8 μm +Bright +V1 = 25.8 μm/s +wno=z - +0 μm/s +Time20 +b) +(un) +a +20 +Velocity (μm/s) +displacement ( +10 +30 +40 +10 +Z +50 +-20 +20 +20.2 +20.42 +20.6 +20.8 +0 +2 +4 +6 +8 +10 +¥121416 +X displacement (μm) +time (sec)simulations is also observed in experiments. This is indeed the case - and we observe clear +signatures of trapped particles oscillating in the z direction using Mode 1 [see Video1 in +Appendix] of the multi-mode fiber. We have also quantified the average axial oscillation +by tracking the trapped particle’s position along the x − z and y − z planes by analyzing +videos of its motion using the Matlab software. For representation, the x − z trajectory of a +trapped particle, and the corresponding velocity plot along the z axis is shown in Fig. 9(a) +and (b), respectively. We determine the average z oscillation of particles to be 29.4(4.1) +µm from the data of 15 trapped particles of similar size. The oscillation amplitude is in +reasonable agreement (around 17 %) with the value provided by our simulations (∼ 24 µm). +Also, the maximum velocity we measure is around 20 µm/s, which is about 40 % different +from the simulations (∼ 34.2 µm/s), but this difference could well be due to the fact that +we have ignored the drag force by air in the simulation, and also the fact that our camera +has a limited frame rate [60 FPS in this case]. +Very interestingly, we observe oscillations of around 0.4-0.5 µm in the radial direction as +well in Fig. 9(a), which are of almost constant amplitude as the particle moves axially. This +is understandable since the multi-mode beam has a speckle structure in all three dimensions, +but the intensity of the speckles fall off faster in the radial direction (close to a Gaussian +profile) compared to that in the axial direction - so that the particle displacement amplitude +is smaller. +FIG. 10. (a) Simulation for finding out the z drifting of a trapped particle in case of Gaussian +beam.(b) Experimental X-Z plot of a trapped particle’s trajectory using Gaussian beam +Finally, we carry out a similar exercise for a particle trapped in a Gaussian beam. A +calculation of all forces based on the location where the particle is trapped, as described +23 + +98 +0.20 +For25 mm I.ens +n +b) +lacement +100 +0.10 +0.05 +0.061 +F +102 +0.00 +displ +-0.05 +Z +12 μm +104 +71.2 +71.4 +71.6 +71.8 +72 +-30 +-20 +-10 +0 +10 +20 +30 +X displecment (μum) +z variation (um)in Table IX, reveals that the total upward force FU is slightly higher than the downward +force FG. As a result, the particle can move in the upward direction. Let us assume that +the location of the trapped particle is a1 as shown in the right inset of Fig. 10(a), where +we represent the propagation of Gaussian beam focused by a convex lens of focal length 25 +mm. Since FU > FG at this location, the particle moves along the upward direction. In the +simulation, we move the particle by small step in this direction, and similar to the previous +case, calculate all relevant forces. So, when the particle moves by 12 µm from the initial +position as depicted by a2 in the right inset of Fig. 10 (a), we obtain FU = FG, so that the +resultant force becomes zero. Ideally, the particle can be stably confined at the a2 position, +but due to perturbations such as laser intensity fluctuations, air turbulence, etc. the particle +may well oscillate around this equilibrium position, which is shown as a black dotted line in +Fig. 10(a). +This is exactly what we observe in experiments. The average z oscillations we measure in +particles trapped by a Gaussian beam [see Video2 in Appendix] is 9.6 (1) µm (from 15 sets +of data), which is again in reasonable agreement (around 20 %) from the simulation results. +The x − z trajectory plot of one of the trapped particles is shown in Fig. 10(b). Radial +oscillations are also observed, but these are on the average between 0.2-0.3 µm, with a few +oscillations reaching an extent of 0.4 µm. This is due to the fact that in comparison to a +multi-mode beam profle - a Gaussian beam has more drastic intensity variation in the radial +direction as compared to that in the axial direction (pure Gaussian versus quadratic). Thus, +for both multi-mode and Gaussian beams, axial and radial oscillations are observed, and +may contribute significantly to the stable trapping of particles. Multi-mode beam profiles, +changing less rapidly in intensity both radially and axially compared to Gaussian ones for +the same focusing lens, offer considerably more robust trapping due to the larger dynamic +equilibrium range in both dimensions. +A relevant question to ask here may be why a particle reaches an intensity region in +the multi-mode profile which produces much higher photophoretic force than that required +to balance its inertia. This, we believe, may to be due to the fact that we use a simple +trapping chamber that is not sealed in any manner, so that particles falling are entirely +exposed to microscopic air currents and turbulence, which may well exert instantaneous +forces much larger than photophoretic forces. Note that the large axial trajectories observed +in the multi-mode case may also be due to the fact that the particle will continue its upward +24 + +trajectory unless it comes into contact with a dark zone, at which point its trajectory will +reverse. Thus, the spatial dynamic range of the particle oscillations are greater in the multi- +mode fiber in almost all cases than that for single-mode fiber. We also believe that these +oscillations are demonstrative of the existence of a restoring force in the case of photophoretic +trapping even in the axial direction. The magnitude of the restoring force appears to be +higher for a multi-mode fiber compared to a single-mode case, with the presence of dark +zones contributing in the final dynamic equilibrium achieved by the particle. In addition, +the threshold power of trapping in the case of multi-mode fibers (see Table I) is also lower +than that for a pure Gaussian trap, since the intensity per speckle is much higher than the +overall intensity measured from the beam waist size - something which is not the case for a +Gaussian beam. +IV. +CONCLUSION +In conclusion, we employ a single multi-mode fiber to develop a robust three-dimensional +optical trap for trapping absorbing particles in air employing photophoretic forces. +We +observe that the intensity profile created by the multi-mode fiber provides around eight +times higher trapping force compared to that produced by a single-mode fiber that produces +a pure Gaussian beam. This is because the intensity a particle experiences in the speckle +pattern generated by a multi-mode fiber is higher than the beam profile at the output +of a single-mode fiber, so that the trapping force is correspondingly higher. Our studies +reveal that a beam profile where the speckle size is similar to the particle size produces +the strongest traps, using which we achieve axial and radial velocities of 5 mm/s, which is +presently limited by our experimental capabilities. We validate our experimental results by +developing a COMSOL-based simulation to calculate all the forces experienced by a trapped +particle, and applying force balance to study the particle dynamics. Our simulations reveal +clear axial oscillations of the trapped particles in the case of both single and multi-mode +fibers, with the multi-mode having higher spread due to the inherently high intensity of the +individual speckles that constitute the beam profile. We validate our simulation results with +experimental observations, where both single and multi-mode fibers give rise to axial as well +as radial particle trajectories. The trajectories in the multi-mode case have considerably +higher spread compared to the single mode case, as confirmed by our simulations. Indeed, +25 + +our results also point out to the existence of an effective restoring force on the trapped +particle in the axial direction, as is known to be the case in the radial direction [6–8]. These +need to be carefully studied in future research, along with more detailed and intensive +modeling of the dynamics of trapped particles that are confined using photophoretic forces +generated by a multi-mode and a single mode beam profile. +While the detailed theory of photophoretic trapping itself is not available yet, with only +quasi-emperical models proposed, our experiments definitively confirm the significant advan- +tage provided by single multi-mode fiber-based photophoretic traps in terms of robustness, +portability, ease of use, inexpensiveness, and the facilitation of diverse applications towards +simultaneous trapping and spectroscopy of aerosols/bio-aerosols, and other diverse applica- +tions. We hope to see exciting research in these directions in the near future. +Acknowledgements +The authors acknowledge IISER Kolkata, an autonomous institution funded by the Min- +istry of Education (MoE), Govt of India for funding and laboratory space. SS thanks CSIR, +MoE for fellowship support. +V. +APPENDIX +A. +Speckle Size Measurement +We know that speckle is a random distribution of light field - consisting of a multitude of +dark and bright spots resulting from destructive and constructive interference[17]. There are +different speckle parameters such as mean speckle size, contrast, intensity and polarization +etc[25]. But here, we only consider the mean speckle size, defined as the average size of bright +or dark spots present in the pattern[17]. Thus, in order to find out the mean speckle size, we +need to measure the Wiener spectrum of the pattern, which is the average strengths of all +possible spatial frequency components of the pattern[17]. This can be done by calculating +the normalized autocovariance function of the intensity speckle pattern obtained in the +observation or image plane (x,y). Further, this function can be considered as the normalized +autocorrelation function of the intensity, which has a zero base, and its width provides a +good measurement of the average width of a speckle[25, 26]. +Let us consider, I(i1, j1) and I(i2, j2) to be the gray values of two pixel points in the +26 + +image plane (i,j). Then, the intensity autocorrelation function is defined as, +RI(∆i, ∆j) = ⟨I(i1, j1)I(i2, j2)⟩ +(4) +where, ∆i = i1 − i2 and ∆j = j1 − j2; and ⟨..⟩ represents a spatial average. Now, for +simplicity, we assume i2 = 0, j2 = 0 and consider i1 = i and j1 = j, so the Eq. 4 can be +written as, +RI(∆i, ∆j) = RI(i, j) +(5) +So, the normalized autocorrelation function of the intensity (CI(i, j)) can be expressed as, +CI(i, j) = RI(i, j) − ⟨I(i, j)⟩2 +⟨I(i, j)2⟩ − ⟨I(i, j)⟩2 +(6) +Again, according to the Wiener-Khinchin theorem, the power spectral density of the wide- +sense-stationary random process is the Fourier transform of the corresponding autocorre- +lation function, which is again the square modulus of the Fourier transform of the signal +(I(i,j)). Hence, we can write, +PSDI(νi, νj) = FT[RI(i, j)] = |FT[I(i, j)]|2 +(7) +Here FT represents the Fourier Transform. +So, using the Eq. 7, the normalized auto- +correlation function of the intensity (CI(i, j)) [Eq. 6] can be expressed as: +CI(i, j) = FT −1[|FT[I(i, j)]|2] − ⟨I(i, j)⟩2 +⟨I(i, j)2⟩ − ⟨I(i, j)⟩2 +(8) +Thus, we determine the normalized auto-correlation intensity distribution (CI(i, j)) of any +given pattern image using the algorithm described by Eq. 8. +B. +Numerical estimation of Photophoretic Forces +We now numerically estimate the value of the photophoretic forces and radiation pres- +sure force experienced by the particle. Hence, we employ the analytical formula for pho- +tophoretic ∆T and ∆α forces acting on a spherical particle provided by Rohatschek in his +semi-empirical model of photophoretic forces[23]. Note that the quantitative analysis of +photophoretic forces acting on a particle is quite complex, as many factors are involved with +this force - such as pressure, different parameters of light (beam profile, intensity, wavelength +27 + +of the laser, etc.), and most importantly, particle properties (i.e., particle size, morphology, +thermal conductivity, absorptivity, etc.)[4]. Thus, only semi empirical estimates of the forces +are available from the literature. However, the calculation of the photophoretic forces sig- +nificantly depend on the Knudsen number (kn) - defined as the ratio of the mean free path +of the gas molecule (λ) and the size of the particle (a), Kn = λ +a [4]. When Kn > 1 i.e., +the particle size is considerably smaller than the mean free path of the gas molecules. This +also includes conditions corresponding to very low pressure (p → 0) (mean free path of the +gas molecules increases), where the free-molecular regime is applied for the calculation of +photophoretic forces. For Kn < 1 i.e., when the particles size is much larger than the λ, or +for atmospheric and high pressures, the continuum regime can be applied. Since we trap +particles in air at atmospheric pressure, where the mean free path of the air molecules are +in the order of nanometers and the particle size is in the order of mirometers, Kn << 1 - +hence the calculation of the photophoretic forces are based on the continuum regime[4]. +Photophoretic forces may be generated both by the difference in the surface temperature +(Ts) and by variations in the thermal accommodation coefficient (α) of the particle. In our +case, we assume a spherical particle of radius a, heated to a certain temperature (Ts) due +to laser radiation. When gas molecules having temperature Ti (< Ts) are incident on the +surface of the particle, they are reflected off the particle and reach a higher temperature +Tr. This elevated temperature can be written using Knudsen’s concept of energy transfer +by individual gas molecules interacting with a hotter surface as, +Tr = Ti + α(Ts − Ti) +(9) +where, α is the thermal accommodation coefficient. Let us consider the temperature of the +gas layer adjacent to the surface of the particle to be (Ta), which can be expressed in terms +of Ti and Tr as, +Ta = niTi + nrTr +(ni + nr) +(10) +where, ni and nr depicts the number density of the incident and reflected air molecules +respectively, and the continuity at the surface signifies - nrcr = nici, so that, nr +√Tr = ni +√Ti, +where c [= +� +8RT/πM] is the mean velocity of the gas molecules. Substituting the above +equation in Eq. 10, and further approximating the geometric mean by the arithmetic mean, +the expression of Ta becomes, +Ta = +� +Ti Tr = Ti + Tr +2 +(11) +28 + +As we consider a spherical particle, we assume that the distribution of the difference in +temperature (∆Ts), and accommodation coefficient (∆α) are rotationally symmetric, where +Ts is measured about the direction of incident light, and α about an axis fixed to the particle. +Besides, the temperature of the gas layer adjacent to the surface of the particle (Ta) is also +assumed to have rotational symmetry. Thus, all the relevant quantities Ts, α and Ta can be +expanded in terms of the Legendre polynomial Pn(cosθ), so that the surface temperature +(Ts) of the particle can be written as, +Ts = T∞ + +∞ +� +n=0 +AnPn(cosθ) = T ′ +s + A1cosθ + ... +(12) +where, T∞ denotes the temperature of the gas far from the sphere and T ′ +s = T∞ + A0. +Similarly, α can be expressed as, +α = +∞ +� +n=0 +anPn(cosθ) = a0 + a1cosθ + ... +(13) +And, the gas temperature next to the surface Ta can be represented as, +Ta = T∞ + +∞ +� +n=0 +BnPn(cosθ) = T ′ +a + B1cosθ +(14) +where, T ′ +a = T∞ + B0. +In the following section, we calculate the photophoretic ∆Ts and ∆α forces where for +the ∆Ts force, α is assumed to be constant, while for the ∆α force, we consider a constant +average surface temperature of the particle (TS). +1. +Calculation of Photophoretic ∆Ts force +We consider a spherical particle of radius a, which is highly light-absorbing, and has very +low thermal conductivity kp. The particle is placed in an air medium at normal atmospheric +pressure (p), and has a molecular weight M and viscosity η. The particle is illuminated by +intense laser light in a direction opposite to gravity. Due to the high absorptivity of the +particle at the operating wavelength of laser light, the surface facing the illumination source +is warmer than the opposite side - resulting in a force in the direction of propagating light, +termed as positive photophoresis force. The direction of this force is solely determined by +the incident laser light direction - and is independent of the particle orientation, and hence +29 + +called space-fixed. As the temperature difference across the particle surface causes the force, +which is directed longitudinally, it is also named as longitudinal photophoresis force (∆Ts) +force. +However, for the continuum regime, the photophoretic ∆Ts force is derived from the +’thermal creep’ flow around the particle and the resulting viscous forces. In this regime, it +is generally considered in the literature that the gas molecules adjacent to the particle have +a similar temperature as the particle’s surface. As shown in Fig. 11, it is expected that for +such a highly absorbing particle, the left side has a higher temperature Ts1 compared to the +right side Ts2, in accordance with the illumination on the particle. Thus, the air molecules +impacting the left (hot) side are faster than those impacting the right (cold) side. +FIG. 11. Photophoretic ∆Ts force acting on a particle arising from thermal creep flow +Now, due to the thermal accommodation, a symmetric velocity distribution of the gas +molecules is obtained with respect to the perpendicular direction of the surface. Hence, the +warmer molecules coming from the left side transfer larger momentum to the particle along +in the right direction compared to the colder molecules to the left - resulting in the particle +experiencing a net force that is directed from the hot to the cold side. The air molecules +correspondingly lose the same amount of momentum, so that a creeping flow around the +particle from the cold side to the hot side occurs simultaneously. Now, the thermal creep +velocity can be written as[23], +us = κ +η +ρairT +dT +ds +(15) +where, us, η, and ρair are denoted the tangential velocity of the gas, the dynamic vis- +cosity, and the mass density, respectively. T and dT +ds are the temperature and tangential +30 + +Incoming +radiation +Colder +molecules +Hotter +molecules +Creep flowtemperature gradient in the gas adjoining the particle surface, respectively. T is written +as Ta, κ is defined as the thermal creep coefficient, which is connected to the momentum +accommodation coefficient having value κ = 1.14. The net photophoretic force can then be +obtained by integrating the stress components in the z-direction over the surface[23] (Eq.15), +as, +F = 4πκ η2 +ρTa +A1 = 4πκRη2 +Mp A1, +(16) +where, A1 is the first order Legendre coefficient corresponding to the particle’s surface tem- +perature Ts. We can rewrite Eq.16 in terms of two other parameters D and p∗, as: +F = 4πκη2 +p +� R +M +� +A1 = 4πκη2 +p +�c2π +8T +� +A1 = 2D p∗ +p aA1 +(17) +where D denotes a constant, determined entirely by the state of the gas and p∗ is the +characteristic pressure that depends on particle radius, and is expressed as, +D = π +2 +�π +3 κ cη +Ta +(18) +p∗ = 1 +2 +√ +3πκ cη 1 +a +(19) +However, the parameter A1 can be calculated either by knowing the value of the surface +temperature difference of the particle or the laser irradiance. Here we consider only the +known surface temperature difference of the particle (∆Ts) that can be written as[23], +Ts = Ts + 1 +2∆Tscosθ +(20) +Again, comparing Eq. 20 with Eq. 12, we obtain, +A1 = 1 +2∆Ts +(21) +Hence, the final form of the photophoretic ∆Ts force can be found by putting the expression +of Eq. 21 for A1 into the Eq. 12, as: +F = D p∗ +p a∆Ts +(22) +2. +Estimation of the Photophoretic ∆α force +The photophoretic ∆α force arises due to the difference in accommodation coefficient of +the particle surface, which might be caused due to differences in surface roughness or com- +position of the particle. For the calculation of F∆α we consider that the particle’s surface +31 + +has two different thermal accommodation coefficient values α1 and α2, where α1 > α2, and +assume that the particle has an average surface temperature (Ts) which is hotter than the +surrounding air molecules. Note that a higher value of the thermal accommodation coeffi- +cient signifies a higher heat transfer rate. Thus, the surface of the particle with a higher +value of α transfers more heat to the air molecules compared to the other surface having a +lower accommodation coefficient value - resulting in the particle experiencing a thrust in the +direction of the high accommodation (α1) surface to the low accommodation surface (α2). +However, the photophoretic ∆α force calculation is based on a common photophoretic func- +tion (φ), and an estimation of B1 - which is a first-order Legendre coefficient of temperature +distribution in the gas layer next to the surface - arises due to the difference in the accom- +modation coefficient (α ̸= 0), and not by a difference in the surface temperature(A1 = 0). +So, the photophoretic ∆α force can be written as, +F∆α = φ ∗ B1 +(23) +This photophoretic function φ is entirely dependent on the gas temperature, and hence it +covers both ∆Ts and ∆α forces and can be expressed as[23, 28] +φ = D +2 +� +p +p∗ + p∗ +p +�a +(24) +The next step is to calculate the B1 value, and for that, the molecular energy transfer in the +Knudsen layer needs to be considered. As the gas temperature next to surface Ta depends +on the accommodation distribution values of the particle surface, a relationship between +B1 and a1 - where the latter is the first order Legendre coefficient of the accommodation +coefficient - can be found out using Eqs. (9), (11),(13) and (14), assuming that Ts = Ts. +2Ta = α(Ts − Ti) + 2Ti +[Putting Eq. (11) into Eq. (9) ] +⇒ Ta = α +2 (Ts − Ti) + Ti +⇒ Ta = 1 +2(a0 + a1cosθ)(Ts − Ti) + Ti +[From Eq. (14) α = a0 + a1cosθ ] +⇒ Ta = +�1 +2(Ts − Ti)a0 + Ti +� ++ a1 +2 (Ts − Ti)cosθ +Comparing this with Eq. (14) [Ta = Ta + B1cosθ], we obtain, +B1 = a1 +2 (Ts − Ti) +(25) +32 + +Again, the value of coefficient a0 and a1 can be obtained as, +a0 = α; +a1 = 3 +4∆α +(26) +where, α = α1+α2 +2 +, and ∆α = α1 − α2. Plugging Eq.(26) into (25), the value of B1 becomes, +B1 = 3 +8(Ts − Ti)∆α +(27) +So, the photophoretic ∆α force can be obtained by putting the expression of φ [Eq.24] and +B1 [Eq.27] into the Eq.23 and the result is +F∆φ = φ ∗ B1 = 3 +4D +1 +� +p +p∗ + p∗ +p +�a(Ts − Ti)∆α +(28) +Thus, we use the expression of Eq. 22 and Eq. 28 for the determination of the photophoretic +∆T and ∆α forces, respectively. +[1] V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Optics +Express 17, 5743 (2009). +[2] A. S. Desyatnikov, V. G. Shvedov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Optics +Express 17, 8201 (2009). +[3] V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. +Kivshar, Physical review letters 105, 118103 (2010). +[4] H. Horvath, KONA Powder and Particle Journal 31, 181 (2014). +[5] Teiser, J. and Dodson-Robinson, S. E., Astronomy & Astrophysics 555, A98 (2013). +[6] S. K. Bera, A. Kumar, S. Sil, T. K. Saha, T. Saha, and A. Banerjee, Optics letters 41, 4356 +(2016). +[7] S. Sil, T. K. Saha, A. Kumar, S. K. Bera, and A. Banerjee, Journal of Optics 19, 12LT02 +(2017). +[8] S. Sil, P. Basak, A. Pahi, and A. Banerjee, Applied Physics Letters 117, 221106 (2020). +[9] S. Sil, A. Pahi, A. A. Punse, and A. Banerjee, Journal of Optics (2022). +[10] V. G. Shvedov, C. Hnatovsky, N. Shostka, A. V. Rode, and W. Krolikowski, Optics letters +37, 1934 (2012). +[11] F. Liu, Z. Zhang, Y. Wei, Q. Zhang, T. Cheng, and X. Wu, Optics express 22, 23716 (2014). +33 + +[12] A. Porfirev and R. Skidanov, Optics express 23, 8373 (2015). +[13] B. Redding and Y.-L. Pan, Optics letters 40, 2798 (2015). +[14] Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Physical review letters 105, 163906 (2010). +[15] P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, +and Z. Chen, Optics letters 36, 1491 (2011). +[16] C. Alpmann, M. Esseling, P. Rose, and C. Denz, Applied Physics Letters 100, 111101 (2012). +[17] J. W. Goodman, JOSA 66, 1145 (1976). +[18] V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. +Kivshar, Optics express 18, 3137 (2010). +[19] V. Shvedov, A. V. Rode, Y. V. Izdebskaya, D. Leykam, A. S. Desyatnikov, W. Krolikowski, +and Y. S. Kivshar, Journal of Optics 12, 124003 (2010). +[20] G. Volpe, G. Volpe, and S. Gigan, Scientific reports 4, 1 (2014). +[21] R. Jamali, F. Nazari, A. Ghaffari, S. K. Velu, and A.-R. Moradi, Nanophotonics 10, 2915 +(2021). +[22] A. Kotnala, P. S. Kollipara, and Y. Zheng, Nanophotonics 9, 927 (2020). +[23] H. Rohatschek, Journal of Aerosol Science 26, 717 (1995). +[24] A. Ghatak, K. Thyagarajan, and K. Thyagarajan, An introduction to fiber optics (Cambridge +university press, 1998). +[25] Y. Piederri`ere, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, Optics Express +12, 176 (2004). +[26] I. Hamarov´a, P. ˇSm´ıd, P. Horv´ath, and M. Hrabovsk`y, Measurement Science Review 14, 177 +(2014). +[27] M. A. de Ara´ujo, R. Silva, E. de Lima, D. P. Pereira, and P. C. de Oliveira, Applied optics +48, 393 (2009). +[28] L. D. Reed, Journal of Aerosol Science 8, 123 (1977). +34 + diff --git a/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/load_file.txt b/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f4e59a38bfee86f28e09de5dffddbaa551fb0f8c --- /dev/null +++ b/ZNE2T4oBgHgl3EQfvQhy/content/tmp_files/load_file.txt @@ -0,0 +1,965 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf,len=964 +page_content='An ultra-stable three-dimensional photophoretic trap in air facilitated by a single multimode fiber Souvik Sil,1 Anita Pahi,1 Aman Anil Punse,1 and Ayan Banerjee1, ∗ 1Department of Physical Sciences, IISER-Kolkata, Mohanpur 741246, India (Dated: January 11, 2023) Abstract Photophoretic forces - which are of thermal origin - have defined an alternative route of optical trapping of absorbing microparticles in air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Here, we show that a single multi-mode fiber facilitates significantly more robust optical traps compared to a pure Gaussian beam emanating from a single mode fiber for the trapping and manipulation of absorbing particles using photophoretic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We carefully study the dependency of trapping on speckle patterns generated from different modes from a multimode fiber, and experimentally observe that maximum trapping force can be obtained when the mean speckle size is comparable to the diameter of a trapped particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We explain this observation by numerical simulations carried out to calculate the photophoretic force, and also determine stable trapping conditions from force balance equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Interestingly, we also observe large oscillations of the trapped particle along the z-direction for multimode beams, which may be demonstrative of an effective restoring force for photophoretic trapping even in the axial direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Our work may presage a new route for exciting applications on optical trapping and spectroscopy with photophoretic forces due to the inherent ease-of-use, portability, and flexibility of single muti- mode fiber based optical traps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' ∗ ayan@iiserkol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='in 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='04089v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='optics] 10 Jan 2023 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' INTRODUCTION Photophoretic forces - that arise due to the inhomogeneous heating of an absorbing particle in a gaseous medium by a intense light (such as a laser beam) - have introduced a new paradigm in optical trapping and manipulation of absorbing particles as demonstrated by a series of experiments[1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The photophoretic force[4] - which is also responsible for giant planet formation[5] - can be categorized into two types of forces,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' F∆T and F∆α,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' where the former arises from an inhomogeneous temperature distribution across an absorbing particle’s surface due to laser heating of that particle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and is directed from the hotter side to the colder side of the particle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' while the later results from a difference in the accommodation coefficient of the particle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and measures the efficiency of heat exchange between the heated particle and ambient molecules of the medium[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Though it is clear that the magnitude of photophoretic forces depends on the intensity of light, it needs to be pondered whether the magnitude only depends on intensity or the gradient of intensity - especially if one uses structured light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In our earlier works[6–8], we showed that particles are confined in at least one dimension due to the photophoretic forces balancing the gravitational force, while in the other dimension, there exists a restoring force possibly generated due to the complex motion of the particle in the light field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, due to the force balance, particles of a certain mass can be trapped with the appropriate intensity of the trapping light[9], with higher and lower intensities leading to particles escaping the trap[7, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' But in the presence of a structured intensity profile, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', adjacent patterns of light and dark regions - there could be opposite forces on a particle as it traverses the intensity profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This would result in a complex restoring force on the particle even in the direction of gravity, and not merely a force balance - leading to a more efficient trap and a definite dependence of the trapping efficiency on the intensity profile of the trapping beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The challenge, however, is to create such light beams having a complex intensity profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Several experimental configurations have been developed to achieve such intensity profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' These include counter-propagating vortex beams[2], doughnut-like vortex beam shapes cre- ated by two hollow beams overlapping in the trapping volume[3],optical lattices[10], tapered rings[11], dark-hollow[12] and optical hollow-cone beams[13, 14], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Moreover, to increase flexibility, holographic beam shaping has been utilized to form optical bottle beams, either by a Moire´technique employing spatial light modulators[15], or by creating discrete trapping 2 sites[16], that lead to a vanishing intensity region surrounded by light in all three dimen- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, such structured light fields can be created using a speckle pattern[17], that can be generated in various ways, such as the scattering of laser light from a rough surface or transverse mode-mixing in a multi-mode fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For example, Shvedov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' demonstrated that a volume speckle field generated by a coherent laser beam and diffuser can be used to confine a massive numbers of carbon particles in air using photophoretic forces[18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, the optical configurations to achieve such structured profiles are quite complex and have very small alignment tolerance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Recently, speckle optical tweezers (ST) have been developed where a speckle pattern, generated using a multi-mode fiber, has been used for performing collective optical manipulation of high-refractive-index particles[20], and even controlled manipulation of high and low refractive index micro-particles and nano-particle loaded vesicles[21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Besides, opto-thermoelectric speckle tweezers have been developed very recently where an optical speckle field was fed into a thermal speckle field through in- teraction with plasmonic substrates, thus converting the high-intensity speckle grains into corresponding thermal speckle grains[22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The speckle optical tweezers described above have predominantly been employed in liquid media and demonstrate trapping in two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In this paper, however, we report for the first time the use of a multi-mode fiber to create a photophoretic trap in air for trapping and manipulating mesoscopic absorbing particles in all three dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' It is important to note that speckle patterns generated from a multi-mode fiber have advantages of uniform speckle distribution, easy alignment, high optical transmission efficiency, and high flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Besides, optical fiber traps provide substantial benefits over conventional microscope-based optical tweezers and are more advantageous than free-space photophoretic traps - the main advantages being large working distance and ease of alignment, which finally results in significantly increased convenience in trapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In addition, we observe that a multi-mode beam profile exerts a radial trapping force that is about eight times stronger than that by a single-mode (Gaussian) beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We also attain large manipulation velocities of around 5 mm/s, both axially and radially, for the trapped particles using the multi-mode beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that this velocity is presently limited by our experimental capabilities, and can possibly reach even higher values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We also determine the dependence of the trapping force on the nature of the speckle pattern, and show that the maximum trapping force is exerted when the average speckle size is similar to that of the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We perform an 3 analysis using the multiphysics tool COMSOL to explain our experimental observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, we also attempt to explain the origin of the large trapping force exerted by the speckle pattern compared to that by a Gaussian beam profile from a simple model based on a balance of all the forces that a trapped particle experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Our model predicts axial trajectories of the trapped particles with the different beam profiles which we compare with those measured in our experiments, and achieve reasonable agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' MATERIALS AND METHODS Earlier, we demonstrated through a series of experiments that an absorbing particle could be trapped employing photophoretic forces, generated by a fundamental Gaussian beam in free space [6, 8], or through a single-mode fiber[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In these experiments, it was clear that in our experimental configuration, the particles are confined in the axial direction due to the photophoretic ∆T force, while in the radial direction, a restoring force appears to be generated by the helical motion of the particle caused by the transverse photophoretic body force (F∆α), which applies a torque on particles due to its interaction with gravity[8, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As a result of this, the particle trajectories are found to be radially shifted off-axis with respect to the trapping beam center[6], with the trap stiffness being linearly proportional to the laser power or intensity[6, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, it is apparent that any beam profile which has a large transverse extent resulting in a high off-axis intensity, would increase the trapping efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is indeed the case - as we showed experimentally - where the trapping efficiency due to a beam profile that was the superposition of a fundamental Gaussian and the first-excited state (Hermite-Gaussian mode) generated by a quasi-single mode optical fiber, was higher by around 80% compared to just the fundamental Gaussian mode[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Extrapolating from this observation, we considered coupling the trapping laser using a multi-mode fiber for our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This was due to the fact that a multi-mode fiber has a higher mode volume than a single-mode one, giving even higher off-axis intensity compared to that we achieved in our previous experiments, and our intuition was that this would increase the trapping efficiency even further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, in the first set of results we report, we quantify the trapping efficiency for input laser mode profiles generated by a multi-mode, and a single-mode fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We determine the radial trapping force by the well-known viscous drag method[6], and also measure the threshold laser power for trapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 In the experiments, we use a graded-index multi-mode optical fiber (Thorlabs GIF625) with core diameter 62 µm, around ten times higher mode volume compared to a single- mode fiber with a core diameter of 6 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The total number of guided modes (N) for a typical graded-index fiber can be defined as N = q 2(q+2)V 2[24],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' where q is the exponent of the power-law profile which has a value of 2 for typical graded-index multi-mode fibers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and V [= K0aNA] is the waveguide parameter - signifying,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' the number of linearly polarized (LP) modes propagating through the fiber for a given wavelength,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' where K0 (= 2π λ ) is free space propagation constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' a is the core radius,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and NA is the numerical aperture of the fiber[24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' By putting the value of K0 where λ = 671nm, a(= 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='5µm) and NA(= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='275), the value of V becomes 80 - signifying that the multi-mode fiber can support around 1200 LP modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, due to the superposition of all those LP modes, a completely random distribution of electric fields, which are typical termed as a speckle pattern - appears at the output of the fiber, which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (a) Typical speckle pattern of Multimode fiber;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (b) & (c) 1-D plot profile of Gaussian and Multimode beam profiles, respectively The line plot of Gaussian and multi-mode beam profile for the same beam size are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11 (b) and (c) respectively, in which the raw data (black line) of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11 b) is fitted with a standard Gaussian function (gray line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' But for the multi-mode case, we can approximate the 1-D profile with a top hat function as shown in the blue line of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11 c) - demonstrating the increased transverse extent, as well as higher off-axis intensity compared to the Gaussian beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Our expectation was that this would increase the trapping efficiency for the multi-mode beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We now describe the experiment towards measuring trapping efficiency for both beam profiles, keeping all other trapping parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', laser power, beam size, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=') invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A schematic of the experimental setup is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2 where we use a 671 nm laser source 5 RawData Intensity (Arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Unit) 100 b) Intensity (Arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Unit) 140- c) RawData Fitted with Gaussian 0 120 100 80 80 70 60 40- 20- 50 0 3400 3500 3600 3700 3800 3900 500 1000 1500 2000 2500 x (pixel) x (pixel)of maximum power 300 mW as a trapping beam for trapping printer toner particles that have very high absorptivity at our operating wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then, we couple the laser beam into a multi-mode fiber using the mirrors M1, M2, and the fiber coupler (FC) [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2] after passing through an optical isolator (for preventing feedback from the fiber which destabilizes laser output) and a combination of a half-wave plate (HWP) and a polarizing beamsplitter (BS) [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2] for changing the laser power in a controlled manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The output beam from the fiber is then collimated and focused into the sample chamber via a home-built mount which contains an aspheric lens (AL) for collimation and a 25 mm plano-convex lens (CL1) for focusing [see bottom right inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This mount is then attached to a motorized translation stage TS, so that when the stage is translated, so is the trapping beam within the sample chamber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is what employ for the drag force measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Schematic of the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A: aperture;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' AL: Aspheric lens;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' C: Camera;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' CCD: Charge coupled device CL: Convex lens;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' F: Filter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FC: Fiber Coupler;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' HWP: Half wave plate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' I: isolator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' M: Mirror;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' MMF: Multimode fiber;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' MO: 10x objective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' PBS: Polarizing beam splitter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' SC: Sample chamber;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TL: Trapping Laser;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TP: Trapped particle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' WLS: White light source The trapped particles are imaged along in the x and y directions for determining the size and mass of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For imaging, we use a white light source (WLS) which is collimated by CL2 and passes through the sample chamber and trapped particle with the 6 F CL3 C1 M5 CCD2 M1 M01 TL X 40 um HWP M02 C2 M3 PBS F CCD1 SC SCH A WLS CL2 CL1 AL M4 M2 FC MMFhelp of mirrors M1 and M2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' After that, the trapped particles are imaged on camera CCD1 in the x-direction using a 10x collection objective MO2, and a notch-filter F to block the trapping beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In the y-direction, the particles are imaged on a Sony fast video camera C1 (1000 FPS) with the help of a 3-f imaging system, which is composed of a 10x objective lens (MO1), the lens CL3, and the lens placed inside the camera C1, where MO1 is used for the collection and another filter F is used to cut off the light at 671 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This 3-f imaging system provides a high contrast zoomed-in image of the trapped particles - a representative image of which is shown in the top right inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In addition, another video camera, C2, is used to determine the axial position of a trapped particle in the z-direction by taking an image of the trapped particle along with a measuring scale affixed to the sample chamber, and imaging the motion of the trapped particle in order to measure the radial velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A representative zoomed-in image of the sample chamber with two particles trapped taken using C2 is shown in the top-left inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' RESULTS AND DISCUSSIONS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Comparison of Trapping force for Single and Multi-mode fiber We keep the laser power at 70 mW throughout the experiments and trap 20 particles using both the multi-mode and single-mode fiber, and make a comparison of the trap parameters for radial trapping between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The results are shown in Table I, with the number in parenthesis-denoting 1 σ errors in the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' First, we determine the average particle size (a) using the methodology described in Ref[8], where we observe that the average particle size for both beam profiles is almost the same [see table I].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then we determine radial trapping force by the viscous drag method, where we accelerate the stage TS with an acceleration of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='1 mm/s2 and thereby reach a maximum velocity of 5 mm/s along radially - so that the trapped particle also translates radially with the same acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, the drag force experienced by the particle increases till when it overcomes the trapping force, at which time the particle leaves the trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We record the particle movement using our camera CCD1 while moving the stage, and perform a frame-by-frame analysis to measure the distance traversed by the particle before it leaves the trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We use the ImageJ software and correspondingly measure the velocity of the particle (ve) at the point of escape from Newton’s equations 7 of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, the escape velocity (ve) achieved by the particle in the single-mode fiber trap is measured to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='33 (6) mm/s, while that in the multi-mode fiber trap is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='53 (16) mm/s [see Table I].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We are then able to calculate the radial trapping force Ftrap by using the equation F = 6πηave for both trap systems, assuming the particle to be spherical, where η is the viscosity of the air, and a is the trapped particle radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The trapping force measurements come out to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01 (17) mm/s and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='87 (51) mm/s for single-mode and multi-mode fiber trap, respectively [see Table I].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, from the results, it is clear that the trapping force in the case of a multi-mode fiber trap is around eight times higher compared to that by a single-mode fiber trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Comparison of trap parameters for Multimode and Gaussian beams Trap parameters Multi-mode (1) Single-mode (2) Ratio (1)/(2) Average particle size (µm) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='96 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='30) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='15 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='33) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='08) Average ve (mm/s) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='53 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='33 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='06) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='67 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95) Average Ftrap (pN) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='87 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='51) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='17) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='79 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='87) Average threshold power (mW) 10(2) 47(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='05) Next, we measure the threshold power for trapping where we trap a particle at a moderate laser power and then reduce the laser power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' While lowering, the trapped particle moves closer to the focus, where the intensity is high enough to provide enough photophoretic force to balance gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' But, if we keep lowering the laser power, a point comes where the laser intensity is no longer able to generate a photophoretic force that can balance the particle’s weight - thus, the laser power at which the particle leaves the trap is called the threshold power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The result is shown in Table I, where we observe that the threshold power is around 47 (2) mW for single-mode trap and 10 (2) mW for Multi-mode trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This signifies that the multi-mode beam profile can be trap particles at around 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='7 times % less power than the Gaussian beam, which indicates the multi-mode trap is about 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='7 times more stable than the single-mode trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, it is clear from our measurements that a multi-mode trapping beam is considerably more effective in trapping absorbing particles compared to a fundamental Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Trapping force for different modes of Multi-mode beam profile However, while performing the experiment for measuring the trapping force using the drag force method, we observe that the escape velocity of the trapped particle changes when we modify the speckle pattern, which signifies that not only the transverse extent and off- axis intensity would affect the trap efficiency, but also the speckle presents in the pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we systematically generate three different speckle patterns at the output of the multi- mode fiber by changing the coupling angle of the fiber coupler - so that different modes are excited inside the fiber, and their interference creates different types of final mode or speckle pattern at the output of the fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Three modes, which are hereafter referred to as Mode 1, Mode 2, and Mode 3, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 3 (a), (b) and (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Speckle patterns created from Multimode fiber;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' a) Mode 1, b) Mode 2 c) Mode 3 In the experiment, we trap around 15 particles for each mode, and take the images of each by the cameras CCD1 (x-axis), C1 (y-axis), and C2 (axial position) [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We introduce another camera, CCD2, for monitoring speckle patterns for further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Here, we also use the viscous drag method (discussed earlier) for radial trapping force measurement by measuring the radial escape velocity of a particle trapped using each mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The average escape velocity (ve) and the corresponding average radial trapping force (Ftrap) are shown in Table II for different modes, with the number in parenthesis-denoting 1 σ errors in the mean as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that, while doing the experiment we keep the laser power beam size invariant for each mode, and for determining the Ftrap, we consider an experimentally measured average particle radius of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01(10) µm and viscosity of air η = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='96×10−5 kg/(ms) From Table II, it is clear that the Mode 1 pattern provides 41% and 27% higher trapping force compared to Mode 2 and Mode 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Also, Mode 3 provides gives 20% higher trapping force than Mode 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we can conclude that the speckle distribution and 9 b) a c)TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Radial trapping force for all three mode Mode name Average vescape (mm/s) Average Ftrap (pN) Mode 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='64 (14) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='81 (45) Mode 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='54 (12) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='57 (34) Mode 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='93 (12) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='70 (35) size definitely affect the efficiency of photophoretic trapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' To obtain a more quantitative understanding of this observation, we further measure the average speckle size for all three modes and determine the average intensity per speckle by counting the number of bright spots present in each mode pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We describe this in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Numerical Simulation and Analysis 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Speckle Size Measurement We know that speckle is a random distribution of light field - consisting of a multitude of dark and bright spots resulting from destructive and constructive interference[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' There are different speckle parameters such as mean speckle size, contrast, intensity and polarization etc[25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' But here, we only consider the mean speckle size, defined as the average size of bright or dark spots present in the pattern[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, in order to find out the mean speckle size, we need to measure the Wiener spectrum of the pattern, which is the average intensities of all possible spatial frequency components of the pattern[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This can be done by calculating the normalized autocovariance function of the intensity speckle pattern obtained in the observation or image plane (x,y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, this function can be considered as the normalized autocorrelation function of the intensity, which has a zero base, and its width provides a good measurement of the average width of a speckle[25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The methodology for finding out the speckle size is discussed in the Appendix Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we determine the normalized auto- correlation intensity distribution (CI(i, j)) of any given pattern image using the algorithm described by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5 in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, for representation, the speckle pattern of Mode 1, and the corresponding nor- malized auto-correlation function CI(i, j) of that pattern are shown in Fig 4 (a) and (b), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, the mean speckle size is defined as a value where the horizontal (X) or 10 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (a) Speckle pattern image of mode 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (b) Normalized auto-correlation intensity distribution CI(i, j) profile of the image (a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' c) & (d) Horizontal profile CI(i, 0) and Vertical profile CI(0, j) of normalized auto-correlation function CI(i, j) (b), respectively vertical (Y) profile of normalized auto-correlation of intensity function CI(i, j) decays to 1/e [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, CI(i, 0) and CI(0, j) give the horizontal (X) and vertical (Y) profile of CI(i, j), which are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 (c) and (d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then, we obtain the widths dx and dy, where CI(0, dy) = CI(0, dy) = 1/e, for the horizontal (x) and vertical (y) directions, respectively [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 (c) and (d)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We observe experimentally that on increasing the size of the beam, the speckle size also increases correspondingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, if we consider the ratio between the speckle size and beam waist size at a particular plane of the respective pattern, the ratio should be invariant irrespective of the beam size, which implies that we can exactly determine the speckle size at any transverse plane along the laser propagation direction, if we know the beam size in that plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We now describe the methodology of determining this ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 (a) depicts the speckle image of Mode 1 of dimension (1540 × 1864) (pixel)2 - implying the total length along the horizontal direction (Lx) and vertical direction (Ly), are 1864 and 1540 pixel, respectively [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 (c) and (d)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Next, we find the width dx and dy both horizontally and vertically to be 114 and 126 pixel, respectively, so the ratio along both the horizontal and vertical direction becomes Rx = dx/Lx and Ry = dy/Ly, and finally take the average (R) between Rx and Ry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This algorithm is applied for the other two modes (Mode 2 and Mode 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The speckle size along both x− and y−axes, and the average speckle size for all three modes are shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, using these ratios, we can find out the exact speckle size at the trapping region of the respective modes from a knowledge of the beam size at that region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, the particles are trapped at a different position axially for each mode, so first we find out the 11 b) c) d) 200 a 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='34 (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='U) (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='U) axis (pixel) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 (pixel) 400 400 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='335 600 600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6 Amplitude 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='33 Amplitude dx dy axis 800 800 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='325 1000 1000 1200 1200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 1400 1400 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='315 05 05 500 1000 1500 500 1000 1500 0 500 1000 1500 2000 0 500 1000 1500 X axis (pixel) X axis (pixel) Distance (pixel) Distance (pixel)TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Speckle size ratio for all three modes Mode name Horizontal (X) speckle Vertical (Y) speckle Average speckle size ratio (Rx) size ratio (Ry) size ratio (R) Mode 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='061 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='082 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='071 Mode 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='226 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='184 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='205 Mode 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='026 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='029 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='027 exact z position of the trapped particles by analyzing the camera images of C2 [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The mean z positions of the trapped particles for each mode are shown in the first column of Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Next, we find out the beam sizes at those z positions by measuring the beam radii using the well-known knife-edge technique[27], which are shown in the second column of Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then, we find out the speckle size at the respective z positions by multiplying the mean beam size (Table IV second column) with the respective average speckle size ratio (R) [Table III] of each mode which are shown in the third column of Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Finally, we determine the trapped particles’ size and mass from their images, taken using cameras CCD1 and C1 [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2] using the methodology given in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [8], and find out the average trapped particle diameter for each mode which we display in the last column of Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This shows that the average diameter of trapped particles is almost the same for each mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Mean speckle size and particle diameter for all three modes Mode name Mean z position Mean Beam size Mean speckle size Mean particle diameter (mm) (µm) (µm) (µm) Mode 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='1) 235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='97 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='78) 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='75 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='77) 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='02 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='32) Mode 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='80 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='16) 218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='17 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='54) 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='72 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='19) 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='76 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='86) Mode 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='90 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='09) 220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='49 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='27) 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='64) Thus, we generate three modes pattern with different speckle sizes, which are 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='75 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='77) µm, 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='72 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='19) µm, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='27) µm for Mode 1, Mode 2 and Mode 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The radial trapping force is different for different modes, but interestingly for Mode 1, we get maximum trapping force where the mean speckle size and particle diameter are almost the same (see Table II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we may reasonably conclude that the trapping efficiency is better when the particle dimension and speckle size are comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Besides, we also observe that 12 for both bigger and smaller speckle sizes compared to the particle size, the trapping force decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We attempt to understand this more elaborately in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Average Intensity per speckle: We make use of the fact that the photophoretic forces depends on laser intensity[7, 23], so that the average intensity per speckle will serve as a crucial parameter for controlling the trapping force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We therefore proceed to estimate the average intensity per speckle for each mode by counting the total number of bright spots present in the pattern, and determining their average intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This can be considered as an average intensity per speckle (⟨Ispeckle⟩), which notation we use hereafter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We first describe the methodology for counting the total number of bright spots present in each speckle pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we consider an rgb speckle image of any mode, say Mode 1, which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We then split the image into three channels (red, blue, and green) using the ImageJ software, and work with the green channel image as it has good contrast, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We proceed to performing the threshold of that green channel image, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' the binary image as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that we adjust the threshold value in such a way that, the bright spots in the green channel image [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5(b)] are converted into complimentary dark spots in the threshold image [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' After that, we locate these dark spots with a curve using the software (‘Analyze Particles’ tool) by setting up the appropriate size ranges in pixels based on the speckle size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Finally, we use the software to count the total number of dark spots in the bounded region - which gives us a count of the high intensity speckles present in the pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (a) Speckle image for Mode 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (b) Green channel image of a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (c) After doing threshold of the image b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (d) Locate and count the Bright spot present in the pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For Mode 1 Mode 2 and Mode 3 [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='3 (b) and (c)], we obtain numbers of 35, 10, and 308, 13 bright spots respectively [see Table V, second row].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that these number of bright spots should be invariant for any beam size, which we experimentally verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Understandably, there also exists an inverse relationship between the speckle size and the number of bright spots present in the speckle pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' On another note, the particles are trapped at different locations, which implies different beam sizes and speckle size as well for the respective modes [see Table IV first, second and third column].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, we find out the mean speckle size which are depicted in the first row of Table V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The laser power (P) is kept constant throughout the experiment for each mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, the laser power per speckle (p) for each mode should be p = P N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then we find out ⟨Ispeckle⟩ = p A where A is the area of the average speckle size of the respective mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The p and ⟨Ispeckle⟩ values for each mode are shown in Table V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TABLE V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Number of bright speckle and average intensity per speckle for the three modes Mode name Mode 1 Mode 2 Mode 3 Average speckle size (µm) 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='75 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='77) 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='72 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='19) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='27) Total number of bright speckle (N) 35 10 308 Laser Power/speckle (p) (mW) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='23 Laser Intensity/speckle (µW/µm2) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='65) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='50 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='51) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='50 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='60) Effective Intensity for Gaussian ⟨Ieff⟩ (µW/µm2) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='62 As shown in the Table V, average intensity per speckle is maximum for Mode 1 with ⟨Ispeckle⟩ = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='13(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='65) µW/µm2 followed by Mode 3, which is 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='50 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='60) µW/µm2, with Mode 2 being the lowest at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='50 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='51) µW/µm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Importantly, we observe a similar trend for the radial trapping force as shown in Table II, where the radial trapping force is maximum for Mode 1, followed by Mode 3 and Mode 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Again, for the Gaussian beam, we determine the effective intensity, which is the actual intensity perceived by the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that the particle is smaller than the beam waist size, and thus does not perceive the entire beam intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This effective intensity is then given by an average of the intensity values of different non-overlapping sections of the beam where the particles of average diameter 16 µm can be trapped[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Besides, we observe from experiments that for the Gaussian beam, the average beam size where the particles are trapped is 200 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, for the 200 µm beam diameter, ⟨Ieff⟩ becomes 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='62 µW/µm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that, since Mode 1 gives the maximum 14 trapping force experimentally, we use this mode to compare with the Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In our experiments, we compare the trapping force for both Multi-mode and Gaussian beam profiles by trapping the particles at the same beam size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, the average intensity per speckle (⟨Ispeckle⟩) for 200 µm beam size is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='92 µW/µm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, the experimentally measured force enhancement factor of eight also compares well with our numerical estimation of six.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' COMSOL simulation to determine temperature distribution across a trapped spherical par- ticle due to laser heating We now numerically estimate the values of the photophoretic forces and radiation pres- sure force experienced by the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, we employ the analytical formula for pho- tophoretic ∆T and ∆α forces acting on a spherical particle provided by Rohatschek in his semi-empirical model of photophoretic forces [23], which we have described in detail in the Appendix (Section II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that the quantitative analysis of photophoretic forces acting on a particle is quite complex, as many factors are involved with this force - such as pres- sure, different parameters of light (beam profile, intensity, wavelength of the laser, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' ), and most importantly, particle properties (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', particle size, morphology, thermal conductivity, absorptivity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=')[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, only semi empirical estimates of the forces are available from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, the photophoretic forces significantly depend on the temperature distribution across the particle’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, we perform a COMSOL simulation to find out the temperature distribution across a particle due to laser heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We use the ’Heat transfer in solid (time-dependent) model’ and assume a spherical particle of radius 8 µm again, as our experiments revealed this to be the average radius of the trapped particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, we choose the incident heat flux (H) as H = χ < I >, where χ is the absorptivity of the particle, and < I > is the average laser intensity which can be ⟨Ispeckle⟩ for a multi- mode and ⟨Ieff⟩ for a Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that this heat flux is considered as a spatially distributed heat source on the particle surface - introduced at the lower hemisphere [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(a) and (b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, according to our earlier estimation of the speckle size, it is clear that for Mode 1 (16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='75 µm), the speckle diameter is comparable to our particle diameter (16 µm), while both for Mode 2 and the Gaussian beam, the speckle (44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='72 µm) and waist diameter (∼ 200 µm), respectively, are much bigger than the particle diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Therefore, in these cases, we fill 15 up the lower hemisphere of the particle by the laser beam - to replicate which, we set the heat flux (H) over the entire region of the lower hemisphere of the particle as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The situation is more complex for Mode 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Here, the average speckle size is FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Schematic for providing heat flux (H) to the lower surface of the particle (a) for Mode 1, Mode 2 of the multi-mode fiber, and the Gaussian beam, (b) for mode 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (c) Temperature distribution across the particle surface due to the laser intensity corresponding to the Mode 1 of the multi-mode beam profile;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (d) Iso-surface of the temperature of the particle for input Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95 µm, so that the lower hemisphere experiences alternate bright and dark regions of the trapping light, both radially and axially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, to simulate this situation in the model, we create two partitions on the lower hemisphere of the particle - one at -5 µm, and the other at -2 µm from the bottom of the lower hemisphere [refer to the -8 µm position in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, we obtain three domains, of which the lowest one is of diameter 6 µm, so that we set this as ‘Heat flux 1’ where H = χ ∗ ⟨Ispeckle⟩Mode 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Next, we have the middle region, once more of diameter 6 µm, which we set ‘as Heat flux 2’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that here the intensity is virtually zero (since we assume a volume speckle field, where the bright and dark speckles are distributed uniformly in all three dimensions) , as the particle encounters a dark region here 16 b) a) 5 5 um 0 μm 0 5 5 Heat Flux 1 Z Z 0 0 ly-x 5 0 5 um V 5 0 um μm um Heat Flux Heat Flux 2 Heat Flux 1 Time=1sSurface:Temperature(K) D Time=1s lsosurface:Temperature(K) D d) c) 304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='42 335 303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='98 303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='54 330 303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='09 302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='65 325 5 302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='21 301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='77 320 301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='32 μm 0 um 315 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='44 310 299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='99 5 5 299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='55 0 305 z μm 299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='11 5 μm 0 5 5 0 5 298.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='66 300 μm 从m 298.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='22[see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Finally, for the uppermost region of 4 µm diameter at the lower hemisphere, we again set ‘Heat flux 1’ [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Moreover, as the particle blocks the beam, we do not provide any heat flux at the upper hemisphere and set the ambient temperature of the particle at 298 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The thermal conductivity, density, and specific heat of the printer toner particle we trap are provided as user-defined values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' With this arrangement for multi-mode and Gaussian beams, we carry out our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The temperature distribution across the particle surface are noted down for all particular simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A representative temperature distribution across the particle surface for Mode 1 of the multi-mode profile is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that we calculate the ∆Ts - which determines both the ∆T and ∆α forces - by calculating the temperature difference between two hemispheres, and for that, we take very thin iso-surface temperature shells of both upper and lower hemispheres of the particle and correspondingly measure the average values of the lower hemisphere (T1) and upper hemisphere (T2) which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6 (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The difference between T1 and T2 gives the ∆Ts value, while we approximate the Ts by taking the average between T1 and T2 without going into too much complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The results for T1, T2, ∆Ts and Ts for all speckle patterns of the multi-mode fibre are depicted in Table VI TABLE VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Temperature difference across the particle surface for all beam profiles Beam Profile T1 (K) T2 (K) ∆Ts Ts At lower hemisphere At upper hemisphere (T1 - T2) (K) (K) Mode 1 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='31 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='49) 307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='82) 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='30 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='67) 316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='16 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='66) Mode 2 311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='41 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='93) 302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='42 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='63) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='99 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='31) 306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='92 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='28) Mode 3 313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='91 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='46) 303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='47) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='77 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='99) 308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='53 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='96) As the heat flux (H) is proportional to the laser intensity for the same particle, we obtain higher temperature difference at higher intensity, resulting in a maximum ∆Ts value for Mode 1 - by a factor of about 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='7 over Mode 2 and Mode 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, while the average intensity per speckle ⟨Ispeckle⟩ for Mode 2 is 46% less compared to Mode 3, the ∆Ts value is only 17% less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This occurs since for Mode 3, some regions of the lower hemisphere of the particle interacts with the dark regions of the optical mode, which lowers the average temperature of that region, and thereby decreases the temperature difference 17 between the two hemispheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The results for T1, T2, ∆Ts and Ts for the Gaussian beam and Mode 1 of multi-mode beam for the same beam size of 200 µm are shown in Table VII .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We see from the table that the ∆Ts value for Mode 1 of the multi-mode profile is around six times higher compared to the Gaussian beam (generated from single-mode fiber), which is similar to the numerical estimation of intensities for both the beam profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TABLE VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Temperature difference across the particle surface for mode 1 of multi- mode and Gaussian beam Beam Profile T1 (K) T2 (K) ∆Ts Ts At lower hemisphere At upper hemisphere (T1 - T2) (K) (K) Gaussian 304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='20 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='04 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='15 302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='12 Mode 1 335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='99 310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='54 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='46 323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Calculation of total force acting on a spherical particle We now consider a force balance on the particle, by considering the effects of the pho- tophoretic ∆T force, radiation pressure force FRP and buoyancy force FB - that always point along the laser propagation direction (vertically upward in our configuration) - and the gravity FG, that points away from the laser (vertically downwards in our configuration) as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, there also exists the photophoretic ∆α force, which is a body-fixed force, and so is directed from higher α to lower α as depicted by the green arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' All the estimated forces acting on the particle for all modes of the multi-mode fiber and the Gaussian beam are summarized in Table VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' First, we calculate the photophoretic ∆T force by plugging in the ∆Ts values [see the fourth column of Table VI] into the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4, F = D p∗ p a∆Ts (1) where, D denotes a constant, determined entirely by the state of the gas and p∗ is the characteristic pressure that depends on particle radius a, p is the atmospheric pressure and ∆Ts is the temperature difference across the particle surface [For more details see Appendix Section 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The values of F∆Ts for all modes of the multi-mode fiber are shown in the second column of Table VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Next, we calculate the radiation pressure force using the formula 18 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Illustration of all the forces acting on a spherical particle FRP = πa2 I c(1 + R), where R is the reflectivity of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For absorbing particles, this should be almost negligible, but we choose R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='1 as an upper limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For intensity I, we take the average intensity per speckle (⟨Ispeckle⟩) for all modes from the multi-mode fiber, and the effective intensity (⟨Ieff⟩) for the Gaussian beam [see Table V], which are shown in the third column of Table VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then, we calculate the gravitational force of the particle, and since we consider the particles to be spherical, FG = 4 3πa3ρ = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 pN, where a is the radius ( ∼ 8µm), and ρ is the density of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The buoyancy force, FB = ρairgV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 pN, is negligible compared to the FG, where ρair is the density of air, g is the gravitational constant, and V is the volume of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Finally, we calculate the photophoretic ∆α force using the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 5 as depicted below (discussed in detail in Appendix), F∆α = φ ∗ B1 = 3 4D 1 � p p∗ + p∗ p �a(Ts − Ti)∆α (2) The F∆α values are shown in the sixth column of Table VIII, where Ti is 298 K and the Ts values are taken from the last column of Table VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that it is impossible to know the exact distribution of accommodation coefficient α value over the particle surface, so that based on the literature [23], we assume the α1 and α2 of the particle as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='9 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 - giving ∆α value to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, while we know that F∆α dominates over F∆T at atmospheric pressure, in our case it is the F∆T values which dominate over F∆α, as the thermal conductivity of the particles we use is minimal, (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='072 W/(m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='K), which creates a substantial temperature difference across the particle surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Similarly, we calculate all the forces acting on the particle for both the Gaussian beam and mode 1 of multi-mode beam with the same beam size, which are shown in Table IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For 19 FAT + FRP + FB ↑FAαL Fμα α2 b F△αT α1 α1 >α2 FG Incident Laser BeamTABLE VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Calculation of all forces acting on the particle Beam Profile F∆Ts (pN) FRP (pN) FG (pN) FB (pN) F∆α (pN) Ftrap (pN) Mode 1 130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='10 (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='87) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='56 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='42) 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='68 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='94) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='81 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='45) Mode 2 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='91 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='28) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='24 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='32) 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='75 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='68) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='57 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='34) Mode 3 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='57 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='04) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='16 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='38) 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='61 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='51) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='70 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='36) the calculation of the photophoretic forces, we take the values of ∆Ts and Ts values from Table VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' TABLE IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Calculation of all forces acting on the particle Beam Profile F∆Ts (pN) FRP (pN) FG (pN) FB (pN) F∆α (pN) Ftrap (pN) Gaussian 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='52 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='38 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01 Mode 1 181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='01 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='95 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='038 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='46 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='79 Since the F∆α force is responsible for radial trapping (as we have mentioned earlier), the experimentally measured Ftrap values (shown in the last column of Table VIII and IX) can be compared with the F∆α values, obtained numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' It is clear from Table VIII and IX that we achieve good agreement between these values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' It is also important to note that in the experiments, we measure only the radial component of the F∆α force, which is not the case in the numerical estimation - so that it is reasonable to expect that the experimentally measured values would be lower than that estimated by the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is indeed what we obtain, as is clear from Table VIII and IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that, for Mode 3, we obtain a lower numerical value than the experimental one, as the size of bright and dark spots present in the pattern is lower than the trapped particle size, which might affect the numerical estimation of the number of spots illuminating the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, in our system, a particle is confined in a position axially when the gravitational force (FG) balances the other three forces, F∆T, FRP and FB) [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 7], though F∆T dominates the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' It can be observed from Table VIII and IX that in general, for the multi-mode beam profile, the total upward force (FU = F∆T +FRP +FB) is significantly larger compared to the gravity FG, as a result of which particles should shoot upwards in the propagation direction, and should thus not be confined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, we do observe very strong and stable trapping in our experiments with the multi-mode fiber with the same beam parameters used 20 in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We now attempt to explain this discrepancy using a simple model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In order to simulate the multi-mode profile consisting of alternate bright and dark regions, we assume a beam structure in which these regions are stacked one after another axially, as shown in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For simplicity, we assume that the particle experiences bright and dark spots in sequence, which may be the case if there is a small angle between the beam axis and the trajectory of the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, when we perform the experiments to compare the trapping forces for the multi-mode and single-mode cases, the experimentally measured particle location data shows that the average beam waist diameter where the particles are trapped for the multi-mode profile is around 200 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, in the simulation, we start from this position, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', assume z = 0 µm here (depicted as a dotted line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8), and correspondingly measure average intensity per speckle (⟨Ispeckle⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Once again, we consider the speckle size for the beam profile corresponding to Mode 1, since this is the mode we choose for the experiments to compare performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, using our earlier estimation of all forces acting on the particle, we define a resultant force (FRE), which is [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8]: FRE = FU − FG (3) where FU = F∆T + FRP + FB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' It is clear that FU >> FG, so that a particle experiences a force axially and moves with a resultant acceleration ar = Fre m − g, where m is the particle mass and g is the gravitational constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Here, we assume that initial velocity (u) at the starting point is zero (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', at z = 0 µm), and then determine the velocity v1 when the particle moves 8µm (h) using Newton’s motion laws, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' v = √u2 + 2arh, which gives v1 = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 µ m/s [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' After the particle traverses 8 µm from the initial position axially, we recalculate all the forces (we ignore the viscous drag by the air for simplicity), and determine FRE using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6, followed by the resultant acceleration ar of the particle at the new axial position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Since, FRE >> 1, the particle continues to move in the upward direction with an estimated velocity v2 = 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 µm/s [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' After this, however, the particle is at z = 16 µm, and arrives in a dark region of the beam, where the photophoretic ∆T and FRP forces are almost zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, the resultant acceleration ar of the particle would be −g, but due to the initial large acceleration of the particle - it continues to move in the upward direction by another 8 µm - albeit with a reduced velocity v3 = 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 µm/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Interestingly, at this position (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', at z = 24 µm, the upper surface of the particle interacts with the bright region of the beam, while the lower 21 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Model for particle oscillation along the z direction while being confined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' region samples a dark region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As a result, the F∆T force and FR force are reversed, and directed towards gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, the particle falls under gravity almost immediately, and back into a bright speckle again [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, the particle undergoes a stable oscillation in the axial direction, and remains confined in the photophoretic trap, even with the laser intensity generating a photophoretic force higher than the gravitational force corresponding to the weight of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (a) X-Z plot of a trapped particle’s trajectory using multimode fiber of Mode 1 profile (b) Corresponding velocity plot of that trajectory along the z direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A crucial issue now is to verify whether the mechanism we suggest for trapping from our 22 z = 64 μm z = 48 μm ↑ z = 40 μm Z axis z=32 μm 个 z = 24 μm Dark V3 = 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 um/s _ z = 16 μm V2 = 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 μm/s Z = 8 μm Bright V1 = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 μm/s wno=z - 0 μm/s Time20 b) (un) a 20 Velocity (μm/s) displacement ( 10 30 40 10 Z 50 20 20 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='42 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 0 2 4 6 8 10 ¥121416 X displacement (μm) time (sec)simulations is also observed in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is indeed the case - and we observe clear signatures of trapped particles oscillating in the z direction using Mode 1 [see Video1 in Appendix] of the multi-mode fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We have also quantified the average axial oscillation by tracking the trapped particle’s position along the x − z and y − z planes by analyzing videos of its motion using the Matlab software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For representation, the x − z trajectory of a trapped particle, and the corresponding velocity plot along the z axis is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 9(a) and (b), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We determine the average z oscillation of particles to be 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='1) µm from the data of 15 trapped particles of similar size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The oscillation amplitude is in reasonable agreement (around 17 %) with the value provided by our simulations (∼ 24 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Also, the maximum velocity we measure is around 20 µm/s, which is about 40 % different from the simulations (∼ 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 µm/s), but this difference could well be due to the fact that we have ignored the drag force by air in the simulation, and also the fact that our camera has a limited frame rate [60 FPS in this case].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Very interestingly, we observe oscillations of around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='5 µm in the radial direction as well in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 9(a), which are of almost constant amplitude as the particle moves axially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is understandable since the multi-mode beam has a speckle structure in all three dimensions, but the intensity of the speckles fall off faster in the radial direction (close to a Gaussian profile) compared to that in the axial direction - so that the particle displacement amplitude is smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (a) Simulation for finding out the z drifting of a trapped particle in case of Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (b) Experimental X-Z plot of a trapped particle’s trajectory using Gaussian beam Finally, we carry out a similar exercise for a particle trapped in a Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A calculation of all forces based on the location where the particle is trapped, as described 23 98 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='20 For25 mm I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='ens n b) lacement 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='061 F 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='00 displ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='05 Z 12 μm 104 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='8 72 30 20 10 0 10 20 30 X displecment (μum) z variation (um)in Table IX, reveals that the total upward force FU is slightly higher than the downward force FG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As a result, the particle can move in the upward direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Let us assume that the location of the trapped particle is a1 as shown in the right inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10(a), where we represent the propagation of Gaussian beam focused by a convex lens of focal length 25 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Since FU > FG at this location, the particle moves along the upward direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In the simulation, we move the particle by small step in this direction, and similar to the previous case, calculate all relevant forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, when the particle moves by 12 µm from the initial position as depicted by a2 in the right inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10 (a), we obtain FU = FG, so that the resultant force becomes zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Ideally, the particle can be stably confined at the a2 position, but due to perturbations such as laser intensity fluctuations, air turbulence, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' the particle may well oscillate around this equilibrium position, which is shown as a black dotted line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is exactly what we observe in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The average z oscillations we measure in particles trapped by a Gaussian beam [see Video2 in Appendix] is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='6 (1) µm (from 15 sets of data), which is again in reasonable agreement (around 20 %) from the simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The x − z trajectory plot of one of the trapped particles is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Radial oscillations are also observed, but these are on the average between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='2-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='3 µm, with a few oscillations reaching an extent of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='4 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is due to the fact that in comparison to a multi-mode beam profle - a Gaussian beam has more drastic intensity variation in the radial direction as compared to that in the axial direction (pure Gaussian versus quadratic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, for both multi-mode and Gaussian beams, axial and radial oscillations are observed, and may contribute significantly to the stable trapping of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Multi-mode beam profiles, changing less rapidly in intensity both radially and axially compared to Gaussian ones for the same focusing lens, offer considerably more robust trapping due to the larger dynamic equilibrium range in both dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A relevant question to ask here may be why a particle reaches an intensity region in the multi-mode profile which produces much higher photophoretic force than that required to balance its inertia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This, we believe, may to be due to the fact that we use a simple trapping chamber that is not sealed in any manner, so that particles falling are entirely exposed to microscopic air currents and turbulence, which may well exert instantaneous forces much larger than photophoretic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that the large axial trajectories observed in the multi-mode case may also be due to the fact that the particle will continue its upward 24 trajectory unless it comes into contact with a dark zone, at which point its trajectory will reverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, the spatial dynamic range of the particle oscillations are greater in the multi- mode fiber in almost all cases than that for single-mode fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We also believe that these oscillations are demonstrative of the existence of a restoring force in the case of photophoretic trapping even in the axial direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The magnitude of the restoring force appears to be higher for a multi-mode fiber compared to a single-mode case, with the presence of dark zones contributing in the final dynamic equilibrium achieved by the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In addition, the threshold power of trapping in the case of multi-mode fibers (see Table I) is also lower than that for a pure Gaussian trap, since the intensity per speckle is much higher than the overall intensity measured from the beam waist size - something which is not the case for a Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' CONCLUSION In conclusion, we employ a single multi-mode fiber to develop a robust three-dimensional optical trap for trapping absorbing particles in air employing photophoretic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We observe that the intensity profile created by the multi-mode fiber provides around eight times higher trapping force compared to that produced by a single-mode fiber that produces a pure Gaussian beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This is because the intensity a particle experiences in the speckle pattern generated by a multi-mode fiber is higher than the beam profile at the output of a single-mode fiber, so that the trapping force is correspondingly higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Our studies reveal that a beam profile where the speckle size is similar to the particle size produces the strongest traps, using which we achieve axial and radial velocities of 5 mm/s, which is presently limited by our experimental capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We validate our experimental results by developing a COMSOL-based simulation to calculate all the forces experienced by a trapped particle, and applying force balance to study the particle dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Our simulations reveal clear axial oscillations of the trapped particles in the case of both single and multi-mode fibers, with the multi-mode having higher spread due to the inherently high intensity of the individual speckles that constitute the beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We validate our simulation results with experimental observations, where both single and multi-mode fibers give rise to axial as well as radial particle trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The trajectories in the multi-mode case have considerably higher spread compared to the single mode case, as confirmed by our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Indeed, 25 our results also point out to the existence of an effective restoring force on the trapped particle in the axial direction, as is known to be the case in the radial direction [6–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' These need to be carefully studied in future research, along with more detailed and intensive modeling of the dynamics of trapped particles that are confined using photophoretic forces generated by a multi-mode and a single mode beam profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' While the detailed theory of photophoretic trapping itself is not available yet, with only quasi-emperical models proposed, our experiments definitively confirm the significant advan- tage provided by single multi-mode fiber-based photophoretic traps in terms of robustness, portability, ease of use, inexpensiveness, and the facilitation of diverse applications towards simultaneous trapping and spectroscopy of aerosols/bio-aerosols, and other diverse applica- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We hope to see exciting research in these directions in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Acknowledgements The authors acknowledge IISER Kolkata, an autonomous institution funded by the Min- istry of Education (MoE), Govt of India for funding and laboratory space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' SS thanks CSIR, MoE for fellowship support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Speckle Size Measurement We know that speckle is a random distribution of light field - consisting of a multitude of dark and bright spots resulting from destructive and constructive interference[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' There are different speckle parameters such as mean speckle size, contrast, intensity and polarization etc[25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' But here, we only consider the mean speckle size, defined as the average size of bright or dark spots present in the pattern[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, in order to find out the mean speckle size, we need to measure the Wiener spectrum of the pattern, which is the average strengths of all possible spatial frequency components of the pattern[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This can be done by calculating the normalized autocovariance function of the intensity speckle pattern obtained in the observation or image plane (x,y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Further, this function can be considered as the normalized autocorrelation function of the intensity, which has a zero base, and its width provides a good measurement of the average width of a speckle[25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Let us consider, I(i1, j1) and I(i2, j2) to be the gray values of two pixel points in the 26 image plane (i,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Then, the intensity autocorrelation function is defined as, RI(∆i, ∆j) = ⟨I(i1, j1)I(i2, j2)⟩ (4) where, ∆i = i1 − i2 and ∆j = j1 − j2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and ⟨.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='.⟩ represents a spatial average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, for simplicity, we assume i2 = 0, j2 = 0 and consider i1 = i and j1 = j, so the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 4 can be written as, RI(∆i, ∆j) = RI(i, j) (5) So, the normalized autocorrelation function of the intensity (CI(i, j)) can be expressed as, CI(i, j) = RI(i, j) − ⟨I(i, j)⟩2 ⟨I(i, j)2⟩ − ⟨I(i, j)⟩2 (6) Again, according to the Wiener-Khinchin theorem, the power spectral density of the wide- sense-stationary random process is the Fourier transform of the corresponding autocorre- lation function, which is again the square modulus of the Fourier transform of the signal (I(i,j)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, we can write, PSDI(νi, νj) = FT[RI(i, j)] = |FT[I(i, j)]|2 (7) Here FT represents the Fourier Transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, using the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 7, the normalized auto- correlation function of the intensity (CI(i, j)) [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 6] can be expressed as: CI(i, j) = FT −1[|FT[I(i, j)]|2] − ⟨I(i, j)⟩2 ⟨I(i, j)2⟩ − ⟨I(i, j)⟩2 (8) Thus, we determine the normalized auto-correlation intensity distribution (CI(i, j)) of any given pattern image using the algorithm described by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Numerical estimation of Photophoretic Forces We now numerically estimate the value of the photophoretic forces and radiation pres- sure force experienced by the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, we employ the analytical formula for pho- tophoretic ∆T and ∆α forces acting on a spherical particle provided by Rohatschek in his semi-empirical model of photophoretic forces[23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that the quantitative analysis of photophoretic forces acting on a particle is quite complex, as many factors are involved with this force - such as pressure, different parameters of light (beam profile, intensity, wavelength 27 of the laser, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' ), and most importantly, particle properties (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', particle size, morphology, thermal conductivity, absorptivity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=')[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, only semi empirical estimates of the forces are available from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, the calculation of the photophoretic forces sig- nificantly depend on the Knudsen number (kn) - defined as the ratio of the mean free path of the gas molecule (λ) and the size of the particle (a), Kn = λ a [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' When Kn > 1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', the particle size is considerably smaller than the mean free path of the gas molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This also includes conditions corresponding to very low pressure (p → 0) (mean free path of the gas molecules increases), where the free-molecular regime is applied for the calculation of photophoretic forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For Kn < 1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', when the particles size is much larger than the λ, or for atmospheric and high pressures, the continuum regime can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Since we trap particles in air at atmospheric pressure, where the mean free path of the air molecules are in the order of nanometers and the particle size is in the order of mirometers, Kn << 1 - hence the calculation of the photophoretic forces are based on the continuum regime[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Photophoretic forces may be generated both by the difference in the surface temperature (Ts) and by variations in the thermal accommodation coefficient (α) of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In our case, we assume a spherical particle of radius a, heated to a certain temperature (Ts) due to laser radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' When gas molecules having temperature Ti (< Ts) are incident on the surface of the particle, they are reflected off the particle and reach a higher temperature Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' This elevated temperature can be written using Knudsen’s concept of energy transfer by individual gas molecules interacting with a hotter surface as, Tr = Ti + α(Ts − Ti) (9) where, α is the thermal accommodation coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Let us consider the temperature of the gas layer adjacent to the surface of the particle to be (Ta), which can be expressed in terms of Ti and Tr as, Ta = niTi + nrTr (ni + nr) (10) where, ni and nr depicts the number density of the incident and reflected air molecules respectively, and the continuity at the surface signifies - nrcr = nici, so that, nr √Tr = ni √Ti, where c [= � 8RT/πM] is the mean velocity of the gas molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Substituting the above equation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 10, and further approximating the geometric mean by the arithmetic mean, the expression of Ta becomes, Ta = � Ti Tr = Ti + Tr 2 (11) 28 As we consider a spherical particle, we assume that the distribution of the difference in temperature (∆Ts), and accommodation coefficient (∆α) are rotationally symmetric, where Ts is measured about the direction of incident light, and α about an axis fixed to the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Besides, the temperature of the gas layer adjacent to the surface of the particle (Ta) is also assumed to have rotational symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, all the relevant quantities Ts, α and Ta can be expanded in terms of the Legendre polynomial Pn(cosθ), so that the surface temperature (Ts) of the particle can be written as, Ts = T∞ + ∞ � n=0 AnPn(cosθ) = T ′ s + A1cosθ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (12) where, T∞ denotes the temperature of the gas far from the sphere and T ′ s = T∞ + A0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Similarly, α can be expressed as, α = ∞ � n=0 anPn(cosθ) = a0 + a1cosθ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (13) And, the gas temperature next to the surface Ta can be represented as, Ta = T∞ + ∞ � n=0 BnPn(cosθ) = T ′ a + B1cosθ (14) where, T ′ a = T∞ + B0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In the following section, we calculate the photophoretic ∆Ts and ∆α forces where for the ∆Ts force, α is assumed to be constant, while for the ∆α force, we consider a constant average surface temperature of the particle (TS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Calculation of Photophoretic ∆Ts force We consider a spherical particle of radius a, which is highly light-absorbing, and has very low thermal conductivity kp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The particle is placed in an air medium at normal atmospheric pressure (p), and has a molecular weight M and viscosity η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The particle is illuminated by intense laser light in a direction opposite to gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Due to the high absorptivity of the particle at the operating wavelength of laser light, the surface facing the illumination source is warmer than the opposite side - resulting in a force in the direction of propagating light, termed as positive photophoresis force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The direction of this force is solely determined by the incident laser light direction - and is independent of the particle orientation, and hence 29 called space-fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As the temperature difference across the particle surface causes the force, which is directed longitudinally, it is also named as longitudinal photophoresis force (∆Ts) force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, for the continuum regime, the photophoretic ∆Ts force is derived from the ’thermal creep’ flow around the particle and the resulting viscous forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' In this regime, it is generally considered in the literature that the gas molecules adjacent to the particle have a similar temperature as the particle’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11, it is expected that for such a highly absorbing particle, the left side has a higher temperature Ts1 compared to the right side Ts2, in accordance with the illumination on the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, the air molecules impacting the left (hot) side are faster than those impacting the right (cold) side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Photophoretic ∆Ts force acting on a particle arising from thermal creep flow Now, due to the thermal accommodation, a symmetric velocity distribution of the gas molecules is obtained with respect to the perpendicular direction of the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hence, the warmer molecules coming from the left side transfer larger momentum to the particle along in the right direction compared to the colder molecules to the left - resulting in the particle experiencing a net force that is directed from the hot to the cold side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The air molecules correspondingly lose the same amount of momentum, so that a creeping flow around the particle from the cold side to the hot side occurs simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Now, the thermal creep velocity can be written as[23], us = κ η ρairT dT ds (15) where, us, η, and ρair are denoted the tangential velocity of the gas, the dynamic vis- cosity, and the mass density, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' T and dT ds are the temperature and tangential 30 Incoming radiation Colder molecules Hotter molecules Creep flowtemperature gradient in the gas adjoining the particle surface, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' T is written as Ta, κ is defined as the thermal creep coefficient, which is connected to the momentum accommodation coefficient having value κ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' The net photophoretic force can then be obtained by integrating the stress components in the z-direction over the surface[23] (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='15), as, F = 4πκ η2 ρTa A1 = 4πκRη2 Mp A1, (16) where, A1 is the first order Legendre coefficient corresponding to the particle’s surface tem- perature Ts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' We can rewrite Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='16 in terms of two other parameters D and p∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' as: F = 4πκη2 p � R M � A1 = 4πκη2 p �c2π 8T � A1 = 2D p∗ p aA1 (17) where D denotes a constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' determined entirely by the state of the gas and p∗ is the characteristic pressure that depends on particle radius,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and is expressed as,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' D = π 2 �π 3 κ cη Ta (18) p∗ = 1 2 √ 3πκ cη 1 a (19) However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' the parameter A1 can be calculated either by knowing the value of the surface temperature difference of the particle or the laser irradiance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Here we consider only the known surface temperature difference of the particle (∆Ts) that can be written as[23], Ts = Ts + 1 2∆Tscosθ (20) Again, comparing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 20 with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 12, we obtain, A1 = 1 2∆Ts (21) Hence, the final form of the photophoretic ∆Ts force can be found by putting the expression of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 21 for A1 into the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 12, as: F = D p∗ p a∆Ts (22) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Estimation of the Photophoretic ∆α force The photophoretic ∆α force arises due to the difference in accommodation coefficient of the particle surface, which might be caused due to differences in surface roughness or com- position of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' For the calculation of F∆α we consider that the particle’s surface 31 has two different thermal accommodation coefficient values α1 and α2, where α1 > α2, and assume that the particle has an average surface temperature (Ts) which is hotter than the surrounding air molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Note that a higher value of the thermal accommodation coeffi- cient signifies a higher heat transfer rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thus, the surface of the particle with a higher value of α transfers more heat to the air molecules compared to the other surface having a lower accommodation coefficient value - resulting in the particle experiencing a thrust in the direction of the high accommodation (α1) surface to the low accommodation surface (α2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' However, the photophoretic ∆α force calculation is based on a common photophoretic func- tion (φ), and an estimation of B1 - which is a first-order Legendre coefficient of temperature distribution in the gas layer next to the surface - arises due to the difference in the accom- modation coefficient (α ̸= 0), and not by a difference in the surface temperature(A1 = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' So, the photophoretic ∆α force can be written as, F∆α = φ ∗ B1 (23) This photophoretic function φ is entirely dependent on the gas temperature, and hence it covers both ∆Ts and ∆α forces and can be expressed as[23, 28] φ = D 2 � p p∗ + p∗ p �a (24) The next step is to calculate the B1 value, and for that, the molecular energy transfer in the Knudsen layer needs to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' As the gas temperature next to surface Ta depends on the accommodation distribution values of the particle surface, a relationship between B1 and a1 - where the latter is the first order Legendre coefficient of the accommodation coefficient - can be found out using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (9), (11),(13) and (14), assuming that Ts = Ts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 2Ta = α(Ts − Ti) + 2Ti [Putting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (11) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (9) ] ⇒ Ta = α 2 (Ts − Ti) + Ti ⇒ Ta = 1 2(a0 + a1cosθ)(Ts − Ti) + Ti [From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (14) α = a0 + a1cosθ ] ⇒ Ta = �1 2(Ts − Ti)a0 + Ti � + a1 2 (Ts − Ti)cosθ Comparing this with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (14) [Ta = Ta + B1cosθ], we obtain, B1 = a1 2 (Ts − Ti) (25) 32 Again, the value of coefficient a0 and a1 can be obtained as, a0 = α;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' a1 = 3 4∆α (26) where, α = α1+α2 2 , and ∆α = α1 − α2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Plugging Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' (26) into (25), the value of B1 becomes, B1 = 3 8(Ts − Ti)∆α (27) So, the photophoretic ∆α force can be obtained by putting the expression of φ [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='24] and B1 [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='27] into the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='23 and the result is F∆φ = φ ∗ B1 = 3 4D 1 � p p∗ + p∗ p �a(Ts − Ti)∆α (28) Thus, we use the expression of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 22 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 28 for the determination of the photophoretic ∆T and ∆α forces, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Desyatnikov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kivshar, Optics Express 17, 5743 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Desyatnikov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kivshar, Optics Express 17, 8201 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [3] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Izdebskaya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Desyatnikov, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kivshar, Physical review letters 105, 118103 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Horvath, KONA Powder and Particle Journal 31, 181 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [5] Teiser, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' and Dodson-Robinson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=', Astronomy & Astrophysics 555, A98 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Bera, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Sil, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Saha, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Saha, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Banerjee, Optics letters 41, 4356 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Sil, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Saha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Bera, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Banerjee, Journal of Optics 19, 12LT02 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Sil, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Basak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Pahi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Banerjee, Applied Physics Letters 117, 221106 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Sil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Pahi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Punse, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Banerjee, Journal of Optics (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [10] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hnatovsky, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shostka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, Optics letters 37, 1934 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Wei, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Cheng, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Wu, Optics express 22, 23716 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 33 [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Porfirev and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Skidanov, Optics express 23, 8373 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Redding and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Pan, Optics letters 40, 2798 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Lamhot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Barak, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Peleg, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Segev, Physical review letters 105, 163906 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Prakash, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Huang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hernandez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Salazar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Christodoulides, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Chen, Optics letters 36, 1491 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Alpmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Esseling, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rose, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Denz, Applied Physics Letters 100, 111101 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Goodman, JOSA 66, 1145 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [18] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Izdebskaya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Desyatnikov, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kivshar, Optics express 18, 3137 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [19] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Shvedov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rode, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Izdebskaya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Leykam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Desyatnikov, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Krolikowski, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kivshar, Journal of Optics 12, 124003 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [20] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Volpe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Volpe, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Gigan, Scientific reports 4, 1 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Jamali, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Nazari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Ghaffari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Velu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Moradi, Nanophotonics 10, 2915 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kotnala, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Kollipara, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Zheng, Nanophotonics 9, 927 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Rohatschek, Journal of Aerosol Science 26, 717 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Ghatak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thyagarajan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Thyagarajan, An introduction to fiber optics (Cambridge university press, 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Piederri`ere, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Cariou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Guern, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Le Jeune, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Le Brun, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Lotrian, Optics Express 12, 176 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [26] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hamarov´a, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' ˇSm´ıd, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Horv´ath, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Hrabovsk`y, Measurement Science Review 14, 177 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' de Ara´ujo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Silva, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' de Lima, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Pereira, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' de Oliveira, Applied optics 48, 393 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' Reed, Journal of Aerosol Science 8, 123 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} +page_content=' 34' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNE2T4oBgHgl3EQfvQhy/content/2301.04089v1.pdf'} diff --git a/ZtA0T4oBgHgl3EQfF_9p/vector_store/index.pkl b/ZtA0T4oBgHgl3EQfF_9p/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..42fb3cf8ba7f53a0c0b48a938847113ddc040c85 --- /dev/null +++ b/ZtA0T4oBgHgl3EQfF_9p/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:af7a685a505f148a7fb0f285930fb0736d456541eaea0cd4e6a3db4893ee2072 +size 182246 diff --git a/_tE2T4oBgHgl3EQfmwdA/vector_store/index.pkl b/_tE2T4oBgHgl3EQfmwdA/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..223c1bc08c30b0058a9c521efc905ed9856040c1 --- /dev/null +++ b/_tE2T4oBgHgl3EQfmwdA/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9f15c6accd1e7a5d8eedc20b1d2ac8124e33063f45c1d7d734b9ca8b4e500129 +size 265439 diff --git a/adE1T4oBgHgl3EQfwwXB/content/2301.03415v1.pdf b/adE1T4oBgHgl3EQfwwXB/content/2301.03415v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..23e10d99feb0568f2f1a16b427016b65e76ae412 --- /dev/null +++ b/adE1T4oBgHgl3EQfwwXB/content/2301.03415v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a49b5fb35ec95902191ffa77102f3e1f138975c319320f0d93add7b4ebb6290c +size 1247099 diff --git a/adE1T4oBgHgl3EQfwwXB/vector_store/index.pkl b/adE1T4oBgHgl3EQfwwXB/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..5fd946fd6cd8c63d84447b0a4ea23fabf7b662af --- /dev/null +++ b/adE1T4oBgHgl3EQfwwXB/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4fceb7068efda516a28b4ceb539efaaa27c805da9170a0fbc6a7c187835d5777 +size 256063 diff --git a/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/2301.05412v1.pdf.txt b/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/2301.05412v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..cae82e8f9ca2b7342da651cf14dcc2b5f5ba8d7d --- /dev/null +++ b/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/2301.05412v1.pdf.txt @@ -0,0 +1,2270 @@ +Evolve Path Tracer: Early Detection of Malicious Addresses in +Cryptocurrency +Ling Cheng +Singapore Management University +Singapore +Feida Zhu +Singapore Management University +Singapore +Yong Wang +Singapore Management University +Singapore +Ruicheng Liang +Hefei University of Technology +Heifei, China +Huiwen Liu +Singapore Management University +Singapore +ABSTRACT +With the ever-increasing boom of Cryptocurrency, detecting fraudu- +lent behaviors and associated malicious addresses draws significant +research effort. However, most existing studies still rely on the full +history features or full-fledged address transaction networks, thus +cannot meet the requirements of early malicious address detection, +which is urgent but seldom discussed by existing studies. To de- +tect fraud behaviors of malicious addresses in the early stage, we +present Evolve Path Tracer which consists of Evolve Path Encoder +LSTM, Evolve Path Graph GCN, and Hierarchical Survival Predictor. +Specifically, in addition to the general address features, we propose +asset transfer paths and corresponding path graphs to characterize +early transaction patterns. Further, since the transaction patterns +are changing rapidly during the early stage, we propose Evolve Path +Encoder LSTM and Evolve Path Graph GCN to encode asset transfer +path and path graph under an evolving structure setting. Hierar- +chical Survival Predictor then predicts addresses’ labels with nice +scalability and faster prediction speed. We investigate the effective- +ness and versatility of Evolve Path Tracer on three real-world illicit +bitcoin datasets. Our experimental results demonstrate that Evolve +Path Tracer outperforms the state-of-the-art methods. Extensive +scalability experiments demonstrate the model’s adaptivity under +a dynamic prediction setting. +KEYWORDS +Early malice detection, Asset transfer path, Evolve encoder, Cryp- +tocurrency, Bitcoin +1 +INTRODUCTION +Cryptocurrency has rapidly grown into a decentralized global finan- +cial system in the past decade. Unfortunately, it has long been criti- +cized for accommodating various cybercrime due to its anonymity. +According to the recent Crypto Crime Report by chainalysis1, mali- +cious addresses’ illegal profits exceeded 2.5 billion dollars. Among +all cryptocurrency platforms, Bitcoin (BTC) has the largest vol- +ume, while the on-chain record data for a certain address are much +scarcer than other popular platforms (e.g., ETH, EOS with smart +contracts). Thus, researchers and practitioners have made signifi- +cant efforts to fight against these fraudulent activities and identify +the associated malicious addresses on BTC. Moreover, these methods +are compatible with those on other cryptocurrency platforms. +1https://go.chainalysis.com/2021-Crypto-Crime-Report.html +Spend TX j +Spend TX i +Recieve TX n +… +… +j +i +Path & Graph +Extractor +… +Recieve TX m +n +m +… +… +… +LSTM/GCN +Forward +LSTM/GCN +Attention +P +Survival Prediction +Module +λAF +λBK-Path +λBK-Graph +λFR-Path +λFR-Graph +Backward +Address +Feature +Evolve Path-Graph +Encoder +∑ +Figure 1: The framework of our Evolve Path Tracer. At +each time step, the path extractor first extracts forward (FR: +pink arrows) and backward (BK: green arrows) asset transfer +paths. The graph extractor builds the path graph to link re- +lated asset transfer paths. Then, the Evolve Path-Graph En- +coder encodes asset transfer paths with corresponding Path- +LSTM models. The Path-GCN module refines the path rep- +resentations with the Path-Graphs. The attention module +will propose corresponding features with an attention sum- +mation. The weights of the Path-LSTM, Path-GCN, and at- +tention modules are provided by address features. Finally, +based on five types of features (Address Feature, BK/FR Path +Feature, BK/FR Graph Feature), the survival probability is +given by the corresponding survival rates 𝜆. TX stands for a +transaction, P stands for predictions. +Most existing detection methods focus on designing features +to characterize specific types of malicious activity with detailed +case studies. Besides, by combining statistic analysis and visualiza- +tion technology, they successfully identified some representative +malicious transaction patterns. Recent studies [3, 5, 30] further +leverage deep-learning techniques to detect malicious addresses. +By encoding account features and the transaction network struc- +ture with deep-learning models, they achieve great performance +improvement in malicious address detection. +However, malicious activities are evolving faster than ever before, +and it is impossible to build a unique feature set for every newly +emerging malicious activity. Although some studies [13] can detect +categories of malicious activities, they are still only available for +post-hoc analysis. Most of them invariably require a full-history +feature observation, which is consequentially scarce at the early +stage of fraud activities, thus they can’t be directly deployed to +detect illicit activities at the early stage. Recently, Random walk +and graph neural network [3, 7, 30, 31] are adopted to encode the +topological feature of transaction network automatically, which +improves the performance of general malice detection tasks. But +arXiv:2301.05412v1 [cs.AI] 13 Jan 2023 + +Conference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +most of them require a full-fledged address transaction network +which is also unavailable under the early stage settings, as the +newly created transaction graphs are usually small, unconnected +and fast-evolving. Also, traditional address transaction networks +may suffer from the issue of scalability, shadow addresses, and the +dilution of the minority class. +Considering the essence of blockchain is a ledger of transactions +(TXs), malicious addresses’ objective is to transfer illicit money to +a legal place. We can derive their intentions by monitoring their +real-time transactions. Thus, in this work, we first set up the Early +Malicious Address Detection (EMAD) task, which is urgent but sel- +dom discussed by existing studies. Then, we develop a path ex- +tractor to focus on transaction paths, especially those significant +paths, which can characterize the early-stage transactions of illicit +addresses effectively. As shown in Figure 1, two kinds of asset trans- +fer paths, i.e., forward and backward transition paths, are proposed +to describe the flow-in and flow-out transition patterns. The asset +transfer paths focus on the token (BTC) flow, thus can relieve the +problem of shadow addresses. +Besides, illicit activities are usually organized together for spe- +cific purposes, and the behavior patterns evolve fast during the +early stage. As a result, encoding each path individually may miss +critical information. Furthermore, static encoding models can’t cap- +ture the dynamism of evolving graphs. Thus, we build an asset path +GCN module to encode the path’s inter-relation. In this graph, asset +transfer paths connect to each other if they share the same intersec- +tion addresses. Inspired by [23], we equip our path encoder and path +GCN module with an evolving mechanism for more sophisticated +path representations under the dynamic setting. +Considering the scalability issue, we implement a Hierarchical +Survival Prediction module to alleviate the workload of feature +preparation during the prediction. Previous prediction results can +be directly used in the next time step, which empowers the model +with a faster prediction speed and the ability to deal with a dy- +namic setting. In summary, the contributions of this paper can be +summarized as follows: +• The Asset Transfer Paths are proposed for the EMAD task, +which is urgent but seldom discussed. These paths exhibit +high versatility in monitoring transaction patterns of various +malicious behaviors in the early stage and relieve the prob- +lem of shadow addresses. This novel concept can be easily +transplanted to all current blockchain-based cryptocurren- +cies and traditional financial systems. +• We propose the Evolve Path Tracer model that can fully uti- +lize the asset transfer paths to encode various transaction +patterns. Besides, it can also encode the paths’ structural +relationship under a dynamic setting with a novel evolve +path graph encoding module. The versatility and dynamic +flexibility are unachievable by other existing models. +• We conduct extensive evaluations to assess the model’s ef- +fectiveness, and the results show that Evolve Path Tracer +delivered a substantially better performance for three dif- +ferent illicit datasets than the state-of-the-art models. Also, +owing to the Hierarchical Survival Prediction module, our +Evolve Path Tracer can effectively predict addresses’ labels +scales well for the increasing data. +2 +RELATED WORK +Early detection of malicious addresses on Bitcoin is an urgent yet +seldom discussed task. Thus, we first review the related works about +malice detection on Bitcoin and related cryptocurrencies. Then, we +briefly review previous works about early rumor detection, which +discussed similar tasks but under the social media circumstance. +2.1 +Malice Detection on Cryptocurrency +Case Analysis mainly focuses on addresses’ behaviors in a cer- +tain case. Reid et al. [24] identified entities by considering similar +transaction times over an extended timeframe. Androulaki et al. [2] +considered several features of transaction behavior, including the +transaction time, the index of addresses, and the value of transac- +tions. Jourdan et al. [10] explored five types of features, including +address features, entity features, temporal features, centrality fea- +tures, and motif features. Vasek et al. [29] gave a list of Bitcoin scams +and conducted a statistical study. Case-Related features are often +helpful in interpreting certain cases based on heuristic clustering +and tainted fund flow. However, these methods require intensive +case analysis, and most of the insights are only available in some +specific cases, let alone apply to other platforms with complex +heterogeneous relationships in general [12, 27]. +Machine Learning can automatically learn general address fea- +tures to address the poor generalization ability of case-related meth- +ods. Yin et al. [33] applied supervised learning to classify entities +that might involve in cybercriminal activities. Akcora et al. [1] +applied the topological data analysis (TDA) approach to generate +the bitcoin address graph for ransomware payment address de- +tection. Shao et al. [25] embedded the transaction history into a +lower-dimensional feature for entity recognition. Nerurkar et al. +[21] used 9 features to train the model for segregating 28 different +licit-illicit categories of users. The general address features improve +the model’s generality significantly. However, they are challenging +to characterize addresses’ behaviors comprehensively. Particular +transaction patterns of asset flow are difficult to be reflected in +these characteristics. +Graph Based Methods focus on the interaction patterns between +object addresses and related addresses. Harlev et al. [7] consid- +ered transaction features in a supervised machine learning frame- +work to de-anonymize Bitcoin addresses and predict the type of +yet-unidentified entities. Wu et al.[31] proposed two kinds of het- +erogeneous temporal motifs in the Bitcoin transaction network +and applied them to detect mixing service addresses. Weber et +al. [30] encodes address transaction graph with GCN, Skip-GCN, +and Evolve-GCN. Chen et al.[3] proposed E-GCN for phishing node +detection on the ETH platform. Tam et al.[28] proposed EdgeProp, a +GCN-based model, to learn the representations of nodes and edges +in large-scale transaction networks. Lin et al.[16] proposed two +kinds of random walk-based embedding methods to encode specific +network features. By changing the sampling strategy in Node2Vec, +Wu et al.[32] proposed the Trans2Vec model, which can consider +the temporal information. Li et al.[13] proposed TTAGN to model +the temporal information of historical transactions for phishing +detection. Chen et al.[4] proposed the AntiBenford subgraph frame- +work for anomaly detection in the Ethereum transaction network +under an unsupervised setting. Network-based methods perform + +Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency +Conference’17, July 2017, Washington, DC, USA +well for retrospect analysis, as they encode the structural informa- +tion. However, in the early stages, the trading network is often too +small to form a discriminative topological structure. The perfor- +mance will degrade greatly if the networks are of sparse structures +for the emerging networks with few connections[36]. Also, these +methods may lead to Over-Smoothing issues and the dilution of the +minority class [18] under the data-unbalanced setting [9, 35, 37]. +2.2 +Early Rumor Detection +Cho et al. [6] used GRU, a typical neural network for sequence +modeling. At each time split, previous hidden state and current +summation features are fed into the GRU unit to predict the labels +for the given samples. Song et al. [26] proposed CED, which also +uses GRU for sequence modeling. They proposes the concept of +“Credible Detection Point,” to increase the prediction speed. Yuan et +al. [34] developed a multi-source long-short term memory network +(M-LSTM) to model user behaviors by using a variety of user edit +aspects as inputs. Zheng et al. [38] put forward SAFE. Instead +of predicting the labels directly, it generates hazard rates for the +survival models. The positive samples should die out fast, while +the negative samples should stay alive. +3 +PROBLEM DEFINITION +In the BTC system, a transaction 𝑡𝑥 is bound to an address. Each +𝑡𝑥 has a set of inputs 𝐼= {𝑖1,𝑖2, . . .𝑖 |𝐼 |} and a set of outputs 𝐽= +{𝑗1, 𝑗2, . . . 𝑗|𝐽 |}. The input and output are still transactions.𝑡𝑥 records +token distribution between 𝐼 and 𝐽. Narratively speaking, the in- +coming tokens flow into a pool and then flow to the outgoing +transactions according to the prior agreement proportion. There is +no record of how many tokens flow from an Input 𝑖 to an Out- +put 𝑗. Thus, we have to build a complete transaction bipartite +graph for this 𝑡𝑥 and generate |𝐼| × |𝐽 | transaction pairs in total. +In other words, a BTC transaction has |𝐼| × |𝐽 | transaction pairs +inside. 𝐷𝑡𝑚={𝑑𝑖 +𝑡𝑚 }𝑁 +𝑖=1={(𝑙𝑖,𝑇𝑖 +𝑖𝑛,𝑡𝑚,𝑇𝑖 +𝑜𝑢𝑡,𝑡𝑚)}𝑁 +𝑖=1 is the input data by +the 𝑡𝑚-th time step, where 𝑙𝑖 ∈ {0, 1} is the label of Address 𝑖, +and 0 or 1 stands for regular and malicious addresses respectively. +𝑇𝑖 +𝑖𝑛,𝑡𝑚=[𝑡𝑥𝑖 +𝑖𝑛,1,𝑡𝑥𝑖 +𝑖𝑛,2, . . .𝑡𝑥𝑖 +𝑁𝑖𝑛,𝑡𝑚 ] and 𝑇𝑖 +𝑜𝑢𝑡,𝑡𝑚 are the transaction +sets where Address 𝑖 acts as the input and output address by the +𝑡𝑚-th time step respectively. For ease of understanding, we denote +these two transaction sets as 𝑅𝑒𝑐𝑒𝑖𝑣𝑒 set and 𝑆𝑝𝑒𝑛𝑑 set respectively. +Early Malicious Address Detection (EMAD). Given a set of ad- +dresses 𝐴, and 𝐷𝑡𝑚 at timestep 𝑡𝑚, the problem is to build a binary +classifier 𝐹 such that +𝐹 (𝑑𝑖 +𝑡𝑚) = +� +1 +if Address 𝑖 is malicious +0 +Otherwise +. +(1) +In the early detection task, to prevent the model predicts conflict +labels at different timesteps, which will confuse users, thus we +require the prediction to be consistent and predict the correct label +as early as possible. We denote the confident time as 𝑡𝑐, where all +classifier predictions 𝐹 after 𝑡𝑐 are consistent. The smallest 𝑡𝑐 is +denoted as 𝑡𝑓 .𝑐. Our purpose is to train a classifier that predicts the +correct label of an address with a smaller 𝑡𝑓 .𝑐. +4 +ASSET TRANSFER PATH +4.1 +Overview and Motivation +Take Address𝑖’s𝑅𝑒𝑐𝑖𝑒𝑣𝑒 transaction set as an example. For a𝑅𝑒𝑐𝑒𝑖𝑣𝑒 +transaction 𝑗0 in the set, suppose we find its significant asset source +𝑗1, which is also a transaction. Then we link 𝑗1 and 𝑗0 to form an +asset transfer pair. After we trace the asset source iteratively, the +asset transfer pairs form an asset transfer path naturally. As shown +in Fig2 (b), for Receive Tx R-1 in the Flow of Receive Tx, after +we trace its asset source, we can get three critical transfer pairs, +namely (10 →R-1, 11 →R-1, 12 →R-1). As shown in Backward Asset +Transfer Path, iteratively, we can get four paths (P-1, P-2, P-3, P-5) +ended with R-1. Among them, three paths(P-1, P-2, P-3) have the +same source (Tx-1 colored green). Also, another path (P-4) ended +with R-2 is initiated by the same source, thus we group them into a +path graph, which is colored green, as shown in the Backward Path +Graph. +Since every transaction is bound to an address at a specific times- +tamp, thus, if all paths come from the same source, then we can +say that, at a particular time point, an address initiates multiple +transactions at the same time, and all transactions’ destinations are +Address 𝑖. If we encode each path as a node, these nodes can be +connected through this source of funds, thus forming a graph. We +build the path graph to reflect: 1) the characteristics of each path, +2) the interaction between paths, and 3) the characteristics of the +asset source. We believe this information is crucial for the early +detection of malicious behavior, and we will justify the statement +in the experiments. +4.2 +Influence and Trust Transaction Pair +Not all transaction pairs help identify illicit addresses. Those note- +worthy pairs typically constitute a significant amount portion of +the entire transaction. As illustrated in Fig. 2(a), the receive 𝑇𝑋𝑗 +receive assets from three spend TXs (each contributing 35%, 30% +and 35% to the total transaction amount). On the other hand, the +spend 𝑇𝑋𝑖 transfers out BTCs to three receive TXs (with a distribu- +tion of 25%, 45%, and 30% as in this example). Given an Address 𝑖 +and a time step 𝑡𝑚, TXs in the shaded dotted-lined box represent all +spend TXs, and receive TXs occurred up to timestep 𝑡𝑚 associated +with Address 𝑖. +As mentioned in Section 3, given a set 𝐼= {𝑖1,𝑖2, . . .𝑖 |𝐼 |} of |𝐼 | +spend transactions to an receive transaction 𝑗 and the set {𝐼 → 𝑗} of +all transaction pairs, i.e., {𝐼 → 𝑗}={(𝑖1, 𝑗), (𝑖2, 𝑗), . . . , (𝑖 |𝐼 |, 𝑗)}, we +define Influence Transaction Pair as follows: Given an influence +activation threshold 𝜃, (𝑖𝑘, 𝑗) is called an Influence Transaction +Pair for transaction 𝑗, if there exists a 𝑘 (1 ≤ 𝑘 ≤ |𝐼|) such that +the amount of transaction pair (𝑖𝑘, 𝑗) contributes at least a certain +proportion of the received amount of transaction 𝑗, i.e, ˆ𝐴(𝑖𝑘, 𝑗) ≥ +𝜃 × ˆ𝐴({𝐼 → 𝑗}) where ˆ𝐴(·) denotes the amount of a transaction +pair or the sum of all transaction pairs. +Similarly, given a set 𝐽= {𝑗1, 𝑗2, . . . 𝑗|𝐽 |} of |𝐽 | transactions, and +a transaction 𝑖, and the set {𝑖 → 𝐽 } of all transaction pairs whose +spend transaction is 𝑖, i.e., {𝑖 → 𝐽 }={(𝑖, 𝑗1), (𝑖, 𝑗2), . . . , (𝑖, 𝑗|𝐽 |)}. If +there exists a receive transaction 𝑗𝑘, 1 ≤ 𝑘 ≤ |𝐽 | such that trans- +action 𝑖 transfers at least a certain proportion of its spend amount +to it, this transaction pair is called a Trust Transaction Pair for + +Conference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +Spend TX1 +Spend TXi +Spend TX|I| +35% +35% +30% +… +… +1 Day +Spend TXi +Spend TX1 +Spend TXN +Receive TXj +Receive TX1 +Receive TXM +… +… +… +… +Address Involved TXs +Receive TXj +… +… +Backward +… +… +25% +30% +45% +Spend TXi +Receive TX1 +Receive TXj +Receive TX|J| +… +… +Forward +1 Day +R-1 +11 +R-2 +8 +4 +7 +12 +5 +1 +2 +6 +13 +9 +3 +10 +Flow of Receive TX +R-1 +11 +8 +4 +1 +R-1 +10 +7 +4 +1 +R-1 +12 +5 +1 +R-2 +13 +5 +1 +R-1 +12 +5 +2 +R-2 +13 +5 +2 +R-2 +13 +9 +6 +2 +R-2 +13 +9 +3 +P-1 +P-3 +P-2 +P-4 +P-5 +P-6 +P-7 +P-8 +Backward Asset Transfer Path Backward Path Graph +S-1 +S-2 +11 +6 +1 +12 +7 +2 +16 +13 +8 +3 +17 +14 +9 +4 +15 +10 +5 +18 +Flow of Spend TX +16 +11 +6 +1 +S-1 +16 +12 +6 +1 +S-1 +16 +12 +7 +2 +S-1 +16 +12 +7 +3 +S-1 +16 +13 +8 +3 +S-1 +17 +13 +8 +3 +S-1 +18 +14 +9 +4 +S-2 +18 +15 +10 +5 +S-2 +Forward Path Graph +Forward Asset Transfer Path +P-6 +P-8 +P-7 +P-1 +P-3 +P-2 +P-4 +P-5 +(a) Asset Transfer Path +(b) Asset Transfer Path Graph +P-1 +P-2 +P-3 +P-4 +P-1 +P-2 +P-3 +P-4 +P-5 +P-6 +P-7 +P-8 +P-5 +P-6 +P-7 +P-8 +Figure 2: (a) Asset transfer pairs. Given an address, we col- +lect its transaction history (All its Receive and Spend TXs +in the dotted box). For each Receive TX, we trace its asset +source from the inflow (Green Spend TXs) to build Influ- +ence TX pairs. For each Spend TX, we trace its asset desti- +nation from the outflow (Yellow Receive TXs) to build Trust +TX pairs. 𝑁 = 𝑁𝑖𝑛,𝑡𝑚, 𝑀 = 𝑁𝑜𝑢𝑡,𝑡𝑚. (b) Asset transfer path and +path graph. By tracing the asset source iteratively, we get a +series of Influence TX pairs. We combine them end-to-end to +form Backward Asset Transfer Path (Similar to Forward As- +set Transfer Path). If paths have the same source or destina- +tion, we connect them through their intersection to form a +path graph (Graph in the same color). Different colors stand +for different starting or ending points. +transaction 𝑖, as it indicates a certain form of trust from 𝑖 to 𝑗𝑘 in +terms of asset transfer. +Given an influence transaction pair (𝑖𝑘, 𝑗), we can conclude that +transaction 𝑗 obtains at least a significant amount (based on the +threshold) of the asset in this transaction from transaction 𝑖𝑘. Ac- +cordingly, given a transaction 𝑗, if there exists a sequence of transac- +tion pairs such that (I) each pair is an influence transaction pair; (II) +the spend transaction of each pair is the receive transaction of the +previous pair; and (III) the receive TX of the last pair is transaction +𝑗, we call such a sequence an Backward Path for 𝑗 as indicated +by the green arrow in Fig. 2(a). It reveals where 𝑗 obtains the asset +and can be used to trace back to the source of the asset. The detail +to prepare the backward asset transfer path is shown in Appendix. +Similarly, we can define a Forward Path to trace the destinations +of transaction 𝑖’s asset flow. For brevity, we would refer to both the +Backward Path and Forward Path as Asset Transfer Paths. +4.3 +Asset Transfer Path Graph +The transaction graph between addresses has been widely used +in the detection task of cryptocurrency. However, these methods +may suffer from the perturbation of shadow addresses and the +scalability issues caused by mixing services. If the malicious use +mixing services, although we will get more asset transfer paths, +suspicious paths will still converge. +Therefore, unlike the previous address-based graph, we build +graphs based on the asset transfer path. As shown in Fig. 2(b), in the +path graph part, each node represents an asset-transfer path. If two +paths share the same source (for backward paths) or destination +(for forward paths), we then connect them with an edge, thus we +can get a group of fully-connected graphs. Since every source or +destination has a binding address at a specific timestep, we use the +feature of this binding address at this time point to represent the +edge feature in the corresponding graph. The address features and +transaction features are illustrated in Appendix. +5 +EVOLVE PATH TRACER +At the 𝑡-th timestep, We will generate five kinds of features to cal- +culate corresponding hazard rates (𝜆) for prediction (1: Address +Feature Hidden Vector (AF Hidden Vector), 2: Backward Path Fea- +ture (BK-Path), 3: Backward Graph Feature (BK-Graph), 4: Forward +Path Feature (FR-Path), 5: Forward Graph Feature (FR-Graph)). Be- +fore generating the hazard rates, all these features will be encoded +through the corresponding LSTM modules (T-1 to T-5 LSTM). +Besides, to capture the dynamics of path evolution, the param- +eters of forward and backward Evolve Path Encoder LSTM (E-1, +E-2 LSTM) are provided by AF hidden vector. Also, forward and +backward Evolve Path Graph GCN parameters are calculated with +AF hidden vector. As shown in Fig 3, in the Evolve Path Encoder +LSTM and Evolve Path Graph GCN, the parameters (the gray and +white nodes) are consistent with the AF hidden vector to show their +interactions. +5.1 +Evolve Path Encoder LSTM +Address Feature is the basis for modeling and reasoning the address +transaction pattern. We implement an address feature LSTM (T-1 +LSTM), which will guide the processing in other modules. +ℎ𝑇1 +𝑡 ,𝑐𝑇1 +𝑡 += LSTM𝑇1 (𝑓 𝑢 +𝑡 ,ℎ𝑇1 +𝑡−1,𝑐𝑇1 +𝑡−1), +(2) +where ℎ𝑇1 +𝑡 +∈ R𝑑 and 𝑐𝑇1 +𝑡 +∈ R𝑑 are the hidden state and the cell state +of T-1 LSTM at time 𝑡. 𝑓 𝑢 +𝑡 +∈ R𝑑𝑛 is the address feature at time 𝑡. +𝑑 is the dimension of hidden state, 𝑑𝑛 is the dimension of address +feature. +As mentioned in Section 4, asset transfer path is composed of a +series of transaction nodes. The lengths of these paths are different. +To encode them uniformly, we project an original path 𝑃𝑜 to an +uniform path 𝑃𝑢 with length of 𝐿𝑢. Given an original path 𝑃𝑜 with +length of 𝐿𝑜, the zoom ratio is calculated by 𝑅𝑧 = 𝐿𝑜/𝐿𝑢, then the +𝑖-th (start from 0) node in 𝑃𝑢 is calculated by the average feature of +the (⌊𝑖 × 𝑅𝑧⌋)-th node to the (⌈(𝑖 + 1) × 𝑅𝑧⌉-1)-th node of 𝑃𝑜. Then, +we denote the uniform path as: +P1:Lu = [𝑝1, 𝑝2, . . . , 𝑝𝐿𝑢 ], +(3) +Different addresses have different characteristics, their path +structures also differ along the timeline. Thus we may lose dy- +namic information with a static encoder. Inspired by Evolve-GCN, +the parameters of our Path Encoder LSTM are determined by the +current address feature. In Evolve-GCN, the weights are updated +by themselves or those representative nodes, thus may dismiss + +Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency +Conference’17, July 2017, Washington, DC, USA +the individual address property. Instead, we use the combination +of address feature and the temporal path feature to generate the +weights of Path Encoder LSTM module. Take backward asset trans- +fer paths as example, for the 𝑗-th node in the input asset transfer +path, backward Evolve Path Encoder LSTM (E-1 LSTM) computes +the following function: +𝐻𝑝 +𝑡 = [ℎ𝑇1 +𝑡 ||ℎ𝑇2 +𝑡−1], +𝑖𝑗 = 𝜎((𝑊𝑖𝑖𝐻𝑝 +𝑡 )𝑝𝑗 + (𝑊ℎ𝑖𝐻𝑝 +𝑡 )ℎ𝐸1 +𝑗−1 + 𝑏𝑖𝐻𝑝 +𝑡 ), +𝑓𝑗 = 𝜎((𝑊𝑖𝑓 𝐻𝑝 +𝑡 )𝑝𝑗 + (𝑊ℎ𝑓 𝐻𝑝 +𝑡 )ℎ𝐸1 +𝑗−1 + 𝑏𝑓 𝐻𝑝 +𝑡 ), +𝑔𝑗 = tanh((𝑊𝑖𝑔𝐻𝑝 +𝑡 )𝑝𝑗 + (𝑊ℎ𝑔𝐻𝑝 +𝑡 )ℎ𝐸1 +𝑗−1 + 𝑏𝑔𝐻𝑝 +𝑡 ), +𝑜𝑗 = 𝜎((𝑊𝑖𝑜𝐻𝑝 +𝑡 )𝑝𝑗 + (𝑊ℎ𝑜𝐻𝑝 +𝑡 )ℎ𝐸1 +𝑗−1 + 𝑏𝑜𝐻𝑝 +𝑡 ), +𝑐𝑗 = 𝑓𝑗 ⊙ 𝑐𝑗−1 + 𝑖𝑗 ⊙ 𝑔𝑗, +ℎ𝐸1 +𝑗 += 𝑜𝑗 ⊙ tanh(𝑐𝑗), +(4) +where || stands for concatenation,ℎ𝑇2 +𝑡−1 ∈ R𝑑 is the hidden state of T- +2 LSTM at timestep 𝑡-1. T-2 LSTM encodes the temporal information +of the backward asset transfer path set. 𝑊∗∗ ∈ R𝑑×𝑑×2𝑑 and 𝑏∗ ∈ +R𝑑×2𝑑 are learnable weights that transfer 𝐻𝑝 +𝑡 to the weights of +projection layers and bias terms. 𝜎 stands for sigmoid function, ⊙ is +the Hadamard product. Finally, each backward asset transfer path +is denoted as final hidden state ℎ𝐸1 +𝐿𝑢 of E-1 LSTM. The representation +of the 𝑖-th path at timestep 𝑡 is 𝑓 𝑝 +𝑖,𝑡. +Not all paths are equally informative for the prediction. We +expect to select more informative paths, thus we adopt multi-head +attention for the selection. +𝑎𝑗 +𝑖,𝑡 = 𝑊 𝑎,𝑗tanh(𝑊 𝑝,𝑢 [𝑓 𝑝 +𝑖,𝑡 ||ℎ𝑇1 +𝑡 ]), +(5) +𝛼 𝑗 +𝑖,𝑡 = Softmax(𝑎𝑗 +𝑖,𝑡) = exp(𝑎𝑗 +𝑖,𝑡)/ +𝑁𝐸1 +∑︁ +𝑘=1 +exp(𝑎𝑗 +𝑘,𝑡), +(6) +ˆ𝑓 𝑝 +𝑡 = ||𝑀𝑝 +𝑗=1 ˆ𝑓 𝑝,𝑗; +ˆ𝑓 𝑝,𝑗 +𝑡 += +𝑁𝐸1 +∑︁ +𝑖=1 +𝛼 𝑗 +𝑖,𝑡 𝑓 𝑝 +𝑖,𝑡, +(7) +where𝑊 𝑝,𝑢 ∈ R +𝑑 +𝑀𝑝 ×2𝑑 and𝑊 𝑎,𝑗 ∈ R1× 𝑑 +𝑀𝑝 are learnable matrices, +𝑗 stand for the index of the attention head, 𝑀𝑝 is the total head +number. 𝑁𝐸1 is the backward asset transfer path number. where +ˆ𝑓 𝑝,𝑗 +𝑡 +is the weighted summed path feature vector of 𝑗-th head, ˆ𝑓 𝑝 +𝑡 +is the concatenation of all heads’ output. The hidden state ℎ𝑇2 +𝑡 and +cell state 𝑐𝑇2 +𝑡 of T-2 LSTM are updated as: +ℎ𝑇2 +𝑡 ,𝑐𝑇2 +𝑡 += LSTM𝑇2 ( ˆ𝑓 𝑝 +𝑡 ,ℎ𝑇2 +𝑡−1,𝑐𝑇2 +𝑡−1). +(8) +5.2 +Evolve Path Graph GCN +If several paths are initiated by or converge at the same transaction, +it may indicate certain suspicious patterns. By encoding the rela- +tionships between these path, model can capture certain significant +patterns in detection. Similarly, due to the volatility of the path +graph, we may lose the discriminative characteristics with a static +model. To resolve this challenge, we propose Evolve Path Graph +GCN. Take backward asset transfer paths as example, the nodes in +the path graph are updated as follow: +𝐻𝑔 +𝑡 = [ℎ𝑇1 +𝑡 ||ℎ𝑇3 +𝑡−1], +𝑓 𝑔 +𝑡 = 𝜎( ˜D− 1 +2 ˜ +A ˜D− 1 +2 (𝑓 𝑝 +𝑡 𝑊 𝑔𝐻𝑔 +𝑡 )), +˜ +A = A + I, +A𝑖,:,𝑗 = (𝑊 𝑒𝐻𝑔 +𝑡 )𝑆𝑖,𝑗, +˜D = diag( +∑︁ +𝑗 +(𝐴𝑖,𝑗 + I𝑖,𝑗)), +(9) +where ℎ𝑇3 +𝑡−1 ∈ R𝑑 is the hidden state of T-3 LSTM at time 𝑡-1. T- +3 LSTM encodes the temporal information of the backward path +graph. 𝑓 𝑝 +𝑡 ∈ R𝑁𝐸1×𝑑 are the representations of path set at timestep +𝑡. 𝐴 ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 and I ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 are the adjacent matrix +and the identity matrix respectively. If the 𝑖-th path and 𝑗-th path +have the same source, then 𝐴𝑖,:,𝑗=1 ∈ R𝑑. Otherwise, 𝐴𝑖,:,𝑗=0 ∈ R𝑑. +If the 𝑖-th path and 𝑗-th path have the same source, 𝑆𝑖,𝑗 ∈ R𝑑𝑛 is +the intersection address feature of path 𝑖 and path 𝑗. Otherwise, +𝑆𝑖,𝑗=0 ∈ R𝑑𝑛. 𝑊 𝑔 ∈ R𝑑×𝑑×2𝑑 and 𝑊 𝑒 ∈ R𝑑×𝑑𝑛×2𝑑 are learnable +weights, and they project 𝐻𝑔 +𝑡 to the weights of the corresponding +projection layers. Thus A ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 . +We denote the output of Evolve Path Graph GCN encode as +interaction-aware asset transfer paths. Resemble the previous cal- +culation, we adopt multi-head attention to select significant signals +for these interaction-aware paths. We denote the ˆ𝑓 𝑔 +𝑡 as the final re- +sult of multi-head attention of interaction-aware paths. The hidden +state ℎ𝑇3 +𝑡 and cell state 𝑐𝑇3 +𝑡 of T-3 LSTM are updated as: +ℎ𝑇3 +𝑡 ,𝑐𝑇3 +𝑡 += LSTM𝑇3 ( ˆ𝑓 𝑔 +𝑡 ,ℎ𝑇3 +𝑡−1,𝑐𝑇3 +𝑡−1). +(10) +5.3 +Hierarchical Survival Predictor +Due to the property of consistent prediction, survival analysis [38] +is proved to be effective in the early detection task. The survival +function 𝑆(𝑡) of an event represents the probability that this event +has not occurred by time 𝑡. The hazard rate function 𝜆𝑡 is the +event’s instantaneous occurrence rate at time 𝑡 given that the event +does not occur before time 𝑡. In our case, the observation time is +discrete in our case, we use 𝑡 to denote a timestamp. The association +between 𝑆(𝑡) and 𝜆𝑡 can be calculated as: +𝑆(𝑡) = 𝑃(𝑇 ≥ 𝑡) = +∞ +∑︁ +𝑘=𝑡 +𝑓 (𝑥), +𝜆𝑡 = 𝑓 (𝑡)/𝑆(𝑡), +𝑆(𝑡) = exp(− +𝑡∑︁ +𝑘=1 +𝜆𝑘). +(11) +Considering the model’s scalability during the real-time prediction, +we define the event as “the address is benevolent” and we call hazard +rate as benevolent rate. As the majority addresses are negative +(benevolent) in the BTC platform. Once the address is classified as +benevolent, we remove it from the monitoring list to reduce the +computation cost. +To get more consistent predictions, previous work deployed a +Softplus function 𝜆𝑡 (𝑥𝑡) = 𝑙𝑛(1 + exp(𝑥𝑡)) to guarantee the haz- +ard rate 𝜆𝑡 is always positive. Hence, the survival probability 𝑆(𝑡) + +Conference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +Evolve Path Encoder LSTM +P-6 +P-8 +P-7 +P-1 +P-3 +P-2 +P-4 +P-5 +P-6 +P-8 +P-7 +P-1 +P-3 +P-2 +P-4 +P-5 +1 +t +tm +Evolve Path Graph GCN +T-1 +LSTM +E-1 +LSTM +T-2 +LSTM +BK-Graph +Encoder +E-2 +LSTM +T-4 +LSTM +FR-Graph +Encoder +λ BK- +Path +λ BK- +Graph +λ FR- +Path +λ FR- +Graph +λ AF +… +… +Prob. +λ-sum (i-1) +λ-sum (i) +∑ +T-5 +LSTM +T-3 +LSTM +Figure 3: Detailed pipeline of Evolve Path Tracer. Five LSTM +models (T-1 to T-5 LSTM) are implemented to encode tem- +poral information of different features. AF hidden vectors +will update the parameters of Forward and Backward Evolve +Path Encoder LSTM (E-1/2 LSTM) and Evolve Path Graph +GCN (BK/FR-Graph Encoder). Evolve Path Encoder LSTM +and Evolve Path Graph GCN are proposed to encode asset +transfer paths and path graphs dynamically. For detailed de- +scriptions of each module, please refer to Appendix. +monotonically decreases. However, the model can hardly classify +addresses correctly in the early hours. Those false-positive predic- +tions will never be corrected with the monotonically decreasing +survival probability. Thus, we release this restriction with a 𝑡𝑎𝑛ℎ +activation function for benevolent rate calculation. The consistency +is assured by Consistency Loss Function which will be elaborated +later. +We designed five parallel benevolent rates corresponding to each +kind of information (address feature, path feature (backward and +forward), and graph feature (backward and forward)). At time step +𝑡, the calculation of these benevolent rates and the prediction as +follows: +𝜆𝑗,𝑡 = tanh(𝑊 ℎ𝑧 +𝑇𝑗 ℎ𝑇𝑗 +𝑡 ), +ˆ𝑦𝑡 = exp(−ReLU( +𝑡∑︁ +𝑖=1 +5 +∑︁ +𝑗=1 +𝜆𝑗,𝑖)), +(12) +where 𝑊 ℎ𝑧 +𝑇𝑗 ∈ R1×𝑑 is the linear projection matrices for the output +of T-j LSTM. At each time step, survival analysis first sums all pre- +vious benevolent rates, then it sums the current 5 benevolent rates +hierarchically. Once addresses’ current benevolent rates reach a cer- +tain threshold, we can remove them from monitoring list to speed +up the prediction and relieve the computing cost in the following +hours. +5.4 +Training and Dynamical Prediction +Model Training Model should give higher 𝑆(𝑡) to malicious ad- +dresses and lower 𝑆(𝑡) to benevolent addresses in every time split. +For Address𝑖, at timestep 𝑡𝑚, the early detection likelihood function +and the negative logarithm prediction 𝑙𝑜𝑠𝑠𝑃 are shown as below: +𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = (1 − 𝑆(𝑡𝑚))1−𝑙𝑖𝑆(𝑡𝑚)𝑙𝑖 += (1 − exp(− +𝑡𝑚 +∑︁ +𝑡=1 +5 +∑︁ +𝑗=1 +𝜆𝑗,𝑡))1−𝑙𝑖 (exp(− +𝑡𝑚 +∑︁ +𝑡=1 +5 +∑︁ +𝑗=1 +𝜆𝑗,𝑡))𝑙𝑖, +𝑙𝑜𝑠𝑠𝑃 +𝑖,𝑡𝑚 = 𝑙𝑖 +𝑡𝑚 +∑︁ +𝑡=1 +5 +∑︁ +𝑗=1 +𝜆𝑗,𝑡 + (𝑙𝑖 − 1)𝑙𝑛(1 − exp(− +𝑡𝑚 +∑︁ +𝑡=1 +5 +∑︁ +𝑗=1 +𝜆𝑗,𝑡)). +(13) +Besides, 𝑙𝑜𝑠𝑠𝑃 is weighted by √𝑡𝑚 to avoid the perturbation in the +early period due to the data insufficiency. +Consistency-boosted Loss Function Since the rate function is +not guaranteed to be positive in our model, a consistency loss +𝑙𝑜𝑠𝑠𝐶 is necessary for consistent predictions. In every time split, +the benevolent rate should have the same sign as the previous time +split. +𝑙𝑜𝑠𝑠𝐶 +𝑖,𝑡𝑚 = +� +0 +sign(𝜆𝑡𝑚−1 ∗ 𝜆𝑡𝑚) >= 0 +1 +else +, +(14) +where 𝜆𝑡0 = 0. Similarly, model should be able to rectify the poor +prediction in the early period, thus the 𝑙𝑜𝑠𝑠𝐶 is also weighted by +√𝑡𝑚. +Besides, since the numbers of positive and negative instances are +imbalanced, different penalty coefficients are allocated to each class. +Then, given a set of training samples with 𝑁𝑝 malicious addresses +and 𝑁𝑛 legal addresses, the overall loss function is defined as: +ℒ = +𝑡𝑀 +∑︁ +𝑡=1 +√ +𝑡(𝐶+ +𝑁𝑝 +∑︁ +𝑖=1 +(𝑙𝑜𝑠𝑠𝑃 +𝑖,𝑡 + 𝛾𝑙𝑜𝑠𝑠𝐶 +𝑖,𝑡)+ +𝐶− +𝑁𝑛 +∑︁ +𝑖=1 +(𝑙𝑜𝑠𝑠𝑃 +𝑖,𝑡 + 𝛾𝑙𝑜𝑠𝑠𝐶 +𝑖,𝑡)), +(15) +where 𝐶+ and 𝐶− are inversely proportional to the number of pos- +itive and negative instances in our settings. 𝛾 is a coefficient to +control the contribution between 𝑙𝑜𝑠𝑠𝑃 and 𝑙𝑜𝑠𝑠𝐶. +Dynamical Prediction Besides the “Early Stop” mechanism pro- +vided by Hierarchical Survival Predictor, our dynamical construction +scheme of asset transfer paths can also relieve the time cost of fea- +ture preparation. As shown in Fig. 4, the path data can be reused if +no new transaction occurs in this interval. If an address has new +Receive or Spend transactions, model will create new backward +or forward asset transfer paths accordingly. Moreover, model also +check the endpoint of the forward paths to determine whether they +need to be extended or not. +6 +EXPERIMENT AND ANALYSIS +In this section, we perform empirical evaluation to answer the +following research questions: +• RQ1: What is the performance with respect to different +uniform path lengths? +• RQ2: Does Evolve Path Tracer outperform the state-of-the- +art methods for early malicious address detection? +• RQ3: How dose each components benefit the final detection +performance? + +Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency +Conference’17, July 2017, Washington, DC, USA +R-1 +R-2 +S-1 +S-2 +Timestep 1 +Timestep 2 +Timestep 3 +Figure 4: Dynamical Construction of asset transfer path. The +three vectors on the left are Address Features corresponding +to Timestamp 1 to Timestamp 3. Different dash boxes repre- +sent input information at different timestamps. +Table 1: Dataset Statistics +Type +Definition +Posi. +Nega. +P/N(%) +H +Hack and steal tokens +302 +6582 +4.03 +R +Encrypt data for ransoms +3224 +21100 +15.28 +D +Illegal BTC darknets +5838 +109937 +5.31 +• RQ4: Dose the time overhead of the preparation procedure +and scalability satisfy the real-time requirement? +6.1 +Data Collection and Preparation +The transaction data are publicly accessible by running a Bitcoin +client. We obtained all the data from the 1-st to the 700, 000-th +block for higher credibility, as we only collect addresses verified by +enough participants. For a given address, we get the related trans- +action history based on the APIs exposed by BlockSci [11]. Based +on this transaction history, we can calculate the related features +and prepare the asset transfer paths and path graphs. To get the +labels for three different illicit activities (Hack, Ransomware, and +Darknet), we performed a manual search on public forums and +datasets, such as Bitcointalk forum2, Reddit, WalletExplorer3 and +several prior studies [14, 22, 31] to fetch related labels. Negative +(Regular) addresses are collected in the same method as [17, 31]. We +set the activation threshold as 0.01 to prepare the asset transfer path. +One can set a smaller threshold depending on the operating device. +More detail about the statistical properties of the asset transfer path +can be found in Appendix A. Table. 1 shows the summarized de- +scriptions: The definition and numbers of positive (Posi), negative +(Nega), and Positive/Negative ratio (P/N) for each malicious type +(H: Hack, R: Ransomware, D: Darknet). +6.2 +Settings and Metrics +As our purpose is to detect malicious addresses as early as pos- +sible, the model should detect them before the institution’s daily +settlement when the institutions may find the malice by themselves. +Therefore, our experiments focus on early illicit detection during +the first day. Although the experiments investigate the performance +during the first day, our Evolve path Tracer can work with an arbi- +trary timespan. To evaluate the performance of our model, we get +2https://bitcointalk.org/ +3https://www.walletexplorer.com +0.75 +0.00 +2 +4 +6 +8 +10 +12 +2 +4 +6 +8 +10 +12 2 +4 +6 +8 +10 +12 +Hack +Ransomware +Darknet +Figure 5: 𝐹1𝐸 and 𝐹1𝐶 of different uniform path lengths on +three datasets. +24 hours data with 1 hour interval, and we average the evaluation +metrics on all timesteps. +The selected metrics are accuracy (Acc.), precision (Prec.), and +recall (Rec.). Besides, the model should predict correct labels fast +to prevent economic loss earlier. Also, due to data insufficiency, +the model may predict conflict labels at different timesteps, thus +confusing users. Thus we require the predictions to be consistent. +we introduce the early-weighted F1 score 𝐹1𝐸 and consistency- +weighted score 𝐹1𝐶 as follows: +F1E = +�𝑁 +𝑖=1 𝐹1𝑖/ +√ +𝑖 +�𝑁 +𝑖=1 1/ +√ +𝑖 +, +F1C = +�𝑁 −1 +𝑖=1 +√ +𝑖 × 𝐹1𝑖 × 1𝑦𝑐 (𝑦𝑖) +�𝑁−1 +𝑖=1 +√ +𝑖 +, +(16) +where 𝑖 is the timestep, 𝑦𝑐 is the set of predictions where 𝑠𝑖𝑔𝑛((𝑦𝑖 − +0.5) × (𝑦𝑖+1 − 0.5)) > 0. The indicator function 1𝑦𝑐 (𝑦𝑖) = 1 when +𝑦𝑖 ∈ 𝑦𝑐. 𝐹1𝑖 is the 𝐹1 score of the prediction at timestep 𝑖. +6.3 +Effects of Uniform Path Length (RQ1) +As mentioned in Section 5.1, to encode the asset transfer paths, +we need to project asset transfer paths to the same length 𝐿𝑢. We +further analyze the effects of uniform path length with a simplified +AF/Path model (using Address features and Asset Transfer Path +features). We test 6 groups with different path lengths (From 2 to +12 by the interval of 2) on all three datasets. As we use a simplified +model, we focus on the path length that maximizes the performance. +as shown in Figure 5. +A Uniform path with a longer length can preserve more infor- +mation that contributes to better performance. Thus the model +performs better as 𝐿𝑢 increases at the beginning. However, if the +𝐿𝑢 is longer than most asset transfer paths, the uniform path may +introduce more redundant noise. Therefore, the model does not +perform better when the path length is too large. +Since hack addresses get funds directly from the victim’s ac- +count and need to transfer money as soon as possible, its asset +transfer path is shorter. As shown in Fig 5, the model achieves the +best 𝐹1𝐸 and 𝐹1𝐶 scores when setting 𝐿𝑢 to 4 and 6, respectively. +Considering both scores, the model performs best when 𝐿𝑢 equals +6. Ransomware is malicious software that threatens the victims +to pay a ransom fee. In many cases, the ransom demand comes +with a deadline. Victims buy bitcoins from exchanges and transfer +them to criminals, thus slightly increasing the lengths of the asset +transfer paths. As shown in Fig 5, the model performs best When +the 𝐿𝑢 is 6. A darknet is an overlay network within the Internet that +can only be accessed with specific authorization. Thereby, users +could buy and sell illicit goods anonymously via the darknet. Since +platforms need to wait for the activity of buyers and sellers, there + +F1E +F1CF1E +F1CConference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +Positive B.R +Negative B.R +Prediction +Hack +Ransomware +Darknet +AF B.R +FR Path B.R +BK Path B.R +FR Graph B.R +BK Graph B.R +Figure 6: Prediction evolution of different address groups +and corresponding average Benevolent Rates (B.R) of differ- +ent features. +will be a longer asset transfer path. The model performs best When +the 𝐿𝑢 is 8. However, setting 𝐿𝑢 to 6, the model gets similar scores. +Considering the model’s scalability, in the actual experiment, we +also set 𝐿𝑢 to 6. +6.4 +Performance Comparison (RQ2) +To verify the effectiveness and versatility of our Evolve Path Tracer, +we first compare the most common machine learning models, then +compare our encoder module with the encoder in other early de- +tection models. At last, we also compare the address graph-based +models. The models are detailed in the appendix. The main results +for comparing all different methods are shown in Table 2, and the +major findings are summarized as follows: +(1) In terms of the five evaluation metrics, our Evolve Path Tracer +outperforms most compared methods by a significant margin. Es- +pecially for early detection performance metrics F1-E and F1-C, our +Evolve Path Tracer achieves the best performance under all three +datasets. Compared to the second-best methods, Evolve Path Tracer +has an average increase of 14.54% on 𝐹1𝐸 and an average increase +of 15.63% on 𝐹1𝐶. Besides, none of these methods can perform well +on all three datasets. These significant performance margins justify +the effectiveness and versatility of our Evolve Path Tracer. Besides, +the "Early Stop" mechanism accelerates the prediction speed and +helps the model discard subsequent noise, improving the model’s +performance. +(2) Traditional machine learning algorithms do not perform well +on the three datasets because these algorithms are difficult to en- +code temporal information. It is difficult for decision-tree-based +machine learning algorithms to consider shifts in the feature deci- +sion boundary along the times [19, 20]. Therefore, our model has +an average improvement of 80.52% on 𝐹1𝐸 and 83.44% on 𝐹1𝐶 com- +pared to the best decision-tree-based model. The sequential deep +learning methods perform well on the three datasets. However, +our Evolve Path Tracer still has an average 21.82% improvement on +𝐹1𝐸 and 24.11% on 𝐹1𝐶 compared to the best model in this group. +The first reason is that the inter-relationships among asset transfer +paths can reveal specific transaction patterns (e.g., two addresses +transfer money through multiple paths to avoid monitoring). In +addition, since the transaction pattern evolves in the early stage, a +static encoding module can hardly encode evolving information. +(3) Compared with Address Graph methods, our Evolve Path +Tracer has an average increase of 22.74% on 𝐹1𝐸 and an average +increase of 23.36% on 𝐹1𝐶. Among them, Evolve-GCN performs +the best in most datasets, which verifies the fast-evolving of early +transaction networks. However, as [18] implies, the address GCN +may lead to Over-Smoothing issues and the dilution of the minority +class. In our cases, most neighbors of malicious nodes are victims or +shadow addresses. Thus the Address Graph models do not perform +well. To avoid the dilution problem, in Evolve Path Tracer, we set +vertices as transactions to utilize the relevant address information +in a "safer" way. +6.5 +Ablation Study (RQ3) +As shown in Table 3, AF performed poorly on the three datasets. +Because many benevolent addresses (change address, ICO, and legal +market addresses) behave similarly to these malicious addresses. As +shown in Fig. 6, the AF benevolent rates for most negative samples +do not exceed 2.5. The introduction of asset transfer path features +significantly improves the performance. As shown in Fig. 6, for +the Hack addresses, the forward transaction signal is more impor- +tant than the backward one because the Hack address will transfer +the funds faster and more centralized. Ransomware and Darknet +addresses usually require victims or buyers to transfer funds ac- +cording to certain conditions. Thus the backward information is +more valuable. +Comparing +Path and +Graph, by encoding the paths’ interrela- +tionships, the model gives predictions based on transaction patterns +rather than the fluctuation of a single path. As shown in Fig. 6, the +prominent signals of malicious nodes are enhanced by introducing +path graphs. In the cryptocurrency transaction network, There- +fore, the model should be able to handle the differences between +various types of addresses at different times. By comparing the +performance differences between +Graph and +Evolve, we found +that this Evolve mechanism is necessary. +Graph only performs +well if the address has a shorter life span, and these addresses will +be discarded after the first few transactions. However, for other +addresses with longer lifetimes, +Evolve can better reflect changes +in the transaction patterns of these addresses, resulting in better +performance. +6.6 +Scalability and Dynamical Prediction (RQ4) +Feature Preparation Time Cost When a new block appears, real +users will generally monitor the addresses that have transactions +with them. Those new and large-volume addresses are likely to +participate in dangerous activities. Thus, we randomly selected +1, 000 blocks (from the first block of 2018 to the first block of 2022) +and collected the daily BTC price during this period. We filter out +transactions lower than $10, 000 and retrieve address with a lifespan +less than one week. We prepare every address’s data of the first 24 +hours, the time cost is illustrated as follows: During each interval +(1 hour is about 6 blocks), we need to monitor about 1, 166 new +addresses, which will only cost 5 minutes. Moreover, as shown in +Table 4, our time cost resembles address graph preparation, but we +can collect information much further than 2 hops. + +0.8 +0.6 +0.4 +0.2 +0.0 +-0.2 +-0.41.00 +0.75 +0.50 +★★★ +0.25 +0.0015.0 +12.5 +10.0 +7.5 +5.0 +2.5 +0.0 +1 +6 +11 +16 +2110 +0 +-5 +-10 +-151.00 +★★★★★★★★ +0.75 +0.50 +0.25 +0.00★ +Posi.Prediction +- +Nega. Prediction★ +Posi. Prediction +Nega. Prediction★ +Posi. Prediction +Nega. Prediction8 +7 +6 +5 +4 +3 +2 +1 +6 +11 +16 +210.12 +0.10 +0.08 +0.06 +0.041.00 +0.75 +0.50 +0.25 +0.0015.0 +12.5 +10.0 +7.5 +5.0 +2.5 +0.0 +1 +6 +11 +16 +21Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency +Conference’17, July 2017, Washington, DC, USA +Table 2: Scores of different prediction model. Evo-PT and Evo-PT (E) are our Evolve Path Tracer with/wo “Early Stop” mecha- +nism. Underline stands for best score in the group, Bold stands for best score in all groups. +Type +Model +Name +Hack +Ransomware +Darknet +𝐴𝑐𝑐. +𝑃𝑟𝑒𝑐. +𝑅𝑒𝑐. +𝐹1𝐸 +𝐹1𝐶 +𝐴𝑐𝑐. +𝑃𝑟𝑒𝑐. +𝑅𝑒𝑐. +𝐹1𝐸 +𝐹1𝐶 +𝐴𝑐𝑐. +𝑃𝑟𝑒𝑐. +𝑅𝑒𝑐. +𝐹1𝐸 +𝐹1𝐶 +Machine +Learning +DT +0.995 +0.347 +0.137 +0.197 +0.197 +0.955 +0.736 +0.432 +0.545 +0.545 +0.982 +0.448 +0.152 +0.227 +0.227 +RF +0.996 +0.405 +0.242 +0.303 +0.303 +0.955 +0.735 +0.436 +0.547 +0.547 +0.983 +0.519 +0.109 +0.181 +0.181 +XGB +0.997 +0.347 +0.137 +0.197 +0.197 +0.960 +0.865 +0.435 +0.579 +0.579 +0.985 +0.790 +0.191 +0.308 +0.308 +Sequen. +Deep +Learning +GRU +0.928 +0.298 +0.438 +0.354 +0.354 +0.885 +0.558 +0.949 +0.703 +0.703 +0.942 +0.470 +0.838 +0.603 +0.603 +M-LSTM +0.949 +0.418 +0.272 +0.328 +0.333 +0.887 +0.561 +0.969 +0.711 +0.710 +0.951 +0.520 +0.845 +0.642 +0.645 +CED +0.909 +0.265 +0.563 +0.360 +0.360 +0.909 +0.617 +0.960 +0.752 +0.751 +0.943 +0.478 +0.829 +0.606 +0.606 +SAFE +0.918 +0.285 +0.438 +0.271 +0.330 +0.909 +0.616 +0.963 +0.752 +0.752 +0.949 +0.508 +0.838 +0.632 +0.632 +Addr. +Graph +GCN +0.920 +0.433 +0.670 +0.501 +0.507 +0.887 +0.564 +0.936 +0.700 +0.706 +0.942 +0.459 +0.613 +0.525 +0.524 +Skip-GCN +0.917 +0.410 +0.690 +0.443 +0.432 +0.903 +0.603 +0.935 +0.729 +0.735 +0.941 +0.459 +0.629 +0.531 +0.530 +Evo-GCN +0.893 +0.428 +0.749 +0.427 +0.442 +0.906 +0.613 +0.944 +0.736 +0.746 +0.941 +0.459 +0.633 +0.530 +0.533 +TX. +Graph +Evo-PT +0.963 +0.607 +0.739 +0.664 +0.668 +0.938 +0.743 +0.869 +0.799 +0.802 +0.963 +0.624 +0.764 +0.686 +0.686 +Evo-PT (E) +0.969 +0.650 +0.731 +0.689 +0.683 +0.940 +0.751 +0.869 +0.802 +0.807 +0.964 +0.625 +0.754 +0.686 +0.687 +Table 3: Scores of different ablation models on Hack (H), +Ransomware (R), and Darknet (D). Ablation modules in- +clude Address Features (AF), Path features (+Path), Path +Graph features (+Graph), and Evolve schemes (+Evolve). +Model +𝐴𝑐𝑐. +𝑃𝑟𝑒𝑐. +𝑅𝑒𝑐. +𝐹1𝐸 +𝐹1𝐶 +H +AF +0.920 +0.309 +0.590 +0.389 +0.412 ++Path +0.954 +0.537 +0.546 +0.509 +0.538 ++Graph +0.965 +0.686 +0.476 +0.545 +0.559 ++Evolve +0.961 +0.606 +0.553 +0.551 +0.576 +R +AF +0.911 +0.710 +0.632 +0.626 +0.628 ++Path +0.929 +0.727 +0.805 +0.760 +0.765 ++Graph +0.927 +0.696 +0.875 +0.773 +0.776 ++Evolve +0.937 +0.735 +0.871 +0.795 +0.798 +D +AF +0.961 +0.619 +0.571 +0.611 +0.604 ++Path +0.961 +0.611 +0.693 +0.649 +0.650 ++Graph +0.960 +0.586 +0.804 +0.678 +0.678 ++Evolve +0.963 +0.626 +0.758 +0.685 +0.685 +Table 4: Time cost of different input data, includes Block +Number, Transaction Number, Address Number), Address +Feature, Asset Transfer Path, Path Graph, and Address +Graph. +#Blk +#TX +#Addr +A-Feat +Path +P-G +A-G +1,000 +306,258 +194,310 +175s +7.7h +6.9h +14.3h +Avg. +306 +194 +0.2s +27.6s +24.8s +51.4s +Scalability of Early Stop To justify the Scalability of our “Early +Stop” mechanism, we plot the skip ratios with a different threshold. +As shown in Fig. 7, all models can filter out most (80%) addresses by +the fourth hour. The mechanism improves the model’s Scalability +significantly. Moreover, choosing a reasonable threshold helps the +Hack +Ransomware +Darknet +0.2-Recall: 0.91 +0.4-Recall: 0.91 +0.6-Recall: 0.84 +0.8-Recall: 0.72 +1.0-Recall: 0.73 + Inf-Recall: 0.73 +0.2-Recall: 0.92 +0.4-Recall: 0.91 +0.6-Recall: 0.90 +0.8-Recall: 0.87 +1.0-Recall: 0.87 + Inf-Recall: 0.87 +0.2-Recall: 0.76 +0.4-Recall: 0.76 +0.6-Recall: 0.76 +0.8-Recall: 0.75 +1.0-Recall: 0.76 + Inf-Recall: 0.76 +Figure 7: Skip Ratio evolution and 𝑅𝑒𝑐𝑎𝑙𝑙 scores with differ- +ent thresholds. The gray line is the Positive/Negative ratio +of each dataset. +model to discard subsequent noise and improve the model’s per- +formance, as mentioned in Section 6.4. A lower threshold means a +faster prediction speed. +However, there is a concern about missing malicious addresses as +we decrease the threshold for faster prediction speed. Which then +decreases the model’s Recall scores. As shown in Fig, compared to +the model without “Early Stop” (labeled as “Inf”), the model has +better Recall scores as we decrease the threshold. This is because our +model can predict the most benevolent addresses in the early hours. +Removing them from the monitoring list can avoid subsequent +noise, which improves the model’s Recall scores. Thus our Evolve +Path Tracer has a faster prediction speed without missing malicious +addresses. +7 +CONCLUSION AND FUTURE WORK +In this paper, we present Evolve Path Tracer, a novel framework for +early malicious address detection on BTC. We first propose asset +transfer paths and encode them with Evolve Path Encoder LSTM. +The asset transfer paths exhibit high versatility in monitoring trans- +action patterns of various malicious behaviors in the early stage. +To take full advantage of these paths, the Evolve Path Graph GCN +is built to encode corresponding path graphs. The graphs capture +the interrelation among the paths. In particular, all modules are +evolving along with the timeline to encode the dynamics of paths’ +content and inter-relation. Finally, we implement Hierarchical Sur- +vival Predictor with Consistency Loss Function to achieve better + +1.00 +0.95 +0.90 +0.85 +0.80 +4 +8 +12 +16 +20 +240.85 +0.84 +0.83 +0.82 +0.81 +0.80 +0.79 +0.78 +4 +8 +12 +16 +20 +241.00 +0.95 +0.90 +0.85 +0.80 +4 +8 +12 +16 +20 +241.0 +0.8 +0.2-Recall: 0.71 +0.4-Recall:0.71 +0.6 +0.6-Recall: 0.65 +0.8-Recall: 0.53 +0.4 +1.0-Recall: 0.54 +Inf-Recall: 0.54 +0.2 +0.0 +4 +8 +12 +16 +20 +24Conference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +prediction performance, higher consistency, and excellent scalabil- +ity. The model is quantitatively and qualitatively evaluated on three +malicious address datasets. Extensive ablation studies elaborate on +the mechanisms behind the effectiveness and excellent scalability. +In future work, we would like to extend Evolve Path Tracer to ma- +licious address detection in other crypto-currency platforms and +traditional financial domains. +REFERENCES +[1] Cuneyt G Akcora, Yitao Li, Yulia R Gel, and Murat Kantarcioglu. 2020. Bit- +coinheist: Topological data analysis for ransomware prediction on the bitcoin +blockchain. In Proceedings of the twenty-ninth international joint conference on +artificial intelligence. +[2] Elli Androulaki, Ghassan O Karame, Marc Roeschlin, Tobias Scherer, and Srdjan +Capkun. 2013. Evaluating user privacy in bitcoin. In International conference on +financial cryptography and data security. Springer, 34–51. +[3] Liang Chen, Jiaying Peng, Yang Liu, Jintang Li, Fenfang Xie, and Zibin Zheng. +2020. Phishing scams detection in ethereum transaction network. ACM Transac- +tions on Internet Technology (TOIT) 21, 1 (2020), 1–16. +[4] Tianyi Chen and Charalampos Tsourakakis. 2022. Antibenford subgraphs: Un- +supervised anomaly detection in financial networks. In Proceedings of the 28th +ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2762–2770. +[5] Weili Chen, Zibin Zheng, Jiahui Cui, Edith Ngai, Peilin Zheng, and Yuren Zhou. +2018. Detecting ponzi schemes on ethereum: Towards healthier blockchain +technology. In Proceedings of the 2018 world wide web conference. 1409–1418. +[6] Kyunghyun Cho, Bart van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio. +2014. On the Properties of Neural Machine Translation: Encoder–Decoder Ap- +proaches. In Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and +Structure in Statistical Translation. 103–111. +[7] Mikkel Alexander Harlev, Haohua Sun Yin, Klaus Christian Langenheldt, Raghava +Mukkamala, and Ravi Vatrapu. 2018. Breaking bad: De-anonymising entity types +on the bitcoin blockchain using supervised machine learning. In Proceedings of +the 51st Hawaii International Conference on System Sciences. +[8] Mikkel Alexander Harlev, Haohua Sun Yin, Klaus Christian Langenheldt, Raghava +Mukkamala, and Ravi Vatrapu. 2018. Breaking bad: De-anonymising entity types +on the bitcoin blockchain using supervised machine learning. In Proceedings of +the 51st Hawaii international conference on system sciences. +[9] Shuli Jiang, Robson Leonardo Ferreira Cordeiro, and Leman Akoglu. 2022. D. +MCA: Outlier Detection with Explicit Micro-Cluster Assignments. arXiv preprint +arXiv:2210.08212 (2022). +[10] Marc Jourdan, Sebastien Blandin, Laura Wynter, and Pralhad Deshpande. 2018. +Characterizing entities in the bitcoin blockchain. In 2018 IEEE international con- +ference on data mining workshops (ICDMW). IEEE, 55–62. +[11] Harry Kalodner, Malte Möser, Kevin Lee, Steven Goldfeder, Martin Plattner, +Alishah Chator, and Arvind Narayanan. 2020. Blocksci: Design and applications of +a blockchain analysis platform. In 29th {USENIX} Security Symposium ({USENIX} +Security 20). 2721–2738. +[12] Jonathan Kuck, Honglei Zhuang, Xifeng Yan, Hasan Cam, and Jiawei Han. 2015. +Query-based outlier detection in heterogeneous information networks. In Ad- +vances in database technology: proceedings. International Conference on Extending +Database Technology, Vol. 2015. NIH Public Access, 325. +[13] Sijia Li, Gaopeng Gou, Chang Liu, Chengshang Hou, Zhenzhen Li, and Gang +Xiong. 2022. TTAGN: Temporal Transaction Aggregation Graph Network for +Ethereum Phishing Scams Detection. In Proceedings of the ACM Web Conference +2022. 661–669. +[14] Yang Li, Yue Cai, Hao Tian, Gengsheng Xue, and Zibin Zheng. 2020. Identifying +illicit addresses in bitcoin network. In International Conference on Blockchain and +Trustworthy Systems. Springer, 99–111. +[15] Jiaqi Liang, Linjing Li, Daniel Zeng, Shu Luan, and Lu Gan. 2019. Bitcoin exchange +addresses identification and its application in online drug trading regulation. +(2019). +[16] Dan Lin, Jiajing Wu, Qi Yuan, and Zibin Zheng. 2020. T-edge: Temporal weighted +multidigraph embedding for ethereum transaction network analysis. Frontiers in +Physics 8 (2020), 204. +[17] Bing Liu, Yang Dai, Xiaoli Li, Wee Sun Lee, and Philip S Yu. 2003. Building text +classifiers using positive and unlabeled examples. In Third IEEE International +Conference on Data Mining. IEEE, 179–186. +[18] Yang Liu, Xiang Ao, Zidi Qin, Jianfeng Chi, Jinghua Feng, Hao Yang, and Qing +He. 2021. Pick and Choose: A GNN-Based Imbalanced Learning Approach for +Fraud Detection. In Proceedings of the Web Conference 2021. +[19] Mohammad Masud, Jing Gao, Latifur Khan, Jiawei Han, and Bhavani M. Thu- +raisingham. 2011. Classification and Novel Class Detection in Concept-Drifting +Data Streams under Time Constraints. IEEE Transactions on Knowledge and Data +Engineering 23, 6 (2011), 859–874. https://doi.org/10.1109/TKDE.2010.61 +[20] Mohammad M. Masud, Qing Chen, Latifur Khan, Charu C. Aggarwal, Jing +Gao, Jiawei Han, Ashok Srivastava, and Nikunj C. Oza. 2013. +Classifica- +tion and Adaptive Novel Class Detection of Feature-Evolving Data Streams. +IEEE Transactions on Knowledge and Data Engineering 25, 7 (2013), 1484–1497. +https://doi.org/10.1109/TKDE.2012.109 +[21] Pranav Nerurkar, Yann Busnel, Romaric Ludinard, Kunjal Shah, Sunil Bhirud, and +Dhiren Patel. 2020. Detecting illicit entities in bitcoin using supervised learning +of ensemble decision trees. In Proceedings of the 2020 10th international conference +on information communication and management. 25–30. +[22] Masarah Paquet-Clouston, Bernhard Haslhofer, and Benoit Dupont. 2019. Ran- +somware payments in the bitcoin ecosystem. Journal of Cybersecurity 5, 1 (2019), +tyz003. +[23] Aldo Pareja, Giacomo Domeniconi, Jie Chen, Tengfei Ma, Toyotaro Suzumura, +Hiroki Kanezashi, Tim Kaler, Tao Schardl, and Charles Leiserson. 2020. Evolvegcn: +Evolving graph convolutional networks for dynamic graphs. In Proceedings of +the AAAI Conference on Artificial Intelligence, Vol. 34. 5363–5370. +[24] Fergal Reid and Martin Harrigan. 2013. An analysis of anonymity in the bitcoin +system. In Security and privacy in social networks. Springer, 197–223. +[25] Wei Shao, Hang Li, Mengqi Chen, Chunfu Jia, Chunbo Liu, and Zhi Wang. 2018. +Identifying bitcoin users using deep neural network. In International Conference +on Algorithms and Architectures for Parallel Processing. Springer, 178–192. +[26] Changhe Song, Cheng Yang, Huimin Chen, Cunchao Tu, Zhiyuan Liu, and +Maosong Sun. 2019. CED: Credible early detection of social media rumors. +IEEE Transactions on Knowledge and Data Engineering (2019). +[27] Yizhou Sun, Jiawei Han, Charu C. Aggarwal, and Nitesh V. Chawla. 2012. When +Will It Happen? Relationship Prediction in Heterogeneous Information Networks. +In Proceedings of the Fifth ACM International Conference on Web Search and Data +Mining (WSDM ’12). 663–672. https://doi.org/10.1145/2124295.2124373 +[28] Da Sun Handason Tam, Wing Cheong Lau, Bin Hu, Qiu Fang Ying, Dah Ming +Chiu, and Hong Liu. 2019. +Identifying Illicit Accounts in Large Scale E- +payment Networks–A Graph Representation Learning Approach. arXiv preprint +arXiv:1906.05546 (2019). +[29] Marie Vasek and Tyler Moore. 2015. There’s no free lunch, even using Bitcoin: +Tracking the popularity and profits of virtual currency scams. In International +conference on financial cryptography and data security. Springer, 44–61. +[30] Mark Weber, Giacomo Domeniconi, Jie Chen, Daniel Karl I Weidele, Claudio +Bellei, Tom Robinson, and Charles E Leiserson. 2019. Anti-money laundering in +bitcoin: Experimenting with graph convolutional networks for financial forensics. +arXiv preprint arXiv:1908.02591 (2019). +[31] Jiajing Wu, Jieli Liu, Weili Chen, Huawei Huang, Zibin Zheng, and Yan Zhang. +2021. Detecting mixing services via mining bitcoin transaction network with +hybrid motifs. IEEE Transactions on Systems, Man, and Cybernetics: Systems +(2021). +[32] Jiajing Wu, Qi Yuan, Dan Lin, Wei You, Weili Chen, Chuan Chen, and Zibin +Zheng. 2020. Who are the phishers? phishing scam detection on ethereum via +network embedding. IEEE Transactions on Systems, Man, and Cybernetics: Systems +(2020). +[33] Haohua Sun Yin and Ravi Vatrapu. 2017. A first estimation of the proportion +of cybercriminal entities in the bitcoin ecosystem using supervised machine +learning. In 2017 IEEE International Conference on Big Data (Big Data). IEEE, +3690–3699. +[34] Shuhan Yuan, Panpan Zheng, Xintao Wu, and Yang Xiang. 2017. Wikipedia +vandal early detection: from user behavior to user embedding. In Joint European +Conference on Machine Learning and Knowledge Discovery in Databases. Springer, +832–846. +[35] Ge Zhang, Zhenyu Yang, Jia Wu, Jian Yang, Shan Xue, Hao Peng, Jianlin Su, Chuan +Zhou, Quan Z Sheng, Leman Akoglu, et al. 2022. Dual-discriminative Graph +Neural Network for Imbalanced Graph-level Anomaly Detection. In Advances in +Neural Information Processing Systems. +[36] Jiawei Zhang, Congying Xia, Chenwei Zhang, Limeng Cui, Yanjie Fu, and S Yu +Philip. 2017. +BL-MNE: emerging heterogeneous social network embedding +through broad learning with aligned autoencoder. In 2017 IEEE International +Conference on Data Mining (ICDM). IEEE, 605–614. +[37] Lingxiao Zhao, Saurabh Sawlani, Arvind Srinivasan, and Leman Akoglu. 2022. +Graph Anomaly Detection with Unsupervised GNNs. https://doi.org/10.48550/ +ARXIV.2210.09535 +[38] Panpan Zheng, Shuhan Yuan, and Xintao Wu. 2019. Safe: A neural survival +analysis model for fraud early detection. In Proceedings of the AAAI Conference +on Artificial Intelligence, Vol. 33. 1278–1285. + +Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency +Conference’17, July 2017, Washington, DC, USA +A +SUPPLEMENTARY MATERIAL +A.1 +Reproducibility +We release Evolve Path Tracer on GitHub4. We first download +full-node BTC raw data with Bitcoin Core. The whole data size is +about 500GB. After downloading all blocks before the 700,000th +block, we parse all data by Blocksci for querying block, transaction, +and address index. The parsed data size is about 400GB. For each +address in our dataset, We then prepare its asset transfer paths +for the transactions during the first 24 hours. The process was +executed on AMD Ryzen 9 3900X Processor with 64.0GB of memory. +We implement Evolve Path Tracer in Pytorch and Geometric. All +experiments are conducted on a single NVIDIA RTX 2080TI with +11G memory. +A.2 +Address Features +We use the following features to characterize an address at a specific +timestamp. +• the current balance of the address +• the number of receive (spend) transactions, +• the ratio of receive (spend) transactions number, +• the maximum receive (spend) transactions number, +• the life span of the address, +• address active rate. +A.3 +Transaction Features +We use the following features to characterize a transaction, which +is the component of every asset transfer path. +• the height interval to the path source, +• the influence (trust) score with the previous transaction, +• the input amount of the previous transaction, +• the transaction fee, +• the total amount (resp. max, min, avg, and var) of all receive +(spend) transactions, +• the number of receive (spend) transactions. +A.4 +Preparation of Asset Transfer Path +Algo. 1 gives the detail to prepare Backward Asset Transfer Paths +that reveal where 𝑗 obtains the asset. The pipeline to construct +Forward Asset Transfer Path is similar to Backward Asset Transfer +Path. The only difference is the tracing direction The essence of +each node is a transaction, thus we use a sequence of transaction +features to represent an asset transfer path. +A.5 +Baseline Models +We give details of our baseline methods from two related tasks: +Malicious Detection in Cryptocurrency. We compare Evolve +Path-Tracer with several models for malicious address detection in +cryptocurrencies. For decision tree models, we use address features +and path statistic features as the feature set. For GCN models, at +each time step, we get the addresses’ embedding after two graph +convolutional layers as implemented in [30]. Then, we feed the +embeddings into a sequential model for prediction. +4https://github.com/Cranooooooo/ADS-Demo +Algorithm 1: Backward Path Preparation +input :Initial Output Tx 𝑗𝑜, Threshold 𝜃, Time Span 𝑇𝑆𝑝𝑎𝑛. +output:Backward Path Set 𝑃. +1 Initialize Backward Path Set: 𝑃 ← {[−, 1, 𝑗𝑜]}; +2 Initialize Previous hop recorder: 𝑃𝑝𝑟𝑒 ← {[−, 1, 𝑗𝑜]}; +3 Initialize Ending Flag: 𝐹𝑒𝑛𝑑 ← 𝐹𝑎𝑙𝑠𝑒; +4 𝑗𝑜’s Time: 𝑇𝑗𝑜 ← Time of 𝑗𝑜; +5 while 𝐹𝑒𝑛𝑑 ≠ 𝑇𝑟𝑢𝑒 do +6 +Current hop recorder 𝑃𝑛𝑜𝑤 ← {}; +7 +𝐹𝑒𝑛𝑑 ← 𝑇𝑟𝑢𝑒; +8 +for 𝑝 in 𝑃𝑝𝑟𝑒 do +9 +𝑗 ← Output Tx 𝑝[2]; +10 +𝐼 ← Input Tx Set of 𝑗; +11 +for 𝑖 in 𝐼 do +12 +𝑃𝑟𝑜𝑝𝑖 ← 𝐴𝑚𝑡𝑖/𝐴𝑚𝑡𝐼 ; +13 +𝑆𝑐𝑜𝑟𝑒𝑖 ← 𝑃𝑟𝑜𝑝𝑖 ∗ 𝑝[1]; +14 +𝑇𝑖 ← time of 𝑖; +15 +if (𝑆𝑐𝑜𝑟𝑒𝑖 ≥ 𝜃 and 𝑇𝑗𝑜 −𝑇𝑖 ≤ 𝑇𝑆𝑝𝑎𝑛) then +16 +Append [𝑗,𝑆𝑐𝑜𝑟𝑒𝑖,𝑖] to 𝑃𝑛𝑜𝑤; +17 +𝐹𝑒𝑛𝑑 ← 𝐹𝑒𝑛𝑑 && 𝐹𝑎𝑙𝑠𝑒; +18 +𝑃𝑝𝑟𝑒 ← 𝑃𝑛𝑜𝑤; +19 +𝑃 ← 𝑃 ∪ 𝑃𝑝𝑟𝑒; +20 return 𝑃 +• Decision Tree [15, 21] utilize Decision Tree for identifying +these malicious addresses. +• Random Forest [21] utilize Decision Tree for identifying +these malicious addresses. +• XGB [8, 21] predict the type of a yet-unidentified entity with +Gradient Boosting based algorithms. +• GCN [30] encodes the objective address based on its trans- +action address graph. +• Skip-GCN [30] inserts a skip connection between the inter- +mediate embedding and the input node features. +• Evolve-GCN [30] updates GCN weights with an RNN mod- +ule. +Early Rumor Detection on Social Media. For these sequential +models, we build an extra path LSTM encoder for a fair comparison. +We concatenate address features with the path-encoder output and +feed them into the sequential prediction model. +• GRU [6] is a typical neural network for sequence modeling. +At each time split, previous hidden state and current summa- +tion features are fed into the GRU unit to predict the labels +for the given addresses. +• M-LSTM [34] adopts LSTM for every kind of feature to +generate its own temporal features at each timestamp. Here +we build three LSTM models for Address Features, Forward +Paths, and Backward Paths. +• CED [26] also uses GRU for sequence modeling, it proposes +the concept of “Credible Detection Point,” making it possible +to make predictions as early as possible dynamically. + +Conference’17, July 2017, Washington, DC, USA +Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu +Table 5: Key components and module description. TX stands for the transaction. +Name(Notation) +Description +Influence TX pair (𝑗 → 𝑖) +A certain portions of TX i’s BTCs come from TX j +Trust TX pair (𝑖 → 𝑗) +A certain portions of TX i’s BTCs flow to TX j +Backward Asset Transfer Path (𝑗𝑛 → · · · → 𝑖) +Build the Influence TX pairs iteratively and link them to form a path +Forward Asset Transfer Path (𝑖 → · · · → 𝑗𝑛) +Build the Trust TX pairs iteratively and link them to form a path +Backward Path Graph +Backward Asset Transfer paths share the same source TX are grouped to form a graph +Forward Path Graph +Forward Asset Transfer paths share the same destination TX are grouped to form a graph +T-1 LSTM +LSTM to encode temporal information of address features +E-1 LSTM +An Evolve Path Encoder LSTM for encoding Backward Asset Transfer Path to Backward Path feature +E-2 LSTM +An Evolve Path Encoder LSTM for encoding Forward Asset Transfer Path to Forward Path feature +T-2 LSTM +LSTM to encode temporal information of Backward Path feature +T-3 LSTM +LSTM to encode temporal information of Forward Path feature +BK-Graph Encoder +An Evolve Path Graph GCN for encoding Backward Path Graph to Backward Graph feature +BK-Graph Encoder +An Evolve Path Graph GCN for encoding Forward Path Graph to Forward Graph feature +T-4 LSTM +LSTM to encode temporal information of Backward Graph feature +T-5 LSTM +LSTM to encode temporal information of Forward Graph feature +Time (Hour) +Time (Hour) +Time (Hour) +Time (Hour) +Time (Hour) +Time (Hour) +Path Hop-Length +Path Height-Length +Path Max Amount ($ log 10) +Path Related Address Number +Path Max Input Number +Path Max Output Number +Figure 8: Asset transfer path’s statistical properties of different malicious addresses under the backward and forward direction. +• SAFE [38] adopts survival probability as the prediction. In- +stead of predicting the labels directly, it generates hazard +rates for the survival models. The positive samples should +die out fast, while the negative samples should stay alive. + +H-FR 4 +7.0 +H-BK +R-FR +6.5 +R-FR +D-FR +6.0 +D-FR +5.5 +5.0 +4.5 +C +4 +8 +12 +16 +20 +2480 +60 +40 +H-FR +H-BK +R-FR +20 +R-FR +D-FR +D-FR +4 +8 +12 +16 +20 +2410 +8 +H-FR +H-BK +R-FR +6 +R-FR +D-FR +D-FR +4 +2 +4 +8 +12 +16 +20 +24160 +H-FR +140 +H-BK +R-FR +120 +R-FR +100 +D-FR +D-FR +80 +60 +40 +20 +0 +4 +8 +12 +16 +20 +24100 +H-FR +90 +H-BK +R-FR +80 +R-FR +D-FR +70 +D-FR +60 +50 +40 +30 +20 +4 +8 +12 +16 +20 +24250 +200 +150 +H-FR +100 +H-BK +R-FR +R-FR +50 +D-FR +D-FR +4 +8 +12 +16 +20 +24 \ No newline at end of file diff --git a/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/load_file.txt b/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a9bc9b11329c72fdfd33ada5f294b7a53d5ddddc --- /dev/null +++ b/bdE5T4oBgHgl3EQfEQ5e/content/tmp_files/load_file.txt @@ -0,0 +1,1401 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf,len=1400 +page_content='Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Ling Cheng Singapore Management University Singapore Feida Zhu Singapore Management University Singapore Yong Wang Singapore Management University Singapore Ruicheng Liang Hefei University of Technology Heifei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' China Huiwen Liu Singapore Management University Singapore ABSTRACT With the ever-increasing boom of Cryptocurrency,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' detecting fraudu- lent behaviors and associated malicious addresses draws significant research effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, most existing studies still rely on the full history features or full-fledged address transaction networks, thus cannot meet the requirements of early malicious address detection, which is urgent but seldom discussed by existing studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To de- tect fraud behaviors of malicious addresses in the early stage, we present Evolve Path Tracer which consists of Evolve Path Encoder LSTM, Evolve Path Graph GCN, and Hierarchical Survival Predictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Specifically, in addition to the general address features, we propose asset transfer paths and corresponding path graphs to characterize early transaction patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Further, since the transaction patterns are changing rapidly during the early stage, we propose Evolve Path Encoder LSTM and Evolve Path Graph GCN to encode asset transfer path and path graph under an evolving structure setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Hierar- chical Survival Predictor then predicts addresses’ labels with nice scalability and faster prediction speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We investigate the effective- ness and versatility of Evolve Path Tracer on three real-world illicit bitcoin datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Our experimental results demonstrate that Evolve Path Tracer outperforms the state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Extensive scalability experiments demonstrate the model’s adaptivity under a dynamic prediction setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' KEYWORDS Early malice detection, Asset transfer path, Evolve encoder, Cryp- tocurrency, Bitcoin 1 INTRODUCTION Cryptocurrency has rapidly grown into a decentralized global finan- cial system in the past decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Unfortunately, it has long been criti- cized for accommodating various cybercrime due to its anonymity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' According to the recent Crypto Crime Report by chainalysis1, mali- cious addresses’ illegal profits exceeded 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 billion dollars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Among all cryptocurrency platforms, Bitcoin (BTC) has the largest vol- ume, while the on-chain record data for a certain address are much scarcer than other popular platforms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=', ETH, EOS with smart contracts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, researchers and practitioners have made signifi- cant efforts to fight against these fraudulent activities and identify the associated malicious addresses on BTC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Moreover, these methods are compatible with those on other cryptocurrency platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1https://go.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='chainalysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='com/2021-Crypto-Crime-Report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='html Spend TX j Spend TX i Recieve TX n … … j i Path & Graph Extractor … Recieve TX m n m … … … LSTM/GCN Forward LSTM/GCN Attention P Survival Prediction Module λAF λBK-Path λBK-Graph λFR-Path λFR-Graph Backward Address Feature Evolve Path-Graph Encoder ∑ Figure 1: The framework of our Evolve Path Tracer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At each time step, the path extractor first extracts forward (FR: pink arrows) and backward (BK: green arrows) asset transfer paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The graph extractor builds the path graph to link re- lated asset transfer paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, the Evolve Path-Graph En- coder encodes asset transfer paths with corresponding Path- LSTM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The Path-GCN module refines the path rep- resentations with the Path-Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The attention module will propose corresponding features with an attention sum- mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The weights of the Path-LSTM, Path-GCN, and at- tention modules are provided by address features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Finally, based on five types of features (Address Feature, BK/FR Path Feature, BK/FR Graph Feature), the survival probability is given by the corresponding survival rates 𝜆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' TX stands for a transaction, P stands for predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Most existing detection methods focus on designing features to characterize specific types of malicious activity with detailed case studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, by combining statistic analysis and visualiza- tion technology, they successfully identified some representative malicious transaction patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Recent studies [3, 5, 30] further leverage deep-learning techniques to detect malicious addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' By encoding account features and the transaction network struc- ture with deep-learning models, they achieve great performance improvement in malicious address detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, malicious activities are evolving faster than ever before, and it is impossible to build a unique feature set for every newly emerging malicious activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Although some studies [13] can detect categories of malicious activities, they are still only available for post-hoc analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Most of them invariably require a full-history feature observation, which is consequentially scarce at the early stage of fraud activities, thus they can’t be directly deployed to detect illicit activities at the early stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Recently, Random walk and graph neural network [3, 7, 30, 31] are adopted to encode the topological feature of transaction network automatically, which improves the performance of general malice detection tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' But arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='05412v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='AI] 13 Jan 2023 Conference’17, July 2017, Washington, DC, USA Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu most of them require a full-fledged address transaction network which is also unavailable under the early stage settings, as the newly created transaction graphs are usually small, unconnected and fast-evolving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, traditional address transaction networks may suffer from the issue of scalability, shadow addresses, and the dilution of the minority class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Considering the essence of blockchain is a ledger of transactions (TXs), malicious addresses’ objective is to transfer illicit money to a legal place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We can derive their intentions by monitoring their real-time transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, in this work, we first set up the Early Malicious Address Detection (EMAD) task, which is urgent but sel- dom discussed by existing studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, we develop a path ex- tractor to focus on transaction paths, especially those significant paths, which can characterize the early-stage transactions of illicit addresses effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Figure 1, two kinds of asset trans- fer paths, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=', forward and backward transition paths, are proposed to describe the flow-in and flow-out transition patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The asset transfer paths focus on the token (BTC) flow, thus can relieve the problem of shadow addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, illicit activities are usually organized together for spe- cific purposes, and the behavior patterns evolve fast during the early stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As a result, encoding each path individually may miss critical information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Furthermore, static encoding models can’t cap- ture the dynamism of evolving graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, we build an asset path GCN module to encode the path’s inter-relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In this graph, asset transfer paths connect to each other if they share the same intersec- tion addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Inspired by [23], we equip our path encoder and path GCN module with an evolving mechanism for more sophisticated path representations under the dynamic setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Considering the scalability issue, we implement a Hierarchical Survival Prediction module to alleviate the workload of feature preparation during the prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Previous prediction results can be directly used in the next time step, which empowers the model with a faster prediction speed and the ability to deal with a dy- namic setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In summary, the contributions of this paper can be summarized as follows: The Asset Transfer Paths are proposed for the EMAD task, which is urgent but seldom discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' These paths exhibit high versatility in monitoring transaction patterns of various malicious behaviors in the early stage and relieve the prob- lem of shadow addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' This novel concept can be easily transplanted to all current blockchain-based cryptocurren- cies and traditional financial systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We propose the Evolve Path Tracer model that can fully uti- lize the asset transfer paths to encode various transaction patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, it can also encode the paths’ structural relationship under a dynamic setting with a novel evolve path graph encoding module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The versatility and dynamic flexibility are unachievable by other existing models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We conduct extensive evaluations to assess the model’s ef- fectiveness, and the results show that Evolve Path Tracer delivered a substantially better performance for three dif- ferent illicit datasets than the state-of-the-art models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, owing to the Hierarchical Survival Prediction module, our Evolve Path Tracer can effectively predict addresses’ labels scales well for the increasing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2 RELATED WORK Early detection of malicious addresses on Bitcoin is an urgent yet seldom discussed task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, we first review the related works about malice detection on Bitcoin and related cryptocurrencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, we briefly review previous works about early rumor detection, which discussed similar tasks but under the social media circumstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Malice Detection on Cryptocurrency Case Analysis mainly focuses on addresses’ behaviors in a cer- tain case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Reid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [24] identified entities by considering similar transaction times over an extended timeframe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Androulaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [2] considered several features of transaction behavior, including the transaction time, the index of addresses, and the value of transac- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Jourdan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [10] explored five types of features, including address features, entity features, temporal features, centrality fea- tures, and motif features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Vasek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [29] gave a list of Bitcoin scams and conducted a statistical study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Case-Related features are often helpful in interpreting certain cases based on heuristic clustering and tainted fund flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, these methods require intensive case analysis, and most of the insights are only available in some specific cases, let alone apply to other platforms with complex heterogeneous relationships in general [12, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Machine Learning can automatically learn general address fea- tures to address the poor generalization ability of case-related meth- ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Yin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [33] applied supervised learning to classify entities that might involve in cybercriminal activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Akcora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [1] applied the topological data analysis (TDA) approach to generate the bitcoin address graph for ransomware payment address de- tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [25] embedded the transaction history into a lower-dimensional feature for entity recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Nerurkar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [21] used 9 features to train the model for segregating 28 different licit-illicit categories of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The general address features improve the model’s generality significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, they are challenging to characterize addresses’ behaviors comprehensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Particular transaction patterns of asset flow are difficult to be reflected in these characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Graph Based Methods focus on the interaction patterns between object addresses and related addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Harlev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [7] consid- ered transaction features in a supervised machine learning frame- work to de-anonymize Bitcoin addresses and predict the type of yet-unidentified entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [31] proposed two kinds of het- erogeneous temporal motifs in the Bitcoin transaction network and applied them to detect mixing service addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Weber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [30] encodes address transaction graph with GCN, Skip-GCN, and Evolve-GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [3] proposed E-GCN for phishing node detection on the ETH platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Tam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [28] proposed EdgeProp, a GCN-based model, to learn the representations of nodes and edges in large-scale transaction networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [16] proposed two kinds of random walk-based embedding methods to encode specific network features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' By changing the sampling strategy in Node2Vec, Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [32] proposed the Trans2Vec model, which can consider the temporal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [13] proposed TTAGN to model the temporal information of historical transactions for phishing detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [4] proposed the AntiBenford subgraph frame- work for anomaly detection in the Ethereum transaction network under an unsupervised setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Network-based methods perform Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Conference’17, July 2017, Washington, DC, USA well for retrospect analysis, as they encode the structural informa- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, in the early stages, the trading network is often too small to form a discriminative topological structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The perfor- mance will degrade greatly if the networks are of sparse structures for the emerging networks with few connections[36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, these methods may lead to Over-Smoothing issues and the dilution of the minority class [18] under the data-unbalanced setting [9, 35, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 Early Rumor Detection Cho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [6] used GRU, a typical neural network for sequence modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At each time split, previous hidden state and current summation features are fed into the GRU unit to predict the labels for the given samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [26] proposed CED, which also uses GRU for sequence modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' They proposes the concept of “Credible Detection Point,” to increase the prediction speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [34] developed a multi-source long-short term memory network (M-LSTM) to model user behaviors by using a variety of user edit aspects as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [38] put forward SAFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Instead of predicting the labels directly, it generates hazard rates for the survival models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The positive samples should die out fast, while the negative samples should stay alive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 3 PROBLEM DEFINITION In the BTC system, a transaction 𝑡𝑥 is bound to an address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Each 𝑡𝑥 has a set of inputs 𝐼= {𝑖1,𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑖 |𝐼 |} and a set of outputs 𝐽= {𝑗1, 𝑗2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑗|𝐽 |}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The input and output are still transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑡𝑥 records token distribution between 𝐼 and 𝐽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Narratively speaking, the in- coming tokens flow into a pool and then flow to the outgoing transactions according to the prior agreement proportion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' There is no record of how many tokens flow from an Input 𝑖 to an Out- put 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, we have to build a complete transaction bipartite graph for this 𝑡𝑥 and generate |𝐼| × |𝐽 | transaction pairs in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In other words, a BTC transaction has |𝐼| × |𝐽 | transaction pairs inside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐷𝑡𝑚={𝑑𝑖 𝑡𝑚 }𝑁 𝑖=1={(𝑙𝑖,𝑇𝑖 𝑖𝑛,𝑡𝑚,𝑇𝑖 𝑜𝑢𝑡,𝑡𝑚)}𝑁 𝑖=1 is the input data by the 𝑡𝑚-th time step, where 𝑙𝑖 ∈ {0, 1} is the label of Address 𝑖, and 0 or 1 stands for regular and malicious addresses respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑇𝑖 𝑖𝑛,𝑡𝑚=[𝑡𝑥𝑖 𝑖𝑛,1,𝑡𝑥𝑖 𝑖𝑛,2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑡𝑥𝑖 𝑁𝑖𝑛,𝑡𝑚 ] and 𝑇𝑖 𝑜𝑢𝑡,𝑡𝑚 are the transaction sets where Address 𝑖 acts as the input and output address by the 𝑡𝑚-th time step respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For ease of understanding, we denote these two transaction sets as 𝑅𝑒𝑐𝑒𝑖𝑣𝑒 set and 𝑆𝑝𝑒𝑛𝑑 set respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Early Malicious Address Detection (EMAD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Given a set of ad- dresses 𝐴, and 𝐷𝑡𝑚 at timestep 𝑡𝑚, the problem is to build a binary classifier 𝐹 such that 𝐹 (𝑑𝑖 𝑡𝑚) = � 1 if Address 𝑖 is malicious 0 Otherwise .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (1) In the early detection task, to prevent the model predicts conflict labels at different timesteps, which will confuse users, thus we require the prediction to be consistent and predict the correct label as early as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We denote the confident time as 𝑡𝑐, where all classifier predictions 𝐹 after 𝑡𝑐 are consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The smallest 𝑡𝑐 is denoted as 𝑡𝑓 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Our purpose is to train a classifier that predicts the correct label of an address with a smaller 𝑡𝑓 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4 ASSET TRANSFER PATH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Overview and Motivation Take Address𝑖’s𝑅𝑒𝑐𝑖𝑒𝑣𝑒 transaction set as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For a𝑅𝑒𝑐𝑒𝑖𝑣𝑒 transaction 𝑗0 in the set, suppose we find its significant asset source 𝑗1, which is also a transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then we link 𝑗1 and 𝑗0 to form an asset transfer pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' After we trace the asset source iteratively, the asset transfer pairs form an asset transfer path naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig2 (b), for Receive Tx R-1 in the Flow of Receive Tx, after we trace its asset source, we can get three critical transfer pairs, namely (10 →R-1, 11 →R-1, 12 →R-1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Backward Asset Transfer Path, iteratively, we can get four paths (P-1, P-2, P-3, P-5) ended with R-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Among them, three paths(P-1, P-2, P-3) have the same source (Tx-1 colored green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, another path (P-4) ended with R-2 is initiated by the same source, thus we group them into a path graph, which is colored green, as shown in the Backward Path Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Since every transaction is bound to an address at a specific times- tamp, thus, if all paths come from the same source, then we can say that, at a particular time point, an address initiates multiple transactions at the same time, and all transactions’ destinations are Address 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If we encode each path as a node, these nodes can be connected through this source of funds, thus forming a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We build the path graph to reflect: 1) the characteristics of each path, 2) the interaction between paths, and 3) the characteristics of the asset source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We believe this information is crucial for the early detection of malicious behavior, and we will justify the statement in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 Influence and Trust Transaction Pair Not all transaction pairs help identify illicit addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Those note- worthy pairs typically constitute a significant amount portion of the entire transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2(a), the receive 𝑇𝑋𝑗 receive assets from three spend TXs (each contributing 35%, 30% and 35% to the total transaction amount).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' On the other hand, the spend 𝑇𝑋𝑖 transfers out BTCs to three receive TXs (with a distribu- tion of 25%, 45%, and 30% as in this example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Given an Address 𝑖 and a time step 𝑡𝑚, TXs in the shaded dotted-lined box represent all spend TXs, and receive TXs occurred up to timestep 𝑡𝑚 associated with Address 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As mentioned in Section 3, given a set 𝐼= {𝑖1,𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='𝑖 |𝐼 |} of |𝐼 | spend transactions to an receive transaction 𝑗 and the set {𝐼 → 𝑗} of all transaction pairs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=', {𝐼 → 𝑗}={(𝑖1, 𝑗), (𝑖2, 𝑗), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' , (𝑖 |𝐼 |, 𝑗)}, we define Influence Transaction Pair as follows: Given an influence activation threshold 𝜃, (𝑖𝑘, 𝑗) is called an Influence Transaction Pair for transaction 𝑗, if there exists a 𝑘 (1 ≤ 𝑘 ≤ |𝐼|) such that the amount of transaction pair (𝑖𝑘, 𝑗) contributes at least a certain proportion of the received amount of transaction 𝑗, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='e, ˆ𝐴(𝑖𝑘, 𝑗) ≥ 𝜃 × ˆ𝐴({𝐼 → 𝑗}) where ˆ𝐴(·) denotes the amount of a transaction pair or the sum of all transaction pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Similarly, given a set 𝐽= {𝑗1, 𝑗2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑗|𝐽 |} of |𝐽 | transactions, and a transaction 𝑖, and the set {𝑖 → 𝐽 } of all transaction pairs whose spend transaction is 𝑖, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=', {𝑖 → 𝐽 }={(𝑖, 𝑗1), (𝑖, 𝑗2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' , (𝑖, 𝑗|𝐽 |)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If there exists a receive transaction 𝑗𝑘,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1 ≤ 𝑘 ≤ |𝐽 | such that trans- action 𝑖 transfers at least a certain proportion of its spend amount to it,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' this transaction pair is called a Trust Transaction Pair for Conference’17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' July 2017,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Washington,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' DC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' USA Ling Cheng,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Feida Zhu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Yong Wang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ruicheng Liang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' and Huiwen Liu ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TX1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TXi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TX|I| ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='35% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='35% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='30% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Day ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TXi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TX1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TXN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TXj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TX1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TXM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Address Involved TXs ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TXj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Backward ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='25% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='30% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='45% ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Spend TXi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TX1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TXj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Receive TX|J| ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Day ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Flow of Receive TX ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Backward Asset Transfer Path Backward Path Graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='17 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Flow of Spend TX ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='17 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='S-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward Path Graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward Asset Transfer Path ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='(a) Asset Transfer Path ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='(b) Asset Transfer Path Graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='P-8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Figure 2: (a) Asset transfer pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Given an address, we col- lect its transaction history (All its Receive and Spend TXs in the dotted box).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For each Receive TX, we trace its asset source from the inflow (Green Spend TXs) to build Influ- ence TX pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For each Spend TX, we trace its asset desti- nation from the outflow (Yellow Receive TXs) to build Trust TX pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑁 = 𝑁𝑖𝑛,𝑡𝑚, 𝑀 = 𝑁𝑜𝑢𝑡,𝑡𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (b) Asset transfer path and path graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' By tracing the asset source iteratively, we get a series of Influence TX pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We combine them end-to-end to form Backward Asset Transfer Path (Similar to Forward As- set Transfer Path).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If paths have the same source or destina- tion, we connect them through their intersection to form a path graph (Graph in the same color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Different colors stand for different starting or ending points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' transaction 𝑖, as it indicates a certain form of trust from 𝑖 to 𝑗𝑘 in terms of asset transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Given an influence transaction pair (𝑖𝑘, 𝑗), we can conclude that transaction 𝑗 obtains at least a significant amount (based on the threshold) of the asset in this transaction from transaction 𝑖𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ac- cordingly, given a transaction 𝑗, if there exists a sequence of transac- tion pairs such that (I) each pair is an influence transaction pair;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (II) the spend transaction of each pair is the receive transaction of the previous pair;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' and (III) the receive TX of the last pair is transaction 𝑗, we call such a sequence an Backward Path for 𝑗 as indicated by the green arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' It reveals where 𝑗 obtains the asset and can be used to trace back to the source of the asset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The detail to prepare the backward asset transfer path is shown in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Similarly, we can define a Forward Path to trace the destinations of transaction 𝑖’s asset flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For brevity, we would refer to both the Backward Path and Forward Path as Asset Transfer Paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 Asset Transfer Path Graph The transaction graph between addresses has been widely used in the detection task of cryptocurrency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, these methods may suffer from the perturbation of shadow addresses and the scalability issues caused by mixing services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If the malicious use mixing services, although we will get more asset transfer paths, suspicious paths will still converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Therefore, unlike the previous address-based graph, we build graphs based on the asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2(b), in the path graph part, each node represents an asset-transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If two paths share the same source (for backward paths) or destination (for forward paths), we then connect them with an edge, thus we can get a group of fully-connected graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Since every source or destination has a binding address at a specific timestep, we use the feature of this binding address at this time point to represent the edge feature in the corresponding graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The address features and transaction features are illustrated in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 5 EVOLVE PATH TRACER At the 𝑡-th timestep, We will generate five kinds of features to cal- culate corresponding hazard rates (𝜆) for prediction (1: Address Feature Hidden Vector (AF Hidden Vector), 2: Backward Path Fea- ture (BK-Path), 3: Backward Graph Feature (BK-Graph), 4: Forward Path Feature (FR-Path), 5: Forward Graph Feature (FR-Graph)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Be- fore generating the hazard rates, all these features will be encoded through the corresponding LSTM modules (T-1 to T-5 LSTM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, to capture the dynamics of path evolution, the param- eters of forward and backward Evolve Path Encoder LSTM (E-1, E-2 LSTM) are provided by AF hidden vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, forward and backward Evolve Path Graph GCN parameters are calculated with AF hidden vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig 3, in the Evolve Path Encoder LSTM and Evolve Path Graph GCN, the parameters (the gray and white nodes) are consistent with the AF hidden vector to show their interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Evolve Path Encoder LSTM Address Feature is the basis for modeling and reasoning the address transaction pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We implement an address feature LSTM (T-1 LSTM), which will guide the processing in other modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ℎ𝑇1 𝑡 ,𝑐𝑇1 𝑡 = LSTM𝑇1 (𝑓 𝑢 𝑡 ,ℎ𝑇1 𝑡−1,𝑐𝑇1 𝑡−1), (2) where ℎ𝑇1 𝑡 ∈ R𝑑 and 𝑐𝑇1 𝑡 ∈ R𝑑 are the hidden state and the cell state of T-1 LSTM at time 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑓 𝑢 𝑡 ∈ R𝑑𝑛 is the address feature at time 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑑 is the dimension of hidden state, 𝑑𝑛 is the dimension of address feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As mentioned in Section 4, asset transfer path is composed of a series of transaction nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The lengths of these paths are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To encode them uniformly, we project an original path 𝑃𝑜 to an uniform path 𝑃𝑢 with length of 𝐿𝑢.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Given an original path 𝑃𝑜 with length of 𝐿𝑜, the zoom ratio is calculated by 𝑅𝑧 = 𝐿𝑜/𝐿𝑢, then the 𝑖-th (start from 0) node in 𝑃𝑢 is calculated by the average feature of the (⌊𝑖 × 𝑅𝑧⌋)-th node to the (⌈(𝑖 + 1) × 𝑅𝑧⌉-1)-th node of 𝑃𝑜.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, we denote the uniform path as: P1:Lu = [𝑝1, 𝑝2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' , 𝑝𝐿𝑢 ], (3) Different addresses have different characteristics, their path structures also differ along the timeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus we may lose dy- namic information with a static encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Inspired by Evolve-GCN, the parameters of our Path Encoder LSTM are determined by the current address feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Evolve-GCN, the weights are updated by themselves or those representative nodes, thus may dismiss Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Conference’17, July 2017, Washington, DC, USA the individual address property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Instead, we use the combination of address feature and the temporal path feature to generate the weights of Path Encoder LSTM module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Take backward asset trans- fer paths as example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' for the 𝑗-th node in the input asset transfer path,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' backward Evolve Path Encoder LSTM (E-1 LSTM) computes the following function: 𝐻𝑝 𝑡 = [ℎ𝑇1 𝑡 ||ℎ𝑇2 𝑡−1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑖𝑗 = 𝜎((𝑊𝑖𝑖𝐻𝑝 𝑡 )𝑝𝑗 + (𝑊ℎ𝑖𝐻𝑝 𝑡 )ℎ𝐸1 𝑗−1 + 𝑏𝑖𝐻𝑝 𝑡 ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑓𝑗 = 𝜎((𝑊𝑖𝑓 𝐻𝑝 𝑡 )𝑝𝑗 + (𝑊ℎ𝑓 𝐻𝑝 𝑡 )ℎ𝐸1 𝑗−1 + 𝑏𝑓 𝐻𝑝 𝑡 ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑔𝑗 = tanh((𝑊𝑖𝑔𝐻𝑝 𝑡 )𝑝𝑗 + (𝑊ℎ𝑔𝐻𝑝 𝑡 )ℎ𝐸1 𝑗−1 + 𝑏𝑔𝐻𝑝 𝑡 ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑜𝑗 = 𝜎((𝑊𝑖𝑜𝐻𝑝 𝑡 )𝑝𝑗 + (𝑊ℎ𝑜𝐻𝑝 𝑡 )ℎ𝐸1 𝑗−1 + 𝑏𝑜𝐻𝑝 𝑡 ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑐𝑗 = 𝑓𝑗 ⊙ 𝑐𝑗−1 + 𝑖𝑗 ⊙ 𝑔𝑗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ℎ𝐸1 𝑗 = 𝑜𝑗 ⊙ tanh(𝑐𝑗),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (4) where || stands for concatenation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='ℎ𝑇2 𝑡−1 ∈ R𝑑 is the hidden state of T- 2 LSTM at timestep 𝑡-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' T-2 LSTM encodes the temporal information of the backward asset transfer path set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑊∗∗ ∈ R𝑑×𝑑×2𝑑 and 𝑏∗ ∈ R𝑑×2𝑑 are learnable weights that transfer 𝐻𝑝 𝑡 to the weights of projection layers and bias terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝜎 stands for sigmoid function, ⊙ is the Hadamard product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Finally, each backward asset transfer path is denoted as final hidden state ℎ𝐸1 𝐿𝑢 of E-1 LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The representation of the 𝑖-th path at timestep 𝑡 is 𝑓 𝑝 𝑖,𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Not all paths are equally informative for the prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We expect to select more informative paths, thus we adopt multi-head attention for the selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑎𝑗 𝑖,𝑡 = 𝑊 𝑎,𝑗tanh(𝑊 𝑝,𝑢 [𝑓 𝑝 𝑖,𝑡 ||ℎ𝑇1 𝑡 ]), (5) 𝛼 𝑗 𝑖,𝑡 = Softmax(𝑎𝑗 𝑖,𝑡) = exp(𝑎𝑗 𝑖,𝑡)/ 𝑁𝐸1 ∑︁ 𝑘=1 exp(𝑎𝑗 𝑘,𝑡), (6) ˆ𝑓 𝑝 𝑡 = ||𝑀𝑝 𝑗=1 ˆ𝑓 𝑝,𝑗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ˆ𝑓 𝑝,𝑗 𝑡 = 𝑁𝐸1 ∑︁ 𝑖=1 𝛼 𝑗 𝑖,𝑡 𝑓 𝑝 𝑖,𝑡, (7) where𝑊 𝑝,𝑢 ∈ R 𝑑 𝑀𝑝 ×2𝑑 and𝑊 𝑎,𝑗 ∈ R1× 𝑑 𝑀𝑝 are learnable matrices, 𝑗 stand for the index of the attention head, 𝑀𝑝 is the total head number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑁𝐸1 is the backward asset transfer path number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' where ˆ𝑓 𝑝,𝑗 𝑡 is the weighted summed path feature vector of 𝑗-th head, ˆ𝑓 𝑝 𝑡 is the concatenation of all heads’ output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The hidden state ℎ𝑇2 𝑡 and cell state 𝑐𝑇2 𝑡 of T-2 LSTM are updated as: ℎ𝑇2 𝑡 ,𝑐𝑇2 𝑡 = LSTM𝑇2 ( ˆ𝑓 𝑝 𝑡 ,ℎ𝑇2 𝑡−1,𝑐𝑇2 𝑡−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (8) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 Evolve Path Graph GCN If several paths are initiated by or converge at the same transaction, it may indicate certain suspicious patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' By encoding the rela- tionships between these path, model can capture certain significant patterns in detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Similarly, due to the volatility of the path graph, we may lose the discriminative characteristics with a static model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To resolve this challenge, we propose Evolve Path Graph GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Take backward asset transfer paths as example, the nodes in the path graph are updated as follow: 𝐻𝑔 𝑡 = [ℎ𝑇1 𝑡 ||ℎ𝑇3 𝑡−1], 𝑓 𝑔 𝑡 = 𝜎( ˜D− 1 2 ˜ A ˜D− 1 2 (𝑓 𝑝 𝑡 𝑊 𝑔𝐻𝑔 𝑡 )), ˜ A = A + I, A𝑖,:,𝑗 = (𝑊 𝑒𝐻𝑔 𝑡 )𝑆𝑖,𝑗, ˜D = diag( ∑︁ 𝑗 (𝐴𝑖,𝑗 + I𝑖,𝑗)), (9) where ℎ𝑇3 𝑡−1 ∈ R𝑑 is the hidden state of T-3 LSTM at time 𝑡-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' T- 3 LSTM encodes the temporal information of the backward path graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑓 𝑝 𝑡 ∈ R𝑁𝐸1×𝑑 are the representations of path set at timestep 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐴 ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 and I ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 are the adjacent matrix and the identity matrix respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If the 𝑖-th path and 𝑗-th path have the same source, then 𝐴𝑖,:,𝑗=1 ∈ R𝑑.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Otherwise, 𝐴𝑖,:,𝑗=0 ∈ R𝑑.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If the 𝑖-th path and 𝑗-th path have the same source, 𝑆𝑖,𝑗 ∈ R𝑑𝑛 is the intersection address feature of path 𝑖 and path 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Otherwise, 𝑆𝑖,𝑗=0 ∈ R𝑑𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑊 𝑔 ∈ R𝑑×𝑑×2𝑑 and 𝑊 𝑒 ∈ R𝑑×𝑑𝑛×2𝑑 are learnable weights, and they project 𝐻𝑔 𝑡 to the weights of the corresponding projection layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus A ∈ R𝑁𝐸1×𝑑×𝑁𝐸1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We denote the output of Evolve Path Graph GCN encode as interaction-aware asset transfer paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Resemble the previous cal- culation, we adopt multi-head attention to select significant signals for these interaction-aware paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We denote the ˆ𝑓 𝑔 𝑡 as the final re- sult of multi-head attention of interaction-aware paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The hidden state ℎ𝑇3 𝑡 and cell state 𝑐𝑇3 𝑡 of T-3 LSTM are updated as: ℎ𝑇3 𝑡 ,𝑐𝑇3 𝑡 = LSTM𝑇3 ( ˆ𝑓 𝑔 𝑡 ,ℎ𝑇3 𝑡−1,𝑐𝑇3 𝑡−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (10) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 Hierarchical Survival Predictor Due to the property of consistent prediction, survival analysis [38] is proved to be effective in the early detection task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The survival function 𝑆(𝑡) of an event represents the probability that this event has not occurred by time 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The hazard rate function 𝜆𝑡 is the event’s instantaneous occurrence rate at time 𝑡 given that the event does not occur before time 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In our case, the observation time is discrete in our case, we use 𝑡 to denote a timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The association between 𝑆(𝑡) and 𝜆𝑡 can be calculated as: 𝑆(𝑡) = 𝑃(𝑇 ≥ 𝑡) = ∞ ∑︁ 𝑘=𝑡 𝑓 (𝑥), 𝜆𝑡 = 𝑓 (𝑡)/𝑆(𝑡), 𝑆(𝑡) = exp(− 𝑡∑︁ 𝑘=1 𝜆𝑘).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (11) Considering the model’s scalability during the real-time prediction, we define the event as “the address is benevolent” and we call hazard rate as benevolent rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As the majority addresses are negative (benevolent) in the BTC platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Once the address is classified as benevolent, we remove it from the monitoring list to reduce the computation cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To get more consistent predictions, previous work deployed a Softplus function 𝜆𝑡 (𝑥𝑡) = 𝑙𝑛(1 + exp(𝑥𝑡)) to guarantee the haz- ard rate 𝜆𝑡 is always positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Hence, the survival probability 𝑆(𝑡) Conference’17, July 2017, Washington, DC, USA Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu Evolve Path Encoder LSTM P-6 P-8 P-7 P-1 P-3 P-2 P-4 P-5 P-6 P-8 P-7 P-1 P-3 P-2 P-4 P-5 1 t tm Evolve Path Graph GCN T-1 LSTM E-1 LSTM T-2 LSTM BK-Graph Encoder E-2 LSTM T-4 LSTM FR-Graph Encoder λ BK- Path λ BK- Graph λ FR- Path λ FR- Graph λ AF … … Prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' λ-sum (i-1) λ-sum (i) ∑ T-5 LSTM T-3 LSTM Figure 3: Detailed pipeline of Evolve Path Tracer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Five LSTM models (T-1 to T-5 LSTM) are implemented to encode tem- poral information of different features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' AF hidden vectors will update the parameters of Forward and Backward Evolve Path Encoder LSTM (E-1/2 LSTM) and Evolve Path Graph GCN (BK/FR-Graph Encoder).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evolve Path Encoder LSTM and Evolve Path Graph GCN are proposed to encode asset transfer paths and path graphs dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For detailed de- scriptions of each module, please refer to Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' monotonically decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, the model can hardly classify addresses correctly in the early hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Those false-positive predic- tions will never be corrected with the monotonically decreasing survival probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, we release this restriction with a 𝑡𝑎𝑛ℎ activation function for benevolent rate calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The consistency is assured by Consistency Loss Function which will be elaborated later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We designed five parallel benevolent rates corresponding to each kind of information (address feature, path feature (backward and forward), and graph feature (backward and forward)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At time step 𝑡, the calculation of these benevolent rates and the prediction as follows: 𝜆𝑗,𝑡 = tanh(𝑊 ℎ𝑧 𝑇𝑗 ℎ𝑇𝑗 𝑡 ), ˆ𝑦𝑡 = exp(−ReLU( 𝑡∑︁ 𝑖=1 5 ∑︁ 𝑗=1 𝜆𝑗,𝑖)), (12) where 𝑊 ℎ𝑧 𝑇𝑗 ∈ R1×𝑑 is the linear projection matrices for the output of T-j LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At each time step, survival analysis first sums all pre- vious benevolent rates, then it sums the current 5 benevolent rates hierarchically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Once addresses’ current benevolent rates reach a cer- tain threshold, we can remove them from monitoring list to speed up the prediction and relieve the computing cost in the following hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 Training and Dynamical Prediction Model Training Model should give higher 𝑆(𝑡) to malicious ad- dresses and lower 𝑆(𝑡) to benevolent addresses in every time split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For Address𝑖, at timestep 𝑡𝑚, the early detection likelihood function and the negative logarithm prediction 𝑙𝑜𝑠𝑠𝑃 are shown as below: 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = (1 − 𝑆(𝑡𝑚))1−𝑙𝑖𝑆(𝑡𝑚)𝑙𝑖 = (1 − exp(− 𝑡𝑚 ∑︁ 𝑡=1 5 ∑︁ 𝑗=1 𝜆𝑗,𝑡))1−𝑙𝑖 (exp(− 𝑡𝑚 ∑︁ 𝑡=1 5 ∑︁ 𝑗=1 𝜆𝑗,𝑡))𝑙𝑖, 𝑙𝑜𝑠𝑠𝑃 𝑖,𝑡𝑚 = 𝑙𝑖 𝑡𝑚 ∑︁ 𝑡=1 5 ∑︁ 𝑗=1 𝜆𝑗,𝑡 + (𝑙𝑖 − 1)𝑙𝑛(1 − exp(− 𝑡𝑚 ∑︁ 𝑡=1 5 ∑︁ 𝑗=1 𝜆𝑗,𝑡)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (13) Besides, 𝑙𝑜𝑠𝑠𝑃 is weighted by √𝑡𝑚 to avoid the perturbation in the early period due to the data insufficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Consistency-boosted Loss Function Since the rate function is not guaranteed to be positive in our model, a consistency loss 𝑙𝑜𝑠𝑠𝐶 is necessary for consistent predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In every time split, the benevolent rate should have the same sign as the previous time split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑙𝑜𝑠𝑠𝐶 𝑖,𝑡𝑚 = � 0 sign(𝜆𝑡𝑚−1 ∗ 𝜆𝑡𝑚) >= 0 1 else , (14) where 𝜆𝑡0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Similarly, model should be able to rectify the poor prediction in the early period, thus the 𝑙𝑜𝑠𝑠𝐶 is also weighted by √𝑡𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, since the numbers of positive and negative instances are imbalanced, different penalty coefficients are allocated to each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, given a set of training samples with 𝑁𝑝 malicious addresses and 𝑁𝑛 legal addresses, the overall loss function is defined as: ℒ = 𝑡𝑀 ∑︁ 𝑡=1 √ 𝑡(𝐶+ 𝑁𝑝 ∑︁ 𝑖=1 (𝑙𝑜𝑠𝑠𝑃 𝑖,𝑡 + 𝛾𝑙𝑜𝑠𝑠𝐶 𝑖,𝑡)+ 𝐶− 𝑁𝑛 ∑︁ 𝑖=1 (𝑙𝑜𝑠𝑠𝑃 𝑖,𝑡 + 𝛾𝑙𝑜𝑠𝑠𝐶 𝑖,𝑡)), (15) where 𝐶+ and 𝐶− are inversely proportional to the number of pos- itive and negative instances in our settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝛾 is a coefficient to control the contribution between 𝑙𝑜𝑠𝑠𝑃 and 𝑙𝑜𝑠𝑠𝐶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Dynamical Prediction Besides the “Early Stop” mechanism pro- vided by Hierarchical Survival Predictor, our dynamical construction scheme of asset transfer paths can also relieve the time cost of fea- ture preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4, the path data can be reused if no new transaction occurs in this interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' If an address has new Receive or Spend transactions, model will create new backward or forward asset transfer paths accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Moreover, model also check the endpoint of the forward paths to determine whether they need to be extended or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6 EXPERIMENT AND ANALYSIS In this section, we perform empirical evaluation to answer the following research questions: RQ1: What is the performance with respect to different uniform path lengths?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' RQ2: Does Evolve Path Tracer outperform the state-of-the- art methods for early malicious address detection?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' RQ3: How dose each components benefit the final detection performance?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Conference’17, July 2017, Washington, DC, USA R-1 R-2 S-1 S-2 Timestep 1 Timestep 2 Timestep 3 Figure 4: Dynamical Construction of asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The three vectors on the left are Address Features corresponding to Timestamp 1 to Timestamp 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Different dash boxes repre- sent input information at different timestamps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Table 1: Dataset Statistics Type Definition Posi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Nega.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' P/N(%) H Hack and steal tokens 302 6582 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='03 R Encrypt data for ransoms 3224 21100 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='28 D Illegal BTC darknets 5838 109937 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='31 RQ4: Dose the time overhead of the preparation procedure and scalability satisfy the real-time requirement?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Data Collection and Preparation The transaction data are publicly accessible by running a Bitcoin client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We obtained all the data from the 1-st to the 700, 000-th block for higher credibility, as we only collect addresses verified by enough participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For a given address, we get the related trans- action history based on the APIs exposed by BlockSci [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Based on this transaction history, we can calculate the related features and prepare the asset transfer paths and path graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To get the labels for three different illicit activities (Hack, Ransomware, and Darknet), we performed a manual search on public forums and datasets, such as Bitcointalk forum2, Reddit, WalletExplorer3 and several prior studies [14, 22, 31] to fetch related labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Negative (Regular) addresses are collected in the same method as [17, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We set the activation threshold as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='01 to prepare the asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' One can set a smaller threshold depending on the operating device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' More detail about the statistical properties of the asset transfer path can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1 shows the summarized de- scriptions: The definition and numbers of positive (Posi), negative (Nega), and Positive/Negative ratio (P/N) for each malicious type (H: Hack, R: Ransomware, D: Darknet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 Settings and Metrics As our purpose is to detect malicious addresses as early as pos- sible, the model should detect them before the institution’s daily settlement when the institutions may find the malice by themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Therefore, our experiments focus on early illicit detection during the first day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Although the experiments investigate the performance during the first day, our Evolve path Tracer can work with an arbi- trary timespan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To evaluate the performance of our model, we get 2https://bitcointalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='org/ 3https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='walletexplorer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='com 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 Hack Ransomware Darknet Figure 5: 𝐹1𝐸 and 𝐹1𝐶 of different uniform path lengths on three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 24 hours data with 1 hour interval, and we average the evaluation metrics on all timesteps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The selected metrics are accuracy (Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ), precision (Prec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ), and recall (Rec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, the model should predict correct labels fast to prevent economic loss earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Also, due to data insufficiency, the model may predict conflict labels at different timesteps, thus confusing users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus we require the predictions to be consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' we introduce the early-weighted F1 score 𝐹1𝐸 and consistency- weighted score 𝐹1𝐶 as follows: F1E = �𝑁 𝑖=1 𝐹1𝑖/ √ 𝑖 �𝑁 𝑖=1 1/ √ 𝑖 , F1C = �𝑁 −1 𝑖=1 √ 𝑖 × 𝐹1𝑖 × 1𝑦𝑐 (𝑦𝑖) �𝑁−1 𝑖=1 √ 𝑖 , (16) where 𝑖 is the timestep, 𝑦𝑐 is the set of predictions where 𝑠𝑖𝑔𝑛((𝑦𝑖 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5) × (𝑦𝑖+1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5)) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The indicator function 1𝑦𝑐 (𝑦𝑖) = 1 when 𝑦𝑖 ∈ 𝑦𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐹1𝑖 is the 𝐹1 score of the prediction at timestep 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 Effects of Uniform Path Length (RQ1) As mentioned in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1, to encode the asset transfer paths, we need to project asset transfer paths to the same length 𝐿𝑢.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We further analyze the effects of uniform path length with a simplified AF/Path model (using Address features and Asset Transfer Path features).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We test 6 groups with different path lengths (From 2 to 12 by the interval of 2) on all three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As we use a simplified model, we focus on the path length that maximizes the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A Uniform path with a longer length can preserve more infor- mation that contributes to better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus the model performs better as 𝐿𝑢 increases at the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, if the 𝐿𝑢 is longer than most asset transfer paths, the uniform path may introduce more redundant noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Therefore, the model does not perform better when the path length is too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Since hack addresses get funds directly from the victim’s ac- count and need to transfer money as soon as possible, its asset transfer path is shorter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig 5, the model achieves the best 𝐹1𝐸 and 𝐹1𝐶 scores when setting 𝐿𝑢 to 4 and 6, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Considering both scores, the model performs best when 𝐿𝑢 equals 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ransomware is malicious software that threatens the victims to pay a ransom fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In many cases, the ransom demand comes with a deadline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Victims buy bitcoins from exchanges and transfer them to criminals, thus slightly increasing the lengths of the asset transfer paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig 5, the model performs best When the 𝐿𝑢 is 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A darknet is an overlay network within the Internet that can only be accessed with specific authorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thereby, users could buy and sell illicit goods anonymously via the darknet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Since platforms need to wait for the activity of buyers and sellers, there F1E F1CF1E F1CConference’17, July 2017, Washington, DC, USA Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu Positive B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R Negative B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R Prediction Hack Ransomware Darknet AF B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R FR Path B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R BK Path B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R FR Graph B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R BK Graph B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R Figure 6: Prediction evolution of different address groups and corresponding average Benevolent Rates (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='R) of differ- ent features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' will be a longer asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The model performs best When the 𝐿𝑢 is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, setting 𝐿𝑢 to 6, the model gets similar scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Considering the model’s scalability, in the actual experiment, we also set 𝐿𝑢 to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 Performance Comparison (RQ2) To verify the effectiveness and versatility of our Evolve Path Tracer, we first compare the most common machine learning models, then compare our encoder module with the encoder in other early de- tection models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At last, we also compare the address graph-based models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The models are detailed in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The main results for comparing all different methods are shown in Table 2, and the major findings are summarized as follows: (1) In terms of the five evaluation metrics, our Evolve Path Tracer outperforms most compared methods by a significant margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Es- pecially for early detection performance metrics F1-E and F1-C, our Evolve Path Tracer achieves the best performance under all three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Compared to the second-best methods, Evolve Path Tracer has an average increase of 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='54% on 𝐹1𝐸 and an average increase of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='63% on 𝐹1𝐶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, none of these methods can perform well on all three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' These significant performance margins justify the effectiveness and versatility of our Evolve Path Tracer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Besides, the "Early Stop" mechanism accelerates the prediction speed and helps the model discard subsequent noise, improving the model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (2) Traditional machine learning algorithms do not perform well on the three datasets because these algorithms are difficult to en- code temporal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' It is difficult for decision-tree-based machine learning algorithms to consider shifts in the feature deci- sion boundary along the times [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Therefore, our model has an average improvement of 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='52% on 𝐹1𝐸 and 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='44% on 𝐹1𝐶 com- pared to the best decision-tree-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The sequential deep learning methods perform well on the three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, our Evolve Path Tracer still has an average 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='82% improvement on 𝐹1𝐸 and 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='11% on 𝐹1𝐶 compared to the best model in this group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The first reason is that the inter-relationships among asset transfer paths can reveal specific transaction patterns (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=', two addresses transfer money through multiple paths to avoid monitoring).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In addition, since the transaction pattern evolves in the early stage, a static encoding module can hardly encode evolving information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (3) Compared with Address Graph methods, our Evolve Path Tracer has an average increase of 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='74% on 𝐹1𝐸 and an average increase of 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='36% on 𝐹1𝐶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Among them, Evolve-GCN performs the best in most datasets, which verifies the fast-evolving of early transaction networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, as [18] implies, the address GCN may lead to Over-Smoothing issues and the dilution of the minority class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In our cases, most neighbors of malicious nodes are victims or shadow addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus the Address Graph models do not perform well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To avoid the dilution problem, in Evolve Path Tracer, we set vertices as transactions to utilize the relevant address information in a "safer" way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 Ablation Study (RQ3) As shown in Table 3, AF performed poorly on the three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Because many benevolent addresses (change address, ICO, and legal market addresses) behave similarly to these malicious addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6, the AF benevolent rates for most negative samples do not exceed 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The introduction of asset transfer path features significantly improves the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6, for the Hack addresses, the forward transaction signal is more impor- tant than the backward one because the Hack address will transfer the funds faster and more centralized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ransomware and Darknet addresses usually require victims or buyers to transfer funds ac- cording to certain conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus the backward information is more valuable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Comparing +Path and +Graph, by encoding the paths’ interrela- tionships, the model gives predictions based on transaction patterns rather than the fluctuation of a single path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6, the prominent signals of malicious nodes are enhanced by introducing path graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In the cryptocurrency transaction network, There- fore, the model should be able to handle the differences between various types of addresses at different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' By comparing the performance differences between +Graph and +Evolve, we found that this Evolve mechanism is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' +Graph only performs well if the address has a shorter life span, and these addresses will be discarded after the first few transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, for other addresses with longer lifetimes, +Evolve can better reflect changes in the transaction patterns of these addresses, resulting in better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 Scalability and Dynamical Prediction (RQ4) Feature Preparation Time Cost When a new block appears, real users will generally monitor the addresses that have transactions with them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Those new and large-volume addresses are likely to participate in dangerous activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus, we randomly selected 1, 000 blocks (from the first block of 2018 to the first block of 2022) and collected the daily BTC price during this period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We filter out transactions lower than $10, 000 and retrieve address with a lifespan less than one week.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We prepare every address’s data of the first 24 hours, the time cost is illustrated as follows: During each interval (1 hour is about 6 blocks), we need to monitor about 1, 166 new addresses, which will only cost 5 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Moreover, as shown in Table 4, our time cost resembles address graph preparation, but we can collect information much further than 2 hops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='50 ★★★ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 1 6 11 16 2110 0 5 10 151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 ★★★★★★★★ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00★ Posi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Prediction Nega.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Prediction★ Posi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Prediction Nega.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Prediction★ Posi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Prediction Nega.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Prediction8 7 6 5 4 3 2 1 6 11 16 210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 1 6 11 16 21Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Conference’17, July 2017, Washington, DC, USA Table 2: Scores of different prediction model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evo-PT and Evo-PT (E) are our Evolve Path Tracer with/wo “Early Stop” mecha- nism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Underline stands for best score in the group, Bold stands for best score in all groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Type Model Name Hack Ransomware Darknet 𝐴𝑐𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑃𝑟𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑅𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐹1𝐸 𝐹1𝐶 𝐴𝑐𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑃𝑟𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑅𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐹1𝐸 𝐹1𝐶 𝐴𝑐𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑃𝑟𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑅𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐹1𝐸 𝐹1𝐶 Machine Learning DT 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='995 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='347 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='137 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='197 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='197 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='955 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='736 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='432 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='545 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='545 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='982 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='448 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='152 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='227 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='227 RF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='996 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='405 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='242 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='303 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='303 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='955 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='735 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='436 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='547 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='547 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='983 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='519 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='109 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='181 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='181 XGB 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='997 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='347 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='137 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='197 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='197 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='960 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='865 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='435 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='579 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='579 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='985 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='790 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='191 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='308 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='308 Sequen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Deep Learning GRU 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='928 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='298 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='438 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='354 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='354 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='885 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='558 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='949 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='703 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='703 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='942 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='470 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='838 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='603 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='603 M-LSTM 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='949 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='418 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='272 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='328 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='887 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='561 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='969 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='711 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='710 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='951 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='520 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='845 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='642 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='645 CED 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='909 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='265 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='563 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='360 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='360 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='909 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='617 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='960 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='752 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='751 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='478 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='606 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='606 SAFE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='918 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='438 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='271 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='330 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='909 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='616 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='963 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='752 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='752 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='949 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='508 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='838 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='632 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='632 Addr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Graph GCN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='920 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='433 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='670 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='501 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='507 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='887 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='564 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='936 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='700 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='706 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='942 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='459 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='613 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='525 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='524 Skip-GCN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='917 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='410 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='690 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='443 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='432 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='903 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='603 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='935 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='729 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='735 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='941 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='459 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='629 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='531 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='530 Evo-GCN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='893 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='428 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='749 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='427 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='442 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='906 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='613 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='944 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='736 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='746 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='941 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='459 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='633 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='530 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='533 TX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Graph Evo-PT 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='963 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='739 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='664 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='668 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='938 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='743 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='869 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='799 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='802 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='963 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='624 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='764 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='686 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='686 Evo-PT (E) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='969 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='650 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='731 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='689 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='683 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='940 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='751 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='869 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='802 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='807 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='964 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='625 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='754 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='686 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='687 Table 3: Scores of different ablation models on Hack (H), Ransomware (R), and Darknet (D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ablation modules in- clude Address Features (AF), Path features (+Path), Path Graph features (+Graph), and Evolve schemes (+Evolve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Model 𝐴𝑐𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑃𝑟𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝑅𝑒𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 𝐹1𝐸 𝐹1𝐶 H AF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='920 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='309 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='590 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='389 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='412 +Path 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='954 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='537 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='546 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='509 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='538 +Graph 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='965 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='686 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='476 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='545 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='559 +Evolve 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='961 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='606 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='553 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='551 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='576 R AF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='911 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='710 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='632 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='626 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='628 +Path 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='929 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='727 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='805 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='760 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='765 +Graph 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='927 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='696 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='875 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='773 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='776 +Evolve 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='937 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='735 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='795 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='798 D AF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='961 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='571 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='611 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='604 +Path 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='961 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='611 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='693 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='649 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='650 +Graph 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='960 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='586 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='804 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='678 +Evolve 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='963 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='626 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='758 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='685 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='685 Table 4: Time cost of different input data, includes Block Number, Transaction Number, Address Number), Address Feature, Asset Transfer Path, Path Graph, and Address Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' #Blk #TX #Addr A-Feat Path P-G A-G 1,000 306,258 194,310 175s 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='7h 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='9h 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3h Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 306 194 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2s 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6s 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8s 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4s Scalability of Early Stop To justify the Scalability of our “Early Stop” mechanism, we plot the skip ratios with a different threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 7, all models can filter out most (80%) addresses by the fourth hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The mechanism improves the model’s Scalability significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Moreover, choosing a reasonable threshold helps the Hack Ransomware Darknet 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='91 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='91 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='84 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='72 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='73 Inf-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='73 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='91 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='87 Inf-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='87 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='76 Inf-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='76 Figure 7: Skip Ratio evolution and 𝑅𝑒𝑐𝑎𝑙𝑙 scores with differ- ent thresholds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The gray line is the Positive/Negative ratio of each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' model to discard subsequent noise and improve the model’s per- formance, as mentioned in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A lower threshold means a faster prediction speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' However, there is a concern about missing malicious addresses as we decrease the threshold for faster prediction speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Which then decreases the model’s Recall scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' As shown in Fig, compared to the model without “Early Stop” (labeled as “Inf”), the model has better Recall scores as we decrease the threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' This is because our model can predict the most benevolent addresses in the early hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Removing them from the monitoring list can avoid subsequent noise, which improves the model’s Recall scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thus our Evolve Path Tracer has a faster prediction speed without missing malicious addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 7 CONCLUSION AND FUTURE WORK In this paper, we present Evolve Path Tracer, a novel framework for early malicious address detection on BTC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We first propose asset transfer paths and encode them with Evolve Path Encoder LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The asset transfer paths exhibit high versatility in monitoring trans- action patterns of various malicious behaviors in the early stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' To take full advantage of these paths, the Evolve Path Graph GCN is built to encode corresponding path graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The graphs capture the interrelation among the paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In particular, all modules are evolving along with the timeline to encode the dynamics of paths’ content and inter-relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Finally, we implement Hierarchical Sur- vival Predictor with Consistency Loss Function to achieve better 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='80 4 8 12 16 20 240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='84 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='83 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='79 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='78 4 8 12 16 20 241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='80 4 8 12 16 20 241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='71 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4-Recall:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='71 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='6-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='8-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='53 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='54 Inf-Recall: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='54 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 4 8 12 16 20 24Conference’17, July 2017, Washington, DC, USA Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu prediction performance, higher consistency, and excellent scalabil- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The model is quantitatively and qualitatively evaluated on three malicious address datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Extensive ablation studies elaborate on the mechanisms behind the effectiveness and excellent scalability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In future work, we would like to extend Evolve Path Tracer to ma- licious address detection in other crypto-currency platforms and traditional financial domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' REFERENCES [1] Cuneyt G Akcora, Yitao Li, Yulia R Gel, and Murat Kantarcioglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Bit- coinheist: Topological data analysis for ransomware prediction on the bitcoin blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the twenty-ninth international joint conference on artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [2] Elli Androulaki, Ghassan O Karame, Marc Roeschlin, Tobias Scherer, and Srdjan Capkun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evaluating user privacy in bitcoin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In International conference on financial cryptography and data security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 34–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [3] Liang Chen, Jiaying Peng, Yang Liu, Jintang Li, Fenfang Xie, and Zibin Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Phishing scams detection in ethereum transaction network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ACM Transac- tions on Internet Technology (TOIT) 21, 1 (2020), 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [4] Tianyi Chen and Charalampos Tsourakakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Antibenford subgraphs: Un- supervised anomaly detection in financial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2762–2770.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [5] Weili Chen, Zibin Zheng, Jiahui Cui, Edith Ngai, Peilin Zheng, and Yuren Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Detecting ponzi schemes on ethereum: Towards healthier blockchain technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the 2018 world wide web conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1409–1418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [6] Kyunghyun Cho, Bart van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' On the Properties of Neural Machine Translation: Encoder–Decoder Ap- proaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 103–111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [7] Mikkel Alexander Harlev, Haohua Sun Yin, Klaus Christian Langenheldt, Raghava Mukkamala, and Ravi Vatrapu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Breaking bad: De-anonymising entity types on the bitcoin blockchain using supervised machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the 51st Hawaii International Conference on System Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [8] Mikkel Alexander Harlev, Haohua Sun Yin, Klaus Christian Langenheldt, Raghava Mukkamala, and Ravi Vatrapu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Breaking bad: De-anonymising entity types on the bitcoin blockchain using supervised machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the 51st Hawaii international conference on system sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [9] Shuli Jiang, Robson Leonardo Ferreira Cordeiro, and Leman Akoglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' MCA: Outlier Detection with Explicit Micro-Cluster Assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' arXiv preprint arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='08212 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [10] Marc Jourdan, Sebastien Blandin, Laura Wynter, and Pralhad Deshpande.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Characterizing entities in the bitcoin blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In 2018 IEEE international con- ference on data mining workshops (ICDMW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE, 55–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [11] Harry Kalodner, Malte Möser, Kevin Lee, Steven Goldfeder, Martin Plattner, Alishah Chator, and Arvind Narayanan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Blocksci: Design and applications of a blockchain analysis platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In 29th {USENIX} Security Symposium ({USENIX} Security 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2721–2738.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [12] Jonathan Kuck, Honglei Zhuang, Xifeng Yan, Hasan Cam, and Jiawei Han.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Query-based outlier detection in heterogeneous information networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Ad- vances in database technology: proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' International Conference on Extending Database Technology, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' NIH Public Access, 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [13] Sijia Li, Gaopeng Gou, Chang Liu, Chengshang Hou, Zhenzhen Li, and Gang Xiong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' TTAGN: Temporal Transaction Aggregation Graph Network for Ethereum Phishing Scams Detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the ACM Web Conference 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 661–669.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [14] Yang Li, Yue Cai, Hao Tian, Gengsheng Xue, and Zibin Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Identifying illicit addresses in bitcoin network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In International Conference on Blockchain and Trustworthy Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 99–111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [15] Jiaqi Liang, Linjing Li, Daniel Zeng, Shu Luan, and Lu Gan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Bitcoin exchange addresses identification and its application in online drug trading regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [16] Dan Lin, Jiajing Wu, Qi Yuan, and Zibin Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' T-edge: Temporal weighted multidigraph embedding for ethereum transaction network analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Frontiers in Physics 8 (2020), 204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [17] Bing Liu, Yang Dai, Xiaoli Li, Wee Sun Lee, and Philip S Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Building text classifiers using positive and unlabeled examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Third IEEE International Conference on Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE, 179–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [18] Yang Liu, Xiang Ao, Zidi Qin, Jianfeng Chi, Jinghua Feng, Hao Yang, and Qing He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Pick and Choose: A GNN-Based Imbalanced Learning Approach for Fraud Detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the Web Conference 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [19] Mohammad Masud, Jing Gao, Latifur Khan, Jiawei Han, and Bhavani M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Thu- raisingham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Classification and Novel Class Detection in Concept-Drifting Data Streams under Time Constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering 23, 6 (2011), 859–874.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1109/TKDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='61 [20] Mohammad M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Masud, Qing Chen, Latifur Khan, Charu C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Aggarwal, Jing Gao, Jiawei Han, Ashok Srivastava, and Nikunj C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Oza.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Classifica- tion and Adaptive Novel Class Detection of Feature-Evolving Data Streams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering 25, 7 (2013), 1484–1497.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1109/TKDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='109 [21] Pranav Nerurkar, Yann Busnel, Romaric Ludinard, Kunjal Shah, Sunil Bhirud, and Dhiren Patel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Detecting illicit entities in bitcoin using supervised learning of ensemble decision trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the 2020 10th international conference on information communication and management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 25–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [22] Masarah Paquet-Clouston, Bernhard Haslhofer, and Benoit Dupont.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Ran- somware payments in the bitcoin ecosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Journal of Cybersecurity 5, 1 (2019), tyz003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [23] Aldo Pareja, Giacomo Domeniconi, Jie Chen, Tengfei Ma, Toyotaro Suzumura, Hiroki Kanezashi, Tim Kaler, Tao Schardl, and Charles Leiserson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evolvegcn: Evolving graph convolutional networks for dynamic graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 5363–5370.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [24] Fergal Reid and Martin Harrigan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' An analysis of anonymity in the bitcoin system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Security and privacy in social networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 197–223.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [25] Wei Shao, Hang Li, Mengqi Chen, Chunfu Jia, Chunbo Liu, and Zhi Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Identifying bitcoin users using deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In International Conference on Algorithms and Architectures for Parallel Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 178–192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [26] Changhe Song, Cheng Yang, Huimin Chen, Cunchao Tu, Zhiyuan Liu, and Maosong Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' CED: Credible early detection of social media rumors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [27] Yizhou Sun, Jiawei Han, Charu C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Aggarwal, and Nitesh V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Chawla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' When Will It Happen?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Relationship Prediction in Heterogeneous Information Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the Fifth ACM International Conference on Web Search and Data Mining (WSDM ’12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 663–672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1145/2124295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2124373 [28] Da Sun Handason Tam, Wing Cheong Lau, Bin Hu, Qiu Fang Ying, Dah Ming Chiu, and Hong Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Identifying Illicit Accounts in Large Scale E- payment Networks–A Graph Representation Learning Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='05546 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [29] Marie Vasek and Tyler Moore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' There’s no free lunch, even using Bitcoin: Tracking the popularity and profits of virtual currency scams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In International conference on financial cryptography and data security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 44–61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [30] Mark Weber, Giacomo Domeniconi, Jie Chen, Daniel Karl I Weidele, Claudio Bellei, Tom Robinson, and Charles E Leiserson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Anti-money laundering in bitcoin: Experimenting with graph convolutional networks for financial forensics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' arXiv preprint arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='02591 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [31] Jiajing Wu, Jieli Liu, Weili Chen, Huawei Huang, Zibin Zheng, and Yan Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Detecting mixing services via mining bitcoin transaction network with hybrid motifs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE Transactions on Systems, Man, and Cybernetics: Systems (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [32] Jiajing Wu, Qi Yuan, Dan Lin, Wei You, Weili Chen, Chuan Chen, and Zibin Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Who are the phishers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' phishing scam detection on ethereum via network embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE Transactions on Systems, Man, and Cybernetics: Systems (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [33] Haohua Sun Yin and Ravi Vatrapu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A first estimation of the proportion of cybercriminal entities in the bitcoin ecosystem using supervised machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In 2017 IEEE International Conference on Big Data (Big Data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE, 3690–3699.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [34] Shuhan Yuan, Panpan Zheng, Xintao Wu, and Yang Xiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Wikipedia vandal early detection: from user behavior to user embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Joint European Conference on Machine Learning and Knowledge Discovery in Databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Springer, 832–846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [35] Ge Zhang, Zhenyu Yang, Jia Wu, Jian Yang, Shan Xue, Hao Peng, Jianlin Su, Chuan Zhou, Quan Z Sheng, Leman Akoglu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Dual-discriminative Graph Neural Network for Imbalanced Graph-level Anomaly Detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [36] Jiawei Zhang, Congying Xia, Chenwei Zhang, Limeng Cui, Yanjie Fu, and S Yu Philip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' BL-MNE: emerging heterogeneous social network embedding through broad learning with aligned autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In 2017 IEEE International Conference on Data Mining (ICDM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' IEEE, 605–614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' [37] Lingxiao Zhao, Saurabh Sawlani, Arvind Srinivasan, and Leman Akoglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Graph Anomaly Detection with Unsupervised GNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='48550/ ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='09535 [38] Panpan Zheng, Shuhan Yuan, and Xintao Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Safe: A neural survival analysis model for fraud early detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1278–1285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evolve Path Tracer: Early Detection of Malicious Addresses in Cryptocurrency Conference’17, July 2017, Washington, DC, USA A SUPPLEMENTARY MATERIAL A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='1 Reproducibility We release Evolve Path Tracer on GitHub4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We first download full-node BTC raw data with Bitcoin Core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The whole data size is about 500GB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' After downloading all blocks before the 700,000th block, we parse all data by Blocksci for querying block, transaction, and address index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The parsed data size is about 400GB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For each address in our dataset, We then prepare its asset transfer paths for the transactions during the first 24 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The process was executed on AMD Ryzen 9 3900X Processor with 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0GB of memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We implement Evolve Path Tracer in Pytorch and Geometric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' All experiments are conducted on a single NVIDIA RTX 2080TI with 11G memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='2 Address Features We use the following features to characterize an address at a specific timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' the current balance of the address the number of receive (spend) transactions, the ratio of receive (spend) transactions number, the maximum receive (spend) transactions number, the life span of the address, address active rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='3 Transaction Features We use the following features to characterize a transaction, which is the component of every asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' the height interval to the path source, the influence (trust) score with the previous transaction, the input amount of the previous transaction, the transaction fee, the total amount (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' max, min, avg, and var) of all receive (spend) transactions, the number of receive (spend) transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='4 Preparation of Asset Transfer Path Algo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1 gives the detail to prepare Backward Asset Transfer Paths that reveal where 𝑗 obtains the asset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The pipeline to construct Forward Asset Transfer Path is similar to Backward Asset Transfer Path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The only difference is the tracing direction The essence of each node is a transaction, thus we use a sequence of transaction features to represent an asset transfer path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 Baseline Models We give details of our baseline methods from two related tasks: Malicious Detection in Cryptocurrency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We compare Evolve Path-Tracer with several models for malicious address detection in cryptocurrencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For decision tree models, we use address features and path statistic features as the feature set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For GCN models, at each time step, we get the addresses’ embedding after two graph convolutional layers as implemented in [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Then, we feed the embeddings into a sequential model for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='com/Cranooooooo/ADS-Demo Algorithm 1: Backward Path Preparation input :Initial Output Tx 𝑗𝑜, Threshold 𝜃, Time Span 𝑇𝑆𝑝𝑎𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' output:Backward Path Set 𝑃.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 1 Initialize Backward Path Set: 𝑃 ← {[−, 1, 𝑗𝑜]};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 2 Initialize Previous hop recorder: 𝑃𝑝𝑟𝑒 ← {[−, 1, 𝑗𝑜]};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 3 Initialize Ending Flag: 𝐹𝑒𝑛𝑑 ← 𝐹𝑎𝑙𝑠𝑒;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 4 𝑗𝑜’s Time: 𝑇𝑗𝑜 ← Time of 𝑗𝑜;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 5 while 𝐹𝑒𝑛𝑑 ≠ 𝑇𝑟𝑢𝑒 do 6 Current hop recorder 𝑃𝑛𝑜𝑤 ← {};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 7 𝐹𝑒𝑛𝑑 ← 𝑇𝑟𝑢𝑒;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 8 for 𝑝 in 𝑃𝑝𝑟𝑒 do 9 𝑗 ← Output Tx 𝑝[2];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 10 𝐼 ← Input Tx Set of 𝑗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 11 for 𝑖 in 𝐼 do 12 𝑃𝑟𝑜𝑝𝑖 ← 𝐴𝑚𝑡𝑖/𝐴𝑚𝑡𝐼 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 13 𝑆𝑐𝑜𝑟𝑒𝑖 ← 𝑃𝑟𝑜𝑝𝑖 ∗ 𝑝[1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 14 𝑇𝑖 ← time of 𝑖;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 15 if (𝑆𝑐𝑜𝑟𝑒𝑖 ≥ 𝜃 and 𝑇𝑗𝑜 −𝑇𝑖 ≤ 𝑇𝑆𝑝𝑎𝑛) then 16 Append [𝑗,𝑆𝑐𝑜𝑟𝑒𝑖,𝑖] to 𝑃𝑛𝑜𝑤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 17 𝐹𝑒𝑛𝑑 ← 𝐹𝑒𝑛𝑑 && 𝐹𝑎𝑙𝑠𝑒;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 18 𝑃𝑝𝑟𝑒 ← 𝑃𝑛𝑜𝑤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 19 𝑃 ← 𝑃 ∪ 𝑃𝑝𝑟𝑒;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' 20 return 𝑃 Decision Tree [15, 21] utilize Decision Tree for identifying these malicious addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Random Forest [21] utilize Decision Tree for identifying these malicious addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' XGB [8, 21] predict the type of a yet-unidentified entity with Gradient Boosting based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' GCN [30] encodes the objective address based on its trans- action address graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Skip-GCN [30] inserts a skip connection between the inter- mediate embedding and the input node features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Evolve-GCN [30] updates GCN weights with an RNN mod- ule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Early Rumor Detection on Social Media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' For these sequential models, we build an extra path LSTM encoder for a fair comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' We concatenate address features with the path-encoder output and feed them into the sequential prediction model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' GRU [6] is a typical neural network for sequence modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' At each time split, previous hidden state and current summa- tion features are fed into the GRU unit to predict the labels for the given addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' M-LSTM [34] adopts LSTM for every kind of feature to generate its own temporal features at each timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Here we build three LSTM models for Address Features, Forward Paths, and Backward Paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' CED [26] also uses GRU for sequence modeling, it proposes the concept of “Credible Detection Point,” making it possible to make predictions as early as possible dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' Conference’17, July 2017, Washington, DC, USA Ling Cheng, Feida Zhu, Yong Wang, Ruicheng Liang, and Huiwen Liu Table 5: Key components and module description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' TX stands for the transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Name(Notation) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Description ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Influence TX pair (𝑗 → 𝑖) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='A certain portions of TX i’s BTCs come from TX j ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Trust TX pair (𝑖 → 𝑗) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='A certain portions of TX i’s BTCs flow to TX j ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Backward Asset Transfer Path (𝑗𝑛 → · · · → 𝑖) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Build the Influence TX pairs iteratively and link them to form a path ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward Asset Transfer Path (𝑖 → · · · → 𝑗𝑛) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Build the Trust TX pairs iteratively and link them to form a path ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Backward Path Graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Backward Asset Transfer paths share the same source TX are grouped to form a graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward Path Graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Forward Asset Transfer paths share the same destination TX are grouped to form a graph ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='T-1 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='LSTM to encode temporal information of address features ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='E-1 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='An Evolve Path Encoder LSTM for encoding Backward Asset Transfer Path to Backward Path feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='E-2 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='An Evolve Path Encoder LSTM for encoding Forward Asset Transfer Path to Forward Path feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='T-2 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='LSTM to encode temporal information of Backward Path feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='T-3 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='LSTM to encode temporal information of Forward Path feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='BK-Graph Encoder ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='An Evolve Path Graph GCN for encoding Backward Path Graph to Backward Graph feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='BK-Graph Encoder ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='An Evolve Path Graph GCN for encoding Forward Path Graph to Forward Graph feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='T-4 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='LSTM to encode temporal information of Backward Graph feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='T-5 LSTM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='LSTM to encode temporal information of Forward Graph feature ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Time (Hour) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Hop-Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Height-Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Max Amount ($ log 10) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Related Address Number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Max Input Number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Path Max Output Number ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='Figure 8: Asset transfer path’s statistical properties of different malicious addresses under the backward and forward direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' SAFE [38] adopts survival probability as the prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' In- stead of predicting the labels directly, it generates hazard rates for the survival models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' The positive samples should die out fast, while the negative samples should stay alive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content=' H-FR 4 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 H-BK R-FR 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 R-FR D-FR 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 D-FR 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} +page_content='5 C 4 8 12 16 20 2480 60 40 H-FR H-BK R-FR 20 R-FR D-FR D-FR 4 8 12 16 20 2410 8 H-FR H-BK R-FR 6 R-FR D-FR D-FR 4 2 4 8 12 16 20 24160 H-FR 140 H-BK R-FR 120 R-FR 100 D-FR D-FR 80 60 40 20 0 4 8 12 16 20 24100 H-FR 90 H-BK R-FR 80 R-FR D-FR 70 D-FR 60 50 40 30 20 4 8 12 16 20 24250 200 150 H-FR 100 H-BK R-FR R-FR 50 D-FR D-FR 4 8 12 16 20 24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE5T4oBgHgl3EQfEQ5e/content/2301.05412v1.pdf'} diff --git a/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/2301.03648v1.pdf.txt b/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/2301.03648v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b0df02c972a41fdbd95dba0ba78290399375d03e --- /dev/null +++ b/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/2301.03648v1.pdf.txt @@ -0,0 +1,768 @@ +Astronomy & Astrophysics manuscript no. aanda +©ESO 2023 +January 11, 2023 +Letter to the Editor +The Cosmic Web from Perturbation Theory +F.-S. Kitaura12⋆, F. Sinigaglia1234,, A. Balaguera-Antol´ınez12, and G. Favole12 +1 Instituto de Astrof´ısica de Canarias, s/n, E-38205, La Laguna, Tenerife, Spain e-mail: fkitaura@iac.es +2 Departamento de Astrof´ısica, Universidad de La Laguna, E-38206, La Laguna, Tenerife, Spain +3 Department of Physics and Astronomy, Universit`a degli Studi di Padova, Vicolo dell’Osservatorio 3, I-35122, Padova, +Italy +4 INAF—Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122, Padova, Italy +Received XX XX, 20XX; accepted XX XX, 20XX +ABSTRACT +Context. Analyzing the large-scale structure (LSS) with galaxy surveys demands accurate structure formation models. +Such models should ideally be fast and have a clear theoretical framework to rapidly scan a variety of cosmological +parameter spaces without requiring large training data sets. +Aims. This study aims to extend Lagrangian perturbation theory (LPT), including viscosity and vorticity, to reproduce +the cosmic evolution from dark matter N-body calculations at the field level. +Methods. We extend Augmented LPT (ALPT) to an Eulerian framework, dubbed eALPT. This enables modelling +the stress tensor, with this introducing vorticity. To compensate that ALPT assumes curl-free fields, a fraction of the +vorticity, emerging after each Eulerian transformation, is added to the subsequent timestep. The model has three free +parameters apart from the choice of cosmology, redshift snapshots, cosmic volume, and the number of particles-cells. +Results. We find that the cross-correlation of the dark matter distribution as compared to N-body solvers increases at +k = 1hMpc−1 from ∼ 55% with the Zel’dovich approximation (∼ 70% with ALPT); to ∼96 and 97% with eALPT, and +power spectra within percentage accuracy up to k ≃ 0.3 and 0.7 hMpc−1, using three and five steps, respectively. +Key words. cosmology: – theory - large-scale structure of Universe - dark matter; methods: analytical +1. Introduction +The cosmic web is the LSS pattern that emerges as a man- +ifestation of the action of gravity in an expanding back- +ground Universe. It is shaped according to the cosmological +information content set in the initial conditions of cosmic +times. +The scientific community is putting special effort into +mapping the three-dimensional distribution of matter in the +Universe through galaxy surveys such as DESI (Levi et al. +2013), EUCLID (Amendola et al. 2016), J-PAS (Benitez +et al. 2014), or the Nancy Grace Roman Space telescope +(Spergel et al. 2015). +The clustering of the large-scale structure (LSS) yields +powerful constraints on the standard cosmological model, +e.g., the nature of dark energy (e.g. DESI Collaboration +et al. 2016), primordial non-gaussianities (see, e.g., Meer- +burg et al. 2019), and neutrino masses (see, e.g., Chudaykin +& Ivanov 2019). +Since the observable Universe is unique, one needs mock +catalogues for a robust analysis. These permit the compu- +tation of covariance matrices and to study of systematics in +the observational data. However, the computation of mock +catalogues is usually costly, and only a few can be done (see, +e.g., Angulo et al. 2012; Fosalba et al. 2015; Chuang et al. +2019). In this context, bias mapping techniques at the field +level emerged as a solution to save enormous computational +resources while maintaining high accuracy, such as PATCHY +⋆ fkitaura@iac.es +(Kitaura et al. 2014, 2015) applied to the BOSS data (Ki- +taura et al. 2016) or EZmocks (Chuang et al. 2015) applied +to the eBOSS data (Zhao et al. 2021). More recently, the +BAM code has been designed to learn the complex bias rela- +tion from reference simulations (Balaguera-Antol´ınez et al. +2019; Balaguera-Antol´ınez et al. 2020; Kitaura et al. 2022). +These techniques can also accurately map the Lyman-α for- +est (see e.g., Sinigaglia et al. 2021, 2022). +All the methods mentioned above require a dark matter +field defined on a mesh. The accuracy of that matter distri- +bution will determine the precision of the mock catalogues. +A series of ideas have been implemented to accelerate +particle-mesh based N-body solvers (see Tassev et al. 2013; +Feng et al. 2016). +Despite these developments, N-body codes are costly +when aiming to mass-produce mock catalogues cover- +ing large cosmic volumes. Therefore, approximate gravity +solvers are still commonly used. While EZmocks relies on the +Zel’dovich approximation (Zel’dovich 1970), PATCHY and +BAM rely on ALPT, including tidal field corrections (Ki- +taura & Hess 2013). It has been shown that such methods +can correct to a great extent the bias introduced by approx- +imate gravity solvers in the nonlinear and nonlocal bias de- +scription (see the application of BAM to galaxy catalogues, +Balaguera-Antol´ınez et al. 2022). +Machine learning techniques applied to large training +data sets (of thousands of N-body simulations for a given +cosmology) have emerged as an alternative to approximate +gravity solvers (He et al. 2019; Dai & Seljak 2021; Jamieson +Article number, page 1 of 5 +arXiv:2301.03648v1 [astro-ph.CO] 9 Jan 2023 + +A&A proofs: manuscript no. aanda +et al. 2022). For a review of numerical methods in LSS +modelling, see Angulo & Hahn (2022). +This letter presents a novel approach to modelling the +cosmic web, as explained in the following sections. +2. Theoretical background +The Universe is considered a closed Hamiltonian system +where energy is conserved. The dark matter content can be +described by a distribution function f(r,v,t) (with position +r and velocity v), such that the probability of finding a +dark matter particle in the phase-space volume drdv cen- +tred on r,v at time t is given by f(r,v,t)drdv (see, e.g., +Mo et al. 2010). The total number of particles will be then +given by integrating over the whole phase-space volume: N = +� � +drdv f(r,v,t). Given the functional form of the distribu- +tion function, total continuous changes to the phase-space +of the system of particles can be expressed with product +and chain derivative rules as: +d +dt f = ∂ +∂t f + ∂r +∂t +∂ +∂r f + ∂v +∂t +∂ +∂v f = +∂ +∂t f +v ∂ +∂r f +g ∂ +∂v f, with g being the gravity-induced accel- +eration. Due to probability conservation, the generalised +continuity equation in phase-space must be fulfilled (Li- +ouville theorem): +∂f +∂t + ∇ · j = ∂f +∂t + ∂( f ˙q) +∂q + ∂( f ˙v) +∂v += 0. Hence, +∂f +∂t + ∂( f ˙q) +∂q ++ ∂(f ˙v) +∂v += ∂ f +∂t + f ∂ ˙q +∂q + ˙q ∂f +∂q + f ∂ ˙v +∂v + ˙v ∂ f +∂v = 0. Con- +sequently, to get the Vlasov or collisionless Boltzmann +equation, the sum of terms multiplied by f must vanish: +f +� ∂ ˙q +∂q + ∂ ˙p +∂p +� += f +� ∂2H +∂q∂p − ∂2H +∂p∂q +� += 0, which is fulfilled by insert- +ing Hamiltonian equations of motion, yielding: +∂ +∂t f + ∂r +∂t +∂ +∂r f + ∂v +∂t +∂ +∂v f = ∂ +∂t f +v ∂ +∂r f +g ∂ +∂v f = 0. +(1) +Building moments of the Boltzmann equation, one gets +– from the zeroth moment, the continuity equation: +multiplying Boltzmann’s equation with the mass of +the +particles +m = m(v)0 +and +integrating +over +dv: +∂ +∂t +ρ +���������������� +� +d3v f m+ ∂ +∂r +ρu +�������������������� +� +d3v f mv = 0, with ρ being the density +and u the velocity field. Hence, +∂ +∂tρ+∇·(ρu) = ∂ +∂tρ+ρ∇·u+u·∇ρ = 0. +(2) +– from the first moment, the Euler equation: multiplying +Boltzmann’s equation with m = m(v)1 and integrating +over dv: +∂ +∂tρu+ ∂ +∂r (ρuu+ρ⟨ww⟩) = ρg, +(3) +with w ≡ u−v being the random velocity. +The process of virialisation is expressed by a stress ten- +sor T term: ⟨ww⟩ = −∇P + ∇ · T. We can neglect the pres- +sure term −∇P for collisionless dark matter. From the com- +bination of the Euler and continuity equations, we get: +ρ +� ∂ +∂tu+(u·∇)u +� += ∇· T+ρg. Introducing comoving coordi- +nates x: r = a(t)x with the scale factor a encoding the ex- +pansion of the Universe, and conformal time τ determined +by: dt = adτ, we can rewrite the previous equation in terms +of, instead of proper velocity u = ˙r = ˙a(t)x+v, peculiar mo- +tions v ≡ a ˙x, yielding: +∂ +∂τv +v ·∇v = 1 +aρ∇·T−∇ ˜Φ−aHv, +(4) +using the Poisson equation ∇2 ˜Φ = 4πG ¯ρδa2 with density +contrast δ ≡ ρ/¯ρ−1 and average density ¯ρ ≡ ⟨ρ⟩. +One usually assumes curl-free velocity fields, neglect- +ing the stress tensor T. Based on this, one can perform +an Eulerian perturbative expansion of both the continu- +ity and the Euler equations around the density contrast +δ(x,τ) = �∞ +n=1 δ(n)(x,τ) and the divergence of the peculiar +velocity field θ(x,τ) ≡ ∇·v = �∞ +n=1 θ(n)(x,τ) (see Bernardeau +et al. 2002, and references therein). Alternatively, one can +consider Eq. 4 and make an expansion in Lagrangian coor- +dinates considering the total derivative +d +dτv = ∂ +∂τv + v · ∇v, +yielding Lagrangian Perturbation Theory (LPT) solutions +(Buchert & Ehlers 1993; Bouchet et al. 1995; Catelan 1995). +The stress tensor is commonly represented by the linear +elastic model ∇·T ∼ µ∇2v+ 1 +3µ∇∇·v+η∇(∇·v) with viscosity +parameters µ and η (see Bernardeau et al. 2002), which +for irrotational fields (when the velocity is the gradient of +a potential field) simplifies to the adhesion model ∇ · T ∼ +µ′∇2v with a single viscosity parameter µ′ (see Shandarin +& Zeldovich 1989). +However, the generation of vorticity (∇ × v) has been +studied in simulations as an important component when +going to the nonlinear regime (see, e.g., Pueblas & Scocci- +marro 2009; Jelic-Cizmek et al. 2018). +As an alternative to expensive N-body simulations, ef- +fective field theories have emerged in LSS, including a mod- +elling of the stress tensor to compute summary statistics +(see, e.g., Carrasco et al. 2012; Baumann et al. 2012; Pa- +jer & Zaldarriaga 2013; Porto et al. 2014; Mercolli & Pajer +2014; Angulo et al. 2015; Baldauf et al. 2015, 2016; Foreman +et al. 2016). See also other perturbative (McDonald 2011; +Pietroni et al. 2012; Rampf 2012; Cusin et al. 2017), and +non-perturbative approaches (Buchert & Dom´ınguez 2005) +to model the curl. +In this work, we propose to model viscosity induced by +a stress tensor through an Eulerian extension of LPT, con- +sidering subsequent cosmic times until reaching the target +redshift. With this, the gravitational potentials become in- +creasingly deeper, changing their shape. In this way, the +vorticity of the displacement field emerges naturally. +3. Method +Let us start considering the Lagrangian q to Eulerian x +coordinates single-step mapping through a displacement Ψ +(with v = d +dτ Ψ): x = q+Ψ(q). The displacement is obtained +according to Augmented LPT (ALPT), which separates the +total displacement Ψ into a long-range ΨL and a short- +range component ΨS (see Kitaura & Hess 2013): Ψ(q,z) = +ΨL(q,z)+ΨS(q,z). +The long-range displacement field is obtained from the +convolution of a Gaussian kernel with an LPT solution: +ΨL(q,z) = K(q,z,rs) ◦ ΨLPT(q,z). We restrict the present +study to second order LPT: Ψ2LPT(q,z) = −D(z)∇qΦ(1)(q)+ +D(2)(z)∇qΦ(2)(q), where D(z) is the growth factor (see e.g. +Heath 1977), and D(2)(z) ≃ − 3 +7 Ω−1/143 +m +(D(z))2 (Bouchet et al. +1995). The normalised potentials Φi(q) are the solutions of +the Poisson equations ∇2 +qΦ(i) = δ(i), where i = 1 is the linear +primordial density field used as the initial conditions, and +i = 2 is determined by: δ(2) = � +i, j 0, and z1 is the first redshift snapshot. Hence, al- +ready after two steps, vorticity at Lagrangian coordinates +emerges naturally. For this reason, it is wrong to assume +that there are no curl sources after one step, even if one +assumes curl-free fields initially. We can compensate for +this vorticity leakage by adding in the subsequent step l+1 +a fraction of the vorticity generated in the previous step +l, computed as the difference between the total displace- +ment to redshift zl and the corresponding curl-free compo- +nent. The displacement field can be decomposed, according +to Helmholtz theorem, into an irrotational or longitudinal +(curl-free) and a solenoidal or transversal (divergence-free) +component: Ψ = Ψ∇×Ψ=0 + Ψ∇·Ψ=0. To get the solenoidal +component, we exploit the fact that the divergence of the +curl of a vector field vanishes: +Ψ∇·Ψ=0(q,zl) ≡ +� +1−∇∇−2∇ +� +·Ψ(q,zl), +(5) +where Ψ∇×Ψ=0 ≡ ∇∇−2∇·Ψ(q,zl). Hence, from the third step +on (l > 1), we add a pure transversal component whose am- +plitude is modulated with a third free parameter α: +xl+1 = xl +Ψ(xl,zl+1)+αΨ∇·Ψ=0(xl(q),zl). +(6) +4. Numerical results +We consider in this study cubical boxes of 200 h−1 Mpc +side length and 2563 particles using Lambda-CDM cosmol- +ogy with an initial power spectrum obtained from CLASS +(Lesgourgues 2011; Blas et al. 2011) with cosmological pa- +rameters: {ΩM = 0.307,ΩΛ = 0.693,Ωb = 0.048,σ8 = 0.823,w = +−1,ns = 0.95} and a Hubble constant (H0 = 100h km s−1 +Mpc−1) given by h = 0.68. We construct a reference set of 25 +N-body calculations at z = 0 relying on FastPM (Feng et al. +2016) for each cosmology with the same volume and num- +ber of particles, with force resolution ∼ 0.39h−1 Mpc, and 50 +timesteps. Initial conditions are generated via second-order +LPT at z = 99. +Using the same Gaussian initial density field, we run +eALPT with (α > 0) and without (α = 0) vorticity correc- +tions (vc), dubbed eALPT and eALPTvc, respectively. In +particular, we study the cases of eALPT with 2 and 5 steps +and eALPTvc with 3, 5, and 6 steps (see Figs. 1 & 2). +The size of each eALPT (or eALPTvc) timestep is com- +puted based on the difference between the linear growth fac- +tors from subsequent steps: ∆D(zl+1,zl) ≡ D(zl+1)−D(zl). For +a given cosmology, we determine the corresponding redshift: +∆z(zl+1,zl) = D−1(∆D(zl+1,zl)), inverting the D = D(z) relation +through an interpolation based on a previously computed +table. We then use ∆z for D(∆z) and D(2)(∆z) to compute the +displacement field to go to redshift zl+1 starting at redshift +zl in Eulerian coordinates. +Because of numerical uncertainties arising from the +mass assignment scheme and from using significant steps +between Eulerian coordinates at subsequent redshifts, the +power at large scales of the resulting density field does not +correspond to the expected one from linear theory. Hence, +the step size has to be adjusted to get a precise final re- +sult. To this end, single-step ALPT calculations can be ap- +plied as a reference to determine excess or lack of power +following Kitaura et al. (2021) using Gaussian convolu- +tions of the density field to determine the variance and +thus the resulting bias: b(zl+1,zl) = +� +⟨(K(r′′ +S )◦δeALPT(xl+1,zl+1))2⟩ +⟨(K(r′′ +S )◦δALPT(xl+1,zl+1))2⟩ +with r′′ +S ∈ [30,70]h−1 Mpc. We note that the exact choice +of r′′ +S is not critical, and results within percentage accu- +racy are obtained for different values in that range. The +timestep size has to be accordingly corrected: ∆z(zl+1,zl) = +D−1(∆D(zl+1,zl)−(b(zl+1,zl)−1)). These corrections must be +computed only once for a particular setup and can then be +applied for different seed perturbations. +We find that the resulting density fields are very sta- +ble, relying on either cloud-in-cell or triangular-shape-cloud +(TSC) mass-assignment schemes (Hockney & Eastwood +Article number, page 3 of 5 + +A&A proofs: manuscript no. aanda +0 +25 +50 +75 +100 +125 +150 +175 +200 +y[h−1 Mpc] +2LPT +ALPT +0 +25 +50 +75 +100 +125 +150 +175 +200 +y[h−1 Mpc] +eALPTvc (6s) +FastPM +0 +25 +50 +75 +100 +125 +150 +175 +200 +y[h−1 Mpc] +∇ · Ψ∇×Ψ=0 +eALPTvc (6s) +∇ · Ψ∇×Ψ=0 FastPM +0 +25 +50 +75 +100 125 150 175 200 +x[h−1 Mpc] +0 +25 +50 +75 +100 +125 +150 +175 +200 +y[h−1 Mpc] +|Ψ∇·Ψ=0| eALPTvc (6s) +0 +25 +50 +75 +100 125 150 175 200 +x[h−1 Mpc] +|Ψ∇·Ψ=0| FastPM +Fig. 1: Upper panels: Log-density slices (log(1 + δ)) corresponding to differ- +ent gravity solvers, through the three dimensional simulation cubical box of +200 h−1 Mpc side length with a mesh of 2563 cells. Lower panels: Same as +the upper panels but for the divergence of the irrotational (∇q · Ψ∇×Ψ=0(q)) +and the absolute value of the solenoidal component of the displacement field +( +���Ψ∇·Ψ=0(q) +���). The resulting maps have been saturated to the same colour scale +after averaging over five slices corresponding to one simulation. +10−1 +100 +101 +102 +103 +104 +P(k) [(h−1Mpc)3] +Zel’dovich +2LPT +ALPT +eALPT (2s) +eALPT (5s) +eALPTvc (3s) +eALPTvc (5s) +eALPTvc (6s) +FastPM (50s+1s-2LPT-IC) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +P(k)/Pref(k) +0.1 +0.5 +1.0 +4.0 +k [h−1Mpc] +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +C(k) +Fig. 2: Power and cross power spec- +tra for the various approximate gravity +solvers compared to fast particle-mesh +based N-body calculations (FastPM). +The Zel’dovich, 2LPT, and ALPT cases +require only one-step calculation. For +the rest, the number of steps is indi- +cated in parentheses. FastPM needs the +first step for the ICs relying on 2LPT +and then a minimal number of iter- +ations compared to standard N-body +simulations, which require the order of +103 iterations. The 1-sigma contours +from 25 fields are shown for FastPM, +and the eALPT limiting cases with the +lowest and highest cross-correlations, 2 +(w/o vc) and 6 (with vc) steps, respec- +tively. The eALPTvc (6s) case yields +power spectra with precision within a +few per cent up to the Nyquist fre- +quency and a correlation of 98% at +k = 1hMpc−1. +1988) with and without tetrahedral tesselations (THT) +(Abel et al. 2012). We finally use TSC with THT. +Regarding the ideal parameter space of {rs,r′ +s,α}, we find +that: +1. The ideal transition scale parameter rs between long- +and short-range forces has a lower rs > rs−min and an up- +per limit rs < rs−max. While rs−min has to be greater than +zero to suppress shell-crossing in knots of the cosmic +web, the accuracy in the tidal field tensor limits rs−max. +In practice, we find 2 < rs < 10 h−1 Mpc. +2. The scale r′ +s is restricted to the range 0 ≤ r′ +s ≤ 2dL, where +dL is the cell side length. Neither larger smoothing scales +nor additional convolutions have any impact on the re- +sults. +3. The fraction of additional vorticity is constrained to the +range α ∈ [0.01,0.1]. +The parameters are chosen to get unbiased power spectra +starting from the lowest modes and continuing towards the +largest ones. +The concrete values are: for 2 steps: {rs = 5,r′ +s = 2,α = 0}, +3 steps: {rs = 3.1,r′ +s = 1.2,α = 7}, 5 steps: {rs = 7,r′ +s = 2,α = 0} +and {rs = 3,r′ +s = 2,α = 3.5}, and 6 steps: {rs = 2.75,r′ +s = 1.4,α = +3}. The numerical results demonstrate a significantly higher +Article number, page 4 of 5 + +F.-S. Kitaura et al.: The Cosmic Web from Perturbation Theory +accuracy when applying vorticity corrections. We also find +that vorticity partially substitutes the short-range compo- +nent, as the transition scale parameter rS becomes smaller +for α > 0. We have checked that we get an equivalent level +of accuracy with different cosmological parameters. +5. Conclusions +Accurate cosmic web dark matter distribution calculations +can be made very fast with effective models, including vis- +cosity based on iterative applications of ALPT. These re- +quire only one reference N-body simulation to calibrate the +power of density perturbations towards small scales, saving +substantial computational resources and providing a con- +trolled theoretical framework. +Within three steps, we already find cross-correlations at +the level of 96% at k = 1hMpc−1 as compared to N-body +calculations. This model is only about three to four times +more expensive than setting up initial conditions for an N- +body simulation. +We plan to use this method to massively perform light- +cone dark matter fields covering the entire redshift range +up to z ∼ 5 populating them with bright-, luminous red-, +emission line-galaxies, quasars, Lyman-α forests, and lens- +ing maps, to make multi-tracer analysis from galaxy sur- +veys. +Further investigation needs to be done to explore the +accuracy within this framework in modelling the peculiar +velocity field and studying different resolutions and red- +shifts. +The developments presented in this letter have appli- +cations ranging from setting up initial conditions, produc- +ing mock catalogues for galaxy surveys, and performing +Bayesian inference analysis, to providing simulations for +emulators. +Acknowledgements. FSK, FS, ABA, and GF acknowledge the Span- +ish Ministry of Economy and Competitiveness (MINECO) for financ- +ing the Big Data of the Cosmic Web project: PID2020-120612GB- +I00 and the IAC for continuous support to the Cosmology with LSS +probes project. FS thanks financial support from the University of +Padova, ABA thanks support from the SEV-2015-0548 grant, and GF +thanks support from the IJC2020-044343-I grant. +References +Abel, T., Hahn, O., & Kaehler, R. 2012, Monthly Notices of the Royal +Astronomical Society, 427, 61 +Amendola, L., Appleby, S., Avgoustidis, A., et al. 2016, ArXiv e-prints +[arXiv:1606.00180] +Angulo, R. E., Foreman, S., Schmittfull, M., & Senatore, L. 2015, J. +Cosmology Astropart. Phys., 2015, 039 +Angulo, R. E. & Hahn, O. 2022, Living Reviews in Computational +Astrophysics, 8, 1 +Angulo, R. E., Springel, V., White, S. D. M., et al. 2012, MNRAS, +426, 2046 +Balaguera-Antol´ınez, A., Kitaura, F.-S., Alam, S., et al. 2022, arXiv +e-prints, arXiv:2211.10640 +Balaguera-Antol´ınez, A., Kitaura, F.-S., Pellejero-Ib´a˜nez, M., et al. +2020, Monthly Notices of the Royal Astronomical Society, 491, 2565 +Balaguera-Antol´ınez, A., Kitaura, F.-S., Pellejero-Ib´a˜nez, M., Zhao, +C., & Abel, T. 2019, Monthly Notices of the Royal Astronomical +Society, 483, L58 +Baldauf, T., Mercolli, L., & Zaldarriaga, M. 2015, Phys. Rev. D, 92, +123007 +Baldauf, T., Schaan, E., & Zaldarriaga, M. 2016, J. Cosmology As- +tropart. Phys., 2016, 017 +Baumann, D., Nicolis, A., Senatore, L., & Zaldarriaga, M. 2012, J. +Cosmology Astropart. Phys., 2012, 051 +Benitez, N., Dupke, R., Moles, M., et al. 2014, arXiv e-prints, +arXiv:1403.5237 +Bernardeau, F. 1994, The Astrophysical Journal, 427, 51 +Bernardeau, F., Colombi, S., Gazta˜naga, E., & Scoccimarro, R. 2002, +Phys. Rep., 367, 1 +Blas, D., Lesgourgues, J., & Tram, T. 2011, J. Cosmology Astropart. +Phys., 2011, 034 +Bouchet, F. R., Colombi, S., Hivon, E., & Juszkiewicz, R. 1995, As- +tronomy & Astrophysics, 296, 575 +Buchert, T. & Dom´ınguez, A. 2005, A&A, 438, 443 +Buchert, T. & Ehlers, J. 1993, Monthly Notices of the Royal Astro- +nomical Society, 264, 375 +Carrasco, J. J. M., Hertzberg, M. P., & Senatore, L. 2012, Journal of +High Energy Physics, 2012, 82 +Catelan, P. 1995, MNRAS, 276, 115 +Chuang, C.-H., Kitaura, F.-S., Prada, F., Zhao, C., & Yepes, G. 2015, +MNRAS, 446, 2621 +Chuang, C.-H., Yepes, G., Kitaura, F.-S., et al. 2019, Monthly Notices +of the Royal Astronomical Society, 487, 48 +Chudaykin, A. & Ivanov, M. M. 2019, J. Cosmology Astropart. Phys., +2019, 034 +Cusin, G., Tansella, V., & Durrer, R. 2017, Phys. Rev. D, 95, 063527 +Dai, B. & Seljak, U. 2021, Proceedings of the National Academy of +Science, 118, e2020324118 +DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016, arXiv +e-prints, arXiv:1611.00036 +Feng, Y., Chu, M.-Y., Seljak, U., & McDonald, P. 2016, Monthly +Notices of the Royal Astronomical Society, 463, 2273 +Foreman, S., Perrier, H., & Senatore, L. 2016, J. Cosmology Astropart. +Phys., 2016, 027 +Fosalba, P., Crocce, M., Gazta˜naga, E., & Castander, F. J. 2015, +MNRAS, 448, 2987 +He, S., Li, Y., Feng, Y., et al. 2019, Proceedings of the National +Academy of Science, 116, 13825 +Heath, D. J. 1977, Monthly Notices of the Royal Astronomical Society, +179, 351 +Hockney, R. W. & Eastwood, J. W. 1988, Computer simulation using +particles +Jamieson, D., Li, Y., Alves de Oliveira, R., et al. 2022, arXiv e-prints, +arXiv:2206.04594 +Jelic-Cizmek, G., Lepori, F., Adamek, J., & Durrer, R. 2018, J. Cos- +mology Astropart. Phys., 2018, 006 +Kitaura, F.-S. & Angulo, R. E. 2012, MNRAS, 425, 2443 +Kitaura, F.-S., Ata, M., Rodr´ıguez-Torres, S. A., et al. 2021, MNRAS, +502, 3456 +Kitaura, F.-S., Balaguera-Antol´ınez, A., Sinigaglia, F., & Pellejero- +Ib´a˜nez, M. 2022, Monthly Notices of the Royal Astronomical Soci- +ety, 512, 2245 +Kitaura, F.-S., Gil-Mar´ın, H., Sc´occola, C. G., et al. 2015, MNRAS, +450, 1836 +Kitaura, F. S. & Hess, S. 2013, MNRAS, 435, L78 +Kitaura, F.-S., Rodr´ıguez-Torres, S., Chuang, C.-H., et al. 2016, MN- +RAS, 456, 4156 +Kitaura, F. S., Yepes, G., & Prada, F. 2014, MNRAS, 439, L21 +Lesgourgues, J. 2011, arXiv e-prints, arXiv:1104.2932 +Levi, +M., +Bebek, +C., +Beers, +T., +et +al. +2013, +ArXiv +e-prints +[arXiv:1308.0847] +McDonald, P. 2011, J. Cosmology Astropart. Phys., 2011, 032 +Meerburg, P. D., Green, D., Flauger, R., et al. 2019, BAAS, 51, 107 +Mercolli, L. & Pajer, E. 2014, J. Cosmology Astropart. Phys., 2014, +006 +Mo, H., van den Bosch, F. C., & White, S. 2010, Galaxy Formation +and Evolution +Mohayaee, R., Mathis, H., Colombi, S., & Silk, J. 2006, Monthly No- +tices of the Royal Astronomical Society, 365, 939 +Neyrinck, M. C. 2013, Monthly Notices of the Royal Astronomical +Society, 428, 141 +Neyrinck, M. C. 2016, MNRAS, 455, L11 +Pajer, E. & Zaldarriaga, M. 2013, J. Cosmology Astropart. Phys., +2013, 037 +Pietroni, M., Mangano, G., Saviano, N., & Viel, M. 2012, J. Cosmol- +ogy Astropart. Phys., 2012, 019 +Porto, R. A., Senatore, L., & Zaldarriaga, M. 2014, J. Cosmology +Astropart. Phys., 2014, 022 +Pueblas, S. & Scoccimarro, R. 2009, Phys. Rev. D, 80, 043504 +Rampf, C. 2012, Journal of Cosmology and Astroparticle Physics, +2012, 004 +Shandarin, S. F. & Zeldovich, Y. B. 1989, Rev. Mod. Phys., 61, 185 +Sheth, R. K. & van de Weygaert, R. 2004, MNRAS, 350, 517 +Sinigaglia, F., Kitaura, F.-S., Balaguera-Antol´ınez, A., et al. 2021, +The Astrophysical Journal, 921, 66 +Sinigaglia, F., Kitaura, F.-S., Balaguera-Antol´ınez, A., et al. 2022, +The Astrophysical Journal, 927, 230 +Spergel, D., Gehrels, N., Baltay, C., et al. 2015, arXiv e-prints, +arXiv:1503.03757 +Tassev, S., Zaldarriaga, M., & Eisenstein, D. J. 2013, Journal of Cos- +moly and Astroparticle Physics, 6, 036 +Zel’dovich, Y. B. 1970, A&A, 5, 84 +Zhao, C., Chuang, C.-H., Bautista, J., et al. 2021, MNRAS, 503, 1149 +Article number, page 5 of 5 + diff --git a/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/load_file.txt b/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..676260d7620c21ce424999de173ae50d2ee3701a --- /dev/null +++ b/cNE2T4oBgHgl3EQfFgbT/content/tmp_files/load_file.txt @@ -0,0 +1,582 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf,len=581 +page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' aanda ©ESO 2023 January 11, 2023 Letter to the Editor The Cosmic Web from Perturbation Theory F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Kitaura12⋆, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Sinigaglia1234,, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Balaguera-Antol´ınez12, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Favole12 1 Instituto de Astrof´ısica de Canarias, s/n, E-38205, La Laguna, Tenerife, Spain e-mail: fkitaura@iac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='es 2 Departamento de Astrof´ısica, Universidad de La Laguna, E-38206, La Laguna, Tenerife, Spain 3 Department of Physics and Astronomy, Universit`a degli Studi di Padova, Vicolo dell’Osservatorio 3, I-35122, Padova, Italy 4 INAF—Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122, Padova, Italy Received XX XX, 20XX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' accepted XX XX, 20XX ABSTRACT Context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Analyzing the large-scale structure (LSS) with galaxy surveys demands accurate structure formation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Such models should ideally be fast and have a clear theoretical framework to rapidly scan a variety of cosmological parameter spaces without requiring large training data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Aims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' This study aims to extend Lagrangian perturbation theory (LPT), including viscosity and vorticity, to reproduce the cosmic evolution from dark matter N-body calculations at the field level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' We extend Augmented LPT (ALPT) to an Eulerian framework, dubbed eALPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' This enables modelling the stress tensor, with this introducing vorticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' To compensate that ALPT assumes curl-free fields, a fraction of the vorticity, emerging after each Eulerian transformation, is added to the subsequent timestep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The model has three free parameters apart from the choice of cosmology, redshift snapshots, cosmic volume, and the number of particles-cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' We find that the cross-correlation of the dark matter distribution as compared to N-body solvers increases at k = 1hMpc−1 from ∼ 55% with the Zel’dovich approximation (∼ 70% with ALPT);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' to ∼96 and 97% with eALPT, and power spectra within percentage accuracy up to k ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='3 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='7 hMpc−1, using three and five steps, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' cosmology: – theory - large-scale structure of Universe - dark matter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' methods: analytical 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Introduction The cosmic web is the LSS pattern that emerges as a man- ifestation of the action of gravity in an expanding back- ground Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' It is shaped according to the cosmological information content set in the initial conditions of cosmic times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The scientific community is putting special effort into mapping the three-dimensional distribution of matter in the Universe through galaxy surveys such as DESI (Levi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2013), EUCLID (Amendola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2016), J-PAS (Benitez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2014), or the Nancy Grace Roman Space telescope (Spergel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The clustering of the large-scale structure (LSS) yields powerful constraints on the standard cosmological model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', the nature of dark energy (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' DESI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2016), primordial non-gaussianities (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Meer- burg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2019), and neutrino masses (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Chudaykin & Ivanov 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Since the observable Universe is unique, one needs mock catalogues for a robust analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' These permit the compu- tation of covariance matrices and to study of systematics in the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' However, the computation of mock catalogues is usually costly, and only a few can be done (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Angulo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Fosalba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Chuang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' In this context, bias mapping techniques at the field level emerged as a solution to save enormous computational resources while maintaining high accuracy, such as PATCHY ⋆ fkitaura@iac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='es (Kitaura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2014, 2015) applied to the BOSS data (Ki- taura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2016) or EZmocks (Chuang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2015) applied to the eBOSS data (Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' More recently, the BAM code has been designed to learn the complex bias rela- tion from reference simulations (Balaguera-Antol´ınez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Balaguera-Antol´ınez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Kitaura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' These techniques can also accurately map the Lyman-α for- est (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Sinigaglia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2021, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' All the methods mentioned above require a dark matter field defined on a mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The accuracy of that matter distri- bution will determine the precision of the mock catalogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' A series of ideas have been implemented to accelerate particle-mesh based N-body solvers (see Tassev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Feng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Despite these developments, N-body codes are costly when aiming to mass-produce mock catalogues cover- ing large cosmic volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Therefore, approximate gravity solvers are still commonly used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' While EZmocks relies on the Zel’dovich approximation (Zel’dovich 1970), PATCHY and BAM rely on ALPT, including tidal field corrections (Ki- taura & Hess 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' It has been shown that such methods can correct to a great extent the bias introduced by approx- imate gravity solvers in the nonlinear and nonlocal bias de- scription (see the application of BAM to galaxy catalogues, Balaguera-Antol´ınez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Machine learning techniques applied to large training data sets (of thousands of N-body simulations for a given cosmology) have emerged as an alternative to approximate gravity solvers (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Dai & Seljak 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Jamieson Article number, page 1 of 5 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='03648v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='CO] 9 Jan 2023 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' aanda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' For a review of numerical methods in LSS modelling, see Angulo & Hahn (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' This letter presents a novel approach to modelling the cosmic web, as explained in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Theoretical background The Universe is considered a closed Hamiltonian system where energy is conserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The dark matter content can be described by a distribution function f(r,v,t) (with position r and velocity v), such that the probability of finding a dark matter particle in the phase-space volume drdv cen- tred on r,v at time t is given by f(r,v,t)drdv (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Mo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The total number of particles will be then given by integrating over the whole phase-space volume: N = � � drdv f(r,v,t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Given the functional form of the distribu- tion function, total continuous changes to the phase-space of the system of particles can be expressed with product and chain derivative rules as: d dt f = ∂ ∂t f + ∂r ∂t ∂ ∂r f + ∂v ∂t ∂ ∂v f = ∂ ∂t f +v ∂ ∂r f +g ∂ ∂v f, with g being the gravity-induced accel- eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Due to probability conservation, the generalised continuity equation in phase-space must be fulfilled (Li- ouville theorem): ∂f ∂t + ∇ · j = ∂f ∂t + ∂( f ˙q) ∂q + ∂( f ˙v) ∂v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Hence, ∂f ∂t + ∂( f ˙q) ∂q + ∂(f ˙v) ∂v = ∂ f ∂t + f ∂ ˙q ∂q + ˙q ∂f ∂q + f ∂ ˙v ∂v + ˙v ∂ f ∂v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Con- sequently, to get the Vlasov or collisionless Boltzmann equation, the sum of terms multiplied by f must vanish: f � ∂ ˙q ∂q + ∂ ˙p ∂p � = f � ∂2H ∂q∂p − ∂2H ∂p∂q � = 0, which is fulfilled by insert- ing Hamiltonian equations of motion, yielding: ∂ ∂t f + ∂r ∂t ∂ ∂r f + ∂v ∂t ∂ ∂v f = ∂ ∂t f +v ∂ ∂r f +g ∂ ∂v f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' (1) Building moments of the Boltzmann equation, one gets – from the zeroth moment, the continuity equation: multiplying Boltzmann’s equation with the mass of the particles m = m(v)0 and integrating over dv: ∂ ∂t ρ ���������������� � d3v f m+ ∂ ∂r ρu �������������������� � d3v f mv = 0, with ρ being the density and u the velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Hence, ∂ ∂tρ+∇·(ρu) = ∂ ∂tρ+ρ∇·u+u·∇ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' (2) – from the first moment, the Euler equation: multiplying Boltzmann’s equation with m = m(v)1 and integrating over dv: ∂ ∂tρu+ ∂ ∂r (ρuu+ρ⟨ww⟩) = ρg, (3) with w ≡ u−v being the random velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The process of virialisation is expressed by a stress ten- sor T term: ⟨ww⟩ = −∇P + ∇ · T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' We can neglect the pres- sure term −∇P for collisionless dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' From the com- bination of the Euler and continuity equations, we get: ρ � ∂ ∂tu+(u·∇)u � = ∇· T+ρg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Introducing comoving coordi- nates x: r = a(t)x with the scale factor a encoding the ex- pansion of the Universe, and conformal time τ determined by: dt = adτ, we can rewrite the previous equation in terms of, instead of proper velocity u = ˙r = ˙a(t)x+v, peculiar mo- tions v ≡ a ˙x, yielding: ∂ ∂τv +v ·∇v = 1 aρ∇·T−∇ ˜Φ−aHv, (4) using the Poisson equation ∇2 ˜Φ = 4πG ¯ρδa2 with density contrast δ ≡ ρ/¯ρ−1 and average density ¯ρ ≡ ⟨ρ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' One usually assumes curl-free velocity fields, neglect- ing the stress tensor T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Based on this, one can perform an Eulerian perturbative expansion of both the continu- ity and the Euler equations around the density contrast δ(x,τ) = �∞ n=1 δ(n)(x,τ) and the divergence of the peculiar velocity field θ(x,τ) ≡ ∇·v = �∞ n=1 θ(n)(x,τ) (see Bernardeau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2002, and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Alternatively, one can consider Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 4 and make an expansion in Lagrangian coor- dinates considering the total derivative d dτv = ∂ ∂τv + v · ∇v, yielding Lagrangian Perturbation Theory (LPT) solutions (Buchert & Ehlers 1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Bouchet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Catelan 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The stress tensor is commonly represented by the linear elastic model ∇·T ∼ µ∇2v+ 1 3µ∇∇·v+η∇(∇·v) with viscosity parameters µ and η (see Bernardeau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2002), which for irrotational fields (when the velocity is the gradient of a potential field) simplifies to the adhesion model ∇ · T ∼ µ′∇2v with a single viscosity parameter µ′ (see Shandarin & Zeldovich 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' However, the generation of vorticity (∇ × v) has been studied in simulations as an important component when going to the nonlinear regime (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Pueblas & Scocci- marro 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Jelic-Cizmek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' As an alternative to expensive N-body simulations, ef- fective field theories have emerged in LSS, including a mod- elling of the stress tensor to compute summary statistics (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=', Carrasco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Baumann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Pa- jer & Zaldarriaga 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Porto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Mercolli & Pajer 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Angulo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Baldauf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2015, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Foreman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' See also other perturbative (McDonald 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Pietroni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Rampf 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Cusin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 2017), and non-perturbative approaches (Buchert & Dom´ınguez 2005) to model the curl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' In this work, we propose to model viscosity induced by a stress tensor through an Eulerian extension of LPT, con- sidering subsequent cosmic times until reaching the target redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' With this, the gravitational potentials become in- creasingly deeper, changing their shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' In this way, the vorticity of the displacement field emerges naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Method Let us start considering the Lagrangian q to Eulerian x coordinates single-step mapping through a displacement Ψ (with v = d dτ Ψ): x = q+Ψ(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The displacement is obtained according to Augmented LPT (ALPT), which separates the total displacement Ψ into a long-range ΨL and a short- range component ΨS (see Kitaura & Hess 2013): Ψ(q,z) = ΨL(q,z)+ΨS(q,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The long-range displacement field is obtained from the convolution of a Gaussian kernel with an LPT solution: ΨL(q,z) = K(q,z,rs) ◦ ΨLPT(q,z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' We restrict the present study to second order LPT: Ψ2LPT(q,z) = −D(z)∇qΦ(1)(q)+ D(2)(z)∇qΦ(2)(q), where D(z) is the growth factor (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' Heath 1977), and D(2)(z) ≃ − 3 7 Ω−1/143 m (D(z))2 (Bouchet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE2T4oBgHgl3EQfFgbT/content/2301.03648v1.pdf'} +page_content=' The normalised potentials Φi(q) are the solutions of the Poisson equations ∇2 qΦ(i) = δ(i), where i = 1 is the linear primordial density field used as the initial conditions, and i = 2 is determined by: δ(2) = � i, j 0 ∩ max +j∈Dc ALBj < 0) → 1. +(2) +Proof. +Result (2) implies (1), so we only prove the former. +Using the fact that P(A ∩ B) ≥ +1−P(Ac)−P(Bc), it is enough to show that both P(minj∈D ALBj > 0) and P(maxj∈Dc ALBj < 0) +tend to 1. +We only consider P(maxj∈Dc ALBj < 0) as the proof for the other probability is similar. We have +P(max +j∈Dc ALBj < 0) += +P +� +� � +j∈Dc +{ALBj < 0} +� +� += +� +j∈Dc +P(ALBj < 0) +≥ +� +min +j∈Dc P(ALBj < 0) +�N +, +(3) +where N is the number of elements in Dc. For each j ∈ Dc, [Merchant and Hart, 2022] show that +P(ALBj < 0) → 1 as m and n tend to ∞. Since N is finite, this implies that the quantity on the +right-hand side of (3) tends to 1, from which the result follows. ■ +It is clear that if p tends to ∞ at a sufficiently slow rate, then Theorem 1 remains true. However, +determining the precise rate at which p can increase relative to m and n requires stronger results +than provided by [Merchant and Hart, 2022], and we will not pursue this direction further. +We now show simulation results for various values of m = n, p and r, where r represents the +proportion of important variables, i.e., variables for which the class distributions are different. We +generate 500 variables for a binary classification problem in the following fashion. If it is important, +the variable is drawn for one class from a t-distribution with 4 degrees of freedom, and drawn from +the other class from a mixture of two normal distributions, where the mixing parameter is 1/2, the +standard deviation of both normal distributions is 1, and the means are -2.5 and 2.5. If instead +the variable is unimportant, then it is drawn from a standard normal. We will name the method of +generating variables in this setting “a shape difference.” Finally, each variable is determined to be +important or not by performing a binomial trial with success probability r = 1/2. Figures 1, 2, and +3 show how the cdfs of the ALBs change depending on m and n. +As the sample sizes m and n increase, the ALBs for important variables gradually increase. Even +when the total number of observations is only eight percent of the total number of variables, we +achieve the property that the largest ALB of the unimportant variables is smaller than the smallest +ALB of the important variables. The black curve shows the cdf of ALBs computed by permuting +the labels for each variable three times and computing the ALB each time. A cutoff of 0 is not larger +6 + +0.00 +0.25 +0.50 +0.75 +1.00 +−0.4 +−0.2 +0.0 +0.2 +0.4 +0.6 +ALBs +p +Significance +Unimportant +Important +Figure 1: Comparison of ALB CDFs when the training set sizes are equal to 10 and important +variables have a shape difference. The black curve denotes the CDF of ALBs generated from data +where the classes are permuted. +0.00 +0.25 +0.50 +0.75 +1.00 +−0.2 +0.0 +0.2 +0.4 +ALBs +p +Significance +Unimportant +Important +Figure 2: Comparison of ALB CDFs when the training set sizes are equal to 20 and important +variables have a shape difference. The black curve denotes the CDF of ALBs generated from data +where the classes are permuted. +than the largest unimportant variable for any n, but is still useful for discarding a large portion of +the unimportant variables. On the other hand, using a large percentile of the permuted variables can +result in discarding almost all of the unimportant variables, and at the largest sample size, choosing +the cutoff to be the maximum of the permuted ALBs does indeed almost perfectly separate the +important and unimportant variables. +4 +Discussion of classification methods +Ideally, one should choose the screening method and classifier that work best together. Good ex- +amples of this principle are provided by the relationship that classification methods such as logistic +regression, support vector machines, and linear discriminant analysis have with t-test based screen- +7 + +0.00 +0.25 +0.50 +0.75 +1.00 +0.0 +0.2 +0.4 +ALBs +p +Significance +Unimportant +Important +Figure 3: Comparison of ALB CDFs when the training set sizes are equal to 40 and important +variables have a shape difference. The black curve denotes the CDF of ALBs generated from data +where the classes are permuted. +ing. Discriminant analysis, support vector machines without a kernel trick, and logistic regression are +designed to take advantage of location differences between classes. It is therefore natural to precede +them with t-test screening, which, of course, is designed to detect differences between means. On the +other hand, support vector machines that use a kernel trick create a hyper-plane that best separates +the two classes essentially after a transformation is performed, and can therefore deal effectively with +many types of differences between distributions. To take advantage of this ability, it is thus best +to use a screening method that can detect non-location differences. In summary, t-test screening is +a natural method to use when linear discriminant analysis or logistic regression are deemed to be +appropriate classifiers, but is not necessarily a good method when a support vector machine with a +kernel trick is required. By linear SVM, we mean a method that can classify by separating the two +groups by a plane. +In Figures 4 and 5 two (important) variables are generated according to a shape difference. The +bimodality of one of the two class distributions makes the classes hard to separate with a plane. +Figure 4 shows the performance of a support vector machine when only two relevant variables are +used for classification, while Figure 5 shows the improvement in the same situation when the kernel +trick is applied to detect non-location based differences. +Our method seeks to outperform t-test screening by considering differences other than ones of +location type. Of course, this performance is not free. It comes with the cost that we lose some +power in detecting differences of means. For our method to work better with a classifier, the classifier +must have the ability to distinguish classes that display non-location differences. For example, a +set of variables whose classes differ only with respect to scale would not be useful to support vector +machines without the kernel trick and LDA, as there would be no hyperplane that nicely separates the +classes. A kernel trick or increasing the number of variables by considering interactions and squared +8 + +terms can sidestep this issue. But adding variables is not ideal, as a goal of our methodology is to +decrease computational complexity. +−1 +0 +1 +2 +−1 +0 +1 +V1 +V2 +y +0 +1 +fittedvals +0 +1 +Figure 4: Prediction accuracy of two important variables in the setting of “a shape difference” using +a linear SVM. The colors represent the predictions that the SVM produces. +The line represents +the discriminator that a linear SVM produces to discriminate the classes. The triangle and circle +represent which class the observation arises from. +−1 +0 +1 +2 +−1 +0 +1 +V1 +V2 +y +0 +1 +fittedvals +0 +1 +Figure 5: Prediction accuracy of two important variables in the setting of “a shape difference” with +an SVM that uses a kernel trick. The colors represent the predictions that the SVM produces when +a kernel trick is applied. The triangle and circle represent which class the observation arises from. +Classification is much better in this case because the trick enables the classifier to capture differences +other than location shifts. +Finally, we would like to add that even though SVM with the kernel trick is a fine classification +method that uncovers many different types of differences between variables, its performance can be +degraded harshly by the presence of noisy variables. +To illustrate this, we use data in the same +setting as the shape difference. We constructed a training and testing set such that both consist of +9 + +Not Screened +Screened +2.5 +5.0 +7.5 +10.0 +Number guessed belong to class 0 in class 0 +(a) Boxplots of true positives +Not Screened +Screened +0.0 +2.5 +5.0 +7.5 +Number guessed belong to class 0 in class 1 +(b) Boxplots of false positives +Not Screened +Screened +0.0 +2.5 +5.0 +7.5 +Number guessed belong to class 1 in class 0 +(c) Boxplots of false negatives +Not Screened +Screened +2.5 +5.0 +7.5 +10.0 +Number guessed belong to class 1 in class 1 +(d) Boxplots of true negatives +Figure 6: Box plots displaying the accuracy of SVM when the data are generated from model where +10% of the variables are important and have a shape difference. To illustrate the accuracy of the +methods, we do the following. First, suppose a positive case corresponds to an observation being in +class 1 and a negative case corresponds to an observation being in the other class. Then to show +the accuracy of the SVMs, we show boxplots on the number of “True Positives,” “True Negatives,” +“False Positives” and “False Negative” occurrences. +10 observations from each class. Five hundred variables were used, with only 10% on average being +important. All data for unimportant variables have a standard normal distribution. If a variable is +important, then its distribution in one class is a bimodal mixture of two normals and in the other +class a t-distribution with 4 degrees of freedom. The normal distributions in the mixture both have +standard deviation 1 and means of -2.5 and 2.5. We trained an SVM with the radial basis kernel on +all of the observations, and trained another SVM with the radial basis kernel but used only variables +whose ALB value was larger than the interpretative cutoff of 0. We repeat this procedure 100 times, +and report on its accuracy in Figure 6. In general, classification accuracy is greatly improved, false +negatives rarely happen after screening and the number of false positives is reduced. +The ALB screening method need not be the final say as to which variables to include. +Two +variables that are individually important but highly correlated might be selected, although this may +10 + +not be ideal for some classifiers. Screening can simply be a precursor that simplifies the job of a +classifier, which does further variable selection. Even methods that can perform variable selection +and modeling simultaneously can benefit from having the number of variables reduced dramatically +by screening. This is observed in SIRS [Zhu et al., 2011], SIS [Fan and Lv, 2008], and is also true in +our case. +5 +Interaction with BART and a tailored classification method +We have recommended using classification methods that can take advantage of features for which the +classes have non-location differences. Methods that do further variable selection or that can handle +sparse data sets can also fare quite well with our screening methods. BART and DART are methods +having few parametric assumptions and that are able to capture a large variety of features from the +data. BART has issues as the number of predictors grow, and DART has been proposed as a solution +for this issue [Linero and Yang, 2018]. While DART can handle the case where many predictors are +irrelevant, there is a cost. Mixing times of the chains for DART are increased compared to BART, and +a prior that encourages sparsity may cause DART to get trapped in a posterior mode when the MCMC +procedure to estimate it is run [Hill et al., 2020]. While we cannot directly mitigate these problems, +decreasing the number of variables helps speed up the MCMC procedure. Our screening method +can decrease the number of variables at a faster rate than DART can. DART is resilient against +correlated nuisance variables and can therefore eliminate variables that survive ALB screening but +are irrelevant due to collinearity. We provide simulations showing that use of our screening method +before BART or DART can result in improved misclassification rates and computing speeds. +We generate data in the same context as Figure 2, but instead roughly 10% of the variables are +relevant. If a variable is irrelevant, the distribution of the variable for both classes is standard normal. +To assess the performance of a classifier, we computed the Rand index, or the percentage of correct +decisions the classifier has made. We compute the Rand index for the BART and DART procedures +applied to all variables, and the Rand index of the same procedures applied to variables that survive +ALB screening. We consider different training set sizes that vary from 5 to 20. The testing set size +for each simulation is the same as the training set size. We repeat this 100 times for each sample size. +Figures 7 and 9 show how accurate BART and DART alone are in these settings and Figures +8 and 10 show how the methods do when variables are screened for importance beforehand. There +is a notable gain in the Rand index as the training set size gradually increases for both methods. +Of greater note is that the time it takes to run both procedures is decreased. Figure 11 shows the +amount of time it takes the BART method to run before screening and Figure 12 shows how long +the method takes after screening. Screening on average shaves off at least 10 seconds of computation +11 + +time while increasing the average accuracy. This is an interesting result, as the methods themselves, +DART especially, tend to be robust to irrelevant variables. However, the figures suggest that a larger +sample size is required to achieve that robustness. +0.4 +0.6 +0.8 +1.0 +5 +10 +15 +20 +TrainingSize +Rand.index.BART +Figure 7: Box plots of the Rand index of BART in the setting of a shape difference. We vary m with +m = n, and the training size in the plot denotes m+n. We repeat each simulation 100 times for each +sample size. Roughly 10% of the variables are relevant. +0.4 +0.6 +0.8 +1.0 +5 +10 +15 +20 +TrainingSize +Rand.index.Bart.S +Figure 8: Box plots of the Rand index of BART when BART is improved by screening. This is in +the same setting as that used in Figure 7. The difference between the two plots is that we screened +the variables with the ALB procedure before applying BART. We choose variables such that all +generated ALBs are larger than the interpretable cutoff of 0. The power of the classification method +grows large when enough data is accrued. The interpretive cutoff tends to be conservative, and power +of the approach is likely to be even larger if a permutation-based cutoff is used instead. +5.1 +A simple Bayesian classifier +Suppose our goal is to simply leverage the differences between variables, regardless of the type of +difference, and that we assume independence between variables. We can construct a simple Bayesian +method for classification in the following fashion. For each variable, we compute two kernel density +estimates, one for each class. For each variable i, let ˆfi and ˆgi be kernel density estimates using all +variable i data from classes 1 and 2, respectively. The prior probability that a variable arises from a +12 + +0.4 +0.6 +0.8 +1.0 +5 +10 +15 +20 +TrainingSize +Rand.index.DART +Figure 9: Box plots of the Rand index of DART. This is in the same setting as in Figure 7, with the +difference that we use DART instead of BART as it is capable of automatically performing variable +selection. +0.4 +0.6 +0.8 +1.0 +5 +10 +15 +20 +TrainingSize +Rand.index.Dart.S +Figure 10: Box plots of the Rand index of DART improved by screening. This is in the same setting +as in Figure 7. The difference here is we screen the variables with the ALB procedure before applying +DART. We choose variables such that all generated ALBs are larger than 0. +The power of the +classification method has improved after screening for variables, despite DART being fully capable of +automatically performing variable selection automatically. +20 +25 +30 +5 +10 +15 +20 +TrainingSize +Time to run DART +Figure 11: Box plots of the time it took to run DART. The simulation is in the same setting as in +Figure 7. +13 + +13 +15 +17 +19 +5 +10 +15 +20 +TrainingSize +Time to run DART post screen +Figure 12: Box plots of the time it took to run DART post screening. This is in the same setting as +in Figure 7. The difference here is we screen the variables with the ALB procedure before applying +DART. The screening procedure itself takes much less than half a second, and as a result of removing +a large number of irrelevant variables, greatly improves the amount of time it takes for DART to run. +class is assumed to be proportional to the number of observations for that class. Let x = (x1, ..., xp) be +an observation to be classified. If the underlying densities are known, then the conditional probability +that x came from class 1 is +p(x) = P(Y = 1|x) = +n +m+n +� +i∈D fi(xi) +n +m+n +� +i∈D fi(xi) + +m +m+n +� +i∈D gi(xi), +(4) +where D is the set of indices i such that fi ̸≡ gi. Of course, the densities and D are unknown, but +p(x) can be estimated using kernel density estimates, and D can be replaced by �D, the set of indices +such that the corresponding variables survive screening: +ˆp(x) = +n +m+n +� +i∈ � +D ˆfi(xi) +n +m+n +� +i∈ � +D ˆfi(xi) + +m +m+n +� +i∈ � +D ˆgi(xi) +. +(5) +A classifier based on (5) can be a powerful tool for capturing marginal differences in distributions, +but is incapable of leveraging differences that may lie in the dependence structure of the variables. To +use (5), we say that an observation x belongs to class 1 if ˆp(x) > n/(m + n) and to class 2 otherwise. +We have found this classifier to have strong accuracy when dealing with independent variables, or +with settings where the difference in multivariate distributions is dominated by marginal differences. +To illustrate the effectiveness of the classifier based on (5), we perform a simulation similar to the +one referenced in Figure 1 but under a variety of different sample sizes. We repeat this procedure +5 times. For each sample size, we generate a balanced testing set of the same size, and compute a +Rand index. A plot of the Rand indices against the sample size is found in Figure 13. The power of +the classification method grows to be quite large at even small m + n values. Since the interpretive +cutoff tends to be conservative, power of the approach is likely to be even larger if a permutation +based cutoff is utilized instead. At a training size of just 9 samples in each group, the classifier makes +14 + +perfect predictions over 75% of the time. +0.4 +0.6 +0.8 +1.0 +4 +6 +8 +10 +12 +14 +16 +18 +20 +n +rand index +Figure 13: A box plot of the Rand index of the Bayesian classifier. The classifier is defined in terms +of (5). We generate data in the same context as in Figure 2, but vary m and n so that m = n, and +the training size denotes m + n. We choose variables such that all generated ALBs are larger than +the intepretable cutoff of 0. +6 +Application on simulated data sets +We want to compare our method to t-test screening and also compare performance of the different +choices of ALB cutoff. There are at least two ways to go about this. One is to compare the percentage +of variables that survive screening from both procedures, and the other is to apply a classification +method after screening and see which method has a better classification rate. These procedures are +carried out in three cases: +Case 1 – Location differences. +There are 600 variables, and those that are important arise +from a case where there is a mean difference between classes. +If the variable is important, +one class has a standard normal distribution and the other a normal distribution with mean 1 +and standard deviation 1. We let roughly 5% of the variables be important by generating 600 +independent Bernoulli variables, each with success probability 0.05. This way of determining +important variables is used in Cases 2 and 3 as well. Also, in this case and the following two +the unimportant variables have standard normal distributions. The classifier we will use to +compare performance in this case is SVM without the kernel trick. +Case 2 – Scale differences. There are 600 variables, and those that are important arise from +15 + +a case where there is a variance difference between classes. If the variable is important, one +class has a standard normal distribution and the other a normal distribution with mean 0 and +standard deviation 3. We let roughly 20% of the variables be important, and the classifier used +is the support vector machine with a kernel trick. +Case 3 – Shape differences. There are 600 variables, and those that are important arise from a +case where the class distributions have different shapes. If the variable is important, one class +has a standard t-distribution with 4 degrees of freedom and the other a bimodal mixture of two +normal distributions with means -2.5 and 2.5 and the same standard deviation of 1. Roughly +10% of the variables are important, and the classifier used is the support vector machine with +a kernel trick. +For all three cases, screening was done and the classifier built from a training set of m+n observations +on each variable, where m = n. The classifier so built was applied to predict m + n observations, +and the resulting Rand index was calculated. In t-test screening, variables were selected when their +P-values were smaller than 0.005. We repeated this procedure 100 times for each sample size. Figures +14-16 show, respectively, how well the methods performed for three ways of choosing an ALB cutoff: +a “fixed type I error rate” approach, the largest n + m values of ALB, and a cutoff of 0. +The results of these simulations suggest that ALB screening is effective at detecting location +differences, as in Case 1, but not to the same degree as t-test screening. In Case 1, the performance of +the SVM with ALB screening is better than with no screening, but worse than with t-test screening. +The proportion of variables that survive ALB screening steadily increases as sample size increases, +but at a slower rate than with t-test screening. In Cases 2 and 3, t-test screening does no better than +no screening in terms of classification accuracy. Regarding preservation of important variables, t-test +screening does not improve as the sample size increases, but ALB screening does. +7 +Application to the GISETTE data +The GISETTE data are obtained from m = 3000 and n = 3000 handwritten images of the digits 4 +and 9, respectively. For each of the 6000 images, p = 5000 variables are measured, some of which are +irrelevant probes, and the others pixel intensities. We will perform classification on these data, using +different screening methods to choose different subsets of the variables. We will rely on DART to be +the primary classification method and will explore how it performs when aided by different screening +methods. +The data set was randomly split into two halves. The first half was treated as the training data. +We trained our classifier and computed t-statistics and ALB statistics on these data. The second half +was treated as the validation set, and we computed the Rand index from these data. +16 + +0.4 +0.5 +0.6 +0.7 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.4 +0.5 +0.6 +0.7 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.4 +0.5 +0.6 +0.7 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +1.00 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +Figure 14: Simulation results for t-test screening and ALB screening that uses A3. We generate +ALB∗ values by permuting the data labels and computing ALB for the resulting data. We do this +for every variable twice. The ALB cutoff is the 95th percentile of ALB∗. The t-statistic cutoff is +chosen so that the P-value is less than 0.05. Red, green and blue box plots are for no screening, t-test +screening, and ALB screening, respectively. The first, second and third row of plots correspond to +cases 1, 2 and 3, respectively. +17 + +0.4 +0.5 +0.6 +0.7 +0.8 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +1.00 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.4 +0.5 +0.6 +0.7 +0.8 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.4 +0.5 +0.6 +0.7 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +Figure 15: Simulation results for t-test screening and ALB screening that uses variables with n + m +largest values of ALB. The colors of the box plots have the same meaning as they do in Figure 14. +18 + +0.4 +0.5 +0.6 +0.7 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.4 +0.5 +0.6 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +1.00 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +0.35 +0.40 +0.45 +0.50 +0.55 +10 +20 +30 +Total training size +Rand index +0.00 +0.25 +0.50 +0.75 +1.00 +10 +20 +30 +Total training size +Proportion of correct variables that survive screening +Figure 16: Simulation results for t-test screening and ALB screening with cutoff 0. The colors of the +box plots have the same meaning as they do in Figure 14. +19 + +Rand Index +Screening Method +Number of variables chosen +0.947 +ALB > T ∗ +0.005 +1321 +0.942 +ALB > 0 +1946 +0.947 +Pt < 0.005 +1540 +0.935 +No screening +4835 +Table 1: Classification and screening results for GISETTE data. All methods used a balanced training +and testing set that both consisted of 3000 observations. The quantities Pt and T ∗ +0.005 are, respectively, +the P-value of a t-test and the 99.5th percentile of permuted ALBs. +Five screening methods were compared. +We implemented A3, setting B = 1000 and d = 1 +and choosing variables such that ALB was larger than the 99.5th percentile of ALB∗ values. To +compare this with t-test screening, we picked variables whose t-test P-values were less than 0.005. +We tried screening method A1 and compared it to it’s t-test counterpart that picks the same number +of variables. We also checked to see how the method did with no variable screening. We compare the +Rand indices of these methods with that when no screening of variables is used. Before proceeding +with any of the methods, we removed each variable for which all 6000 data values were the same. As +a result there were only 4835 variables in the full data set rather than 5000. A summary of Rand +indices is given in Table 1. +0.6 +0.7 +0.8 +0.9 +0 +1000 +2000 +3000 +4000 +5000 +Number of Variables chosen +Resulting Rand Index +Figure 17: +Rand index for the GISETTE data as a function of number of variables used. The red +points correspond to ALB screening and blue points to t-statistic screening. Rand index is computed +for a DART classifier using only those variables having the largest 2j t-statistics or the largest 2j +values of ALB, where j = 3, . . . , 11. +For these data, t-test screening does as well as ALB screening based on A4 and the 99.5th per- +centile. The difference between the two methods is that ALB retains the same accuracy while picking +roughly 200 fewer variables. The interpretable cutoff rule does the worst, but 75% accuracy using +only four “pixel” measurements is a very interesting result. We believe this is a setting where most +variables, or ”pixels,” that are marginally important are ones that are colored in for one of the two +numbers (4 or 9) but not the other. This can be interpreted as a location difference, since the intensity +of a colored-in pixel is larger than the intensity of a pixel that is rarely touched. We also believe this +20 + +is the reason why t-test screening finds more important variables than does ALB screening based on +the same type I error rate. Despite being a setting where mostly location differences exist, ALB ends +up doing as well as t-test screening in terms of Rand index, at least when using a type I error rate of +0.005. In general we believe that choosing a cutoff based on a type I error rate or using 0 as a cutoff +are good strategies for data sets where n and p are both large. A large amount of data allows us +to choose fairly small significance thresholds while still maintaining good power. Choosing variables +that have the largest n + m values of ALB in this case results in no variables being screened, and so +we elect not to explore that avenue. A cross-validation procedure for selecting a cutoff is expensive +to perform due to the large values of p and n + m. +To explore the impact of choosing a cutoff based on quantiles, we explored the Rand indices when +the cutoff corresponded to using variables with the largest k statistics. We considered values of k that +increased geometrically: k = 8, 16, . . . , 2048. The results can be seen in Figure 17. At each number +of variables used, ALB-based screening has a larger Rand index than does t-test screening. Clearly, +ALB and t-test screening are not choosing the same variables, and the ones chosen by ALB are more +effective. +8 +Application to Leukemia data +The Leukemia data set contains observations on 72 patients, 47 of which have one type of leukemia +and the remainder another type. We have observations of 7129 variables on each patient to build a +classifier that will help decide which type of leukemia a future patient has. This is a case where p is +much larger than n and m. We will apply various screening methods to this problem in conjunction +with DART and compare the accuracy of the methods via Rand indices. +To do this in a fair fashion, we split the data set randomly into two halves. The first half are +validation data, and the second half are training data. We then split the training data in half again +to make two smaller training sets. We do this for two reasons. First, we wish to assess the effect of +training set size on accuracy of the methods. One of the two smaller training sets will be used to build +classifiers, each one corresponding to a different screening method, and then all the training data will +be used to build another set of classifiers. Both sets of classifiers will be used to predict the data in +the validation set. The second reason for dividing the training set in half is that it makes possible a +cross-validation approach for selecting a cutoff. We can train the model on one of the smaller training +data sets, and choose a cutoff that gives the best classification accuracy on the other training data +set. We can then train this best model on the full training set and apply it to the validation set. This +is applying strategy A2 in the methodology, which is feasible because of the small sizes of m and n. +To carry out our analysis we did the following. We performed four ALB based screening methods +21 + +Rand Index +Screening Method Used +Number of variables +0.599 +n + m largest ALBs +19 +0.529 +ALB > T ∗ +0.05 +617 +0.599 +n + m largest t-statistics +19 +0.529 +Pt < 0.05 +847 +0.501 +No screening +7129 +Table 2: Classification and screening results for leukemia data when training set is a quarter of full +set. All results are based on a validation set size that was roughly half that of the full data set. The +quantities Pt and T ∗ +0.05 are, respectively, the P-value of a t-test and the 95th percentile of permuted +ALBs. The classifier used was DART. +Rand Index +Screening Method +Number of variables +0.742 +ALB > TCV +12 +0.742 +ALB > TCV +12 +0.786 +n + m largest ALBs +38 +0.572 +ALB > T ∗ +0.05 +1302 +0.598 +n + m largest t-statistics +38 +0.572 +Pt < .05 +1694 +0.549 +No screening +7129 +Table 3: Classification and screening results for leukemia data when training set is half of full set. +All results are based on a validation set size that was roughly half that of the full data set. The first +two rows of the table correspond to use of the classifier based on (5), and subsequent rows to use of +DART. The quantity TCV is the best cutoff as chosen by cross-validation, and Pt and T ∗ +0.05 are as in +Table 2. See Section 8 for an explanation of how cross-validation was implemented. +and two t-test based screening methods. The four ALB methods were A1 with the n + m largest +ALBs being selected, A2 with the cutoff of 0, and A3 with a type I error rate of 0.05, d = 3 and +B = 7129. +Two methods of t-test screening were used, one using the variables with the m + n largest t- +statistics, and the other using variables whose t-test P-values were smaller than 0.05. The latter +version of t-test screening makes it comparable to choosing a variable using method A3 with signifi- +cance level 0.05. Once we determined relevant variables via screening, DART based on those variables +was used to compute a Rand index from the validation set. Tables 2 and 3 summarize the results. +All screening methods performed similarly when the training set size was a quarter of m + n. +However, ALB screening that chose a cutoff as in A1 or A3 improved remarkably when the sample +sizes were doubled, faring much better than the t-test based screening methods. While DART has +been shown to be an effective classifier, our experience is that it may fail to recover the structure of +the classification problem when the sample size is small. We thus tried the Bayesian classifier based +on (5) with the CV-based method to choose a cutoff, and this classifier was able to achieve decent +classification accuracy, surpassing DART if a different cutoff is chosen. We believe this is the case due +to its simplicity, and there should be enough data to construct reasonable kernel density estimates of +the underlying distributions. +22 + +Figure 18 shows the cross-validated Rand indices of the Bayesian classifier as a function of cutoff. +It turns out that the largest cutoff maximizing the Rand index was .288. (The largest cutoff was +chosen since this corresponds to the smallest number of variables maximizing the Rand index.) Figure +19 shows Rand indices of the Bayesian classifier that was trained on the full training set (i.e., the +training set using half of the full data set). This figure shows how well the CV cutoff fared when it +was used to screen variables in the full training set. Figure 18 shows how the number of variables +chosen is related to cutoff. Finally, Figure 19 also shows how sensitive the Rand index is to the +selected cutoff. +0.75 +0.80 +0.85 +0.90 +−0.25 +0.00 +0.25 +0.50 +Cutoff on training +Rand index on training +Figure 18: Cross-validation performance of the Bayesian classifier on the training set of the leukemia +data. A plot of the Rand index of the method corresponding to (5) against the number of variables +chosen by the method. The Rand indices are the performance of the classifier on one of the training +sets, applied to the other training sets. We chose the cutoff that works best by picking the cutoff (in +blue) that preserves the fewest variables in a sequence that maximizes the Rand index. +We believe the Bayesian classifier has potential in other settings where there may not be sufficient +data to train ensemble methods and there may exist differences between classes that are not of location +type. We note that, like other methods, it’s best to apply screening before using the Bayesian classifier, +as all of their performances will degrade if there are a large amount of variables that are not useful. +It is encouraging that the cutoff of 0 was the largest cutoff before large improvements in Rand index +23 + +0.5 +0.6 +0.7 +0.8 +0.9 +−0.25 +0.00 +0.25 +0.50 +Cutoff on Test +Rand index on Test +Figure 19: Cross-validation performance of the Bayesian classifier on the testing set of the leukemia +data. The Rand indices are on the validation set. The cutoff we chose for cross validation is in blue +?? and was selected by examining Figure 18. +occurred for the Bayesian classifier, but somewhat discouraging that the cross-validation approach +could not pick a cutoff that resulted in the best performance for that classifier. The problem here is +that the cross-validation approach chose an optimal cutoff when the classifier was constructed from +one quarter of all the data, whereas we actually needed to know the optimal cutoff when half of all +the data were used. Future research can focus on how an optimal cutoff depends on training set size. +If the dependence is simple enough, it may be possible to estimate the optimal cutoff for a given +training set size from cross-validation results based on a smaller training set size. +ALB screening tends to do better when using the k variables having the k largest ALBs. Figure +21 shows the Rand index resulting from applying DART after using this method of screening. When +using fewer than 500 variables, ALB screening does a better job than the analogous way of performing +t-test screening. After the number of variables included is large enough, t-test screening does better +than ALB screening, but at this point the number of variables included is large enough that the Rand +index becomes suboptimal for both types of screening. +24 + +−0.25 +0.00 +0.25 +0.50 +0 +2000 +4000 +6000 +Number of Variables picked on Test +ALB Cutoff on Test +Figure 20: Number of variables picked versus the cutoff chosen using the ALB screening method on +the Leukemia test data. +9 +Conclusion and future work +We have proposed a new screening method that searches for differences other than those of location +type. For this method to be more effective than t-test screening it needs to be paired with classification +methods that can leverage these differences. In simulations, we pair ALB screening with BART, +DART and a Bayesian classifier and show that it performs better than t-test screening in situations +where class differences are not of location type. The Bayesian classier outperformed DART when +applied to a leukemia data set. Even if the data contain primarily location differences, ALB screening +performs well, although, as expected, not as well as t-test screening. +Future work includes efforts to increase the speed of computing ALB statistics and their permu- +tation distributions, especially for large data sets. An iterative approach to the screening method +is available for SIS, and future research could involve investigating an ALB procedure that could +capture differences in joint distributions. The simulated data in this paper all leveraged independent +data, and how sensitive the method is to independence is also a property to explore. The interaction +between ALB screening and random projection or sketching methods of dealing with settings where +25 + +0.55 +0.60 +0.65 +0.70 +0.75 +0 +500 +1000 +1500 +2000 +Number of Variables chosen +Resulting Rand Index +Figure 21: DART Rand indices versus number of variables chosen for the Leukemia data set. We plot +the Rand index of the DART methods where we choose relevant variables corresponding to the top +number of ALBs or t-statistics. We vary the number of variables chosen. The red points denote the +Rand index of DART models using the top number of ALBs, while the blue points denote the Rand +index of DART models using the top number of t-statistics. +n and/or p are very large is also a promising direction for future research. +References +[Boser et al., 1992] Boser, B. E., Guyon, I. M., and Vapnik, V. N. (1992). A training algorithm for +optimal margin classifiers. In Proceedings of the fifth annual workshop on Computational learning +theory, pages 144–152. 1, 2 +[Brieman et al., 1984] Brieman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984). Classi- +fication and regression trees. Wadsworth Inc, 67. 1 +[Cui et al., 2015] Cui, H., Li, R., and Zhong, W. (2015). Model-free feature screening for ultrahigh +dimensional discriminant analysis. Journal of the American Statistical Association, 110(510):630– +641. 1, 2 +[Fan and Lv, 2008] Fan, J. and Lv, J. (2008). +Sure independence screening for ultrahigh dimen- +sional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology), +70(5):849–911. 2, 4, 11 +26 + +[Fan et al., 2010] Fan, J., Song, R., et al. (2010). Sure independence screening in generalized linear +models with NP-dimensionality. The Annals of Statistics, 38(6):3567–3604. 2 +[Friedman, 2002] Friedman, J. H. (2002). Stochastic gradient boosting. Computational statistics & +data analysis, 38(4):367–378. 1 +[Hill et al., 2020] Hill, J., Linero, A., and Murray, J. (2020). Bayesian Additive Regression Trees: A +Review and Look Forward. Annual Review of Statistics and Its Application, 7. 11 +[Linero and Yang, 2018] Linero, A. R. and Yang, Y. (2018). Bayesian regression tree ensembles that +adapt to smoothness and sparsity. Journal of the Royal Statistical Society: Series B (Statistical +Methodology), 80(5):1087–1110. 1, 2, 11 +[Mai and Zou, 2012] Mai, Q. and Zou, H. (2012). The Kolmogorov filter for variable screening in +high-dimensional binary classification. Biometrika, 100(1):229–234. 1, 2 +[Merchant and Hart, 2022] Merchant, N. and Hart, J. (2022). A Bayesian motivated two-sample test +based on kernel density estimates. Entropy, 24:1071. 2, 3, 5, 6 +[Tang et al., 2014] Tang, J., Alelyani, S., and Liu, H. (2014). Feature selection for classification: A +review. Data classification: Algorithms and applications, page 37. 2 +[Zhu et al., 2011] Zhu, L.-P., Li, L., Li, R., and Zhu, L.-X. (2011). Model-free feature screening for +ultrahigh-dimensional data. Journal of the American Statistical Association, 106(496):1464–1475. +4, 11 +27 + diff --git a/d9E0T4oBgHgl3EQfWwCZ/content/tmp_files/load_file.txt b/d9E0T4oBgHgl3EQfWwCZ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..1383045bce5761cd311f45119ff5d0c37abc89b0 --- /dev/null +++ b/d9E0T4oBgHgl3EQfWwCZ/content/tmp_files/load_file.txt @@ -0,0 +1,759 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf,len=758 +page_content='Screening Methods for Classification Based on Non-parametric Bayesian Tests Naveed Merchant and Jeffrey D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Hart January 2023 Abstract: Feature or variable selection is a problem inherent to large data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Screening methods scale linearly with the number of predictors by checking each predictor one at a time, and are a tool used to decrease the number of variables to consider before further analysis or variable selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For classification, there is a variety of techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There are parametric based screening tests, such as t-test or SIS based screening, and non-parametric based screening tests, such as Kolmogorov distance based screening [Mai and Zou, 2012], and MV-SIS [Cui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We propose a method for variable screening that uses Bayesian-motivated tests, compare it to SIS based screening, and provide example applications of the method on simulated and real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It is shown that our screening method can lead to improvements in classification rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is so even when our method is used in conjunction with a classifier, such as DART, which is designed to select a sparse subset of variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Finally, we propose a classifier based on kernel density estimates that in some cases can produce dramatic improvements in classification rates relative to DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Keywords: Independent Screening, Variable Selection, Classification, Bayes Factors 1 Introduction Classification involves predicting a class label for an observation, given a set of predictor variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The techniques for doing so are wide ranging, including support vector machines [Boser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 1992], tree based methods [Brieman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 1984], Bayesian trees [Linero and Yang, 2018] and gradient boosting trees [Friedman, 2002].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It is common to encounter a data set with many features, but rarely are all of them important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Picking a subset of these features quickly is a task that is desired, but can be tricky for very large data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Removing unimportant variables can result in dramatic improvement for some of the previously mentioned classification methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Feature selection is not a new field, and can be divided 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='02283v1 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='ME] 5 Jan 2023 into three categories: screening or filter based methods, wrapper methods, and embedded methods [Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Screening methods examine each variable one at a time to see if it provides useful information, and as a result scale linearly with the number of predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' However, examining each variable individually can cause information on joint behavior of variables to be lost, or can cause collinear variables to be selected [Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Wrapper methods fit different models, and then evaluate each one according to some criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The model that does best according to this criterion is selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While this tends to select good variable subsets, fitting every model can be extremely time- consuming, especially if the data set is very large [Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Embedding methods produce a model that has some sparsity built into it, producing a set of useful variables and a model built with them, simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The speed of different embedding methods varies with the strategy used to obtain sparsity, but these are typically slower than screening methods [Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Our focus in this paper will be on screening methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It is a common strategy to employ a screening method and then employ an embedding method (such as LASSO) afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Fan [Fan and Lv, 2008] employs this strategy and improves both the time it takes to run LASSO and the accuracy of the model as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Since then several filter methods have popped up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For classification in particular, maximum marginal likelihood screening [Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2010], MV-SIS [Cui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2015], and Kolmogorov distance screening [Mai and Zou, 2012] are some of the screening tests that have been published.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Most of these methods are applied to linear discriminant analysis and show improvement in applying these methods to a data set after the screening has been performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This paper proposes a new screen- ing method when the number of classes is known to be two, and show that it results in improved classification accuracy in settings where the simple model underlying linear discriminant analysis does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Our screening method identifies informative features by using a two-sample Bayesian test that checks whether two data sets share the same distribution[Merchant and Hart, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' One of our goals is to show that classification methods, including BART [Linero and Yang, 2018], DART [Linero and Yang, 2018] and SVM [Boser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 1992], can be improved when preceded by our screen- ing procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 2 Methodology Our screening method is based on computing a statistic for each individual feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will use kernel density estimates of the two distributions corresponding to the two classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The idea is similar to that of Kolmogorov distance screening: if it seems likely that the two classes have different distributions for a feature, then we will keep the feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We define a test statistic that can make this determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Suppose we observe the data X, an (m + n) × p matrix whose ith row, (Xi1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , Xip), contains the values of the p variables for one subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The ith element, Yi, of vector Y is 0 or 1 and indicates 2 the class to which the ith subject belongs, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , m + n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For now, suppose that Y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , Yn are 0 and Yn+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , Yn+m are 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We have n + m data vectors and p features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Consider the data Xj = (X1j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , X(m+n)j) for feature j and define ˆhi(·|Xj, b) to be a kernel density estimate that has bandwidth b and uses all the data in Xj except that of the ith subject: ˆhi(x|Xj, b) = 1 nb n+m � r=1 r̸=i K �x − Xrj b � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We also compute kernel estimates from the data sets consisting of observations where Y = 0 and Y = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' These are ˆfi(·|Xj, b) = 1 nb n � r=1 r̸=i K �x − Xrj b � and ˆgi(·|Xj, b) = 1 nb n+m � r=n+1 r̸=i K �x − Xrj b � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Then we define the test statistics ALBj, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , p: (m + n)ALBj = m � i=n+1 log � ˆgi(Xij|Xj, b) ˆhi(Xij|Xj, b) � + n � i=1 log � ˆfi(Xij|Xj, b) ˆhi(Xij|Xj, b) � def = m � i=n+1 log(B1ji) + n � i=1 log(B2ji).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The notation ALB stands for Average Log-Bayes factor, since, as argued by [Merchant and Hart, 2022], the statistics B1jr and B2js are Bayes factors based on the data “sets” Xrj and Xsj, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We refer to [Merchant and Hart, 2022] for a thorough exploration of such average log-Bayes factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Another motivation for ALBj is in terms of Kullback-Leibler divergence, which for densities h1 and h2 is KL(h1, h2) = � ∞ −∞ h1(x) log �h1(x) h2(x) � dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Define fj,mix = (nfj + mgj)/(n + m), where fj and gj are the densities of feature j for classes 0 and 1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Then the statistic ALBj is an approximately unbiased estimator of the following quantity: � n m + n � KL (fj, fj,mix) + � m m + n � KL (gj, fj,mix) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In the case f ≡ g, ALBj converges to 0 in probability as m and n tend to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The null distribution of ALBj can be assessed using a permutation-based procedure to determine if two sets of observations arise from a common distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' [Merchant and Hart, 2022] propose selecting the bandwidth b by leave-one-out cross validation, a 3 proposal that tacitly assumes the null hypothesis to be true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While this strategy has potential, we believe it to be too computationally expensive to use for every variable separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We only have to do this p times, suggesting linear scaling with the variable length, but this introduces quadratic scaling with n, which is prohibitive for large data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Instead, we opt to use a normal plug-in bandwidth in conjunction with the heavy tailed Hall kernel, which is: K0(z) = 1 √ 8πe Φ(1) exp � −1 2(log(1 + |z|))2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Simulation results show that the constant for the plug-in is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='162 to 3 decimal places, resulting in the following plug-in rule for variable j: bplug-in,j(Xj) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='162(m + n)−1/5sj, where sj is an estimate of the underlying (null) standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' One possibility is to take sj to be the sample standard deviation for Xj, but we prefer the more robust choice sRj = IQR(Xj)/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Suppose we have computed ALB1, ALB2, ALB3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', ALBp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The matter still remains in choosing a cutoff for the ALBs such that we select all variables with ALB larger than the cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Below are some possible ways of doing so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Choose the cutoff to be some percentile of ALB1, ALB2, ALB3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', ALBp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is in line with what some of the authors in SIS and SIRS propose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Suppose we expect d features to be important in the data set, then we can set our cutoff to be the 100(1 − d/p)th percentile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Clearly, the largest d test statistics are the most likely to be significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A problem with this approach is selecting an appropriate value for d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The authors in SIS [Fan and Lv, 2008] and SIRS [Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2011] argue that a conservative choice for d is n or n log(n), although these choices seem somewhat arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' An empirical but computationally daunting way to approach this problem is to proceed with two training sets and a classification method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We can choose the cutoff that minimizes the error rate of the classification method when it is trained on one of the training sets and then applied to the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To keep the computational scaling of the procedure linear with p, we recommend restricting the number of candidate cutoff values to be fairly small, say no more than ten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Randomly select a covariate, say Xj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For this covariate, permute the labels, and compute the test statistic, call it ALB∗ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Using the same feature Xj, repeat this procedure d times, resulting in ALB∗ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , ALB∗ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We randomly select B−1 more covariates without replacement, and repeat the previous steps for each of them, resulting in a total of Bd values of ALB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Once this is done, we choose the cutoff to be a percentile of these Bd values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This method also approximates the 4 null conditional distribution of ALB for a randomly selected feature, but potentially has the advantage of requiring fewer statistics to be computed than in A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Bayes factor interpretation of ALBj entails that variable j should never survive screening when ALBj < 0, suggesting that we use 0 as a cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While this choice may seem liberal, [Merchant and Hart, 2022] show that an ALB cutoff of 0 produces a test whose type I error probability tends to 0 as m + n tends to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It should be noted that a particular screening method will work differently with different classifiers, although this is perhaps to be expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We encourage the use of a classifier that can take advantage of differences in distribution other than location differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A popular classifier is linear discriminant analysis (LDA), by which we mean the version that assumes equal covariance matrices for the two classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Features identified as important due to a scale difference between classes will usually be of no use to LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Of the methods A1-A4, the least computationally expensive ones are A1 and A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Use of these cutoffs also has the advantage of producing a test with power tending to 1 as m + n tends to ∞, since ALBj converges to 0 in probability when fj ≡ gj [Merchant and Hart, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Method A1 is recommended if there is a strong idea as to how many variables are expected to be relevant or if there is a critical number of variables that are needed for another classifier to work well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Lastly we wish to note that each ALB has a finite upper bound, as it is easily shown that ALBj ≤ log(2) · max � m (m − 1), n (n − 1) � , which implies that ALBj is essentially bounded by log(2) so long as m and n are not too small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 3 Consistency results We begin with the assumption that every variable satisfies conditions A1-A5 in [Merchant and Hart, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will also assume that the numbers, m and n, of samples for the two classes tend to infinity, and the number of variables, p, is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Suppose that a variable belongs to class D if the variable marginally offers information, which means that the variable has a different distribution for one class than it does for the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Finally, we assume that the variables are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the above assumptions hold, then lim n,m→∞ P(max i∈Dc ALBi < min j∈D ALBj) → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (1) 5 Suppose we use a cutoff as in A4 (in our Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Then we also have the following result: lim n,m→∞ P(min j∈D ALBj > 0 ∩ max j∈Dc ALBj < 0) → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Result (2) implies (1), so we only prove the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Using the fact that P(A ∩ B) ≥ 1−P(Ac)−P(Bc), it is enough to show that both P(minj∈D ALBj > 0) and P(maxj∈Dc ALBj < 0) tend to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We only consider P(maxj∈Dc ALBj < 0) as the proof for the other probability is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We have P(max j∈Dc ALBj < 0) = P � � � j∈Dc {ALBj < 0} � � = � j∈Dc P(ALBj < 0) ≥ � min j∈Dc P(ALBj < 0) �N , (3) where N is the number of elements in Dc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For each j ∈ Dc, [Merchant and Hart, 2022] show that P(ALBj < 0) → 1 as m and n tend to ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Since N is finite, this implies that the quantity on the right-hand side of (3) tends to 1, from which the result follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' ■ It is clear that if p tends to ∞ at a sufficiently slow rate, then Theorem 1 remains true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' However, determining the precise rate at which p can increase relative to m and n requires stronger results than provided by [Merchant and Hart, 2022], and we will not pursue this direction further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We now show simulation results for various values of m = n, p and r, where r represents the proportion of important variables, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', variables for which the class distributions are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We generate 500 variables for a binary classification problem in the following fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If it is important, the variable is drawn for one class from a t-distribution with 4 degrees of freedom, and drawn from the other class from a mixture of two normal distributions, where the mixing parameter is 1/2, the standard deviation of both normal distributions is 1, and the means are -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If instead the variable is unimportant, then it is drawn from a standard normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will name the method of generating variables in this setting “a shape difference.” Finally, each variable is determined to be important or not by performing a binomial trial with success probability r = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figures 1, 2, and 3 show how the cdfs of the ALBs change depending on m and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' As the sample sizes m and n increase, the ALBs for important variables gradually increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Even when the total number of observations is only eight percent of the total number of variables, we achieve the property that the largest ALB of the unimportant variables is smaller than the smallest ALB of the important variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The black curve shows the cdf of ALBs computed by permuting the labels for each variable three times and computing the ALB each time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A cutoff of 0 is not larger 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 ALBs p Significance Unimportant Important Figure 1: Comparison of ALB CDFs when the training set sizes are equal to 10 and important variables have a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The black curve denotes the CDF of ALBs generated from data where the classes are permuted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 ALBs p Significance Unimportant Important Figure 2: Comparison of ALB CDFs when the training set sizes are equal to 20 and important variables have a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The black curve denotes the CDF of ALBs generated from data where the classes are permuted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' than the largest unimportant variable for any n, but is still useful for discarding a large portion of the unimportant variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' On the other hand, using a large percentile of the permuted variables can result in discarding almost all of the unimportant variables, and at the largest sample size, choosing the cutoff to be the maximum of the permuted ALBs does indeed almost perfectly separate the important and unimportant variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 4 Discussion of classification methods Ideally, one should choose the screening method and classifier that work best together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Good ex- amples of this principle are provided by the relationship that classification methods such as logistic regression, support vector machines, and linear discriminant analysis have with t-test based screen- 7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 ALBs p Significance Unimportant Important Figure 3: Comparison of ALB CDFs when the training set sizes are equal to 40 and important variables have a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The black curve denotes the CDF of ALBs generated from data where the classes are permuted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Discriminant analysis, support vector machines without a kernel trick, and logistic regression are designed to take advantage of location differences between classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It is therefore natural to precede them with t-test screening, which, of course, is designed to detect differences between means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' On the other hand, support vector machines that use a kernel trick create a hyper-plane that best separates the two classes essentially after a transformation is performed, and can therefore deal effectively with many types of differences between distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To take advantage of this ability, it is thus best to use a screening method that can detect non-location differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In summary, t-test screening is a natural method to use when linear discriminant analysis or logistic regression are deemed to be appropriate classifiers, but is not necessarily a good method when a support vector machine with a kernel trick is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' By linear SVM, we mean a method that can classify by separating the two groups by a plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In Figures 4 and 5 two (important) variables are generated according to a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The bimodality of one of the two class distributions makes the classes hard to separate with a plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figure 4 shows the performance of a support vector machine when only two relevant variables are used for classification, while Figure 5 shows the improvement in the same situation when the kernel trick is applied to detect non-location based differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Our method seeks to outperform t-test screening by considering differences other than ones of location type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Of course, this performance is not free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It comes with the cost that we lose some power in detecting differences of means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For our method to work better with a classifier, the classifier must have the ability to distinguish classes that display non-location differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For example, a set of variables whose classes differ only with respect to scale would not be useful to support vector machines without the kernel trick and LDA, as there would be no hyperplane that nicely separates the classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A kernel trick or increasing the number of variables by considering interactions and squared 8 terms can sidestep this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' But adding variables is not ideal, as a goal of our methodology is to decrease computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' −1 0 1 2 −1 0 1 V1 V2 y 0 1 fittedvals 0 1 Figure 4: Prediction accuracy of two important variables in the setting of “a shape difference” using a linear SVM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The colors represent the predictions that the SVM produces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The line represents the discriminator that a linear SVM produces to discriminate the classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The triangle and circle represent which class the observation arises from.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' −1 0 1 2 −1 0 1 V1 V2 y 0 1 fittedvals 0 1 Figure 5: Prediction accuracy of two important variables in the setting of “a shape difference” with an SVM that uses a kernel trick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The colors represent the predictions that the SVM produces when a kernel trick is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The triangle and circle represent which class the observation arises from.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Classification is much better in this case because the trick enables the classifier to capture differences other than location shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Finally, we would like to add that even though SVM with the kernel trick is a fine classification method that uncovers many different types of differences between variables, its performance can be degraded harshly by the presence of noisy variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To illustrate this, we use data in the same setting as the shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We constructed a training and testing set such that both consist of 9 Not Screened Screened 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 Number guessed belong to class 0 in class 0 (a) Boxplots of true positives Not Screened Screened 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 Number guessed belong to class 0 in class 1 (b) Boxplots of false positives Not Screened Screened 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 Number guessed belong to class 1 in class 0 (c) Boxplots of false negatives Not Screened Screened 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 Number guessed belong to class 1 in class 1 (d) Boxplots of true negatives Figure 6: Box plots displaying the accuracy of SVM when the data are generated from model where 10% of the variables are important and have a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To illustrate the accuracy of the methods, we do the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' First, suppose a positive case corresponds to an observation being in class 1 and a negative case corresponds to an observation being in the other class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Then to show the accuracy of the SVMs, we show boxplots on the number of “True Positives,” “True Negatives,” “False Positives” and “False Negative” occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 10 observations from each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Five hundred variables were used, with only 10% on average being important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' All data for unimportant variables have a standard normal distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If a variable is important, then its distribution in one class is a bimodal mixture of two normals and in the other class a t-distribution with 4 degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The normal distributions in the mixture both have standard deviation 1 and means of -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We trained an SVM with the radial basis kernel on all of the observations, and trained another SVM with the radial basis kernel but used only variables whose ALB value was larger than the interpretative cutoff of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We repeat this procedure 100 times, and report on its accuracy in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In general, classification accuracy is greatly improved, false negatives rarely happen after screening and the number of false positives is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The ALB screening method need not be the final say as to which variables to include.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Two variables that are individually important but highly correlated might be selected, although this may 10 not be ideal for some classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Screening can simply be a precursor that simplifies the job of a classifier, which does further variable selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Even methods that can perform variable selection and modeling simultaneously can benefit from having the number of variables reduced dramatically by screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is observed in SIRS [Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2011], SIS [Fan and Lv, 2008], and is also true in our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 5 Interaction with BART and a tailored classification method We have recommended using classification methods that can take advantage of features for which the classes have non-location differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Methods that do further variable selection or that can handle sparse data sets can also fare quite well with our screening methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' BART and DART are methods having few parametric assumptions and that are able to capture a large variety of features from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' BART has issues as the number of predictors grow, and DART has been proposed as a solution for this issue [Linero and Yang, 2018].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While DART can handle the case where many predictors are irrelevant, there is a cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Mixing times of the chains for DART are increased compared to BART, and a prior that encourages sparsity may cause DART to get trapped in a posterior mode when the MCMC procedure to estimate it is run [Hill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While we cannot directly mitigate these problems, decreasing the number of variables helps speed up the MCMC procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Our screening method can decrease the number of variables at a faster rate than DART can.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' DART is resilient against correlated nuisance variables and can therefore eliminate variables that survive ALB screening but are irrelevant due to collinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We provide simulations showing that use of our screening method before BART or DART can result in improved misclassification rates and computing speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We generate data in the same context as Figure 2, but instead roughly 10% of the variables are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If a variable is irrelevant, the distribution of the variable for both classes is standard normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To assess the performance of a classifier, we computed the Rand index, or the percentage of correct decisions the classifier has made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We compute the Rand index for the BART and DART procedures applied to all variables, and the Rand index of the same procedures applied to variables that survive ALB screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We consider different training set sizes that vary from 5 to 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The testing set size for each simulation is the same as the training set size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We repeat this 100 times for each sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figures 7 and 9 show how accurate BART and DART alone are in these settings and Figures 8 and 10 show how the methods do when variables are screened for importance beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There is a notable gain in the Rand index as the training set size gradually increases for both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Of greater note is that the time it takes to run both procedures is decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figure 11 shows the amount of time it takes the BART method to run before screening and Figure 12 shows how long the method takes after screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Screening on average shaves off at least 10 seconds of computation 11 time while increasing the average accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is an interesting result, as the methods themselves, DART especially, tend to be robust to irrelevant variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' However, the figures suggest that a larger sample size is required to achieve that robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 5 10 15 20 TrainingSize Rand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='BART Figure 7: Box plots of the Rand index of BART in the setting of a shape difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We vary m with m = n, and the training size in the plot denotes m+n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We repeat each simulation 100 times for each sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Roughly 10% of the variables are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 5 10 15 20 TrainingSize Rand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='Bart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='S Figure 8: Box plots of the Rand index of BART when BART is improved by screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is in the same setting as that used in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The difference between the two plots is that we screened the variables with the ALB procedure before applying BART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We choose variables such that all generated ALBs are larger than the interpretable cutoff of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The power of the classification method grows large when enough data is accrued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The interpretive cutoff tends to be conservative, and power of the approach is likely to be even larger if a permutation-based cutoff is used instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='1 A simple Bayesian classifier Suppose our goal is to simply leverage the differences between variables, regardless of the type of difference, and that we assume independence between variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We can construct a simple Bayesian method for classification in the following fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For each variable, we compute two kernel density estimates, one for each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For each variable i, let ˆfi and ˆgi be kernel density estimates using all variable i data from classes 1 and 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The prior probability that a variable arises from a 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 5 10 15 20 TrainingSize Rand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='DART Figure 9: Box plots of the Rand index of DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is in the same setting as in Figure 7, with the difference that we use DART instead of BART as it is capable of automatically performing variable selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 5 10 15 20 TrainingSize Rand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='Dart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='S Figure 10: Box plots of the Rand index of DART improved by screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is in the same setting as in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The difference here is we screen the variables with the ALB procedure before applying DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We choose variables such that all generated ALBs are larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The power of the classification method has improved after screening for variables, despite DART being fully capable of automatically performing variable selection automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 20 25 30 5 10 15 20 TrainingSize Time to run DART Figure 11: Box plots of the time it took to run DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The simulation is in the same setting as in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 13 13 15 17 19 5 10 15 20 TrainingSize Time to run DART post screen Figure 12: Box plots of the time it took to run DART post screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is in the same setting as in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The difference here is we screen the variables with the ALB procedure before applying DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The screening procedure itself takes much less than half a second, and as a result of removing a large number of irrelevant variables, greatly improves the amount of time it takes for DART to run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' class is assumed to be proportional to the number of observations for that class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Let x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', xp) be an observation to be classified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the underlying densities are known, then the conditional probability that x came from class 1 is p(x) = P(Y = 1|x) = n m+n � i∈D fi(xi) n m+n � i∈D fi(xi) + m m+n � i∈D gi(xi), (4) where D is the set of indices i such that fi ̸≡ gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Of course, the densities and D are unknown, but p(x) can be estimated using kernel density estimates, and D can be replaced by �D, the set of indices such that the corresponding variables survive screening: ˆp(x) = n m+n � i∈ � D ˆfi(xi) n m+n � i∈ � D ˆfi(xi) + m m+n � i∈ � D ˆgi(xi) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (5) A classifier based on (5) can be a powerful tool for capturing marginal differences in distributions, but is incapable of leveraging differences that may lie in the dependence structure of the variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To use (5), we say that an observation x belongs to class 1 if ˆp(x) > n/(m + n) and to class 2 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We have found this classifier to have strong accuracy when dealing with independent variables, or with settings where the difference in multivariate distributions is dominated by marginal differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To illustrate the effectiveness of the classifier based on (5), we perform a simulation similar to the one referenced in Figure 1 but under a variety of different sample sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We repeat this procedure 5 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For each sample size, we generate a balanced testing set of the same size, and compute a Rand index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A plot of the Rand indices against the sample size is found in Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The power of the classification method grows to be quite large at even small m + n values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Since the interpretive cutoff tends to be conservative, power of the approach is likely to be even larger if a permutation based cutoff is utilized instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' At a training size of just 9 samples in each group, the classifier makes 14 perfect predictions over 75% of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='0 4 6 8 10 12 14 16 18 20 n rand index Figure 13: A box plot of the Rand index of the Bayesian classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The classifier is defined in terms of (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We generate data in the same context as in Figure 2, but vary m and n so that m = n, and the training size denotes m + n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We choose variables such that all generated ALBs are larger than the intepretable cutoff of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 6 Application on simulated data sets We want to compare our method to t-test screening and also compare performance of the different choices of ALB cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There are at least two ways to go about this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' One is to compare the percentage of variables that survive screening from both procedures, and the other is to apply a classification method after screening and see which method has a better classification rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' These procedures are carried out in three cases: Case 1 – Location differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There are 600 variables, and those that are important arise from a case where there is a mean difference between classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the variable is important, one class has a standard normal distribution and the other a normal distribution with mean 1 and standard deviation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We let roughly 5% of the variables be important by generating 600 independent Bernoulli variables, each with success probability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This way of determining important variables is used in Cases 2 and 3 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Also, in this case and the following two the unimportant variables have standard normal distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The classifier we will use to compare performance in this case is SVM without the kernel trick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Case 2 – Scale differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There are 600 variables, and those that are important arise from 15 a case where there is a variance difference between classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the variable is important, one class has a standard normal distribution and the other a normal distribution with mean 0 and standard deviation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We let roughly 20% of the variables be important, and the classifier used is the support vector machine with a kernel trick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Case 3 – Shape differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' There are 600 variables, and those that are important arise from a case where the class distributions have different shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the variable is important, one class has a standard t-distribution with 4 degrees of freedom and the other a bimodal mixture of two normal distributions with means -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 and the same standard deviation of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Roughly 10% of the variables are important, and the classifier used is the support vector machine with a kernel trick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For all three cases, screening was done and the classifier built from a training set of m+n observations on each variable, where m = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The classifier so built was applied to predict m + n observations, and the resulting Rand index was calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In t-test screening, variables were selected when their P-values were smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We repeated this procedure 100 times for each sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figures 14-16 show, respectively, how well the methods performed for three ways of choosing an ALB cutoff: a “fixed type I error rate” approach, the largest n + m values of ALB, and a cutoff of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The results of these simulations suggest that ALB screening is effective at detecting location differences, as in Case 1, but not to the same degree as t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In Case 1, the performance of the SVM with ALB screening is better than with no screening, but worse than with t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The proportion of variables that survive ALB screening steadily increases as sample size increases, but at a slower rate than with t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In Cases 2 and 3, t-test screening does no better than no screening in terms of classification accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Regarding preservation of important variables, t-test screening does not improve as the sample size increases, but ALB screening does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 7 Application to the GISETTE data The GISETTE data are obtained from m = 3000 and n = 3000 handwritten images of the digits 4 and 9, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For each of the 6000 images, p = 5000 variables are measured, some of which are irrelevant probes, and the others pixel intensities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will perform classification on these data, using different screening methods to choose different subsets of the variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will rely on DART to be the primary classification method and will explore how it performs when aided by different screening methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The data set was randomly split into two halves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The first half was treated as the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We trained our classifier and computed t-statistics and ALB statistics on these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The second half was treated as the validation set, and we computed the Rand index from these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 10 20 30 Total training size Proportion of correct variables that survive screening Figure 14: Simulation results for t-test screening and ALB screening that uses A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We generate ALB∗ values by permuting the data labels and computing ALB for the resulting data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We do this for every variable twice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The ALB cutoff is the 95th percentile of ALB∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The t-statistic cutoff is chosen so that the P-value is less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Red, green and blue box plots are for no screening, t-test screening, and ALB screening, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The first, second and third row of plots correspond to cases 1, 2 and 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 10 20 30 Total training size Proportion of correct variables that survive screening Figure 15: Simulation results for t-test screening and ALB screening that uses variables with n + m largest values of ALB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The colors of the box plots have the same meaning as they do in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 10 20 30 Total training size Proportion of correct variables that survive screening 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='55 10 20 30 Total training size Rand index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 10 20 30 Total training size Proportion of correct variables that survive screening Figure 16: Simulation results for t-test screening and ALB screening with cutoff 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The colors of the box plots have the same meaning as they do in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 19 Rand Index Screening Method Number of variables chosen 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='947 ALB > T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005 1321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='942 ALB > 0 1946 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='947 Pt < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005 1540 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='935 No screening 4835 Table 1: Classification and screening results for GISETTE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' All methods used a balanced training and testing set that both consisted of 3000 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The quantities Pt and T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005 are, respectively, the P-value of a t-test and the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5th percentile of permuted ALBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Five screening methods were compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We implemented A3, setting B = 1000 and d = 1 and choosing variables such that ALB was larger than the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5th percentile of ALB∗ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To compare this with t-test screening, we picked variables whose t-test P-values were less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We tried screening method A1 and compared it to it’s t-test counterpart that picks the same number of variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We also checked to see how the method did with no variable screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We compare the Rand indices of these methods with that when no screening of variables is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Before proceeding with any of the methods, we removed each variable for which all 6000 data values were the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' As a result there were only 4835 variables in the full data set rather than 5000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A summary of Rand indices is given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='9 0 1000 2000 3000 4000 5000 Number of Variables chosen Resulting Rand Index Figure 17: Rand index for the GISETTE data as a function of number of variables used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The red points correspond to ALB screening and blue points to t-statistic screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Rand index is computed for a DART classifier using only those variables having the largest 2j t-statistics or the largest 2j values of ALB, where j = 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For these data, t-test screening does as well as ALB screening based on A4 and the 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5th per- centile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The difference between the two methods is that ALB retains the same accuracy while picking roughly 200 fewer variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The interpretable cutoff rule does the worst, but 75% accuracy using only four “pixel” measurements is a very interesting result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We believe this is a setting where most variables, or ”pixels,” that are marginally important are ones that are colored in for one of the two numbers (4 or 9) but not the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This can be interpreted as a location difference, since the intensity of a colored-in pixel is larger than the intensity of a pixel that is rarely touched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We also believe this 20 is the reason why t-test screening finds more important variables than does ALB screening based on the same type I error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Despite being a setting where mostly location differences exist, ALB ends up doing as well as t-test screening in terms of Rand index, at least when using a type I error rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In general we believe that choosing a cutoff based on a type I error rate or using 0 as a cutoff are good strategies for data sets where n and p are both large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A large amount of data allows us to choose fairly small significance thresholds while still maintaining good power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Choosing variables that have the largest n + m values of ALB in this case results in no variables being screened, and so we elect not to explore that avenue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A cross-validation procedure for selecting a cutoff is expensive to perform due to the large values of p and n + m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To explore the impact of choosing a cutoff based on quantiles, we explored the Rand indices when the cutoff corresponded to using variables with the largest k statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We considered values of k that increased geometrically: k = 8, 16, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' , 2048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The results can be seen in Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' At each number of variables used, ALB-based screening has a larger Rand index than does t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Clearly, ALB and t-test screening are not choosing the same variables, and the ones chosen by ALB are more effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 8 Application to Leukemia data The Leukemia data set contains observations on 72 patients, 47 of which have one type of leukemia and the remainder another type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We have observations of 7129 variables on each patient to build a classifier that will help decide which type of leukemia a future patient has.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is a case where p is much larger than n and m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We will apply various screening methods to this problem in conjunction with DART and compare the accuracy of the methods via Rand indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To do this in a fair fashion, we split the data set randomly into two halves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The first half are validation data, and the second half are training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We then split the training data in half again to make two smaller training sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We do this for two reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' First, we wish to assess the effect of training set size on accuracy of the methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' One of the two smaller training sets will be used to build classifiers, each one corresponding to a different screening method, and then all the training data will be used to build another set of classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Both sets of classifiers will be used to predict the data in the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The second reason for dividing the training set in half is that it makes possible a cross-validation approach for selecting a cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We can train the model on one of the smaller training data sets, and choose a cutoff that gives the best classification accuracy on the other training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We can then train this best model on the full training set and apply it to the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This is applying strategy A2 in the methodology, which is feasible because of the small sizes of m and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' To carry out our analysis we did the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We performed four ALB based screening methods 21 Rand Index Screening Method Used Number of variables 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='599 n + m largest ALBs 19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='529 ALB > T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 617 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='599 n + m largest t-statistics 19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='529 Pt < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 847 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='501 No screening 7129 Table 2: Classification and screening results for leukemia data when training set is a quarter of full set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' All results are based on a validation set size that was roughly half that of the full data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The quantities Pt and T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 are, respectively, the P-value of a t-test and the 95th percentile of permuted ALBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The classifier used was DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Rand Index Screening Method Number of variables 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='742 ALB > TCV 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='742 ALB > TCV 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='786 n + m largest ALBs 38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='572 ALB > T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 1302 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='598 n + m largest t-statistics 38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='572 Pt < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 1694 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='549 No screening 7129 Table 3: Classification and screening results for leukemia data when training set is half of full set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' All results are based on a validation set size that was roughly half that of the full data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The first two rows of the table correspond to use of the classifier based on (5), and subsequent rows to use of DART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The quantity TCV is the best cutoff as chosen by cross-validation, and Pt and T ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05 are as in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' See Section 8 for an explanation of how cross-validation was implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and two t-test based screening methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The four ALB methods were A1 with the n + m largest ALBs being selected, A2 with the cutoff of 0, and A3 with a type I error rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05, d = 3 and B = 7129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Two methods of t-test screening were used, one using the variables with the m + n largest t- statistics, and the other using variables whose t-test P-values were smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The latter version of t-test screening makes it comparable to choosing a variable using method A3 with signifi- cance level 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Once we determined relevant variables via screening, DART based on those variables was used to compute a Rand index from the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Tables 2 and 3 summarize the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' All screening methods performed similarly when the training set size was a quarter of m + n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' However, ALB screening that chose a cutoff as in A1 or A3 improved remarkably when the sample sizes were doubled, faring much better than the t-test based screening methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' While DART has been shown to be an effective classifier, our experience is that it may fail to recover the structure of the classification problem when the sample size is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We thus tried the Bayesian classifier based on (5) with the CV-based method to choose a cutoff, and this classifier was able to achieve decent classification accuracy, surpassing DART if a different cutoff is chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We believe this is the case due to its simplicity, and there should be enough data to construct reasonable kernel density estimates of the underlying distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 22 Figure 18 shows the cross-validated Rand indices of the Bayesian classifier as a function of cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It turns out that the largest cutoff maximizing the Rand index was .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (The largest cutoff was chosen since this corresponds to the smallest number of variables maximizing the Rand index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=') Figure 19 shows Rand indices of the Bayesian classifier that was trained on the full training set (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', the training set using half of the full data set).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' This figure shows how well the CV cutoff fared when it was used to screen variables in the full training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figure 18 shows how the number of variables chosen is related to cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Finally, Figure 19 also shows how sensitive the Rand index is to the selected cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='90 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 Cutoff on training Rand index on training Figure 18: Cross-validation performance of the Bayesian classifier on the training set of the leukemia data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A plot of the Rand index of the method corresponding to (5) against the number of variables chosen by the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Rand indices are the performance of the classifier on one of the training sets, applied to the other training sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We chose the cutoff that works best by picking the cutoff (in blue) that preserves the fewest variables in a sequence that maximizes the Rand index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We believe the Bayesian classifier has potential in other settings where there may not be sufficient data to train ensemble methods and there may exist differences between classes that are not of location type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We note that, like other methods, it’s best to apply screening before using the Bayesian classifier, as all of their performances will degrade if there are a large amount of variables that are not useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' It is encouraging that the cutoff of 0 was the largest cutoff before large improvements in Rand index 23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='9 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 Cutoff on Test Rand index on Test Figure 19: Cross-validation performance of the Bayesian classifier on the testing set of the leukemia data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Rand indices are on the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The cutoff we chose for cross validation is in blue ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and was selected by examining Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' occurred for the Bayesian classifier, but somewhat discouraging that the cross-validation approach could not pick a cutoff that resulted in the best performance for that classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The problem here is that the cross-validation approach chose an optimal cutoff when the classifier was constructed from one quarter of all the data, whereas we actually needed to know the optimal cutoff when half of all the data were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Future research can focus on how an optimal cutoff depends on training set size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' If the dependence is simple enough, it may be possible to estimate the optimal cutoff for a given training set size from cross-validation results based on a smaller training set size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' ALB screening tends to do better when using the k variables having the k largest ALBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Figure 21 shows the Rand index resulting from applying DART after using this method of screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' When using fewer than 500 variables, ALB screening does a better job than the analogous way of performing t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' After the number of variables included is large enough, t-test screening does better than ALB screening, but at this point the number of variables included is large enough that the Rand index becomes suboptimal for both types of screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 24 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='50 0 2000 4000 6000 Number of Variables picked on Test ALB Cutoff on Test Figure 20: Number of variables picked versus the cutoff chosen using the ALB screening method on the Leukemia test data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 9 Conclusion and future work We have proposed a new screening method that searches for differences other than those of location type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' For this method to be more effective than t-test screening it needs to be paired with classification methods that can leverage these differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In simulations, we pair ALB screening with BART, DART and a Bayesian classifier and show that it performs better than t-test screening in situations where class differences are not of location type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Bayesian classier outperformed DART when applied to a leukemia data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Even if the data contain primarily location differences, ALB screening performs well, although, as expected, not as well as t-test screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Future work includes efforts to increase the speed of computing ALB statistics and their permu- tation distributions, especially for large data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' An iterative approach to the screening method is available for SIS, and future research could involve investigating an ALB procedure that could capture differences in joint distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The simulated data in this paper all leveraged independent data, and how sensitive the method is to independence is also a property to explore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The interaction between ALB screening and random projection or sketching methods of dealing with settings where 25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='75 0 500 1000 1500 2000 Number of Variables chosen Resulting Rand Index Figure 21: DART Rand indices versus number of variables chosen for the Leukemia data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We plot the Rand index of the DART methods where we choose relevant variables corresponding to the top number of ALBs or t-statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' We vary the number of variables chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The red points denote the Rand index of DART models using the top number of ALBs, while the blue points denote the Rand index of DART models using the top number of t-statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' n and/or p are very large is also a promising direction for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' References [Boser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 1992] Boser, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Guyon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Vapnik, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A training algorithm for optimal margin classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' In Proceedings of the fifth annual workshop on Computational learning theory, pages 144–152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1, 2 [Brieman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 1984] Brieman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Friedman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Olshen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Stone, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Classi- fication and regression trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Wadsworth Inc, 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1 [Cui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2015] Cui, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Zhong, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Model-free feature screening for ultrahigh dimensional discriminant analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Journal of the American Statistical Association, 110(510):630– 641.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1, 2 [Fan and Lv, 2008] Fan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and Lv, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Sure independence screening for ultrahigh dimen- sional feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(5):849–911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 2, 4, 11 26 [Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2010] Fan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Song, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Sure independence screening in generalized linear models with NP-dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Annals of Statistics, 38(6):3567–3604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 2 [Friedman, 2002] Friedman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Stochastic gradient boosting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Computational statistics & data analysis, 38(4):367–378.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1 [Hill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2020] Hill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Linero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Murray, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Bayesian Additive Regression Trees: A Review and Look Forward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Annual Review of Statistics and Its Application, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 11 [Linero and Yang, 2018] Linero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Bayesian regression tree ensembles that adapt to smoothness and sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(5):1087–1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1, 2, 11 [Mai and Zou, 2012] Mai, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and Zou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' The Kolmogorov filter for variable screening in high-dimensional binary classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Biometrika, 100(1):229–234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 1, 2 [Merchant and Hart, 2022] Merchant, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' and Hart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' A Bayesian motivated two-sample test based on kernel density estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Entropy, 24:1071.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 2, 3, 5, 6 [Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2014] Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Alelyani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Feature selection for classification: A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Data classification: Algorithms and applications, page 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 2 [Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', 2011] Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=', and Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Model-free feature screening for ultrahigh-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' Journal of the American Statistical Association, 106(496):1464–1475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} +page_content=' 4, 11 27' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E0T4oBgHgl3EQfWwCZ/content/2301.02283v1.pdf'} diff --git a/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/2301.04106v1.pdf.txt b/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/2301.04106v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9c3bcae29b01036a3faf5f297a1b85682a225d1b --- /dev/null +++ b/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/2301.04106v1.pdf.txt @@ -0,0 +1,1315 @@ +Simulation of ODMR Spectra from Nitrogen-Vacancy +Ensembles in Diamond for Electric Field Sensing +Yuchun Zhu,∗,† Elena Losero,†,‡ Christophe Galland,†,¶ and Valentin Goblot†,¶ +†Institute of Physics, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, +Switzerland +‡Division of Quantum Metrology and Nanotechnologies, Istituto Nazionale di Ricerca Metrologica +(INRiM), 10135 Torino, Italy +¶Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland +E-mail: yuchun.zhu@epfl.ch +Abstract +Solid state spins in diamond, in particular negatively charged nitrogen-vacancy +centers (NV), are leading contenders in the field of quantum sensing. While ad- +dressing of single NVs offers nanoscale spatial resolution, many implementations +benefit from using large ensembles to increase signal magnitude and therefore +sensitivity. However, sensing with ensembles brings its own challenges given the +random orientation of the spin quantization axis within the diamond crystal lat- +tice. Here, we present an open source simulation tool that models the influence of +arbitrary electric and magnetic fields on the electronic and nuclear spin states of +NV ensembles, and can be extended to other color centers. Specifically, the code +computes the transition strengths and predicts the sensitivity under shot-noise- +limited optically-detected magnetic resonance. We illustrate the use of the code +in the context of electric field sensing, a promising emerging functionality of NV +centers with applications in biosensing and electronics, and bring several subtle +features to light that are due to the interplay between different NV orientations +and the external electric and microwave fields. Moreover, we show that our code +can be used to optimize sensitivity in situations where usual arguments based on +1 +arXiv:2301.04106v1 [quant-ph] 10 Jan 2023 + +neglecting terms in the full Hamiltonian would give sub-optimal results. Finally, +we propose a novel sensing scheme which allows to perform full vector electrome- +try without the need for precise bias magnetic field alignment, thus reducing the +experimental complexity and speeding up the measurement procedure. +keywords: nitrogen-vacancy (NV) centers, diamond, optically detected magnetic resonance +(ODMR) spectroscopy, electric field sensing, numerical simulation, quantum metrology +1 +Introduction +In recent years negatively charged nitrogen-vacancy (NV) centers in diamond, consisting of a +nearest-neighbor pair of a substitutional nitrogen atom and a lattice vacancy (Fig. 1a), have at- +tracted a lot of attention for their long spin coherence times and favorable optical properties, making +them promising candidates for quantum sensing and quantum information processing applications.1 +Their nanoscale resolution, bio-compatibility, long coherence time even at room temperature and +technical simplicity underpin their widespread use in quantum sensing – notably for magnetic field, +but also for electric field, temperature and strain sensing.2–7 NV centers sensing capabilities are +based on optical preparation and readout of their spin states. The energy level structure depends +on the NV center environment and can be probed through optically detected magnetic resonance +(ODMR). The easiest approach is to continuously excite the sample, both optically (with green +light) and with a coherent microwave field (MW), while collecting the photoluminescence (PL) +signal (at red and near infrared wavelengths). In this work, we typically refer to this technique, +named as continuous-wave (CW) ODMR. More advanced pulsed techniques can be used to improve +the sensitivity and are reviewed for example in Ref.8 The spin transition spectra computed by our +code can be used as input for further modeling in such contexts as well. +An ODMR spectrum provides much information, such as the direction and the magnitude of +a magnetic and electric fields at the NV center position. However, the presence of local intrinsic +fields (e.g. due to strain), paramagnetic impurities, surface defects or unknown sample properties +(e.g. random orientations of the NV centers), adds difficulties on the interpretation of the acquired +ODMR spectrum.9 Moreover, due to the interplay between the different quantities, the optimal +sensing configuration is not always obvious. The complexity is increased while using NV ensembles, +due to the presence of all the 4 possible NV crystallographic orientations (each one with two possible +2 + +NV vs. VN configuration) and to the higher concentration of other impurities compared to the +single NV case in ultra-pure diamond substrate.10 Even though a single NV center offers nanoscale +spatial resolution, NV ensembles are a common solution in sensing applications since they allow +to improve the signal-to-noise ratio (which ideally scales as 1/ +√ +N, N being the number of NV +centers involved), even if the sensitivity typically remains below the theoretical shot-noise limited +sensitivity.11,12 +Here, we present a comprehensive sensing-oriented open source simulation tool that computes +the ODMR spectrum from NV ensembles under arbitrary applied electric and magnetic fields. The +two possible orientations for the nitrogen and the vacancy along a certain crystallographic direction +are accounted for. Analytical expressions are essential for understanding the physics of a system, +but they are also typically obtained under simplifying hypotheses not always met in the experiment. +Our simulation tool offers an easy way to interpret ODMR spectra: the user may choose to inspect +one individual NV or all orientations together and can thereby conveniently assess new sensing +schemes. Special attention is dedicated to the CW-ODMR shot noise sensitivity under varying +experimental settings (e.g. magnitude and direction of a bias magnetic field), thus helping the +user to optimize the sensing scheme in a specific scenario. The simulation is based on < 100 > +oriented diamond containing 12C and 14N isotopes. Different situations (e.g. < 111 > surfaces +or implanted 15N) can easily be implemented by the user into the open-source code. Moreover, +the code is most relevant under the condition of low-to-moderate magnetic field, B < 100 G. Our +choice of approximations and their range of validity are described further in the paper. +After providing the necessary theoretical background and describing the open-source code (Sec. +2), we present some application examples in the context of electric field sensing (Sec. 3-4). In +particular, the impact of both the direction and magnitude of a bias magnetic field on the electric +field sensitivity is discussed. This information is essential for the optimal design of an experiment +or a sensing device and for the correct interpretation of experimental results. Moreover, we present +a novel electric-field sensing scheme with NV ensemble that is based on the alignment of a bias +magnetic field orthogonal to two NV families and allows to retrieve the whole vector information. +A quantitative study of this new configuration would not be possible without solving the full +Hamiltonian as our code is doing. +3 + +2 +Methods +The code we developed is written in Python, and can be accessed and downloaded here https: +//github.com/chris-galland/NV-ODMR-simulation. In this section we provide the necessary +theoretical background and detail its main features. More technical details can be found directly +in the code. Note that we did not aim to include all possible physical interactions and variations +of configurations (e.g. nitrogen and carbon isotopes, diamond cut angle, etc.) into the simula- +tion; however, the interested users can further extend its functionalities, based on their specific +requirements. +2.1 +From single NV Hamiltonian to ODMR spectrum +Given an NV center, we define the NV reference frame by a direct orthonormal coordinate system +(x, y, z), where z is along the NV major symmetry axis (also simply referred to as NV axis) and +points from the nitrogen atom to the vacancy. The x axis belongs to one of the defect’s three +symmetry planes containing a carbon atom neighbouring the vacancy, see Fig. 1a. In the following, +we will decompose the fields of interest into parallel (∥) and transverse (⊥) components with respect +to the NV axis. The ground state spin Hamiltonian of an NV center can be written as:1,13 +ˆHtot = ˆHel + ˆHnuc +(1) +where ˆHel refers to the electronic spin Hamiltonian and ˆHnuc to the hyperfine interaction between +the NV electron spin and the nitrogen nuclear spin. In the natural electronic spin-triplet basis +{|ms = −1⟩, |ms = 0⟩, |ms = 1⟩} and in the presence of an external magnetic field ⃗B and electric +field ⃗E, ˆHel can be written as: +1 +h +ˆHel = (Dgs + d∥Ez) +� +ˆS2 +z − 2 +3 +� ++ γNV ⃗B · ˆ⃗S − d⊥Ex( ˆS2 +x − ˆS2 +y) + d⊥Ey( ˆSx ˆSy + ˆSy ˆSx) +(2) +where Dgs is the temperature-dependent zero field splitting (Dgs = 2.870 GHz at room tempera- +ture), γNV = µB +h ·gNV = 2.80 MHz/G is the gyromagnetic ratio, h is the Planck constant, µB is the +Bohr magneton. Additionally, d∥ = 0.35 Hz cmV−1 and d⊥ = 17 Hz cmV−1 are the electric-field +coupling strengths for parallel and transverse components. Note that d⊥ is about 50 times larger +4 + +than d∥, offering correspondingly larger sensitivity to the electric field component normal to the +NV axis. ˆ⃗S = ( ˆSx, ˆSy, ˆSz) is the total electronic spin operator; since for NV centers the total spin +is S = 1, the three operators can be expressed in matrix form as: +ˆSx = +1 +√ +2 +� +� +� +� +� +� +0 +1 +0 +1 +0 +1 +0 +1 +0 +� +� +� +� +� +� +; ˆSy = +1 +√ +2 +� +� +� +� +� +� +0 +−i +0 +i +0 +−i +0 +i +0 +� +� +� +� +� +� +; ˆSz = +1 +√ +2 +� +� +� +� +� +� +1 +0 +0 +0 +0 +0 +0 +0 +−1 +� +� +� +� +� +� +(3) +Strain in the diamond lattice can also be accounted for in ˆHel in the form of an effective electric +field.14,15 +In the case of a 14N nucleus, the contribution ˆHnuc to the hyperfine electronic level structure +can be written as: +1 +h +ˆHnuc = A∥ ˆSz ˆIz + A⊥( ˆSx ˆIx + ˆSy ˆIy) + P +� +ˆI2 +z − 2 +3 +� ++ γN ⃗B · ˆ⃗I +(4) +where A∥ = −2.14 MHz and A⊥ = −2.7 MHz are the 14N axial and transverse magnetic hyperfine +parameters respectively, P = −4.95 MHz is the nuclear quadrupole parameter and γN = µB +h ·gN = +0.31 kHz/G is the nuclear gyromagnetic ratio (gN = 0.404 is the nuclear g-factor and µN the +nuclear magneton). +ˆ⃗I = (ˆIx, ˆIy, ˆIz) is the nuclear spin operator of 14N. Since the total nuclear +spin is I = 1, the Pauli matrices of the cartesian operators in the natural nuclear spin basis +{|mI = −1⟩, |mI = 0⟩, |mI = 1⟩} are exactly the same as reported in Eq. 3. The extension to 15N +nucleus, which has spin I = 1 +2, could be easily implemented by replacing the matrix for nuclear spin +operator and deleting the nuclear quadrupole interaction term since only nuclei with spin I ≥ 1 +may possess electric quadrupole moments. +In the code, the computation of the electronic energy levels in presence of external fields is +straightforward and consists in diagonalizing the complete Hamiltonian in Eq. 1 and extracting +its eigenvalues. The corresponding eigenvectors are represented in the natural spin basis states: +|ms, mI⟩, where ms = 0, ±1 and mI = 0, ±1 refer to the z−projection of the electronic and nuclear +spin respectively. +In CW-ODMR, the spin transitions are probed by sweeping the applied MW field frequency that +interacts with the magnetic dipole moment of the NV center,16,17 see Fig. 1d. In order to reproduce +5 + +𝑑⊥𝐸⊥ +2𝛾𝑁𝑉𝐵∥ +𝐵∥ +a +C +C +N +X +Y +Z +C +V +𝜑𝑀𝑊 +b +c +d +C +C +N +X +Y +Z +C +V +C +C +N +X +Y +Z +C +C +C +Z +C +Y +X +N +V +𝐸⊥ +𝐸⊥ +V +Figure 1: (a) Left panel: Atomic structure of the NV center and its three reflection planes, with the chosen +coordinate system (x, y, z) . Right panel: Computed spin transition strength spectrum without any applied +static field nor strain, at room temperature, assuming an electronic spin transition linewidth δ = 0.3 MHz +(corresponding to T ∗ +2 = 1.1 µs). The hyperfine structure due to the 14N nuclear spin is clearly visible. (b) +Transition strength spectrum in the presence of a static magnetic field (B = 1.8 G) aligned along z. (c) +Transition strength spectrum in the presence of an electric field (E⊥ = 4 · 107 V/m) in the xy plane (no +magnetic field applied). (d) Transition strength spectrum for two different MW linear polarisations lying in +the xy plane (φMW = 0, π/2 with respect to x). An electric field (E⊥ = 4·106 V/m) with the same direction +as in (c) is applied in this case. +6 + +20 +(a.u.) +Transition Strength +15 +10 +5 +0 +2862 +2864 +2866 +2868 +2870 +2872 +2874 +2876 +2878 +Freguency (MHz)10 +Transition Strength (a.u.) +8 +6 +4 +2 +0 +2862 +2864 +2866 +2868 +2870 +2872 +2874 +2876 +2878 +Freguency (MHz)3.0 +(a. +2.0 +1.5 +Transition +1.0 +0.5 +0.0 +2862 +2864 +2866 +2868 +2870 +2872 +2874 +2876 +2878 +Freguency(MHz) Strength (a.u.) +2.0 +1.5 +Transition +1.0 +0.5 +0.0 +2862 +2864 +2866 +2868 +2870 +2872 +2874 +2876 +2878 +Freguency (MHz)the CW-ODMR spectrum, our code models the coupling of a linearly polarized MW magnetic field +⃗BMW = (BMW +x +, BMW +y +, BMW +z +) to the electronic and nuclear spin through the following interaction +Hamiltonian, denoted as ˆHint : +1 +h +ˆHint = γNV ⃗BMW · ˆ⃗S + γN ⃗BMW · ˆ⃗I +(5) +Note that arbitrary MW polarization can be implemented into the code by considering a complex +MW magnetic field vector ⃗BMW .18 The above interaction Hamiltonian induces transitions between +an initial eigenstate |i⟩ of energy Ei = hνi and a final eigenstate |f⟩ of energy Ef = hνf. The +magnetic dipole transition probability between these states is calculated as: +Ti,f ∝ |⟨f| ˆHint|i⟩|2 +(6) +Within the program, we assume that the transition between |i⟩ and |f⟩ has a Lorentzian shape, +with amplitude given by Ti,f and linewidth δ.18 This linewidth depends on the specific experimental +conditions (diamond growth, laser and MW power, etc.) and is given to the code as an input +parameter. The frequency-dependent transition amplitude between the state |i⟩ and the state |f⟩, +induced by the MW with frequency ν is thus: +Ti,f(ν) = +Ti,fδ2 +4 +� +(ν − |νf − νi|)2 + δ2 +4 +� +(7) +Eventually, the total transition strength for a given MW frequency is obtained by summing +over all possible initial and final states: T(ν) = � +i,f Ti,f(ν). Since ms = ±1 and ms = 0 exhibit +different PL intensities, the transition strength T(ν) is proportional to the ODMR contrast. Note +that this is true only in the low magnetic field regime (B < 100 G), which our study is limited +to. Higher magnetic fields induce mixing of the excited states and therefore we cannot assume +anymore that T is proportional to the ODMR contrast. In this case, a model including decay and +pumping rates between each ground, excited and metastable state is needed to reproduce the PL +and ODMR response.19 +To conclude this section, we briefly summarize the influence of external fields on the transition +strength spectrum. Examples of the final computed spectra in different conditions that illustrate +7 + +these influences are shown in Fig. 1. The ground state energy level structure without any perturba- +tion is shown in Fig. 1a. It is dominated by zero field splitting (Dgs = 2.87 GHz) and the hyperfine +interaction due to the 14N nucleus that breaks the degeneracy of the mI = 0, ±1 states, leading to +a characteristic triplet of peaks. +A magnetic field acts on the level structure through the Zeeman effect. In particular, in presence +of an axial ⃗B field, the Zeeman splitting is proportional to the axial component of the field (Fig. 1b), +which is the basis for most magnetic sensing protocols developed in the recent years.4,12,20 +Experimentally, the Stark shift induced by an electric field is more difficult to observe due to +the smaller coupling constants.21,22 An axial electric field shifts all |ms = ±1⟩ states with respect +to the state |ms = 0⟩ by d∥Ez. On the other hand, a transverse electric field makes the electronic +Hamiltonian Hel non-diagonal, which results in mixing of states |ms = ±1⟩. In the absence of +magnetic field, the new eigenvectors are: +|−⟩ = +1 +√ +2(eiφE|ms = +1⟩ + |ms = −1⟩) +|+⟩ = +1 +√ +2(eiφE|ms = +1⟩ − |ms = −1⟩) +(8) +with φE = arctan(Ex/Ey). Correspondingly, the energy levels present a splitting in the central +resonance proportional to E⊥, as illustrated in Fig. 1c. Stark shift has been used to image electric +fields7,21–23 as well as local strain and stress,24–26 both with single NV and ensembles. Noteworthy, +in diamond with high NV concentration, a central splitting can be observed even in absence of +external electric fields, due to local electric fields caused by surrounding NV centers and other spin +impurities27 as well as lattice strain.28 The combined influence of magnetic and electric field is +more complex, and is discussed in Sec. 3. +Finally, the linear MW polarization has an influence on the amplitudes of allowed transitions. +In particular, in the presence of an effective electric field only, an analytical expression for these +amplitudes can be derived. For a MW magnetic field orthogonal to the NV axis and with polar +angle φMW , the transition amplitude between |ms = 0⟩ and |±⟩ eigenstates introduced above is +given by:18,27 +T0,± ∝ (1 − cos(2φMW + φE)) +(9) +8 + +This is illustrated in Fig. 1d, where for mI = 0 states (inner hyperfine states, indicated by black +arrows) the transition amplitude at lower frequency is completely suppressed for φMW = 0 and +the upper frequency transition has maximal amplitude, whereas it is the opposite for φMW = π/2. +Note that the proportionality factor omitted in Eq. 9 depends on the transverse component of +the MW field (transition amplitude is maximized for completely transverse ⃗BMW ) and is different +for the different nuclear spin states mI. The dependence on linear polarization has been used to +reconstruct local effective electric fields (with possible contributions from strain) for single NV +centers.18,27 +The presence of a magnetic field also contributes to the MW polarization dependence, in par- +ticular adding a phase that depends on φB to the cosine term in Eq. 9.18 Deriving an analytical +expression for the combined influence of electric and magnetic field on MW polarization response +is beyond the scope of our discussion. However, this aspect can be explored numerically using our +code. +2.2 +From single NV to NV ensembles +c +a +b +𝑁𝑉1 +𝑁𝑉2 +𝑁𝑉3 +𝑁𝑉4 +y +𝑁𝑉1 +𝑁𝑉2 +𝑁𝑉3 +V +V +V z +N +x +𝑍𝐿 +𝑋𝐿 +𝑌𝐿 +V +𝑁𝑉4 +Figure 2: (a) NV reference frame (x, y, z) vs. lab frame (XL, YL, ZL) for the most usual (100) oriented +diamond crystals; z points along the N-to-V direction. (b) Schematic of the four possible NV orientations +inside the diamond crystal lattice. (c) Transition strength spectrum in the presence of a static magnetic field +(B = 18 G) whose direction is chosen such that all resonances are clearly resolved. There are 3 × 8 peaks +corresponding to the four different NV orientations: each giving rise to two non-degenerate electronic spin +transitions (ms = 0 to ±1) and each with three hyperfine transitions. +The ground state Hamiltonian for a single NV center, Eq. 1, is defined in the NV reference frame. +However, we typically deal with external fields whose direction is expressed in the laboratory frame +9 + + Strength (a.u. +2.0 +1.5 +1.0 +0.5 +0.01 +2820 +2840 +2860 +2880 +2900 +2920 +Freguency (MHz)(XL, YL, ZL), see Fig. 2a. For ease of use, our code employs polar rather than cartesian coordinates +to express external fields. +When dealing with NV ensembles, each NV center is aligned along one of the 4 possible crystallo- +graphic axes (Fig. 2b, upper panel). The four possible NV orientations, named as NVi, i = 1, 2, 3, 4, +are typically equally present (and each one presents two possible directions, NV and VN); excep- +tions are under particular growth conditions leading to preferential orientation along one axis.29–31 +In the code, we assume the NV centers equally distributed among the 4 possible crystallographic +axes, but different situations can be easily implemented by weighting the contributions accordingly. +In order to compute the energy levels and the corresponding transition strength spectra for an NV +ensemble, we proceed in three main steps: +1. The input fields ( ⃗E and ⃗B), given in polar coordinates in the laboratory frame, are converted +into the different NVi frames. The same holds for the MW field used to probe the spin transitions. +The relation between the laboratory and the NVi reference systems depends on the diamond surface +considered. In our case we assume the most commonly used < 100 > surface. Different cases can be +implemented changing the transformation matrices accordingly (or applying an additional global +transformation). +2. +The Hamiltonian in each NVi frame is numerically diagonalized and the corresponding +transition strength spectrum obtained using the procedure explained for the single NV case (See +Sec. 2.1 ). +3. +The transition strength spectra corresponding to the different NVi frames are summed +together, obtaining the complete spectrum. +Referring to Fig. 2a, the transformation matrices between the laboratory frame and the different +NVi frames are given by: +TNV1 = +� +� +� +� +� +� +−1/ +√ +6 +1/ +√ +6 +−2/ +√ +6 +−1/ +√ +2 +−1/ +√ +2 +0 +−1/ +√ +3 +1/ +√ +3 +1/ +√ +3 +� +� +� +� +� +� +TNV2 = +� +� +� +� +� +� +1/ +√ +6 +1/ +√ +6 +2/ +√ +6 +1/ +√ +2 +−1/ +√ +2 +0 +1/ +√ +3 +1/ +√ +3 +−1/ +√ +3 +� +� +� +� +� +� +10 + +TNV3 = +� +� +� +� +� +� +−1/ +√ +6 +−1/ +√ +6 +2/ +√ +6 +−1/ +√ +2 +1/ +√ +2 +0 +−1/ +√ +3 +−1/ +√ +3 +−1/ +√ +3 +� +� +� +� +� +� +TNV4 = +� +� +� +� +� +� +1/ +√ +6 +−1/ +√ +6 +−2/ +√ +6 +1/ +√ +2 +1/ +√ +2 +0 +1/ +√ +3 +−1/ +√ +3 +1/ +√ +3 +� +� +� +� +� +� +Further, as illustrated in Fig. 3a, given a certain crystallographic axis there are two possible +arrangements for the nitrogen atom and the vacancy, that we refer to as NV and VN. In typical +growth conditions we can assume these two configurations to be equally present. In their respective +reference frame, as defined in Sec. 2.1, VN and NV centers experience opposite fields (i.e. for a +magnetic field: +⃗BV N = − ⃗BNV ). +A closer look at Eq. 2 reveals that the Hamiltonian remains +identical upon a simultaneous change ⃗B → − ⃗B and ms = ±1 → ∓1. Thus, NV and VN respond in +an identical way to an external magnetic field. A similar argument can be made for a longitudinal +electric field. However, a transverse electric field breaks this inversion symmetry and has a different +contribution on the two configurations. +This fact can be appreciated in Fig. 3b and c, where we report the transition strength spectrum +for NV and VN configurations in the presence of external fields. Fig. 3b corresponds to the spectrum +in presence of a transverse magnetic field (B⊥ = 20 G): in this case the two curves perfectly overlap, +confirming that NV and VN response is identical. Fig. 3c corresponds to the spectrum in presence +of an electric field transverse to the NV axis (a bias static magnetic field B⊥ = 20 G is applied in the +same direction): the two configurations show different splitting widths, confirming that considering +both NV and VN is essential.32 To fully model NV ensemble within our code, we thus compute the +transition strength spectrum for both NV and VN arrangements, and sum them to obtain the final +spectrum. The full transition strength spectrum per defect center T(ν) is obtained by summing +the contribution of NV and VN for all 4 NV orientations. To correctly model the contribution +of each NV axis and direction to the PL, we divide by the total number of configurations (i.e 8). +The resulting spectrum is illustrated in Fig. 2c in the presence of an external magnetic field. The +direction of magnetic field was chosen in order to allow each NV orientation to be resolved. +11 + +𝜑𝐸 +𝜑𝐸 +Z +x +y +y +𝐸⊥ +Z +x +𝐸⊥ +C +C +E +Z +x +C +V +N +C +C +C +a +𝜑𝐸 +b +y +E +𝜑𝐸 +C +C +Z +x +C +V +N +C +C +C +y +𝐸⊥ +𝐸⊥ +c +𝐵⊥ +𝐵⊥ +Figure 3: (a) Two possible configurations for a given NV axis with their respective reference frames. (b) +Transition strength spectrum containing equal contributions from both NV and VN under an applied static +magnetic field (B⊥ = 20 G) perpendicular to the NV axis. The solid curves corresponding to NV and VN +are perfectly overlapping. The dashed curve indicates the summation of both contributions. (c) Transition +strength spectrum of both NV and VN defects under an applied combination of static electric field (Ebot = +1 · 107 V/m) and static magnetic field (B⊥ = 20 G) perpendicular to the NV axis. The projection of NV +and VN with 3 carbon atoms next to the nitrogen are plotted. In the NV frame the applied electric field +makes an angle φE with respect to x axis resulting in frequency upshift (orange line). The same electric field +vector in the VN frame has a different azimuthal angle resulting in frequency downshift (blue line). +12 + +12 +VN +Transition Strength (a.u.) +10 +VN +NV+VN +8 +6 +4 +2 +0 +2868 +2869 +2870 +2871 +2872 +2873 +2874 +2875 +2876 +Freguency (MHz)VN +Transition Strength (a.u.) +NV +NV+VN +2868 +2869 +2870 +2871 +2872 +2873 +2874 +2875 +2876 +Freguency (MHz)3 +Optimization of electric field sensing +In this section, we illustrate how our code can be used to optimize the sensitivity of electric field +measurements using an NV ensemble. We start with a short general discussion on electric field +sensing with a single NV center. For the sake of simplicity, we neglect the effect of strain and local +stray electric fields. The standard sensing scheme for electric fields relies on a bias magnetic field +applied orthogonal to the NV axis, typically of a few tens of Gauss.21,22,33 In this way, the Zeeman +shift is suppressed and the eigenstates become sensitive to electric fields while being decoupled from +longitudinal magnetic noise. The effect of electric field is maximal on states with mI = 0. In the +presence of both an electric field ⃗E and a transverse magnetic field ⃗B⊥, the transition frequencies +for this sub-ensemble of states are:17,21 +f± +� +⃗E, ⃗B⊥ +� += Dgs + d∥Ez + 2Λ ± +� +d2 +⊥E2 +⊥ − 2Λd⊥E⊥ cos φ + Λ2 +(10) +where Ez and E⊥ are the electric field components respectively longitudinal and transverse to the +NV axis, Λ = γ2 +NV B2 +⊥/2Dgs and φ = 2φB + φE, with φB,E the polar angle of ⃗B⊥ and ⃗E in the +transverse plane (see Fig.4a). Note that for states with mI = ±1, the hyperfine interaction acts +as a small longitudinal magnetic field, hence reducing the sensitivity to electric fields. Taking into +account that d∥ ≪ d⊥, the influence of longitudinal electric field is much weaker than transverse +ones, and in realistic experiments precise sensing of Ez is not possible. In the following we ignore +Ez and focus on transverse electric fields. +We distinguish three regimes of electric fields: (i) weak fields, with d⊥E ≪ Λ, +��A∥ +�� (typically +E ≲ 105 V/m) ; (ii) moderate fields (105 V/m ≲ E < 5 · 107 V/m) ; and (iii) strong fields, +d⊥E > +��A∥ +�� , Λ (E > 5 · 107 V/m). +Even though case (i) requires the best sensitivity and is the most explored case with single +NV,7,21,34,35 cases (ii) and (iii) are still relevant in various contexts.22,23,32 In particular, E field +sensing with NV ensemble may be limited to moderate and strong fields due to the presence of +local electric fields and inhomogenous strain that might screen weak E fields. +In case (i), only states with mI = 0 are affected by ⃗E. Moreover, Eq. 10 can be approximated +as f±( ⃗E⊥, ⃗B⊥) ≈ Dgs +(2±1)Λ∓d⊥E⊥ cos φ, from which it appears that the electric field-induced +13 + +shift of the transitions is independent of | ⃗B⊥|, but is maximal for φ = 2φB + φE = 0 or π. As a +consequence, the B field direction defines the axis of optimal sensing. +In case (ii), Eq. 10 can still be used to compute the transitions frequencies for mI = 0 states. +However, other hyperfine transitions can no longer be ignored, and optimal sensitivity conditions +might deviate from single-transition analytical predictions from Eq. 10. This case is illustrated in +Fig. 4a, which presents the transition amplitudes for a single NV center versus transverse magnetic +field, for E = 5 · 106 V/m, φE = π/4 and φB = 0. We notice that for B > 40 G the inner and outer +transitions begin to merge due to their non-zero linewidth. For simplicity, we consider unpolarized +microwave excitation for the moment. +In order to estimate the sensitivity to electric field for a given B value, we compute the differ- +ential spectrum ∆S(ν) = ∆T(ν)/∆E, with ∆T(ν) = T(ν, ⃗E + ∆ ⃗E, ⃗B) − T(ν, ⃗E, ⃗B) and ∆E ≪ E. +∆S is proportional to the variation of photoluminescence intensity caused by a change of electric +field, thus it is inversely proportional to the usual sensitivity η as defined for example in Ref.12 +In the following we refer to ∆S as sensitivity, which we thus aim to maximize. The differential +spectrum corresponding to Fig. 4a is presented in Fig. 4b, and the extrema of ∆S are presented in +Fig. 4c. Unlike in the weak E case, we observe a non-monotonous sensitivity when increasing B, +with even a drop to 0 expected around 30 G, and a maximal sensitivity obtained when the hyperfine +transitions are merging. When the lines are merged, the sensitivity saturates. It is important to +note that an increase by a factor 2 is also expected in the weak E case when the hyperfine transi- +tions are degenerate (e.g. for B ≳ 50 G with a 1 MHz linewidth), since the transition amplitude is +also increased by a factor 2. +Finally, we note that for strong E fields, i.e. case (iii), hyperfine transitions are degenerate +for any value of B. In this case, Eq. 10 is again relevant. A particular case is d⊥E ≫ Λ, for +which Eq. 10 can be approximated as f±( ⃗E⊥, ⃗B⊥) ≈ Dgs + (2 ∓ cos φ)Λ ± d⊥E⊥. In particular, the +sensitivity is then completely independent of ⃗B, both for its magnitude and direction. +We have seen that even with a single NV center, there exist regimes where analytical formulas +can hardly be applied, and a numerical simulation approach might be necessary for sensitivity +optimization. We now consider electric field sensing with NV ensembles. +Let us assume that a bias field ⃗B is applied orthogonal to a single NV orientation, e.g. NV1. +Thus, all other NVs have Zeeman splitting dominating over Stark shift, and their transition energies +14 + +𝐵⊥ +f +c +d +V +NV1 +NV2 +NV4 +NV3 +V +V +N +V +E +e +E +z +x +V +𝜑𝐸 +y +N +𝐸⊥ +a +b +𝐵⊥ +T(a.u.) +(a.u.) +T(a.u.) +∆𝑆 +(a.u.) +∆𝑆 +Figure 4: Electric field sensitivity optimization with (a-c) a single NV and (d-f) an ensemble. (a) Transition +strength spectrum versus static magnetic field amplitude B. (b) Electric field sensitivity ∆S versus B. (c) +Optimal values of the sensitivity (maximum: solid line; minimum (absolute value): dashed line) of ∆S, +over MW frequency ω, for each B value. +⃗B, ⃗E are orthogonal to the NV axis, with φB = 0, φE = π/4 +and E = 5 · 106 V/m. δ = 1 MHz. MW is unpolarized, with MW field ⃗BMW orthogonal to NV axis. +∆E = 1 · 105 V/m. (d-f) Same plots for an NV ensemble when the MW field is linearly polarized with ⃗BMW +orthogonal to NV1 axis, and φMW = π/2 in NV1 frame. Values for ⃗B, ⃗E are unchanged. +15 + +80 +0.04 +60 +0.02 +40 +0.00 +B +-0.02 +20 +-0.04 +0 - +2860 +2870 +2880 +2890 +Frequency (MHz)80 +60 +B +20 +- 0 +0.0 +0.1 +Sensitivity (arb. units)5580 +- +60 +@ 40 +B +20 - ++0 +0.00 +0.02 +0.04 +Sensitivity (arb. units)080 +5 +-09 +4 +3 +40 - +B +2 +20 - +1 +0 - +2860 +2870 +2880 +2890 +Frequency (MHz)80 +10 +-09 +8 +6 +40 - +B +4 +20 - +2 +2860 +2870 +2880 +2890 +Frequency (MHz)80 +0.15 +0.10 +60 +0.05 +0.00 +B +-0.05 +20 +-0.10 +-0 +-0.15 +2860 +2870 +2880 +2890 +Frequency (MHz)are well separated from the E-sensitive orientation, see Fig. 4d. We consider a linewidth of 1 MHz, +well-representative of NV ensemble. Fig. 4(d-f) presents the transition amplitude and corresponding +sensitivity calculations performed with same ⃗B, ⃗E in NV1 frame as in panels (a-c). To illustrate +how the MW polarization degree of freedom can be exploited for sensitivity optimization, we now +consider linearly polarized MW. The MW field is set orthogonal to NV1 axis, with φMW = π/2. +The main difference with the single NV case is due to the contribution from VN-aligned centers, +which results in up to 8 non-degenerate transitions just for NV1 orientation, thus complicating +the identification of each transition. Additionally, the polarized microwave causes an imbalance +in amplitude between upper and lower frequency transitions, particularly visible for B > 30 G. +Eventually, the sensitivity to electric field, shown in Fig. 4e, is completely different from the single +NV case (Fig. 4b). This illustrates that a thorough analysis with our code is needed in order to +optimize the sensing scheme with NV ensembles. In this precise case, optimal sensitivity is reached +for a magnetic field around B = 60 G. Around this value of B, the chosen MW polarization direction +allows to selectively excite only the lower frequency transition, with transition strength twice as +big as in the unpolarized case. The sensitivity, in turn, is increased by a factor 2. Interestingly, the +microwave frequency for which maximum signal variation is expected is around 2880 MHz, between +two hyperfine transitions. +a +c +b +T(a.u.) +(a.u.) +∆𝑆 +Figure 5: (a) Transition strength spectrum versus misalignement angle δθB away from the plane normal to +NV1 (θB = π/2 in NV1 frame). (b) Corresponding sensitivity ∆S versus δθB. (c) Absolute maximum (solid) +and minimum (dashed line) of ∆S versus δθB. The configuration is identical to Fig. 4(d-f), with B = 60 G +. +To conclude this section, we briefly discuss the influence of bias magnetic field misalignment on +the electric field sensing sensitivity. Fig. 5 illustrates how sensitivity is affected when ⃗B is rotated +out of the plane normal to the NV axis. It is clearly seen that sensitivity drops quickly even for a +16 + +2 +B +0 +60 +-2 : +-4 +0.00 +0.02 +0.04 +Sensitivity (arb. units)4 +0.04 +2 +0.02 +60B ( +0 +0.00 +-2 +-0.02 +-0.04 +-4 - +2870 +2880 +2890 +2900 +Frequency (MHz)3.0 +4 +2.5 +2 - +2.0 +60B ( +-0 +1.5 +-2 - +1.0 +0.5 +-4 - +2870 +2880 +2890 +2900 +Frequency (MHz)few degree of misalignment. This is due to the Zeeman shift induced by the longitudinal component +Bz when B is misaligned slightly out-of-plane (see Fig. 5a). Note that this also illustrates that +in an NV ensemble, the NV orientations different from the chosen E-sensitive one (i.e those with +non-orthogonal bias magnetic field ⃗B) are almost completely insensitive to electric field. +4 +Full vector electometry with a single ODMR spectrum +We now propose a new scheme for the full determination of the electric field vector using a single +value of bias magnetic field ⃗B. The scheme considered in the previous section only allows to extract +the magnitude of ⃗E in the plane normal to a single NV orientation. In theory, an ensemble ODMR +spectrum, with up to 8x3 resonances, contains enough information to extract ⃗E,23 but as already +mentioned, the ratio d∥/d⊥ ≪ 1 leads to significant uncertainty in the longitudinal component Ez. +Thus, the most common solution for vector electrometry is to use several directions of magnetic field +bias ⃗B: rotating ⃗B in the normal plane allows to identify the transverse vector direction, i.e polar +angle φE,21,34,35 and the longitudinal component Ez can be obtained by aligning ⃗B orthogonal to a +second NV orientation.32 However, it can be cumbersome and time consuming to modify the bias +magnetic field in experiments. In Ref.,27 the authors used another approach: they took advantage +of the dependence of transition strength on linear microwave polarization to determine φE, using +the relation from Eq. 9. +Our proposed scheme builds on their approach: the bias magnetic field ⃗B is chosen orthogonal +to 2 NV orientations simultaneously, e.g., along < 011 > as illustrated in Fig. 6a. Consequently, +2 NV orientations become E-sensitive (NV2, NV4). The ODMR spectrum presents two sets of +resonance around 2870 MHz, due to the two different transverse components of ⃗E for the 2 chosen +NV orientations, see Fig. 6b. The transition amplitude versus linear polarization angle φMW is +presented in Fig. 6c, where the MW field is polarized orthogonal to < 001 > direction. φMW = 0 +corresponds to polarization along XL in the lab frame, φMW = π/2 along YL, and so on. For two +transition energies associated with the two different NV orientations, the evolution of transition +amplitude is periodic, with an offset that is different in the two cases. Note that the rotation of +the MW polarization is not normal to any of the 2 NV axis, so strictly speaking the dependence +on φMW is not sinusoidal. Nevertheless, the simulation allows to extract φE for the two transverse +17 + +B +V 𝑁𝑉4 +𝑁𝑉4 +𝑁𝑉4 +𝑁𝑉2 +𝑁𝑉3 +V +V +N +𝑁𝑉1 +V +𝑁𝑉2 +d +a +b +c +T(a.u.) +Figure 6: (a) Geometric configuration for our vector electrometry scheme. To illustrate our method, we +choose a bias magnetic field ⃗B along the < 011 > direction, normal to the plane containing NV4 and NV2. +We set B = 20 G, electric field ⃗E = (45, 15, −15) · 106 V/m, in laboratory coordinate frame, and MW field +orthogonal to ZL direction (θMW = π/2). (b) Transition strength spectrum for linearly polarized MW with +φMW = 0, where φMW is defined with respect to XL. (c) Transition spectrum versus MW polarization angle +φMW . (d) Transition strength versus φMW , at the lower frequency transition associated with NV4 (blue) +and NV2 (orange), as identified in (b) by the two vertical dotted lines. +18 + +Amplitude (arb. units) +1.5 +1.0 +0.5 +0.0 +2850 +2860 +2870 +2880 +2890 +2900 +Frequency (MHz)2.0 +2.0 +1.5 +1.5 +1.0 - +1.0 +0.5 - +0.5 +0.0 +2850 +2860 +2870 +2880 +2890 +2900 +Frequency (MHz)Amplitude (arb. units) +2.0 +1.5 +1.0 +0.5 +0.0 +0.0 +0.5 +1.0 +1.5 +2.0 +MW Polarization angle Φ/πprojections. For example, in Fig. 6d, the maximal transition amplitude for NV4 (blue line) is at +φMW = π/6. Using Eq. 9, and taking into account the correct offset in φMW due to our arbitrary +choice of φMW = 0 along XL, we get φE = π/3, which is precisely the value of φE in the frame of +NV4 for the chosen ⃗E = (45, 15, −15)·106 V/m (expressed in laboratory coordinate frame). Having +determined the amplitude and direction of ⃗E⊥ in one NV frame, the only unknown is Ez in the +same NV frame: we have restricted the possible solutions for vector ⃗E to a single line. Eventually, +the knowledge of the transverse projection vector in the two NV axes combines into a unique vector +⃗E, at the intersection of the two lines of solution associated with the two axes. Thus, the electric +field vector can be determined unambiguously. The advantage of our methods is that, with proper +design of the MW antenna, rotation of the linear MW polarization can be achieved all-electrically,36 +with much faster timescale than a change of magnetic field. +5 +Conclusion +To conclude, in this work we developed an open-source Python based code (accessible at https: +//github.com/chris-galland/NV-ODMR-simulation) to compute the NV electronic energy levels +and the corresponding ODMR spectrum in presence of external magnetic and electric fields. This +code is a convenient tool to explore how the ODMR spectrum varies with different parameters +of interest (e.g. fields intensity and direction or linewidth), for both single NV and ensembles of +them. In particular, having the NV sensing application in mind, we focused on the sensitivity +computation. Optimizing the sensitivity with respect to the experimental conditions is not always +straightforward: even with a single NV center, there exist regimes where analytical formulas can +hardly be applied, and a numerical simulation is necessary. With our code we try to meet this +need. In particular, sensitivity maps can be simulated under varying experimental parameters, +thus facilitating the working point optimization and allowing for the development of new sensing +schemes. +In the second part of the paper, we showed how our code can provide new insights into electric +field sensing and we suggested a novel electrometry scheme, which relaxes the effort on dynamic +bias magnetic fields alignment. On the one hand, we discussed electric field sensing in different +regimes, presenting sensitivity maps and exploring the impact of experimental imperfections, like +19 + +the misalignement of the bias magnetic field. +On the other hand, we showed how full vector +electrometry using an NV ensemble is possible without having to dynamically re-align the bias +magnetic field in different directions. Our method is based on the change of ODMR amplitudes +with MW polarization angle and only requires a properly designed antenna. This method will allow +to significantly decrease the experimental complexity and speed up the measurement. Finally, we +believe that our open source code will help students and researchers explore the physics of NV +center ensembles, optimize quantum sensors based on them, and generalise the simulation to other +color centers. +Acknowledgement +This project has received funding from the Swiss National Science Foundation (grants No. 198898 +and 204036) and from EPFL Interdisciplinary Seed Fund. +References +(1) Doherty, M. W.; Manson, N. B.; Delaney, P.; Jelezko, F.; Wrachtrup, J.; Hollenberg, L. C. +The nitrogen-vacancy colour centre in diamond. Physics Reports 2013, 528, 1–45. +(2) Budker, D.; Romalis, M. Optical magnetometry. Nature physics 2007, 3, 227–234. +(3) Schirhagl, R.; Chang, K.; Loretz, M.; Degen, C. L. Nitrogen-vacancy centers in diamond: +nanoscale sensors for physics and biology. Annual review of physical chemistry 2014, 65, +83–105. +(4) Casola, F.; Van Der Sar, T.; Yacoby, A. Probing condensed matter physics with magnetometry +based on nitrogen-vacancy centres in diamond. Nature Reviews Materials 2018, 3, 1–13. +(5) Radtke, M.; Bernardi, E.; Slablab, A.; Nelz, R.; Neu, E. Nanoscale sensing based on nitrogen +vacancy centers in single crystal diamond and nanodiamonds: achievements and challenges. +Nano Futures 2019, 3, 042004. +(6) Ho, K. O.; Shen, Y.; Pang, Y. Y.; Leung, W. K.; Zhao, N.; Yang, S. Diamond quantum +20 + +sensors: from physics to applications on condensed matter research. Functional Diamond +2022, 1, 160–173. +(7) Qiu, Z.; Hamo, A.; Vool, U.; Zhou, T. X.; Yacoby, A. Nanoscale electric field imaging with an +ambient scanning quantum sensor microscope. npj Quantum Information 2022, 8, 107. +(8) Vandersypen, L. M.; Chuang, I. L. NMR techniques for quantum control and computation. +Reviews of modern physics 2005, 76, 1037. +(9) Jensen, K.; Acosta, V.; Jarmola, A.; Budker, D. Light narrowing of magnetic resonances in +ensembles of nitrogen-vacancy centers in diamond. Physical Review B 2013, 87, 014115. +(10) Matsuzaki, Y.; Morishita, H.; Shimooka, T.; Tashima, T.; Kakuyanagi, K.; Semba, K.; +Munro, W.; Yamaguchi, H.; Mizuochi, N.; Saito, S. Optically detected magnetic resonance +of high-density ensemble of NV- centers in diamond. Journal of Physics: Condensed Matter +2016, 28, 275302. +(11) Bauch, E.; Singh, S.; Lee, J.; Hart, C. A.; Schloss, J. M.; Turner, M. J.; Barry, J. F.; +Pham, L. M.; Bar-Gill, N.; Yelin, S. F.; others Decoherence of ensembles of nitrogen-vacancy +centers in diamond. Physical Review B 2020, 102, 134210. +(12) Barry, J. F.; Schloss, J. M.; Bauch, E.; Turner, M. J.; Hart, C. A.; Pham, L. M.; +Walsworth, R. L. Sensitivity optimization for NV diamond magnetometry. Reviews of Modern +Physics 2020, 92, 015004. +(13) Gali, ´A. Ab initio theory of the nitrogen-vacancy center in diamond. Nanophotonics 2019, 8, +1907–1943. +(14) Udvarhelyi, P.; Shkolnikov, V. O.; Gali, A.; Burkard, G.; P´alyi, A. Spin-strain interaction in +nitrogen-vacancy centers in diamond. Phys. Rev. B 2018, 98, 075201. +(15) Barson, M. S. J. et al. Nanomechanical Sensing Using Spins in Diamond. Nano Letters 2017, +17, 1496–1503. +(16) Dobrovitski, V.; Fuchs, G.; Falk, A.; Santori, C.; Awschalom, D. Quantum control over single +spins in diamond. Annu. Rev. Condens. Matter Phys. 2013, 4, 23–50. +21 + +(17) Doherty, M.; Dolde, F.; Fedder, H.; Jelezko, F.; Wrachtrup, J.; Manson, N.; Hollenberg, L. +Theory of the ground-state spin of the NV- center in diamond. Physical Review B 2012, 85, +205203. +(18) K¨olbl, J.; Kasperczyk, M.; B¨urgler, B.; Barfuss, A.; Maletinsky, P. Determination of intrinsic +effective fields and microwave polarizations by high-resolution spectroscopy of single nitrogen- +vacancy center spins. New Journal of Physics 2019, 21, 113039. +(19) Tetienne, J.-P.; Rondin, L.; Spinicelli, P.; Chipaux, M.; Debuisschert, T.; Roch, J.-F.; +Jacques, V. Magnetic-field-dependent photodynamics of single NV defects in diamond: an +application to qualitative all-optical magnetic imaging. New Journal of Physics 2012, 14, +103033. +(20) Rondin, L.; Tetienne, J.-P.; Hingant, T.; Roch, J.-F.; Maletinsky, P.; Jacques, V. Magne- +tometry with nitrogen-vacancy defects in diamond. Reports on progress in physics 2014, 77, +056503. +(21) Dolde, F.; Fedder, H.; Doherty, M. W.; N¨obauer, T.; Rempp, F.; Balasubramanian, G.; +Wolf, T.; Reinhard, F.; Hollenberg, L. C.; Jelezko, F.; others Electric-field sensing using single +diamond spins. Nature Physics 2011, 7, 459–463. +(22) Michl, J.; Steiner, J.; Denisenko, A.; Bulau, A.; Zimmermann, A.; Nakamura, K.; Sumiya, H.; +Onoda, S.; Neumann, P.; Isoya, J.; others Robust and accurate electric field sensing with solid +state spin ensembles. Nano letters 2019, 19, 4904–4910. +(23) Broadway, D. A.; Dontschuk, N.; Tsai, A.; Lillie, S. E.; Lew, C.-K.; McCallum, J. C.; John- +son, B.; Doherty, M.; Stacey, A.; Hollenberg, L.; others Spatial mapping of band bending in +semiconductor devices using in situ quantum sensors. Nature Electronics 2018, 1, 502–507. +(24) Trusheim, M. E.; Englund, D. Wide-field strain imaging with preferentially aligned nitrogen- +vacancy centers in polycrystalline diamond. New Journal of Physics 2016, 18, 123023. +(25) Kehayias, P.; Turner, M. J.; Trubko, R.; Schloss, J. M.; Hart, C. A.; Wesson, M.; Glenn, D. R.; +Walsworth, R. L. Imaging crystal stress in diamond using ensembles of nitrogen-vacancy +centers. Phys. Rev. B 2019, 100, 174103. +22 + +(26) Barfuss, A.; Kasperczyk, M.; K¨olbl, J.; Maletinsky, P. Spin-stress and spin-strain coupling in +diamond-based hybrid spin oscillator systems. Physical Review B 2019, 99, 174102. +(27) Mittiga, T.; Hsieh, S.; Zu, C.; Kobrin, B.; Machado, F.; Bhattacharyya, P.; Rui, N.; Jar- +mola, A.; Choi, S.; Budker, D.; others Imaging the local charge environment of nitrogen- +vacancy centers in diamond. Physical review letters 2018, 121, 246402. +(28) Levchenko, A.; Vasil’Ev, V.; Zibrov, S.; Zibrov, A.; Sivak, A.; Fedotov, I. Inhomogeneous +broadening of optically detected magnetic resonance of the ensembles of nitrogen-vacancy +centers in diamond by interstitial carbon atoms. Applied Physics Letters 2015, 106, 102402. +(29) Michl, J.; Teraji, T.; Zaiser, S.; Jakobi, I.; Waldherr, G.; Dolde, F.; Neumann, P.; Do- +herty, M. W.; Manson, N. B.; Isoya, J.; others Perfect alignment and preferential orientation of +nitrogen-vacancy centers during chemical vapor deposition diamond growth on (111) surfaces. +Applied Physics Letters 2014, 104, 102407. +(30) Pham, L. M.; Bar-Gill, N.; Le Sage, D.; Belthangady, C.; Stacey, A.; Markham, M.; +Twitchen, D.; Lukin, M. D.; Walsworth, R. L. Enhanced metrology using preferential ori- +entation of nitrogen-vacancy centers in diamond. Physical Review B 2012, 86, 121202. +(31) Edmonds, A.; D’Haenens-Johansson, U.; Cruddace, R.; Newton, M.; Fu, K.-M.; Santori, C.; +Beausoleil, R.; Twitchen, D.; Markham, M. Production of oriented nitrogen-vacancy color +centers in synthetic diamond. Physical Review B 2012, 86, 035201. +(32) Yang, B.; Murooka, T.; Mizuno, K.; Kim, K.; Kato, H.; Makino, T.; Ogura, M.; Yamasaki, S.; +Schmidt, M. E.; Mizuta, H.; others Vector electrometry in a wide-gap-semiconductor device +using a spin-ensemble quantum sensor. Physical Review Applied 2020, 14, 044049. +(33) Li, R.; Kong, F.; Zhao, P.; Cheng, Z.; Qin, Z.; Wang, M.; Zhang, Q.; Wang, P.; Wang, Y.; +Shi, F.; others Nanoscale electrometry based on a magnetic-field-resistant spin sensor. Physical +Review Letters 2020, 124, 247701. +(34) Doherty, M. W.; Michl, J.; Dolde, F.; Jakobi, I.; Neumann, P.; Manson, N. B.; Wrachtrup, J. +Measuring the defect structure orientation of a single NV- centre in diamond. New Journal of +Physics 2014, 16, 063067. +23 + +(35) Barson, M. S.; Oberg, L. M.; McGuinness, L. P.; Denisenko, A.; Manson, N. B.; Wrachtrup, J.; +Doherty, M. W. Nanoscale vector electric field imaging using a single electron spin. Nano +Letters 2021, 21, 2962–2967. +(36) Staacke, R.; John, R.; Kneiß, M.; Osterkamp, C.; Diziain, S.; Jelezko, F.; Grundmann, M.; +Meijer, J. Method of full polarization control of microwave fields in a scalable transparent +structure for spin manipulation. Journal of Applied Physics 2020, 128, 194301. +24 + diff --git a/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/load_file.txt b/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..372f93134ed8e8c73632873644ac07b9b6ca315b --- /dev/null +++ b/ddE2T4oBgHgl3EQfxAhM/content/tmp_files/load_file.txt @@ -0,0 +1,1183 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf,len=1182 +page_content='Simulation of ODMR Spectra from Nitrogen-Vacancy Ensembles in Diamond for Electric Field Sensing Yuchun Zhu,∗,† Elena Losero,†,‡ Christophe Galland,†,¶ and Valentin Goblot†,¶ †Institute of Physics, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland ‡Division of Quantum Metrology and Nanotechnologies, Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy ¶Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland E-mail: yuchun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='zhu@epfl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='ch Abstract Solid state spins in diamond, in particular negatively charged nitrogen-vacancy centers (NV), are leading contenders in the field of quantum sensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' While ad- dressing of single NVs offers nanoscale spatial resolution, many implementations benefit from using large ensembles to increase signal magnitude and therefore sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, sensing with ensembles brings its own challenges given the random orientation of the spin quantization axis within the diamond crystal lat- tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Here, we present an open source simulation tool that models the influence of arbitrary electric and magnetic fields on the electronic and nuclear spin states of NV ensembles, and can be extended to other color centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Specifically, the code computes the transition strengths and predicts the sensitivity under shot-noise- limited optically-detected magnetic resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We illustrate the use of the code in the context of electric field sensing, a promising emerging functionality of NV centers with applications in biosensing and electronics, and bring several subtle features to light that are due to the interplay between different NV orientations and the external electric and microwave fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Moreover, we show that our code can be used to optimize sensitivity in situations where usual arguments based on 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04106v1 [quant-ph] 10 Jan 2023 neglecting terms in the full Hamiltonian would give sub-optimal results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Finally, we propose a novel sensing scheme which allows to perform full vector electrome- try without the need for precise bias magnetic field alignment, thus reducing the experimental complexity and speeding up the measurement procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' keywords: nitrogen-vacancy (NV) centers, diamond, optically detected magnetic resonance (ODMR) spectroscopy, electric field sensing, numerical simulation, quantum metrology 1 Introduction In recent years negatively charged nitrogen-vacancy (NV) centers in diamond, consisting of a nearest-neighbor pair of a substitutional nitrogen atom and a lattice vacancy (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1a), have at- tracted a lot of attention for their long spin coherence times and favorable optical properties, making them promising candidates for quantum sensing and quantum information processing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1 Their nanoscale resolution, bio-compatibility, long coherence time even at room temperature and technical simplicity underpin their widespread use in quantum sensing – notably for magnetic field, but also for electric field, temperature and strain sensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2–7 NV centers sensing capabilities are based on optical preparation and readout of their spin states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The energy level structure depends on the NV center environment and can be probed through optically detected magnetic resonance (ODMR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The easiest approach is to continuously excite the sample, both optically (with green light) and with a coherent microwave field (MW), while collecting the photoluminescence (PL) signal (at red and near infrared wavelengths).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In this work, we typically refer to this technique, named as continuous-wave (CW) ODMR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' More advanced pulsed techniques can be used to improve the sensitivity and are reviewed for example in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='8 The spin transition spectra computed by our code can be used as input for further modeling in such contexts as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' An ODMR spectrum provides much information, such as the direction and the magnitude of a magnetic and electric fields at the NV center position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, the presence of local intrinsic fields (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' due to strain), paramagnetic impurities, surface defects or unknown sample properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' random orientations of the NV centers), adds difficulties on the interpretation of the acquired ODMR spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='9 Moreover, due to the interplay between the different quantities, the optimal sensing configuration is not always obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The complexity is increased while using NV ensembles, due to the presence of all the 4 possible NV crystallographic orientations (each one with two possible 2 NV vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' VN configuration) and to the higher concentration of other impurities compared to the single NV case in ultra-pure diamond substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='10 Even though a single NV center offers nanoscale spatial resolution, NV ensembles are a common solution in sensing applications since they allow to improve the signal-to-noise ratio (which ideally scales as 1/ √ N, N being the number of NV centers involved), even if the sensitivity typically remains below the theoretical shot-noise limited sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='11,12 Here, we present a comprehensive sensing-oriented open source simulation tool that computes the ODMR spectrum from NV ensembles under arbitrary applied electric and magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The two possible orientations for the nitrogen and the vacancy along a certain crystallographic direction are accounted for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Analytical expressions are essential for understanding the physics of a system, but they are also typically obtained under simplifying hypotheses not always met in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Our simulation tool offers an easy way to interpret ODMR spectra: the user may choose to inspect one individual NV or all orientations together and can thereby conveniently assess new sensing schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Special attention is dedicated to the CW-ODMR shot noise sensitivity under varying experimental settings (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' magnitude and direction of a bias magnetic field), thus helping the user to optimize the sensing scheme in a specific scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The simulation is based on < 100 > oriented diamond containing 12C and 14N isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Different situations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' < 111 > surfaces or implanted 15N) can easily be implemented by the user into the open-source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Moreover, the code is most relevant under the condition of low-to-moderate magnetic field, B < 100 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Our choice of approximations and their range of validity are described further in the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' After providing the necessary theoretical background and describing the open-source code (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2), we present some application examples in the context of electric field sensing (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3-4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, the impact of both the direction and magnitude of a bias magnetic field on the electric field sensitivity is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This information is essential for the optimal design of an experiment or a sensing device and for the correct interpretation of experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Moreover, we present a novel electric-field sensing scheme with NV ensemble that is based on the alignment of a bias magnetic field orthogonal to two NV families and allows to retrieve the whole vector information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A quantitative study of this new configuration would not be possible without solving the full Hamiltonian as our code is doing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3 2 Methods The code we developed is written in Python, and can be accessed and downloaded here https: //github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='com/chris-galland/NV-ODMR-simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In this section we provide the necessary theoretical background and detail its main features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' More technical details can be found directly in the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that we did not aim to include all possible physical interactions and variations of configurations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' nitrogen and carbon isotopes, diamond cut angle, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') into the simula- tion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' however, the interested users can further extend its functionalities, based on their specific requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1 From single NV Hamiltonian to ODMR spectrum Given an NV center, we define the NV reference frame by a direct orthonormal coordinate system (x, y, z), where z is along the NV major symmetry axis (also simply referred to as NV axis) and points from the nitrogen atom to the vacancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The x axis belongs to one of the defect’s three symmetry planes containing a carbon atom neighbouring the vacancy, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the following, we will decompose the fields of interest into parallel (∥) and transverse (⊥) components with respect to the NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The ground state spin Hamiltonian of an NV center can be written as:1,13 ˆHtot = ˆHel + ˆHnuc (1) where ˆHel refers to the electronic spin Hamiltonian and ˆHnuc to the hyperfine interaction between the NV electron spin and the nitrogen nuclear spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the natural electronic spin-triplet basis {|ms = −1⟩, |ms = 0⟩, |ms = 1⟩} and in the presence of an external magnetic field ⃗B and electric field ⃗E, ˆHel can be written as: 1 h ˆHel = (Dgs + d∥Ez) � ˆS2 z − 2 3 � + γNV ⃗B · ˆ⃗S − d⊥Ex( ˆS2 x − ˆS2 y) + d⊥Ey( ˆSx ˆSy + ˆSy ˆSx) (2) where Dgs is the temperature-dependent zero field splitting (Dgs = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='870 GHz at room tempera- ture), γNV = µB h ·gNV = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='80 MHz/G is the gyromagnetic ratio, h is the Planck constant, µB is the Bohr magneton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Additionally, d∥ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='35 Hz cmV−1 and d⊥ = 17 Hz cmV−1 are the electric-field coupling strengths for parallel and transverse components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that d⊥ is about 50 times larger 4 than d∥, offering correspondingly larger sensitivity to the electric field component normal to the NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ˆ⃗S = ( ˆSx, ˆSy, ˆSz) is the total electronic spin operator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' since for NV centers the total spin is S = 1, the three operators can be expressed in matrix form as: ˆSx = 1 √ 2 � � � � � � 0 1 0 1 0 1 0 1 0 � � � � � � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ˆSy = 1 √ 2 � � � � � � 0 −i 0 i 0 −i 0 i 0 � � � � � � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ˆSz = 1 √ 2 � � � � � � 1 0 0 0 0 0 0 0 −1 � � � � � � (3) Strain in the diamond lattice can also be accounted for in ˆHel in the form of an effective electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='14,15 In the case of a 14N nucleus, the contribution ˆHnuc to the hyperfine electronic level structure can be written as: 1 h ˆHnuc = A∥ ˆSz ˆIz + A⊥( ˆSx ˆIx + ˆSy ˆIy) + P � ˆI2 z − 2 3 � + γN ⃗B · ˆ⃗I (4) where A∥ = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='14 MHz and A⊥ = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='7 MHz are the 14N axial and transverse magnetic hyperfine parameters respectively, P = −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='95 MHz is the nuclear quadrupole parameter and γN = µB h ·gN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='31 kHz/G is the nuclear gyromagnetic ratio (gN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='404 is the nuclear g-factor and µN the nuclear magneton).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ˆ⃗I = (ˆIx, ˆIy, ˆIz) is the nuclear spin operator of 14N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Since the total nuclear spin is I = 1, the Pauli matrices of the cartesian operators in the natural nuclear spin basis {|mI = −1⟩, |mI = 0⟩, |mI = 1⟩} are exactly the same as reported in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The extension to 15N nucleus, which has spin I = 1 2, could be easily implemented by replacing the matrix for nuclear spin operator and deleting the nuclear quadrupole interaction term since only nuclei with spin I ≥ 1 may possess electric quadrupole moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the code, the computation of the electronic energy levels in presence of external fields is straightforward and consists in diagonalizing the complete Hamiltonian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1 and extracting its eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The corresponding eigenvectors are represented in the natural spin basis states: |ms, mI⟩, where ms = 0, ±1 and mI = 0, ±1 refer to the z−projection of the electronic and nuclear spin respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In CW-ODMR, the spin transitions are probed by sweeping the applied MW field frequency that interacts with the magnetic dipole moment of the NV center,16,17 see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In order to reproduce 5 𝑑⊥𝐸⊥ 2𝛾𝑁𝑉𝐵∥ 𝐵∥ a C C N X Y Z C V 𝜑𝑀𝑊 b c d C C N X Y Z C V C C N X Y Z C C C Z C Y X N V 𝐸⊥ 𝐸⊥ V Figure 1: (a) Left panel: Atomic structure of the NV center and its three reflection planes, with the chosen coordinate system (x, y, z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Right panel: Computed spin transition strength spectrum without any applied static field nor strain, at room temperature, assuming an electronic spin transition linewidth δ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 MHz (corresponding to T ∗ 2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1 µs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The hyperfine structure due to the 14N nuclear spin is clearly visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Transition strength spectrum in the presence of a static magnetic field (B = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='8 G) aligned along z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Transition strength spectrum in the presence of an electric field (E⊥ = 4 · 107 V/m) in the xy plane (no magnetic field applied).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (d) Transition strength spectrum for two different MW linear polarisations lying in the xy plane (φMW = 0, π/2 with respect to x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' An electric field (E⊥ = 4·106 V/m) with the same direction as in (c) is applied in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 6 20 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') Transition Strength 15 10 5 0 2862 2864 2866 2868 2870 2872 2874 2876 2878 Freguency (MHz)10 Transition Strength (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') 8 6 4 2 0 2862 2864 2866 2868 2870 2872 2874 2876 2878 Freguency (MHz)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 Transition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 2862 2864 2866 2868 2870 2872 2874 2876 2878 Freguency(MHz) Strength (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 Transition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 2862 2864 2866 2868 2870 2872 2874 2876 2878 Freguency (MHz)the CW-ODMR spectrum, our code models the coupling of a linearly polarized MW magnetic field ⃗BMW = (BMW x , BMW y , BMW z ) to the electronic and nuclear spin through the following interaction Hamiltonian, denoted as ˆHint : 1 h ˆHint = γNV ⃗BMW · ˆ⃗S + γN ⃗BMW · ˆ⃗I (5) Note that arbitrary MW polarization can be implemented into the code by considering a complex MW magnetic field vector ⃗BMW .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='18 The above interaction Hamiltonian induces transitions between an initial eigenstate |i⟩ of energy Ei = hνi and a final eigenstate |f⟩ of energy Ef = hνf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The magnetic dipole transition probability between these states is calculated as: Ti,f ∝ |⟨f| ˆHint|i⟩|2 (6) Within the program, we assume that the transition between |i⟩ and |f⟩ has a Lorentzian shape, with amplitude given by Ti,f and linewidth δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='18 This linewidth depends on the specific experimental conditions (diamond growth, laser and MW power, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') and is given to the code as an input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The frequency-dependent transition amplitude between the state |i⟩ and the state |f⟩, induced by the MW with frequency ν is thus: Ti,f(ν) = Ti,fδ2 4 � (ν − |νf − νi|)2 + δ2 4 � (7) Eventually, the total transition strength for a given MW frequency is obtained by summing over all possible initial and final states: T(ν) = � i,f Ti,f(ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Since ms = ±1 and ms = 0 exhibit different PL intensities, the transition strength T(ν) is proportional to the ODMR contrast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that this is true only in the low magnetic field regime (B < 100 G), which our study is limited to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Higher magnetic fields induce mixing of the excited states and therefore we cannot assume anymore that T is proportional to the ODMR contrast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In this case, a model including decay and pumping rates between each ground, excited and metastable state is needed to reproduce the PL and ODMR response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='19 To conclude this section, we briefly summarize the influence of external fields on the transition strength spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Examples of the final computed spectra in different conditions that illustrate 7 these influences are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The ground state energy level structure without any perturba- tion is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' It is dominated by zero field splitting (Dgs = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='87 GHz) and the hyperfine interaction due to the 14N nucleus that breaks the degeneracy of the mI = 0, ±1 states, leading to a characteristic triplet of peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A magnetic field acts on the level structure through the Zeeman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, in presence of an axial ⃗B field, the Zeeman splitting is proportional to the axial component of the field (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1b), which is the basis for most magnetic sensing protocols developed in the recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='4,12,20 Experimentally, the Stark shift induced by an electric field is more difficult to observe due to the smaller coupling constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='21,22 An axial electric field shifts all |ms = ±1⟩ states with respect to the state |ms = 0⟩ by d∥Ez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' On the other hand, a transverse electric field makes the electronic Hamiltonian Hel non-diagonal, which results in mixing of states |ms = ±1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the absence of magnetic field, the new eigenvectors are: |−⟩ = 1 √ 2(eiφE|ms = +1⟩ + |ms = −1⟩) |+⟩ = 1 √ 2(eiφE|ms = +1⟩ − |ms = −1⟩) (8) with φE = arctan(Ex/Ey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Correspondingly, the energy levels present a splitting in the central resonance proportional to E⊥, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Stark shift has been used to image electric fields7,21–23 as well as local strain and stress,24–26 both with single NV and ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Noteworthy, in diamond with high NV concentration, a central splitting can be observed even in absence of external electric fields, due to local electric fields caused by surrounding NV centers and other spin impurities27 as well as lattice strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='28 The combined influence of magnetic and electric field is more complex, and is discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Finally, the linear MW polarization has an influence on the amplitudes of allowed transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, in the presence of an effective electric field only, an analytical expression for these amplitudes can be derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For a MW magnetic field orthogonal to the NV axis and with polar angle φMW , the transition amplitude between |ms = 0⟩ and |±⟩ eigenstates introduced above is given by:18,27 T0,± ∝ (1 − cos(2φMW + φE)) (9) 8 This is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1d, where for mI = 0 states (inner hyperfine states, indicated by black arrows) the transition amplitude at lower frequency is completely suppressed for φMW = 0 and the upper frequency transition has maximal amplitude, whereas it is the opposite for φMW = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that the proportionality factor omitted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 9 depends on the transverse component of the MW field (transition amplitude is maximized for completely transverse ⃗BMW ) and is different for the different nuclear spin states mI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The dependence on linear polarization has been used to reconstruct local effective electric fields (with possible contributions from strain) for single NV centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='18,27 The presence of a magnetic field also contributes to the MW polarization dependence, in par- ticular adding a phase that depends on φB to the cosine term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='18 Deriving an analytical expression for the combined influence of electric and magnetic field on MW polarization response is beyond the scope of our discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, this aspect can be explored numerically using our code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 From single NV to NV ensembles c a b 𝑁𝑉1 𝑁𝑉2 𝑁𝑉3 𝑁𝑉4 y 𝑁𝑉1 𝑁𝑉2 𝑁𝑉3 V V V z N x 𝑍𝐿 𝑋𝐿 𝑌𝐿 V 𝑁𝑉4 Figure 2: (a) NV reference frame (x, y, z) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' lab frame (XL, YL, ZL) for the most usual (100) oriented diamond crystals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' z points along the N-to-V direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Schematic of the four possible NV orientations inside the diamond crystal lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Transition strength spectrum in the presence of a static magnetic field (B = 18 G) whose direction is chosen such that all resonances are clearly resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' There are 3 × 8 peaks corresponding to the four different NV orientations: each giving rise to two non-degenerate electronic spin transitions (ms = 0 to ±1) and each with three hyperfine transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The ground state Hamiltonian for a single NV center, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 1, is defined in the NV reference frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, we typically deal with external fields whose direction is expressed in the laboratory frame 9 Strength (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='01 2820 2840 2860 2880 2900 2920 Freguency (MHz)(XL, YL, ZL), see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For ease of use, our code employs polar rather than cartesian coordinates to express external fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' When dealing with NV ensembles, each NV center is aligned along one of the 4 possible crystallo- graphic axes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2b, upper panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The four possible NV orientations, named as NVi, i = 1, 2, 3, 4, are typically equally present (and each one presents two possible directions, NV and VN);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' excep- tions are under particular growth conditions leading to preferential orientation along one axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='29–31 In the code, we assume the NV centers equally distributed among the 4 possible crystallographic axes, but different situations can be easily implemented by weighting the contributions accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In order to compute the energy levels and the corresponding transition strength spectra for an NV ensemble, we proceed in three main steps: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The input fields ( ⃗E and ⃗B), given in polar coordinates in the laboratory frame, are converted into the different NVi frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The same holds for the MW field used to probe the spin transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The relation between the laboratory and the NVi reference systems depends on the diamond surface considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In our case we assume the most commonly used < 100 > surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Different cases can be implemented changing the transformation matrices accordingly (or applying an additional global transformation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The Hamiltonian in each NVi frame is numerically diagonalized and the corresponding transition strength spectrum obtained using the procedure explained for the single NV case (See Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The transition strength spectra corresponding to the different NVi frames are summed together, obtaining the complete spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Referring to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' the transformation matrices between the laboratory frame and the different ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='NVi frames are given by: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='TNV1 = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−2/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='TNV2 = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='TNV3 = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='TNV4 = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−2/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='−1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='Further,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3a, given a certain crystallographic axis there are two possible arrangements for the nitrogen atom and the vacancy, that we refer to as NV and VN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In typical growth conditions we can assume these two configurations to be equally present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In their respective reference frame, as defined in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1, VN and NV centers experience opposite fields (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' for a magnetic field: ⃗BV N = − ⃗BNV ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A closer look at Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2 reveals that the Hamiltonian remains identical upon a simultaneous change ⃗B → − ⃗B and ms = ±1 → ∓1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Thus, NV and VN respond in an identical way to an external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A similar argument can be made for a longitudinal electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, a transverse electric field breaks this inversion symmetry and has a different contribution on the two configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This fact can be appreciated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3b and c, where we report the transition strength spectrum for NV and VN configurations in the presence of external fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3b corresponds to the spectrum in presence of a transverse magnetic field (B⊥ = 20 G): in this case the two curves perfectly overlap, confirming that NV and VN response is identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 3c corresponds to the spectrum in presence of an electric field transverse to the NV axis (a bias static magnetic field B⊥ = 20 G is applied in the same direction): the two configurations show different splitting widths, confirming that considering both NV and VN is essential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='32 To fully model NV ensemble within our code, we thus compute the transition strength spectrum for both NV and VN arrangements, and sum them to obtain the final spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The full transition strength spectrum per defect center T(ν) is obtained by summing the contribution of NV and VN for all 4 NV orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' To correctly model the contribution of each NV axis and direction to the PL, we divide by the total number of configurations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='e 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The resulting spectrum is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2c in the presence of an external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The direction of magnetic field was chosen in order to allow each NV orientation to be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 11 𝜑𝐸 𝜑𝐸 Z x y y 𝐸⊥ Z x 𝐸⊥ C C E Z x C V N C C C a 𝜑𝐸 b y E 𝜑𝐸 C C Z x C V N C C C y 𝐸⊥ 𝐸⊥ c 𝐵⊥ 𝐵⊥ Figure 3: (a) Two possible configurations for a given NV axis with their respective reference frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Transition strength spectrum containing equal contributions from both NV and VN under an applied static magnetic field (B⊥ = 20 G) perpendicular to the NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The solid curves corresponding to NV and VN are perfectly overlapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The dashed curve indicates the summation of both contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Transition strength spectrum of both NV and VN defects under an applied combination of static electric field (Ebot = 1 · 107 V/m) and static magnetic field (B⊥ = 20 G) perpendicular to the NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The projection of NV and VN with 3 carbon atoms next to the nitrogen are plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the NV frame the applied electric field makes an angle φE with respect to x axis resulting in frequency upshift (orange line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The same electric field vector in the VN frame has a different azimuthal angle resulting in frequency downshift (blue line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 12 12 VN Transition Strength (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') 10 VN NV+VN 8 6 4 2 0 2868 2869 2870 2871 2872 2873 2874 2875 2876 Freguency (MHz)VN Transition Strength (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') NV NV+VN 2868 2869 2870 2871 2872 2873 2874 2875 2876 Freguency (MHz)3 Optimization of electric field sensing In this section, we illustrate how our code can be used to optimize the sensitivity of electric field measurements using an NV ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We start with a short general discussion on electric field sensing with a single NV center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For the sake of simplicity, we neglect the effect of strain and local stray electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The standard sensing scheme for electric fields relies on a bias magnetic field applied orthogonal to the NV axis, typically of a few tens of Gauss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='21,22,33 In this way, the Zeeman shift is suppressed and the eigenstates become sensitive to electric fields while being decoupled from longitudinal magnetic noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The effect of electric field is maximal on states with mI = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the presence of both an electric field ⃗E and a transverse magnetic field ⃗B⊥, the transition frequencies for this sub-ensemble of states are:17,21 f± � ⃗E, ⃗B⊥ � = Dgs + d∥Ez + 2Λ ± � d2 ⊥E2 ⊥ − 2Λd⊥E⊥ cos φ + Λ2 (10) where Ez and E⊥ are the electric field components respectively longitudinal and transverse to the NV axis, Λ = γ2 NV B2 ⊥/2Dgs and φ = 2φB + φE, with φB,E the polar angle of ⃗B⊥ and ⃗E in the transverse plane (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that for states with mI = ±1, the hyperfine interaction acts as a small longitudinal magnetic field, hence reducing the sensitivity to electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Taking into account that d∥ ≪ d⊥, the influence of longitudinal electric field is much weaker than transverse ones, and in realistic experiments precise sensing of Ez is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the following we ignore Ez and focus on transverse electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We distinguish three regimes of electric fields: (i) weak fields, with d⊥E ≪ Λ, ��A∥ �� (typically E ≲ 105 V/m) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (ii) moderate fields (105 V/m ≲ E < 5 · 107 V/m) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' and (iii) strong fields, d⊥E > ��A∥ �� , Λ (E > 5 · 107 V/m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Even though case (i) requires the best sensitivity and is the most explored case with single NV,7,21,34,35 cases (ii) and (iii) are still relevant in various contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='22,23,32 In particular, E field sensing with NV ensemble may be limited to moderate and strong fields due to the presence of local electric fields and inhomogenous strain that might screen weak E fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In case (i), only states with mI = 0 are affected by ⃗E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Moreover, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 10 can be approximated as f±( ⃗E⊥, ⃗B⊥) ≈ Dgs +(2±1)Λ∓d⊥E⊥ cos φ, from which it appears that the electric field-induced 13 shift of the transitions is independent of | ⃗B⊥|, but is maximal for φ = 2φB + φE = 0 or π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' As a consequence, the B field direction defines the axis of optimal sensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In case (ii), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 10 can still be used to compute the transitions frequencies for mI = 0 states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' However, other hyperfine transitions can no longer be ignored, and optimal sensitivity conditions might deviate from single-transition analytical predictions from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This case is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4a, which presents the transition amplitudes for a single NV center versus transverse magnetic field, for E = 5 · 106 V/m, φE = π/4 and φB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We notice that for B > 40 G the inner and outer transitions begin to merge due to their non-zero linewidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For simplicity, we consider unpolarized microwave excitation for the moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In order to estimate the sensitivity to electric field for a given B value, we compute the differ- ential spectrum ∆S(ν) = ∆T(ν)/∆E, with ∆T(ν) = T(ν, ⃗E + ∆ ⃗E, ⃗B) − T(ν, ⃗E, ⃗B) and ∆E ≪ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ∆S is proportional to the variation of photoluminescence intensity caused by a change of electric field, thus it is inversely proportional to the usual sensitivity η as defined for example in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='12 In the following we refer to ∆S as sensitivity, which we thus aim to maximize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The differential spectrum corresponding to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4a is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4b, and the extrema of ∆S are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Unlike in the weak E case, we observe a non-monotonous sensitivity when increasing B, with even a drop to 0 expected around 30 G, and a maximal sensitivity obtained when the hyperfine transitions are merging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' When the lines are merged, the sensitivity saturates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' It is important to note that an increase by a factor 2 is also expected in the weak E case when the hyperfine transi- tions are degenerate (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' for B ≳ 50 G with a 1 MHz linewidth), since the transition amplitude is also increased by a factor 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Finally, we note that for strong E fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' case (iii), hyperfine transitions are degenerate for any value of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In this case, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 10 is again relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A particular case is d⊥E ≫ Λ, for which Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 10 can be approximated as f±( ⃗E⊥, ⃗B⊥) ≈ Dgs + (2 ∓ cos φ)Λ ± d⊥E⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, the sensitivity is then completely independent of ⃗B, both for its magnitude and direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We have seen that even with a single NV center, there exist regimes where analytical formulas can hardly be applied, and a numerical simulation approach might be necessary for sensitivity optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We now consider electric field sensing with NV ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Let us assume that a bias field ⃗B is applied orthogonal to a single NV orientation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' NV1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Thus, all other NVs have Zeeman splitting dominating over Stark shift, and their transition energies 14 𝐵⊥ f c d V NV1 NV2 NV4 NV3 V V N V E e E z x V 𝜑𝐸 y N 𝐸⊥ a b 𝐵⊥ T(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') T(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') ∆𝑆 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') ∆𝑆 Figure 4: Electric field sensitivity optimization with (a-c) a single NV and (d-f) an ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (a) Transition strength spectrum versus static magnetic field amplitude B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Electric field sensitivity ∆S versus B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Optimal values of the sensitivity (maximum: solid line;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' minimum (absolute value): dashed line) of ∆S, over MW frequency ω, for each B value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ⃗B, ⃗E are orthogonal to the NV axis, with φB = 0, φE = π/4 and E = 5 · 106 V/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' δ = 1 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' MW is unpolarized, with MW field ⃗BMW orthogonal to NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' ∆E = 1 · 105 V/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (d-f) Same plots for an NV ensemble when the MW field is linearly polarized with ⃗BMW orthogonal to NV1 axis, and φMW = π/2 in NV1 frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Values for ⃗B, ⃗E are unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 15 80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='00 B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 0 - 2860 2870 2880 2890 Frequency (MHz)80 60 B 20 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='1 Sensitivity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' units)5580 60 @ 40 B 20 - +0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 Sensitivity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' units)080 5 09 4 3 40 - B 2 20 - 1 0 - 2860 2870 2880 2890 Frequency (MHz)80 10 09 8 6 40 - B 4 20 - 2 2860 2870 2880 2890 Frequency (MHz)80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='10 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='00 B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='05 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='15 2860 2870 2880 2890 Frequency (MHz)are well separated from the E-sensitive orientation, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We consider a linewidth of 1 MHz, well-representative of NV ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4(d-f) presents the transition amplitude and corresponding sensitivity calculations performed with same ⃗B, ⃗E in NV1 frame as in panels (a-c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' To illustrate how the MW polarization degree of freedom can be exploited for sensitivity optimization, we now consider linearly polarized MW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The MW field is set orthogonal to NV1 axis, with φMW = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The main difference with the single NV case is due to the contribution from VN-aligned centers, which results in up to 8 non-degenerate transitions just for NV1 orientation, thus complicating the identification of each transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Additionally, the polarized microwave causes an imbalance in amplitude between upper and lower frequency transitions, particularly visible for B > 30 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Eventually, the sensitivity to electric field, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4e, is completely different from the single NV case (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This illustrates that a thorough analysis with our code is needed in order to optimize the sensing scheme with NV ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In this precise case, optimal sensitivity is reached for a magnetic field around B = 60 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Around this value of B, the chosen MW polarization direction allows to selectively excite only the lower frequency transition, with transition strength twice as big as in the unpolarized case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The sensitivity, in turn, is increased by a factor 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Interestingly, the microwave frequency for which maximum signal variation is expected is around 2880 MHz, between two hyperfine transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' a c b T(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') ∆𝑆 Figure 5: (a) Transition strength spectrum versus misalignement angle δθB away from the plane normal to NV1 (θB = π/2 in NV1 frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Corresponding sensitivity ∆S versus δθB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Absolute maximum (solid) and minimum (dashed line) of ∆S versus δθB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The configuration is identical to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4(d-f), with B = 60 G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' To conclude this section, we briefly discuss the influence of bias magnetic field misalignment on the electric field sensing sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 5 illustrates how sensitivity is affected when ⃗B is rotated out of the plane normal to the NV axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' It is clearly seen that sensitivity drops quickly even for a 16 2 B 0 60 2 : 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 Sensitivity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' units)4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 60B ( 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='00 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='04 4 - 2870 2880 2890 2900 Frequency (MHz)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 2 - 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 60B ( 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 2 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 4 - 2870 2880 2890 2900 Frequency (MHz)few degree of misalignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This is due to the Zeeman shift induced by the longitudinal component Bz when B is misaligned slightly out-of-plane (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 5a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that this also illustrates that in an NV ensemble, the NV orientations different from the chosen E-sensitive one (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='e those with non-orthogonal bias magnetic field ⃗B) are almost completely insensitive to electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 4 Full vector electometry with a single ODMR spectrum We now propose a new scheme for the full determination of the electric field vector using a single value of bias magnetic field ⃗B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The scheme considered in the previous section only allows to extract the magnitude of ⃗E in the plane normal to a single NV orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In theory, an ensemble ODMR spectrum, with up to 8x3 resonances, contains enough information to extract ⃗E,23 but as already mentioned, the ratio d∥/d⊥ ≪ 1 leads to significant uncertainty in the longitudinal component Ez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Thus, the most common solution for vector electrometry is to use several directions of magnetic field bias ⃗B: rotating ⃗B in the normal plane allows to identify the transverse vector direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='e polar angle φE,21,34,35 and the longitudinal component Ez can be obtained by aligning ⃗B orthogonal to a second NV orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='32 However, it can be cumbersome and time consuming to modify the bias magnetic field in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=',27 the authors used another approach: they took advantage of the dependence of transition strength on linear microwave polarization to determine φE, using the relation from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Our proposed scheme builds on their approach: the bias magnetic field ⃗B is chosen orthogonal to 2 NV orientations simultaneously, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=', along < 011 > as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 6a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Consequently, 2 NV orientations become E-sensitive (NV2, NV4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The ODMR spectrum presents two sets of resonance around 2870 MHz, due to the two different transverse components of ⃗E for the 2 chosen NV orientations, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 6b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The transition amplitude versus linear polarization angle φMW is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 6c, where the MW field is polarized orthogonal to < 001 > direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' φMW = 0 corresponds to polarization along XL in the lab frame, φMW = π/2 along YL, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For two transition energies associated with the two different NV orientations, the evolution of transition amplitude is periodic, with an offset that is different in the two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Note that the rotation of the MW polarization is not normal to any of the 2 NV axis, so strictly speaking the dependence on φMW is not sinusoidal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nevertheless, the simulation allows to extract φE for the two transverse 17 B V 𝑁𝑉4 𝑁𝑉4 𝑁𝑉4 𝑁𝑉2 𝑁𝑉3 V V N 𝑁𝑉1 V 𝑁𝑉2 d a b c T(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=') Figure 6: (a) Geometric configuration for our vector electrometry scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' To illustrate our method, we choose a bias magnetic field ⃗B along the < 011 > direction, normal to the plane containing NV4 and NV2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' We set B = 20 G, electric field ⃗E = (45, 15, −15) · 106 V/m, in laboratory coordinate frame, and MW field orthogonal to ZL direction (θMW = π/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (b) Transition strength spectrum for linearly polarized MW with φMW = 0, where φMW is defined with respect to XL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (c) Transition spectrum versus MW polarization angle φMW .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (d) Transition strength versus φMW , at the lower frequency transition associated with NV4 (blue) and NV2 (orange), as identified in (b) by the two vertical dotted lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 18 Amplitude (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' units) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 2850 2860 2870 2880 2890 2900 Frequency (MHz)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 2850 2860 2870 2880 2890 2900 Frequency (MHz)Amplitude (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' units) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='0 MW Polarization angle Φ/πprojections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' For example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 6d, the maximal transition amplitude for NV4 (blue line) is at φMW = π/6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 9, and taking into account the correct offset in φMW due to our arbitrary choice of φMW = 0 along XL, we get φE = π/3, which is precisely the value of φE in the frame of NV4 for the chosen ⃗E = (45, 15, −15)·106 V/m (expressed in laboratory coordinate frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Having determined the amplitude and direction of ⃗E⊥ in one NV frame, the only unknown is Ez in the same NV frame: we have restricted the possible solutions for vector ⃗E to a single line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Eventually, the knowledge of the transverse projection vector in the two NV axes combines into a unique vector ⃗E, at the intersection of the two lines of solution associated with the two axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Thus, the electric field vector can be determined unambiguously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The advantage of our methods is that, with proper design of the MW antenna, rotation of the linear MW polarization can be achieved all-electrically,36 with much faster timescale than a change of magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 5 Conclusion To conclude, in this work we developed an open-source Python based code (accessible at https: //github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='com/chris-galland/NV-ODMR-simulation) to compute the NV electronic energy levels and the corresponding ODMR spectrum in presence of external magnetic and electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This code is a convenient tool to explore how the ODMR spectrum varies with different parameters of interest (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' fields intensity and direction or linewidth), for both single NV and ensembles of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, having the NV sensing application in mind, we focused on the sensitivity computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Optimizing the sensitivity with respect to the experimental conditions is not always straightforward: even with a single NV center, there exist regimes where analytical formulas can hardly be applied, and a numerical simulation is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' With our code we try to meet this need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In particular, sensitivity maps can be simulated under varying experimental parameters, thus facilitating the working point optimization and allowing for the development of new sensing schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' In the second part of the paper, we showed how our code can provide new insights into electric field sensing and we suggested a novel electrometry scheme, which relaxes the effort on dynamic bias magnetic fields alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' On the one hand, we discussed electric field sensing in different regimes, presenting sensitivity maps and exploring the impact of experimental imperfections, like 19 the misalignement of the bias magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' On the other hand, we showed how full vector electrometry using an NV ensemble is possible without having to dynamically re-align the bias magnetic field in different directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Our method is based on the change of ODMR amplitudes with MW polarization angle and only requires a properly designed antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' This method will allow to significantly decrease the experimental complexity and speed up the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Finally, we believe that our open source code will help students and researchers explore the physics of NV center ensembles, optimize quantum sensors based on them, and generalise the simulation to other color centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Acknowledgement This project has received funding from the Swiss National Science Foundation (grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 198898 and 204036) and from EPFL Interdisciplinary Seed Fund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' References (1) Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Manson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Delaney, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jelezko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wrachtrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hollenberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' The nitrogen-vacancy colour centre in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physics Reports 2013, 528, 1–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (2) Budker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Romalis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Optical magnetometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nature physics 2007, 3, 227–234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (3) Schirhagl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Loretz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Degen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Annual review of physical chemistry 2014, 65, 83–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (4) Casola, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Van Der Sar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yacoby, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nature Reviews Materials 2018, 3, 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (5) Radtke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bernardi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Slablab, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nelz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Neu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nanoscale sensing based on nitrogen vacancy centers in single crystal diamond and nanodiamonds: achievements and challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nano Futures 2019, 3, 042004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (6) Ho, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Shen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Pang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Leung, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zhao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Diamond quantum 20 sensors: from physics to applications on condensed matter research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Functional Diamond 2022, 1, 160–173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (7) Qiu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hamo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Vool, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zhou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yacoby, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nanoscale electric field imaging with an ambient scanning quantum sensor microscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' npj Quantum Information 2022, 8, 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (8) Vandersypen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Chuang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' NMR techniques for quantum control and computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Reviews of modern physics 2005, 76, 1037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (9) Jensen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Acosta, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jarmola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Budker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Light narrowing of magnetic resonances in ensembles of nitrogen-vacancy centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2013, 87, 014115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (10) Matsuzaki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Morishita, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Shimooka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Tashima, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kakuyanagi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Semba, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Munro, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yamaguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Mizuochi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Saito, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Optically detected magnetic resonance of high-density ensemble of NV- centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Journal of Physics: Condensed Matter 2016, 28, 275302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (11) Bauch, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Singh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hart, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Schloss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Turner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Barry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Pham, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bar-Gill, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yelin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Decoherence of ensembles of nitrogen-vacancy centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2020, 102, 134210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (12) Barry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Schloss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bauch, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Turner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hart, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Pham, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Walsworth, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Sensitivity optimization for NV diamond magnetometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Reviews of Modern Physics 2020, 92, 015004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (13) Gali, ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Ab initio theory of the nitrogen-vacancy center in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nanophotonics 2019, 8, 1907–1943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (14) Udvarhelyi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Shkolnikov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Gali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Burkard, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' P´alyi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Spin-strain interaction in nitrogen-vacancy centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B 2018, 98, 075201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (15) Barson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nanomechanical Sensing Using Spins in Diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nano Letters 2017, 17, 1496–1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (16) Dobrovitski, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fuchs, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Falk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Santori, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Awschalom, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Quantum control over single spins in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 2013, 4, 23–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 21 (17) Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Dolde, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fedder, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jelezko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wrachtrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Manson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hollenberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Theory of the ground-state spin of the NV- center in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2012, 85, 205203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (18) K¨olbl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kasperczyk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B¨urgler, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Barfuss, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Maletinsky, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Determination of intrinsic effective fields and microwave polarizations by high-resolution spectroscopy of single nitrogen- vacancy center spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' New Journal of Physics 2019, 21, 113039.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (19) Tetienne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rondin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Spinicelli, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Chipaux, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Debuisschert, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Roch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jacques, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Magnetic-field-dependent photodynamics of single NV defects in diamond: an application to qualitative all-optical magnetic imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' New Journal of Physics 2012, 14, 103033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (20) Rondin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Tetienne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hingant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Roch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Maletinsky, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jacques, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Magne- tometry with nitrogen-vacancy defects in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Reports on progress in physics 2014, 77, 056503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (21) Dolde, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fedder, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' N¨obauer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rempp, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Balasubramanian, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wolf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Reinhard, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hollenberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jelezko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Electric-field sensing using single diamond spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nature Physics 2011, 7, 459–463.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (22) Michl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Steiner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Denisenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bulau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zimmermann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nakamura, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Sumiya, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Onoda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Neumann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Isoya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Robust and accurate electric field sensing with solid state spin ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nano letters 2019, 19, 4904–4910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (23) Broadway, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Dontschuk, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Tsai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Lillie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Lew, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' McCallum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' John- son, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Stacey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hollenberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Spatial mapping of band bending in semiconductor devices using in situ quantum sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nature Electronics 2018, 1, 502–507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (24) Trusheim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Englund, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wide-field strain imaging with preferentially aligned nitrogen- vacancy centers in polycrystalline diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' New Journal of Physics 2016, 18, 123023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (25) Kehayias, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Turner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Trubko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Schloss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hart, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wesson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Glenn, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Walsworth, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Imaging crystal stress in diamond using ensembles of nitrogen-vacancy centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B 2019, 100, 174103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 22 (26) Barfuss, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kasperczyk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' K¨olbl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Maletinsky, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Spin-stress and spin-strain coupling in diamond-based hybrid spin oscillator systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2019, 99, 174102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (27) Mittiga, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Hsieh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kobrin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Machado, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bhattacharyya, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Rui, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jar- mola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Choi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Budker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Imaging the local charge environment of nitrogen- vacancy centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical review letters 2018, 121, 246402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (28) Levchenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Vasil’Ev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zibrov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zibrov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Sivak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fedotov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Inhomogeneous broadening of optically detected magnetic resonance of the ensembles of nitrogen-vacancy centers in diamond by interstitial carbon atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Applied Physics Letters 2015, 106, 102402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (29) Michl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Teraji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zaiser, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jakobi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Waldherr, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Dolde, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Neumann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Do- herty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Manson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Isoya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Perfect alignment and preferential orientation of nitrogen-vacancy centers during chemical vapor deposition diamond growth on (111) surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Applied Physics Letters 2014, 104, 102407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (30) Pham, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Bar-Gill, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Le Sage, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Belthangady, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Stacey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Markham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Twitchen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Lukin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Walsworth, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Enhanced metrology using preferential ori- entation of nitrogen-vacancy centers in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2012, 86, 121202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (31) Edmonds, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' D’Haenens-Johansson, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Cruddace, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Newton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Fu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Santori, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Beausoleil, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Twitchen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Markham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Production of oriented nitrogen-vacancy color centers in synthetic diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review B 2012, 86, 035201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (32) Yang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Murooka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Mizuno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kato, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Makino, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Ogura, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Yamasaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Schmidt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Mizuta, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Vector electrometry in a wide-gap-semiconductor device using a spin-ensemble quantum sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review Applied 2020, 14, 044049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (33) Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kong, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zhao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Cheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Zhang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Shi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' others Nanoscale electrometry based on a magnetic-field-resistant spin sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Physical Review Letters 2020, 124, 247701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (34) Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Michl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Dolde, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jakobi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Neumann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Manson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wrachtrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Measuring the defect structure orientation of a single NV- centre in diamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' New Journal of Physics 2014, 16, 063067.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 23 (35) Barson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Oberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' McGuinness, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Denisenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Manson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Wrachtrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Doherty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nanoscale vector electric field imaging using a single electron spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Nano Letters 2021, 21, 2962–2967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' (36) Staacke, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' John, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Kneiß, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Osterkamp, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Diziain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Jelezko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Grundmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Meijer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Method of full polarization control of microwave fields in a scalable transparent structure for spin manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' Journal of Applied Physics 2020, 128, 194301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} +page_content=' 24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ddE2T4oBgHgl3EQfxAhM/content/2301.04106v1.pdf'} diff --git a/e9E1T4oBgHgl3EQfegRi/content/2301.03207v1.pdf b/e9E1T4oBgHgl3EQfegRi/content/2301.03207v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..fe5fbdd71bb4d78ac7222d5b57cf863aa1979392 --- /dev/null +++ b/e9E1T4oBgHgl3EQfegRi/content/2301.03207v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b0e76f2259a0763ee9d9af96dc7ea6ef687832bd6402defe60b8dbdb4b001c25 +size 665417 diff --git a/e9E1T4oBgHgl3EQfegRi/vector_store/index.pkl b/e9E1T4oBgHgl3EQfegRi/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..05535f1a68f30a25296815b5851bd2926f186eb0 --- /dev/null +++ b/e9E1T4oBgHgl3EQfegRi/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:df724ac97c074e431e7522c8907a43e15990e09a080e420a876841abc0881876 +size 180346 diff --git a/f9E1T4oBgHgl3EQfewTK/content/tmp_files/2301.03211v1.pdf.txt b/f9E1T4oBgHgl3EQfewTK/content/tmp_files/2301.03211v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c702b7533a181cd07b92406fad8371733a97f96 --- /dev/null +++ b/f9E1T4oBgHgl3EQfewTK/content/tmp_files/2301.03211v1.pdf.txt @@ -0,0 +1,807 @@ +Nonlinear Topological Magnon Spin Hall Effect +Zhejunyu Jin1, Xianglong Yao1, Zhenyu Wang1, H. Y. Yuan2, Zhaozhuo Zeng1, Yunshan Cao1, and Peng Yan1∗ +1School of Electronic Science and Engineering and State Key Laboratory of Electronic Thin Films and Integrated Devices, +University of Electronic Science and Technology of China, Chengdu 610054, China +2Institute for Theoretical Physics, Utrecht University, 3584 CC Utrecht, The Netherlands +When a magnon passes through two-dimensional magnetic textures, it will experience a fictitious magnetic +field originating from the 3 × 3 skew-symmetric gauge fields. To date, only one of the three independent +components of the gauge fields has been found to play a role in generating the fictitious magnetic field while the +rest two are perfectly hidden. In this work, we show that they are concealed in the nonlinear magnon transport in +magnetic textures. Without loss of generality, we theoretically study the nonlinear magnon-skyrmion interaction +in antiferromagnets. By analyzing the scattering features of three-magnon processes between the circularly- +polarized incident magnon and breathing skyrmion, we predict a giant Hall angle of both the confluence and +splitting modes. Furthermore, we find that the Hall angle reverses its sign when one switches the handedness +of the incident magnons. We dub it nonlinear topological magnon spin Hall effect. Our findings are deeply +rooted in the bosonic nature of magnons that the particle number is not conserved, which has no counterpart in +low-energy fermionic systems, and may open the door for probing gauge fields by nonlinear means. +Introduction.—Topology dictates the particle or wave trans- +port in many branches of physics, ranging from solid state +physics to geophysics and astrophysics [1, 2]. One outstand- +ing example in condensed matter physics is the intrinsic spin +Hall effect which originates from the momentum-space topol- +ogy, i.e., the Berry curvature of the band structure [3–11]. On +the other hand, non-collinear spin textures, such as the mag- +netic vortex, meron, and skyrmion, can give rise to the real- +space topology. When a spinful particle propagates through +the topological spin texture, it will experience an effective +Lorentz force, resulting in the so-called topological (spin-) +Hall effect [12–17]. +Magnons, quanta of spin waves, are the collective excita- +tions of ordered magnets [18, 19]. Very recently, magnon- +based spintronics has attracted enormous interest due to pecu- +liar advantages of magnons, such as the long-distance trans- +port and low-energy consumption. Magnons carry spin angu- +lar momentum as well, so that they can experience an effective +Lorentz force from the spin texture, leading to the topological +magnon Hall effect [20–24]. In antiferromagnets, magnons +have two degenerate modes with opposite spins, i.e., right- +and left-handed magnons [25]. Therefore, when a magnon +passes through the antiferromagnetic (AFM) skyrmion, for in- +stance, it will experience a spin-dependent Lorentz force, re- +sulting in the topological magnon spin Hall effect [15, 26, 27]. +These topological magnon Hall effects originate from the +gauge fields in transforming the non-collinear magnetic tex- +ture to the collinear state. The gauge transformation generates +the covariant form of the differential operator ∂µ + Aµ with +µ = x, y. Here, the 3×3 skew-symmetric matrix Aµ = R−1∂µR +with the rotation matrix R contains three independent gauge +fields [28, 29]. So far, only one of the three elements, i.e., +Aµ,12, has been identified to play a role in the Hall transport +of magnons while the rest two (Aµ,13 and Aµ,23) are concealed +from the community. +In the past few years, the nonlinear Hall effect due to the +momentum-space topology, e.g., Berry curvature dipole, has +attracted much attention [30–41]. However, its counterpart +induced by the real-space topology has not been reported till +now. It is well known that the geometric phase derived from +the adiabatic evolution is crucial for the Hall transport. No- +tably, in the three-wave mixing process, the accumulation of +adiabatic geometric phase takes place not only on incident +waves but also on nonlinear ones [42–44]. One thus expects +that magnons generated in the nonlinear three-magnon pro- +cess in spin textures [45–51] may also experience a topologi- +cal Hall effect subject to the conventional gauge field, but it is +not clear whether the rest two gauge fields play any role. +In this Letter, we aim to reveal the concealed gauge fields +by addressing the nonlinear Hall transport of magnons in spin +textures. To this end, we theoretical study the nonlinear inter- +action between polarized magnons and magnetic skyrmions +in antiferromagnets. We show that the two long-sought gauge +fields are actually hidden in the nonlinear magnon transport. +By analyzing the “bunny ears” scattering pattern of three- +magnon processes between the circularly-polarized magnon +and breathing skyrmion in an antiferromagnet, we discover a +giant Hall angle of both confluence and splitting modes. The +Hall angle reverses its sign when one switches the handedness +of incident AFM magnons. We dub it nonlinear topological +magnon spin Hall effect. Our findings are deeply connected +to both the nonconservation of magnon number and the spin- +texture-induced Berry curvature in real space, as shown in Fig. +1. +Model.—Let us consider a chiral antiferromagnet described +by the following Lagrangian [16] +L = +� +(∂tl)2dr − H, +(1) +where l is the normalized N´eel vector and H = +� �J(∇l)2 + +Dl · (∇ × l) − Kl2 +z +�dr is the system Hamiltonian including the +exchange energy, Dzyaloshinskii-Moriya interaction (DMI), +and magnetic anisotropy, with J, D, and K being the ex- +change stiffness, DMI strength, and anisotropy coefficient, re- +spectively. To facilitate the analysis, we use the 3 × 3 ma- +trix R =exp(φLz)exp(θLy) to rotate the z−axis to the equi- +arXiv:2301.03211v1 [cond-mat.mes-hall] 9 Jan 2023 + +2 +FIG. 1: Schematic illustration of the nonlinear topological magnon +spin Hall effect in magnon-AFM skyrmion scattering. +Circles +with arrows indicate the handedness of AFM magnons. Incident, +skyrmion breathing, sum-frequency, and difference-frequency modes +are denoted by black, green, red, and blue colors, respectively. vs,p,q +represent the velocity of three propagating magnon wavepackets. +The bottom panel shows the magnon splitting (left) and confluence +(right) processes. It is noted that magnons with opposite handedness +will experience magnitude-equal but opposite Lorentz forces, result- +ing in the opposite transverse displacement (not shown). +librium direction of the stagger vector l0, i.e., Rez = l0 = +(sin θ cos φ, sin θ sin φ, cos θ) with the polar angle θ and az- +imuthal angle φ. Here, Lz and Ly are generators of the three- +dimensional rotations about the z and y axis, respectively. To +investigate the magnon excitation and transport in spin tex- +tures, we introduce the magnon creation (a†) and annihilation +(a) operators by the Holstein-Primakoff transformation on the +vector n = R−1l [53]. We expand the bosonic operator as +a = aseiks·r + apeikp·r + aqeikq·r + arψr, where as, ap, aq, and ar +are operators of incident magnon, sum-frequency, difference- +frequency, and the skyrmion breathing modes [54], respec- +tively. ks, kp, and kq are the corresponding wave vectors of +three propagating modes in the far-field region, and ψr is the +wavefunction of the localized breathing mode. Furthermore, +we assume that the magnon excitation is in the form of a wave +packet, which has a fixed shape and can be described by its +central position ri(t), with i = s, p, q. In terms of these col- +lective coordinates [55], the Lagrangian can be simplified as +a function of the position ri and the group velocity vi = ˙ri of +the magnon wavepacket [24]. Keeping up to third-order terms, +the total Hamiltonian can be expressed as H = H2+H3. Here, +the quadratic Hamiltonian is +H2 = +� +i=s,p,q +2a† +i ai +� �1 +J ω2 +i v2 +i − (2A12 + Dl0 +J ) · ωivi +� +dr, +(2) +which determines the magnon dispersion relation. The cu- +bic Hamiltonian H3 = H3s + H3p + H3q includes contribu- +tions from the incident term H3s, sum-frequency term H3p, +and difference-frequency term H3q +H3s = +� +ωsvs · +� +− 1√ +2 +�(iA13 + A23) + D +2J (ieφ + eθ)� +�3aqara† +sei(−ks+kq)·r + a† +parasei(ks−kp)·r�ψr + H.c. +� +dr, +H3p = +� +ωpvp · +� +− 3√ +2 +�(iA13 + A23) + D +2J (ieφ + eθ)� +asara† +pei(ks−kp)·rψr + H.c. +� +dr, +H3q = +� +ωqvq · +� +− 1√ +2 +�(iA13 + A23) + D +2J (ieφ + eθ)� +asa† +ra† +qei(ks−kq)·rψ∗ +r + H.c. +� +dr, +(3) +where Aνν′ = Ax,νν′ex + Ay,νν′ey are the gauge fields (ν, ν′ = +1, 2, 3), eθ and eφ are two unit vectors in spherical coordinates, +and ωs, ωp, and ωq are, respectively, the frequencies of the in- +cident, confluence, and splitting magnons meeting law of en- +ergy conservation, i.e., ωp(q) = ωs ± ωr with ωr the skyrmion +breathing frequency, see the bottom panel of Fig. 1. Equa- +tions (2) and (3) show that the conventional gauge field A12 +only appears in the quadratic term, while gauge fields A13 and +A23 emerge in the nonlinear three-magnon processes. To re- +veal their role in the magnon transport, we employ the Euler- +Lagrangian formula to derive equations of motion of magnon +wavepackets +a† +i ai +ℏω2 +i +eJ ˙vi − a† +i aiωivi × B − Fcubic +i += 0, (i = s, p, q), +(4) +where B = Bzez with Bz = ℏ +e +�∇ × (A12 + Dl0 +2J )� +z = ℏ +e +�l0 · (∂xl0 × +∂yl0) + (∇ × Dl0 +2J )z +� is the conventional fictitious magnetic field +for the linear magnon transport with the reduced Planck con- +stant ℏ and elementary charge e. See Supplemental Material +[56] for the derivation of (4). It is noted that we have ig- +nored the effective electric field associated with the skyrmion +static energy due to its negligible role in the magnon Hall ef- +fect. The extra force Fcubic +i +originates from the three-magnon +process and the newfound gauge fields, with the following ex- +pression +Fcubic +i += civi × B′, (i = s, p, q), +(5) +where B′ = B′ +zez with B′ +z = ℏ +e(∇×A23)z+ ℏD +2Je(∇×eθ)z = ℏ +e +�∂yl0· +∂x(n× +ez +sin θ)−∂xl0 ·∂y(n× +ez +sin θ)�+ ℏD +2Je(∇× ez+cos θl0 +sin θ +)z represents +the new fictitious magnetic field playing a role merely when +the nonlinear three-magnon process occurs. Due to the circu- +lar symmetry of skyrmion, the A13 component is absent. Here, +cs = ωs +4 (gpa† +paras + 3gqa† +qa† +ras + H.c.), cp = 3ωp +4 (gpasara† +p + +H.c.), and cq = +ωq +4 (gpasa† +ra† +q + H.c.), with overlap integrals +gp = +1 +√ +2V +� +ei(ks−kp)·rψrdr, gq = +1 +√ +2V +� +ei(ks−kq)·rψ∗ +rdr, and V +being the system volume. As shown in Eq. (4), the spin-wave +packet can be regarded as a particle-like object moving in its +own parameter space [57] subject to fictitious magnetic fields + +3 +(B and B′). The first term on the left-hand side of Eq. (4) char- +acterizes the acceleration of magnons. The second term rep- +resents the effective Lorentz force from the quadratic Hamil- +ton H2, resulting in the conventional topological magnon Hall +effect. Interestingly enough, the third term induces an ex- +tra Lorentz force on the wavepacket, leading to the nonlinear +topological magnon Hall effect. The spatial distributions of +the dimensionless magnetic fields Bz/B0 and B′ +z/B0 are shown +in Figs. 2(a) and 2(b), respectively, where B0 = ℏ/a2e with a +being the lattice constant. It is noted that B0 ≈ 660 T for a = 1 +nm. Due to the rotational symmetry of the Bloch skyrmion, +both magnetic fields B/B0 and B′/B0 have the circular sym- +metry. For B/B0, its main origin comes from the topological +charge density of skyrmion, and the total magnetic flux is 4π +[58]. The spatial distribution of B′/B0, however, is similar to +the fictitious magnetic field distribution of the target skyrmion +[59, 60] with a vanishing total flux but a singularity at the +skyrmion core. +Revealing the concealed fictitious magnetic field.—In non- +linear magnon-skyrmion scatterings, the time-evolution of +populations of confluence and splitting modes is governed by +the coupled Heisenberg equations: i˙ap = (∆p − iαωp)ap + +˜gpasar and i˙aq = (∆q − iαωq)aq + ˜gqasa† +r. Here, the detun- +ing parameter ∆p(q) = ωp(q) − ω0 with the driving microwave +frequency ω0, ˜gp = +� � − 2g1,µikp,µψr + g∗ +2,µ(∂µψr + iks,µ) − +5√ +2K sin θ cos θ�ei(ks−kp)·rdr and ˜gq = +� �g2,µ(∂µψ∗ +r + ikq,µ) + +2g∗ +1,µiks,µψ∗ +r − +5√ +2K sin θ cos θ�ei(ks−kq)·rdr where the Einstein +summation rule is applied, coefficients g1,µ = +3J +2 +√ +2(Aµ,13 − +iAµ,23) + +3D +4 +√ +2(eφ,µ − ieθ,µ) and g2,µ = +J√ +2(−Aµ,13 − iAµ,23) + +D +2 +√ +2(−eφ,µ − ieθ,µ) denote the strength of the three-magnon +confluence and splitting, respectively, and α is the Gilbert +damping constant. +Then, one can analytically derive the +steady-state magnon populations as ap = +gasar +ϵ+iα(ωs+ωr) and aq = +gasa† +r +ϵ−iα(ωs−ωr) with ϵ = ωs − ωr. Here, we have adopted the +approximation ˜gp ≈ ˜gq ≈ g which is justified by the small +difference between confluence and splitting frequencies since +ωr ≪ ωs. We therefore obtain +msw, i˙vi − evi × σ(B + λiB′) = 0, (i = s, p, q), +(6) +which is the main result of this work (see Supplemental Ma- +terial [56] for detailed derivations). Here, msw,i = ℏωi/J is +the effective mass of the spin-wave packet in antiferromag- +nets, σ = ∓1 represents the left/right-hand magnon polar- +izations, λs = nr( ggp +4ϵ + 3ggq +4ϵ ++ H.c.), λp = +3 +4( ϵgp +g + H.c.), +and λq = 1 +4( ϵgq +g + H.c.) with the particle number of skyrmion +breathing mode nr = ⟨a† +rar⟩. Equation (6) shows that the ex- +tra effective Lorentz force eλivi × σB′ (i = s, p, q) is mode- +dependent. For incident magnons, the extra Lorentz force is +proportional to the product of the skyrmion breathing number +nr (≪ 1), the coupling parameter g/ϵ, and the overlap inte- +gral gp,q. In general, magnon populations of confluence and +splitting modes are far less than the incident one. It implies +g/ϵ, gp,q ≪ 1. The effect of B′ on incident magnons is thus +(a) +0 +50 +100 +50 +100 +(c) +0 +50 +100 +50 +100 +(d) +(b) +0 +50 +100 +50 +100 +50 +100 +0 +50 +100 +FIG. 2: Spatial distribution of dimensionless field Bz/B0 (a) and +B′ +z/B0 (b). Spin wave trajectories in real space under fictitious mag- +netic field B (c) and B+B′ (d), where different black curves represent +trajectories of magnon wavepackets with different impact parame- +ters, the red curve indicates the averaged trajectory of 51 magnon +wavepackets, and the dashed green circle labels skyrmion’s wall cen- +ter (lz = 0). +negligible. However, for the confluence and splitting modes, +parameters λp,q are inversely proportional to g/ϵ, the addi- +tional effective Lorentz force is therefore expected to bring an +enormous effect. +To explore the role of fictitious magnetic fields on the +magnon transport, we numerically solve Eq. (6) both without +and with the new fictitious magnetic field B′. In calculations, +we consider a right-handed magnon wavepacket (σ = 1), and +set the incident-magnon’s initial velocity vs(t = 0) = 2.65 +(with unit J/aω) along x direction, magnon mass msw = 0.31 +(with unit ℏω/J), and coefficient λs,p,q = 1. It is observed +that the effective magnetic field B′ significantly enhances the +magnon Hall effect, as displayed in Figs. 2(c) and 2(d). Due +to the singularity of the fictitious magnetic field B′, we note +anomalous magnon trajectories near the skyrmion center. Be- +low, we verify our theoretical predictions by full micromag- +netic simulations using MUMAX3 package [61]. +We consider an AFM thin film of dimension 1000 ×1000 +×1 nm3, hosting a Bloch-type skyrmion at the film center [62– +64]. Magnetic parameters of KMnF3 [65]: J = 6.59 pJ/m, +K = 1.16 × 105 J/m3, and D = 1 mJ/m2 are used in the +simulations, which gives rise to a skyrmion radius ≈ 11 nm +(defineds as the radius of circle lz = 0). The Gilbert damp- +ing is set as α = 0.001. To efficiently generate polarized +magnons and the three-wave mixing, we apply a microwave +field hRH/LH(t) = h0[cos(ωst)ex ∓ sin(ωst)ey] with amplitude +h0 = 50 mT and frequency ωs/2π = 1.205 THz (generating +the incident magnon of wavelength ≈ 15.2 nm) on one sublat- +tice in a narrow region: −401 nm≤ x ≤ −399 nm and a local +field hr(t) = hr sin(ωrt)ez over the skyrmion with amplitude + +0 +10.0 +80.0 +B"\Bo17.0- +↑7.0- +20.0- +r0.04 +-55.56 +-20.8 +-29.87 +-4.18 +-50.52 +-19.74 +20.56 +56 +4.19 +29.76 +50.44 +19.38 +0.05 +0.2 +FFT amplitude (arb. units) +0.2 +0.4 +0.05 +0.2 +1.11 THz +1.11 THz +1.205 THz +1.205 THz +1.3 THz +1.3 THz +(a) +(b) +FIG. 3: (a) MFC in the nonlinear scattering between the incident +magnon and AFM skyrmion. (b) Isoline maps for righted-handed +(top panel) and left-handed (bottom panel) magnons scattered by the +skrymion at the origin. In each panel, modes from left to right corre- +spond to splitting, incident, and confluence magnons, respectively. +hr = 5 mT and ωr/2π = 0.095 THz (the skyrmion breathing +frequency) [56]. Here, RH and LH represent the abbrevia- +tion of microwave with right and left handedness, respectively. +Absorbing boundary conditions are adopted to eliminate the +spin-wave reflection by film edges [66]. +To analyze the magnon spectrum in the skyrmion area, we +implement fast Fourier transform of local magnetic moments. +Figure 3(a) shows the emerging magnon frequency comb +(MFC) [52] in the terahertz region, where the mode spacing +of the comb is exactly the skyrmion breathing frequency. Fur- +thermore, we plot the isoline map of incident, confluence, and +splitting modes to analyze the Hall angle of each mode, as +shown in Fig. 3(b). We observe an interesting “bunny ears” +pattern of magnons scattering off the AFM skyrmion, with +red and blue lines denoting the propagation direction of two +branches. Here, the Hall angle is defined as the included angle +between each branch and the horizontal line. Compared with +the incident mode, the Hall angle of nonlinear modes nearly +doubles (quintuples) for the main (secondary) branch of the +“bunny ears” [see Fig. 3(b)], where the major (secondary) +branch is referred to as the one with a large (small) Hall an- +gle. More importantly, by flipping the chirality of incident +magnons, we observe an opposite magnon Hall motion [com- +paring the top and bottom panels in Fig. 3(b)]. The small dif- +ference of Hall angles between right-handed and left-handed +magnons results from the dipolar field [56]. Micromagnetic +(a) +(b) +sim. +fitting +theo. +sim. +mode +s +p +q +FIG. 4: (a) The Hall angle of the main branch of “bunny ears” as a +function of the driving frequency for the incident (black), confluence +(blue), and splitting (red) modes. Symbols are micromagnetic simu- +lations and curves are analytical fitting by solving Eq. (6). (b) The +Hall angle as a function of the mode index m for different incident +magnon frequencies. Symbols and lines represent micromagnetic +simulations and linear fittings, respectively. +simulations thus offer solid evidences for the nonlinear topo- +logical magnon spin Hall effect as we predicted above. +Furthermore, we derive the frequency-dependent Hall angle +by fitting the flow direction of the main branch of the isosur- +face of each mode. Figure 4(a) plots the quantitative compar- +ison between theoretical calculations and micromagnetic sim- +ulations for incident (black), confluence (blue), and splitting +(red) modes. It shows that the Hall angle monotonically de- +creases with the increase of the mode frequency. Simulation +results can be well explained by the analytical model (6) with +parameters nr = 0, g = 49 MHz, and gp = 1 +3gq = 9.4 × 10−6. +A vanishing mode number of skyrmion breathing is justified +by its small wave amplitude. The coupling coefficient g is +independently obtained by numerically solving the coupled +Heisenberg equations. +Acceptable deviations could be at- +tributed to the simplified wavepacket treatment in the present +formalism and the neglected topological electric-field compo- +nent of the gauge fields. Figure 4(b) shows the Hall angle of +nonlinear magnons over a broad frequencies ωs + mωr in the +MFC with integer m labeling the order of the spectrum line. +Their “bunny ears” scattering patterns are plotted in Supple- +mental Material [56]. It is found that the noninear Hall an- +gle increases linearly with |m|. This monotonic dependence +is reminiscent of the refraction process of light waves through +multilayer media [67], where the refraction angle accumulates +upon each scattering layer. It is noted that the slope of the lin- +ear trendline decreases as the incident magnon’s frequency ωs +increases. +Discussion.—In the above calculations, we have considered +rotationally symmetric spin textures, the A13 gauge field thus +vanishes. However, the curl of gauge field induced by DMI +becomes finite when the rotational symmetry is broken. We +then envision contributions from A13 in generating the ficti- +tious magnetic field for elliptical skyrmions [68]. +To summarize, we revealed the long-sought gauge fields +concealed in the nonlinear magnon transport. By investigat- +ing the three-wave mixing between propagating magnons and + +S.0 +8.0 +0'4S.0 +8.0 +0'4S.0 +8.0 +0'45 +breathing skyrmions, we found giant Hall angles emerging for +each nonlinear spectrum line of the MFC. We further identi- +fied that the sign of the Hall angle is reversed by switching the +chirality of incident magnons, and we dub it nonlinear topo- +logical magnon spin Hall effect. Our findings are intimately +connected to the particle number nonconservation of magnons +and thus applicable to generic bosons, which does not have the +low-energy fermionic counterpart. Our results significantly +advance the understanding of the nonlinear Hall effect and +pave the way to probing the gauge field by frequency comb. +This work was funded by the National Key Research Devel- +opment Program under Contract No. 2022YFA1402802 and +the National Natural Science Foundation of China (NSFC) +(Grant No. 12074057). Z.W. acknowledges financial support +from the NSFC (Grant No. 12204089) and the China Post- +doctoral Science Foundation under Grant No. 2019M653063. +H.Y.Y. acknowledges the European Union’s Horizon 2020 re- +search and innovation programme under Marie Skłodowska- +Curie Grant Agreement SPINCAT No. 101018193. +∗ yan@uestc.edu.cn +[1] P. Delplace, J. B. Marston, and A. Venaille, Topological origin +of equatorial waves, Science 358, 1075 (2017). +[2] J. B. Parker, J. B. Marston, S. M. Tobias, and Z. Zhu, Topolog- +ical Gaseous Plasmon Polariton in Realistic Plasma, Phys. Rev. +Lett. 124, 195001 (2020). +[3] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, +Observation of the spin Hall effect in semiconductors, Science +306, 1910 (2004). +[4] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Ex- +perimental Observation of the Spin-Hall Effect in a Two- +Dimensional Spin-Orbit Coupled Semiconductor System, Phys. +Rev. Lett. 94, 047204 (2005). +[5] J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. +Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015). +[6] A. Kavokin, G. Malpuech, and M. Glazov, Optical Spin Hall +Effect, Phys. Rev. Lett. 95, 136601 (2005). +[7] C. Leyder, M. Romanelli, J. Ph. Karr, E. Giacobino, T. C. H. +Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bra- +mati, Observation of the optical spin Hall effect, Nat. Phys. 3, +628 (2007). +[8] Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. +Tokura, Observation of the magnon Hall effect, Science 329, +297 (2010). +[9] K. Shen, Magnon Spin Relaxation and Spin Hall Effect Due to +the Dipolar Interaction in Antiferromagnetic Insulators, Phys. +Rev. Lett. 124, 077201 (2020). +[10] J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and +A. H. MacDonald, Universal Intrinsic Spin Hall Effect, Phys. +Rev. Lett. 92, 126603 (2004). +[11] G. Y. Guo, S. Murakami, T.-W. Chen, and N. Nagaosa, Intrin- +sic Spin Hall Effect in Platinum: First-Principles Calculations, +Phys. Rev. Lett. 100, 096401 (2008). +[12] G. Yin, Y. Liu, Y. Barlas, J. Zang, and R. K. Lake, Topological +spin Hall effect resulting from magnetic skyrmions, Phys. Rev. +B 92, 024411 (2015). +[13] B. G¨obel, A. Mook, J. Henk, and I. Mertig, Antiferromagnetic +skyrmion crystals: Generation, topological Hall, and topologi- +cal spin Hall effect, Phys. Rev. B 96, 060406 (2017). +[14] C. A. Akosa, O. A. Tretiakov, G. Tatara, and A. Manchon, The- +ory of the Topological Spin Hall Effect in Antiferromagnetic +Skyrmions: Impact on Current-Induced Motion, Phys. Rev. +Lett. 121, 097204 (2018). +[15] M. W. Daniels, W. Yu, R. Cheng, J. Xiao, and D. Xiao, Topo- +logical spin Hall effects and tunable skyrmion Hall effects in +uniaxial antiferromagnetic insulators, Phys. Rev. B 99, 224433 +(2019). +[16] S. K. Kim, K. Nakata, D. Loss, and Y. Tserkovnyak, Tunable +Magnonic Thermal Hall Effect in Skyrmion Crystal Phases of +Ferrimagnets, Phys. Rev. Lett. 122, 057204 (2019). +[17] Q. Du, Z. Hu, M. G. Han, F. Camino, Y. Zhu, and C. Petrovic, +Topological Hall Effect Anisotropy in Kagome Bilayer Metal +Fe3Sn2, Phys. Rev. Lett. 129, 236601 (2022). +[18] P. Yan, X. S. Wang, and X. R. Wang, All-Magnonic Spin- +Transfer Torque and Domain Wall Propagation, Phys. Rev. Lett. +107, 177207 (2011). +[19] H. Y. Yuan, Y. Cao, A. Kamra, R. A. Duine, and P. Yan, Quan- +tum magnonics: When magnon spintronics meets quantum in- +formation science, Phys. Rep. 965, 1 (2022). +[20] V. K. Dugaev, P. Bruno, B. Canals, and C. Lacroix, Berry phase +of magnons in textured ferromagnets, Phys. Rev. B 72, 024456 +(2005). +[21] A. A. Kovalev and Y. Tserkovnyak, Thermomagnonic spin +transfer and Peltier effects in insulating magnets, EPL 97, +67002 (2012). +[22] K. A. van Hoogdalem, Y. Tserkovnyak, and D. Loss, Magnetic +texture-induced thermal Hall effects Phys. Rev. B 87, 024402 +(2013). +[23] C. Sch¨utte and M. Garst, Magnon-skyrmion scattering in chiral +magnets, Phys. Rev. B 90, 094423 (2014). +[24] J. Lan and J. Xiao, Skew scattering and side jump of spin wave +across magnetic texture, Phys. Rev. B 103, 054428 (2021). +[25] Z. Wang, W. Bao, Y. Cao, and P. Yan, All-magnonic Stern- +Gerlach effect in antiferromagnets, Appl. Phys. Lett. 120, +242403 (2022). +[26] Z. Jin, C. Y. Meng, T. T. Liu, D. Y. Chen, Z. Fan, M. Zeng, X. +B. Lu, X. S. Gao, M. H. Qin, and J.-M. Liu, Magnon-driven +skyrmion dynamics in antiferromagnets: Effect of magnon po- +larization, Phys. Rev. B 104, 054419 (2021). +[27] Y. Liu, T. T. Liu, Z. Jin, Z. P. Hou, D. Y. Chen, Z. Fan, M. +Zeng, X. B. Lu, X. S. Gao, M. H. Qin, and J.-M. Liu, Spin- +wave-driven skyrmion dynamics in ferrimagnets: Effect of net +angular momentum, Phys. Rev. B 106, 064424 (2022). +[28] S. G. Tan, S.-H. Chen, C. S. Ho, C.-C. Huang, M. B. A. Jalil, C. +R. Chang, and S. Murakami, Yang-Mills physics in spintronics, +Phys. Rep. 882, 1 (2020). +[29] G. Tatara, Effective gauge field theory of spintronics, Physica E +106, 208 (2019). +[30] I. Sodemann and L. Fu, Quantum Nonlinear Hall Effect Induced +by Berry Curvature Dipole in Time-Reversal Invariant Materi- +als, Phys. Rev. Lett. 115, 216806 (2015). +[31] Q. Ma, S.-Y. Xu, H. Shen, D. MacNeill, V. Fatemi, T.-R. Chang, +A. M. M. Valdivia, S. Wu, Z. Du, C.-H. Hsu, S. Fang, Q. D. +Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, E. Kaxiras, H.- +Z. Lu, H. Lin, L. Fu, N. Gedik, and P. J. Herrero, Observation +of the nonlinear Hall effect under time-reversal-symmetric con- +ditions, Nature (London) 565, 337 (2019). +[32] K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nonlinear +anomalous Hall effect in few-layer WTe2, Nat. Mater. 18, 324 +(2019). +[33] Z. Z. Du, C. M. Wang, H.-Z. Lu, and X. C. Xie, Band Signatures +for Strong Nonlinear Hall Effect in Bilayer WTe2, Phys. Rev. + +6 +Lett. 121, 266601 (2018). +[34] P. He, S. S.-L. Zhang, D. Zhu, S. Shi, O. G. Heinonen, G. Vi- +gnale, and H. Yang, Nonlinear Planar Hall Effect, Phys. Rev. +Lett. 123, 016801 (2019). +[35] D.-F. Shao, S.-H. Zhang, G. Gurung, W. Yang, and E. Y. Tsym- +bal, Nonlinear Anomalous Hall Effect for N´eel Vector Detec- +tion, Phys. Rev. Lett. 124, 067203 (2020). +[36] S. Lai, H. Liu, Z. Zhang, J. Zhao, X. Feng, N. Wang, C. Tang, Y. +Liu, K. S. Novoselov, S. A. Yang, and W.-B. Gao, Third-order +nonlinear Hall effect induced by the Berry-connection polariz- +ability tensor, Nat. Nano. 16, 869 (2021). +[37] J. Duan, Y. Jian, Y. Gao, H. Peng, J. Zhong, Q. Feng, J. +Mao, and Y. Yao, Giant Second-Order Nonlinear Hall Effect +in Twisted Bilayer Graphene, Phys. Rev. Lett. 129, 186801 +(2022). +[38] Y. M. Itahashi, T. Ideue, S. Hoshino, C. Goto, H. Namiki, T. +Sasagawa, and Y. Iwasa, Giant second harmonic transport un- +der time-reversal symmetry in a trigonal superconductor, Nat. +Commun. 13, 1659 (2022). +[39] Z. Z. Du, H. Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. +Rev. Phys 3, 744 (2021). +[40] A. Mook, B. G¨obel, J. Henk, and I. Mertig, Taking an electron- +magnon duality shortcut from electron to magnon transport, +Phys. Rev. B 97, 140401 (2018). +[41] H. Kondo and Y. Akagi, Nonlinear magnon spin Nernst effect +in antiferromagnets and strain-tunable pure spin current, Phys. +Rev. Research 4, 013186 (2022). +[42] M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. +Belkin, and A. Al`u, Gradient Nonlinear Pancharatnam-Berry +Metasurfaces, Phys. Rev. Lett. 115, 207403 (2015). +[43] G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. +Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, Continuous +control of the nonlinearity phase for harmonic generations, Nat. +Mat. 14, 607 (2015). +[44] Y. Li, O. Yesharim, I. Hurvitz, A. Karnieli, S. Fu, G. Porat, +and A. Arie, Adiabatic geometric phase in fully nonlinear three- +wave mixing, Phys. Rev. A 101, 033807 (2020). +[45] Z. Wang, H. Y. Yuan, Y. Cao, Z.-X. Li, R. A. Duine, and P. +Yan, Magnonic Frequency Comb through Nonlinear Magnon- +Skyrmion Scattering, Phys. Rev. Lett. 127, 037202 (2021). +[46] Z. Wang, H. Y. Yuan, Y. Cao, and P. Yan, Twisted Magnon +Frequency Comb and Penrose Superradiance, Phys. Rev. Lett. +129, 107203 (2022). +[47] H. Schultheiss, X. Janssens, M. van Kampen, F. Ciubotaru, S. J. +Hermsdoerfer, B. Obry, A. Laraoui, A. A. Serga, L. Lagae, A. +N. Slavin, B. Leven, and B. Hillebrands, Direct Current Control +of Three Magnon Scattering Processes in Spin-Valve Nanocon- +tacts, Phys. Rev. Lett. 103, 157202 (2009). +[48] J. Iwasaki, A. J. Beekman, and N. Nagaosa, Theory of magnon- +skyrmion scattering in chiral magnets, Phys. Rev. B 89, 064412 +(2014). +[49] B. Zhang, Z. Wang, Y. Cao, P. Yan, and X. R. Wang, Eaves- +dropping on spin waves inside the domain-wall nanochannel +via three-magnon processes, Phys. Rev. B 97, 094421 (2018). +[50] K. Schultheiss, R. Verba, F. Wehrmann, K. Wagner, L. K¨orber, +T. Hula, T. Hache, A. K´akay, A. A. Awad, V. Tiberkevich, A. N. +Slavin, J. Fassbender, and H. Schultheiss, Excitation of Whis- +pering Gallery Magnons in a Magnetic Vortex, Phys. Rev. Lett. +122, 097202 (2019). +[51] L. K¨orber, K. Schultheiss, T. Hula, R. Verba, J. Fassbender, +A. K´akay, and H. Schultheiss, Nonlocal Stimulation of Three- +Magnon Splitting in a Magnetic Vortex, Phys. Rev. Lett. 125, +207203 (2020). +[52] T. Hula, K. Schultheiss, F. J. T. Goncalves, L. K¨orber, M. Be- +jarano, M. Copus, L. Flacke, L. Liensberger, A. Buzdakov, A. +K´akay, M. Weiler, R. Camley, J. Fassbender, and H. Schultheiß, +Spin-wave frequency combs, Appl. Phys. Lett. 121, 112404 +(2022). +[53] T. Holstein and H. Primakoff, Field dependence of the intrinsic +domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 +(1940). +[54] M. Mochizuki, Spin-Wave Modes and Their Intense Excita- +tion Effects in Skyrmion Crystals, Phys. Rev. Lett. 108, 017061 +(2012). +[55] A. A. Thiele, Steady-State Motion of Magnetic Domains, Phys. +Rev. Lett. 30, 230 (1973). +[56] See Supplemental Material at http://link.aps.org/supplemental/ +for the derivation of equations of motion for magnon wavepack- +ets, the numerical verification of the skyrmion breathing and its +frequency, the analysis of magnon polarizations on their non- +linear topological Hall transport, and the isolines of incident +magnons scattered by skyrmions with and without breathing, +which includes Refs. [16, 45, 53]. +[57] G. Sundaram and Q. Niu, Wave-packet dynamics in slowly per- +turbed crystals: Gradient corrections and Berry-phase effects, +Phys. Rev. B 59, 14915 (1999). +[58] G. E. Volovik, Linear momentum in ferromagnets, J. Phys. C +20, L83 (1987). +[59] J. Tang, Y. Wu, W. Wang, L. Kong, B. Lv, W. Wei, J. Zang, M. +Tian, and H. Du, Magnetic skyrmion bundles and their current- +driven dynamics, Nat. Nanotechnol. 16, 1086 (2021). +[60] P. B. Ndiaye, C. A. Akosa, and A. Manchon, Topological Hall +and spin Hall effects in disordered skyrmionic textures, Phys. +Rev. B 95, 064426 (2017). +[61] A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia- +Sanchez, and B. V. Waeyenberge, The design and verification of +MUMAX3, AIP Adv. 4, 107133 (2014). +[62] S. M¨uhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. +Neubauer, R. Georgii, and P. B¨oni, Skyrmion Lattice in a Chiral +Magnet, Science 323, 915 (2009). +[63] X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. +Matsui, N. Nagaosa, and Y. Tokura, Real-space observation of +a two-dimensional skyrmion crystal, Nature (London) 465, 901 +(2010). +[64] S. X. Huang and C. L. Chien, Extended Skyrmion Phase in +Epitaxial FeGe (111) Thin Films, Phys. Rev. Lett. 108, 267201 +(2012). +[65] J. Barker and O. A. Tretiakov, Static and Dynamical Proper- +ties of Antiferromagnetic Skyrmions in the Presence of Applied +Current and Temperature, Phys. Rev. Lett. 116, 147203 (2016). +[66] G. Venkat, H. Fangohr, and A. Prabhakar, Absorbing boundary +layers for spin wave micromagnetics, J. Magn. Magn. Mater. +450, 34 (2018). +[67] M. Lax, Multiple Scattering of Waves, Rev. Mod. Phys. 23, 287 +(1951). +[68] J. Jena, B. G¨obel, T. Ma, V. Kumar, R. Saha, I. Mertig, C. +Felser, and S. S. P. Parkin, Elliptical Bloch skyrmion chi- +ral twins in an antiskyrmion system, Nat. Commun. 11, 1115 +(2020). + diff --git a/f9E1T4oBgHgl3EQfewTK/content/tmp_files/load_file.txt b/f9E1T4oBgHgl3EQfewTK/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..bcd5a3de792f5b3bada60cdf45e3f738c214df9e --- /dev/null +++ b/f9E1T4oBgHgl3EQfewTK/content/tmp_files/load_file.txt @@ -0,0 +1,962 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf,len=961 +page_content='Nonlinear Topological Magnon Spin Hall Effect Zhejunyu Jin1, Xianglong Yao1, Zhenyu Wang1, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yuan2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhaozhuo Zeng1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yunshan Cao1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' and Peng Yan1∗ 1School of Electronic Science and Engineering and State Key Laboratory of Electronic Thin Films and Integrated Devices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' University of Electronic Science and Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chengdu 610054,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' China 2Institute for Theoretical Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Utrecht University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3584 CC Utrecht,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The Netherlands When a magnon passes through two-dimensional magnetic textures,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' it will experience a fictitious magnetic field originating from the 3 × 3 skew-symmetric gauge fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To date, only one of the three independent components of the gauge fields has been found to play a role in generating the fictitious magnetic field while the rest two are perfectly hidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In this work, we show that they are concealed in the nonlinear magnon transport in magnetic textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Without loss of generality, we theoretically study the nonlinear magnon-skyrmion interaction in antiferromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' By analyzing the scattering features of three-magnon processes between the circularly- polarized incident magnon and breathing skyrmion, we predict a giant Hall angle of both the confluence and splitting modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Furthermore, we find that the Hall angle reverses its sign when one switches the handedness of the incident magnons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We dub it nonlinear topological magnon spin Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Our findings are deeply rooted in the bosonic nature of magnons that the particle number is not conserved, which has no counterpart in low-energy fermionic systems, and may open the door for probing gauge fields by nonlinear means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='—Topology dictates the particle or wave trans- port in many branches of physics, ranging from solid state physics to geophysics and astrophysics [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' One outstand- ing example in condensed matter physics is the intrinsic spin Hall effect which originates from the momentum-space topol- ogy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', the Berry curvature of the band structure [3–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' On the other hand, non-collinear spin textures, such as the mag- netic vortex, meron, and skyrmion, can give rise to the real- space topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' When a spinful particle propagates through the topological spin texture, it will experience an effective Lorentz force, resulting in the so-called topological (spin-) Hall effect [12–17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Magnons, quanta of spin waves, are the collective excita- tions of ordered magnets [18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Very recently, magnon- based spintronics has attracted enormous interest due to pecu- liar advantages of magnons, such as the long-distance trans- port and low-energy consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Magnons carry spin angu- lar momentum as well, so that they can experience an effective Lorentz force from the spin texture, leading to the topological magnon Hall effect [20–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In antiferromagnets, magnons have two degenerate modes with opposite spins, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', right- and left-handed magnons [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Therefore, when a magnon passes through the antiferromagnetic (AFM) skyrmion, for in- stance, it will experience a spin-dependent Lorentz force, re- sulting in the topological magnon spin Hall effect [15, 26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' These topological magnon Hall effects originate from the gauge fields in transforming the non-collinear magnetic tex- ture to the collinear state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The gauge transformation generates the covariant form of the differential operator ∂µ + Aµ with µ = x, y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, the 3×3 skew-symmetric matrix Aµ = R−1∂µR with the rotation matrix R contains three independent gauge fields [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' So far, only one of the three elements, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', Aµ,12, has been identified to play a role in the Hall transport of magnons while the rest two (Aµ,13 and Aµ,23) are concealed from the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In the past few years, the nonlinear Hall effect due to the momentum-space topology, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', Berry curvature dipole, has attracted much attention [30–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' However, its counterpart induced by the real-space topology has not been reported till now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is well known that the geometric phase derived from the adiabatic evolution is crucial for the Hall transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' No- tably, in the three-wave mixing process, the accumulation of adiabatic geometric phase takes place not only on incident waves but also on nonlinear ones [42–44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' One thus expects that magnons generated in the nonlinear three-magnon pro- cess in spin textures [45–51] may also experience a topologi- cal Hall effect subject to the conventional gauge field, but it is not clear whether the rest two gauge fields play any role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In this Letter, we aim to reveal the concealed gauge fields by addressing the nonlinear Hall transport of magnons in spin textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To this end, we theoretical study the nonlinear inter- action between polarized magnons and magnetic skyrmions in antiferromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We show that the two long-sought gauge fields are actually hidden in the nonlinear magnon transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' By analyzing the “bunny ears” scattering pattern of three- magnon processes between the circularly-polarized magnon and breathing skyrmion in an antiferromagnet, we discover a giant Hall angle of both confluence and splitting modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The Hall angle reverses its sign when one switches the handedness of incident AFM magnons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We dub it nonlinear topological magnon spin Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Our findings are deeply connected to both the nonconservation of magnon number and the spin- texture-induced Berry curvature in real space, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='—Let us consider a chiral antiferromagnet described by the following Lagrangian [16] L = � (∂tl)2dr − H, (1) where l is the normalized N´eel vector and H = � �J(∇l)2 + Dl · (∇ × l) − Kl2 z �dr is the system Hamiltonian including the exchange energy, Dzyaloshinskii-Moriya interaction (DMI), and magnetic anisotropy, with J, D, and K being the ex- change stiffness, DMI strength, and anisotropy coefficient, re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To facilitate the analysis, we use the 3 × 3 ma- trix R =exp(φLz)exp(θLy) to rotate the z−axis to the equi- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='03211v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='mes-hall] 9 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 1: Schematic illustration of the nonlinear topological magnon spin Hall effect in magnon-AFM skyrmion scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Circles with arrows indicate the handedness of AFM magnons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Incident, skyrmion breathing, sum-frequency, and difference-frequency modes are denoted by black, green, red, and blue colors, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' vs,p,q represent the velocity of three propagating magnon wavepackets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The bottom panel shows the magnon splitting (left) and confluence (right) processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is noted that magnons with opposite handedness will experience magnitude-equal but opposite Lorentz forces, result- ing in the opposite transverse displacement (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' librium direction of the stagger vector l0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', Rez = l0 = (sin θ cos φ, sin θ sin φ, cos θ) with the polar angle θ and az- imuthal angle φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, Lz and Ly are generators of the three- dimensional rotations about the z and y axis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To investigate the magnon excitation and transport in spin tex- tures, we introduce the magnon creation (a†) and annihilation (a) operators by the Holstein-Primakoff transformation on the vector n = R−1l [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We expand the bosonic operator as a = aseiks·r + apeikp·r + aqeikq·r + arψr, where as, ap, aq, and ar are operators of incident magnon, sum-frequency, difference- frequency, and the skyrmion breathing modes [54], respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' ks, kp, and kq are the corresponding wave vectors of three propagating modes in the far-field region, and ψr is the wavefunction of the localized breathing mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Furthermore, we assume that the magnon excitation is in the form of a wave packet, which has a fixed shape and can be described by its central position ri(t), with i = s, p, q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In terms of these col- lective coordinates [55], the Lagrangian can be simplified as a function of the position ri and the group velocity vi = ˙ri of the magnon wavepacket [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Keeping up to third-order terms, the total Hamiltonian can be expressed as H = H2+H3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, the quadratic Hamiltonian is H2 = � i=s,p,q 2a† i ai � �1 J ω2 i v2 i − (2A12 + Dl0 J ) · ωivi � dr, (2) which determines the magnon dispersion relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The cu- bic Hamiltonian H3 = H3s + H3p + H3q includes contribu- tions from the incident term H3s, sum-frequency term H3p, and difference-frequency term H3q H3s = � ωsvs · � − 1√ 2 �(iA13 + A23) + D 2J (ieφ + eθ)� �3aqara† sei(−ks+kq)·r + a† parasei(ks−kp)·r�ψr + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' � dr, H3p = � ωpvp · � − 3√ 2 �(iA13 + A23) + D 2J (ieφ + eθ)� asara† pei(ks−kp)·rψr + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' � dr, H3q = � ωqvq · � − 1√ 2 �(iA13 + A23) + D 2J (ieφ + eθ)� asa† ra† qei(ks−kq)·rψ∗ r + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' � dr, (3) where Aνν′ = Ax,νν′ex + Ay,νν′ey are the gauge fields (ν, ν′ = 1, 2, 3), eθ and eφ are two unit vectors in spherical coordinates, and ωs, ωp, and ωq are, respectively, the frequencies of the in- cident, confluence, and splitting magnons meeting law of en- ergy conservation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=', ωp(q) = ωs ± ωr with ωr the skyrmion breathing frequency, see the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Equa- tions (2) and (3) show that the conventional gauge field A12 only appears in the quadratic term, while gauge fields A13 and A23 emerge in the nonlinear three-magnon processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To re- veal their role in the magnon transport, we employ the Euler- Lagrangian formula to derive equations of motion of magnon wavepackets a† i ai ℏω2 i eJ ˙vi − a† i aiωivi × B − Fcubic i = 0, (i = s, p, q), (4) where B = Bzez with Bz = ℏ e �∇ × (A12 + Dl0 2J )� z = ℏ e �l0 · (∂xl0 × ∂yl0) + (∇ × Dl0 2J )z � is the conventional fictitious magnetic field for the linear magnon transport with the reduced Planck con- stant ℏ and elementary charge e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' See Supplemental Material [56] for the derivation of (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is noted that we have ig- nored the effective electric field associated with the skyrmion static energy due to its negligible role in the magnon Hall ef- fect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The extra force Fcubic i originates from the three-magnon process and the newfound gauge fields, with the following ex- pression Fcubic i = civi × B′, (i = s, p, q), (5) where B′ = B′ zez with B′ z = ℏ e(∇×A23)z+ ℏD 2Je(∇×eθ)z = ℏ e �∂yl0· ∂x(n× ez sin θ)−∂xl0 ·∂y(n× ez sin θ)�+ ℏD 2Je(∇× ez+cos θl0 sin θ )z represents the new fictitious magnetic field playing a role merely when the nonlinear three-magnon process occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Due to the circu- lar symmetry of skyrmion, the A13 component is absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, cs = ωs 4 (gpa† paras + 3gqa† qa† ras + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='), cp = 3ωp 4 (gpasara† p + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='), and cq = ωq 4 (gpasa† ra† q + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='), with overlap integrals gp = 1 √ 2V � ei(ks−kp)·rψrdr, gq = 1 √ 2V � ei(ks−kq)·rψ∗ rdr, and V being the system volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (4), the spin-wave packet can be regarded as a particle-like object moving in its own parameter space [57] subject to fictitious magnetic fields 3 (B and B′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The first term on the left-hand side of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (4) char- acterizes the acceleration of magnons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The second term rep- resents the effective Lorentz force from the quadratic Hamil- ton H2, resulting in the conventional topological magnon Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Interestingly enough, the third term induces an ex- tra Lorentz force on the wavepacket, leading to the nonlinear topological magnon Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The spatial distributions of the dimensionless magnetic fields Bz/B0 and B′ z/B0 are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 2(a) and 2(b), respectively, where B0 = ℏ/a2e with a being the lattice constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is noted that B0 ≈ 660 T for a = 1 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Due to the rotational symmetry of the Bloch skyrmion, both magnetic fields B/B0 and B′/B0 have the circular sym- metry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' For B/B0, its main origin comes from the topological charge density of skyrmion, and the total magnetic flux is 4π [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The spatial distribution of B′/B0, however, is similar to the fictitious magnetic field distribution of the target skyrmion [59, 60] with a vanishing total flux but a singularity at the skyrmion core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Revealing the concealed fictitious magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='—In non- linear magnon-skyrmion scatterings, the time-evolution of populations of confluence and splitting modes is governed by the coupled Heisenberg equations: i˙ap = (∆p − iαωp)ap + ˜gpasar and i˙aq = (∆q − iαωq)aq + ˜gqasa† r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' the detun- ing parameter ∆p(q) = ωp(q) − ω0 with the driving microwave frequency ω0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' ˜gp = � � − 2g1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µikp,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µψr + g∗ 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ(∂µψr + iks,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ) − 5√ 2K sin θ cos θ�ei(ks−kp)·rdr and ˜gq = � �g2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ(∂µψ∗ r + ikq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ) + 2g∗ 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µiks,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µψ∗ r − 5√ 2K sin θ cos θ�ei(ks−kq)·rdr where the Einstein summation rule is applied,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' coefficients g1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ = 3J 2 √ 2(Aµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='13 − iAµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='23) + 3D 4 √ 2(eφ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ − ieθ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ) and g2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ = J√ 2(−Aµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='13 − iAµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='23) + D 2 √ 2(−eφ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ − ieθ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='µ) denote the strength of the three-magnon confluence and splitting,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' and α is the Gilbert damping constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Then, one can analytically derive the steady-state magnon populations as ap = gasar ϵ+iα(ωs+ωr) and aq = gasa† r ϵ−iα(ωs−ωr) with ϵ = ωs − ωr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, we have adopted the approximation ˜gp ≈ ˜gq ≈ g which is justified by the small difference between confluence and splitting frequencies since ωr ≪ ωs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We therefore obtain msw, i˙vi − evi × σ(B + λiB′) = 0, (i = s, p, q), (6) which is the main result of this work (see Supplemental Ma- terial [56] for detailed derivations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, msw,i = ℏωi/J is the effective mass of the spin-wave packet in antiferromag- nets, σ = ∓1 represents the left/right-hand magnon polar- izations, λs = nr( ggp 4ϵ + 3ggq 4ϵ + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='), λp = 3 4( ϵgp g + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='), and λq = 1 4( ϵgq g + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=') with the particle number of skyrmion breathing mode nr = ⟨a† rar⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Equation (6) shows that the ex- tra effective Lorentz force eλivi × σB′ (i = s, p, q) is mode- dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' For incident magnons, the extra Lorentz force is proportional to the product of the skyrmion breathing number nr (≪ 1), the coupling parameter g/ϵ, and the overlap inte- gral gp,q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In general, magnon populations of confluence and splitting modes are far less than the incident one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It implies g/ϵ, gp,q ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The effect of B′ on incident magnons is thus (a) 0 50 100 50 100 (c) 0 50 100 50 100 (d) (b) 0 50 100 50 100 50 100 0 50 100 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 2: Spatial distribution of dimensionless field Bz/B0 (a) and B′ z/B0 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Spin wave trajectories in real space under fictitious mag- netic field B (c) and B+B′ (d), where different black curves represent trajectories of magnon wavepackets with different impact parame- ters, the red curve indicates the averaged trajectory of 51 magnon wavepackets, and the dashed green circle labels skyrmion’s wall cen- ter (lz = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' However, for the confluence and splitting modes, parameters λp,q are inversely proportional to g/ϵ, the addi- tional effective Lorentz force is therefore expected to bring an enormous effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To explore the role of fictitious magnetic fields on the magnon transport, we numerically solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (6) both without and with the new fictitious magnetic field B′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In calculations, we consider a right-handed magnon wavepacket (σ = 1), and set the incident-magnon’s initial velocity vs(t = 0) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='65 (with unit J/aω) along x direction, magnon mass msw = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='31 (with unit ℏω/J), and coefficient λs,p,q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is observed that the effective magnetic field B′ significantly enhances the magnon Hall effect, as displayed in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 2(c) and 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Due to the singularity of the fictitious magnetic field B′, we note anomalous magnon trajectories near the skyrmion center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Be- low, we verify our theoretical predictions by full micromag- netic simulations using MUMAX3 package [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We consider an AFM thin film of dimension 1000 ×1000 ×1 nm3, hosting a Bloch-type skyrmion at the film center [62– 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Magnetic parameters of KMnF3 [65]: J = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='59 pJ/m, K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='16 × 105 J/m3, and D = 1 mJ/m2 are used in the simulations, which gives rise to a skyrmion radius ≈ 11 nm (defineds as the radius of circle lz = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The Gilbert damp- ing is set as α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To efficiently generate polarized magnons and the three-wave mixing, we apply a microwave field hRH/LH(t) = h0[cos(ωst)ex ∓ sin(ωst)ey] with amplitude h0 = 50 mT and frequency ωs/2π = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='205 THz (generating the incident magnon of wavelength ≈ 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='2 nm) on one sublat- tice in a narrow region: −401 nm≤ x ≤ −399 nm and a local field hr(t) = hr sin(ωrt)ez over the skyrmion with amplitude 0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0 B"\\Bo17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0- ↑7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0- 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0- r0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='04 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='56 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='8 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='87 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='18 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='52 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='74 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='56 56 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='19 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='76 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='44 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='2 FFT amplitude (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' units) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='11 THz 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='11 THz 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='205 THz 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='205 THz 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='3 THz 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='3 THz (a) (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3: (a) MFC in the nonlinear scattering between the incident magnon and AFM skyrmion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (b) Isoline maps for righted-handed (top panel) and left-handed (bottom panel) magnons scattered by the skrymion at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' In each panel, modes from left to right corre- spond to splitting, incident, and confluence magnons, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' hr = 5 mT and ωr/2π = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='095 THz (the skyrmion breathing frequency) [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, RH and LH represent the abbrevia- tion of microwave with right and left handedness, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Absorbing boundary conditions are adopted to eliminate the spin-wave reflection by film edges [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To analyze the magnon spectrum in the skyrmion area, we implement fast Fourier transform of local magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Figure 3(a) shows the emerging magnon frequency comb (MFC) [52] in the terahertz region, where the mode spacing of the comb is exactly the skyrmion breathing frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fur- thermore, we plot the isoline map of incident, confluence, and splitting modes to analyze the Hall angle of each mode, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We observe an interesting “bunny ears” pattern of magnons scattering off the AFM skyrmion, with red and blue lines denoting the propagation direction of two branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Here, the Hall angle is defined as the included angle between each branch and the horizontal line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Compared with the incident mode, the Hall angle of nonlinear modes nearly doubles (quintuples) for the main (secondary) branch of the “bunny ears” [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3(b)], where the major (secondary) branch is referred to as the one with a large (small) Hall an- gle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' More importantly, by flipping the chirality of incident magnons, we observe an opposite magnon Hall motion [com- paring the top and bottom panels in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The small dif- ference of Hall angles between right-handed and left-handed magnons results from the dipolar field [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Micromagnetic (a) (b) sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' fitting theo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' mode s p q FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 4: (a) The Hall angle of the main branch of “bunny ears” as a function of the driving frequency for the incident (black), confluence (blue), and splitting (red) modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Symbols are micromagnetic simu- lations and curves are analytical fitting by solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' (b) The Hall angle as a function of the mode index m for different incident magnon frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Symbols and lines represent micromagnetic simulations and linear fittings, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' simulations thus offer solid evidences for the nonlinear topo- logical magnon spin Hall effect as we predicted above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Furthermore, we derive the frequency-dependent Hall angle by fitting the flow direction of the main branch of the isosur- face of each mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Figure 4(a) plots the quantitative compar- ison between theoretical calculations and micromagnetic sim- ulations for incident (black), confluence (blue), and splitting (red) modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It shows that the Hall angle monotonically de- creases with the increase of the mode frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Simulation results can be well explained by the analytical model (6) with parameters nr = 0, g = 49 MHz, and gp = 1 3gq = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='4 × 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A vanishing mode number of skyrmion breathing is justified by its small wave amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' The coupling coefficient g is independently obtained by numerically solving the coupled Heisenberg equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Acceptable deviations could be at- tributed to the simplified wavepacket treatment in the present formalism and the neglected topological electric-field compo- nent of the gauge fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Figure 4(b) shows the Hall angle of nonlinear magnons over a broad frequencies ωs + mωr in the MFC with integer m labeling the order of the spectrum line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Their “bunny ears” scattering patterns are plotted in Supple- mental Material [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is found that the noninear Hall an- gle increases linearly with |m|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' This monotonic dependence is reminiscent of the refraction process of light waves through multilayer media [67], where the refraction angle accumulates upon each scattering layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' It is noted that the slope of the lin- ear trendline decreases as the incident magnon’s frequency ωs increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='—In the above calculations, we have considered rotationally symmetric spin textures, the A13 gauge field thus vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' However, the curl of gauge field induced by DMI becomes finite when the rotational symmetry is broken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We then envision contributions from A13 in generating the ficti- tious magnetic field for elliptical skyrmions [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' To summarize, we revealed the long-sought gauge fields concealed in the nonlinear magnon transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' By investigat- ing the three-wave mixing between propagating magnons and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content="0 0'4S." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content="0 0'4S." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content="0 0'45 breathing skyrmions, we found giant Hall angles emerging for each nonlinear spectrum line of the MFC." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' We further identi- fied that the sign of the Hall angle is reversed by switching the chirality of incident magnons, and we dub it nonlinear topo- logical magnon spin Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Our findings are intimately connected to the particle number nonconservation of magnons and thus applicable to generic bosons, which does not have the low-energy fermionic counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Our results significantly advance the understanding of the nonlinear Hall effect and pave the way to probing the gauge field by frequency comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' This work was funded by the National Key Research Devel- opment Program under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 2022YFA1402802 and the National Natural Science Foundation of China (NSFC) (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 12074057).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' acknowledges financial support from the NSFC (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 12204089) and the China Post- doctoral Science Foundation under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 2019M653063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' acknowledges the European Union’s Horizon 2020 re- search and innovation programme under Marie Skłodowska- Curie Grant Agreement SPINCAT No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 101018193.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' ∗ yan@uestc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='cn [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Delplace, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Marston, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Venaille, Topological origin of equatorial waves, Science 358, 1075 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Parker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Marston, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tobias, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhu, Topolog- ical Gaseous Plasmon Polariton in Realistic Plasma, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 124, 195001 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [3] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kato, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Myers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gossard, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Awschalom, Observation of the spin Hall effect in semiconductors, Science 306, 1910 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wunderlich, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kaestner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sinova, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jungwirth, Ex- perimental Observation of the Spin-Hall Effect in a Two- Dimensional Spin-Orbit Coupled Semiconductor System, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 94, 047204 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sinova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Valenzuela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wunderlich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Back, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jungwirth, Spin Hall effects, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 87, 1213 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kavokin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Malpuech, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Glazov, Optical Spin Hall Effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 95, 136601 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Leyder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Romanelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Karr, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Giacobino, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liew, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Glazov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kavokin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Malpuech, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Bra- mati, Observation of the optical spin Hall effect, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 3, 628 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Onose, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ideue, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Katsura, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shiomi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nagaosa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [9] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shen, Magnon Spin Relaxation and Spin Hall Effect Due to the Dipolar Interaction in Antiferromagnetic Insulators, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 124, 077201 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sinova, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Culcer, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Niu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sinitsyn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jungwirth, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' MacDonald, Universal Intrinsic Spin Hall Effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 92, 126603 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [11] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Guo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Murakami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chen, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nagaosa, Intrin- sic Spin Hall Effect in Platinum: First-Principles Calculations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 100, 096401 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [12] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Barlas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zang, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lake, Topological spin Hall effect resulting from magnetic skyrmions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 92, 024411 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G¨obel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mook, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Henk, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mertig, Antiferromagnetic skyrmion crystals: Generation, topological Hall, and topologi- cal spin Hall effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 96, 060406 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Akosa, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tretiakov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tatara, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Manchon, The- ory of the Topological Spin Hall Effect in Antiferromagnetic Skyrmions: Impact on Current-Induced Motion, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 121, 097204 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Daniels, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xiao, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xiao, Topo- logical spin Hall effects and tunable skyrmion Hall effects in uniaxial antiferromagnetic insulators, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 99, 224433 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nakata, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Loss, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tserkovnyak, Tunable Magnonic Thermal Hall Effect in Skyrmion Crystal Phases of Ferrimagnets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 122, 057204 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [17] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Du, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Han, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Camino, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhu, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Petrovic, Topological Hall Effect Anisotropy in Kagome Bilayer Metal Fe3Sn2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 129, 236601 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, All-Magnonic Spin- Transfer Torque and Domain Wall Propagation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 107, 177207 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kamra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Duine, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, Quan- tum magnonics: When magnon spintronics meets quantum in- formation science, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 965, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [20] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Dugaev, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Bruno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Canals, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lacroix, Berry phase of magnons in textured ferromagnets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 72, 024456 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kovalev and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tserkovnyak, Thermomagnonic spin transfer and Peltier effects in insulating magnets, EPL 97, 67002 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' van Hoogdalem, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tserkovnyak, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Loss, Magnetic texture-induced thermal Hall effects Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 87, 024402 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sch¨utte and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Garst, Magnon-skyrmion scattering in chiral magnets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 90, 094423 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lan and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xiao, Skew scattering and side jump of spin wave across magnetic texture, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 103, 054428 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [25] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Bao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cao, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, All-magnonic Stern- Gerlach effect in antiferromagnets, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 120, 242403 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [26] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Meng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zeng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Qin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, Magnon-driven skyrmion dynamics in antiferromagnets: Effect of magnon po- larization, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 104, 054419 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [27] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zeng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Qin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, Spin- wave-driven skyrmion dynamics in ferrimagnets: Effect of net angular momentum, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 106, 064424 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ho, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jalil, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Murakami, Yang-Mills physics in spintronics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 882, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [29] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tatara, Effective gauge field theory of spintronics, Physica E 106, 208 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [30] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sodemann and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fu, Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materi- als, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 115, 216806 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [31] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ma, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' MacNeill, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fatemi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Valdivia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Du, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hsu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gibson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Taniguchi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cava, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kaxiras, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='- Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gedik, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Herrero, Observation of the nonlinear Hall effect under time-reversal-symmetric con- ditions, Nature (London) 565, 337 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Li, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sohn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mak, Nonlinear anomalous Hall effect in few-layer WTe2, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 18, 324 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [33] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Du, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xie, Band Signatures for Strong Nonlinear Hall Effect in Bilayer WTe2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 6 Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 121, 266601 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [34] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' He, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Heinonen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Vi- gnale, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yang, Nonlinear Planar Hall Effect, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 123, 016801 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [35] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Shao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gurung, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yang, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tsym- bal, Nonlinear Anomalous Hall Effect for N´eel Vector Detec- tion, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 124, 067203 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Feng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Novoselov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yang, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gao, Third-order nonlinear Hall effect induced by the Berry-connection polariz- ability tensor, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nano.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 16, 869 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Duan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Peng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Feng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mao, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yao, Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 129, 186801 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Itahashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ideue, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hoshino, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Goto, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Namiki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sasagawa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Iwasa, Giant second harmonic transport un- der time-reversal symmetry in a trigonal superconductor, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 13, 1659 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [39] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Du, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Xie, Nonlinear Hall effects, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys 3, 744 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mook, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G¨obel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Henk, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mertig, Taking an electron- magnon duality shortcut from electron to magnon transport, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 97, 140401 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [41] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kondo and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Akagi, Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Research 4, 013186 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tymchenko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Gomez-Diaz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lee, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nookala, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Belkin, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Al`u, Gradient Nonlinear Pancharatnam-Berry Metasurfaces, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 115, 207403 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [43] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Pholchai, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Reineke, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wong, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Pun, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cheah, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zentgraf, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhang, Continuous control of the nonlinearity phase for harmonic generations, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 14, 607 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [44] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Li, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yesharim, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hurvitz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Karnieli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Porat, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Arie, Adiabatic geometric phase in fully nonlinear three- wave mixing, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A 101, 033807 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [45] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Duine, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, Magnonic Frequency Comb through Nonlinear Magnon- Skyrmion Scattering, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 127, 037202 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [46] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cao, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, Twisted Magnon Frequency Comb and Penrose Superradiance, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 129, 107203 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [47] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Janssens, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' van Kampen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ciubotaru, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hermsdoerfer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Obry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Laraoui, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Serga, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lagae, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Slavin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Leven, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hillebrands, Direct Current Control of Three Magnon Scattering Processes in Spin-Valve Nanocon- tacts, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 103, 157202 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [48] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Iwasaki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Beekman, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nagaosa, Theory of magnon- skyrmion scattering in chiral magnets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 89, 064412 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [49] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Cao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, Eaves- dropping on spin waves inside the domain-wall nanochannel via three-magnon processes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 97, 094421 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [50] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Verba, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wehrmann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wagner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K¨orber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hula, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hache, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K´akay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Awad, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tiberkevich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Slavin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fassbender, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, Excitation of Whis- pering Gallery Magnons in a Magnetic Vortex, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 122, 097202 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [51] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K¨orber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hula, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Verba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fassbender, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K´akay, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, Nonlocal Stimulation of Three- Magnon Splitting in a Magnetic Vortex, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 125, 207203 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Hula, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiss, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Goncalves, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K¨orber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Be- jarano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Copus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Flacke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Liensberger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Buzdakov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' K´akay, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Weiler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Camley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fassbender, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Schultheiß, Spin-wave frequency combs, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 121, 112404 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [53] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Holstein and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 58, 1098 (1940).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [54] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mochizuki, Spin-Wave Modes and Their Intense Excita- tion Effects in Skyrmion Crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 108, 017061 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Thiele, Steady-State Motion of Magnetic Domains, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 30, 230 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [56] See Supplemental Material at http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content='org/supplemental/ for the derivation of equations of motion for magnon wavepack- ets, the numerical verification of the skyrmion breathing and its frequency, the analysis of magnon polarizations on their non- linear topological Hall transport, and the isolines of incident magnons scattered by skyrmions with and without breathing, which includes Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [16, 45, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [57] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Sundaram and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Niu, Wave-packet dynamics in slowly per- turbed crystals: Gradient corrections and Berry-phase effects, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 59, 14915 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [58] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Volovik, Linear momentum in ferromagnets, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' C 20, L83 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [59] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lv, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Wei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Zang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tian, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Du, Magnetic skyrmion bundles and their current- driven dynamics, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nanotechnol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 16, 1086 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [60] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ndiaye, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Akosa, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Manchon, Topological Hall and spin Hall effects in disordered skyrmionic textures, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B 95, 064426 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Vansteenkiste, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Leliaert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Dvornik, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Helsen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Garcia- Sanchez, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Waeyenberge, The design and verification of MUMAX3, AIP Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 4, 107133 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' M¨uhlbauer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Binz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jonietz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Pfleiderer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rosch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Neubauer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Georgii, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' B¨oni, Skyrmion Lattice in a Chiral Magnet, Science 323, 915 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [63] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Onose, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kanazawa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Matsui, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Nagaosa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature (London) 465, 901 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [64] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Huang and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Chien, Extended Skyrmion Phase in Epitaxial FeGe (111) Thin Films, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 108, 267201 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [65] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Barker and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Tretiakov, Static and Dynamical Proper- ties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 116, 147203 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [66] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Venkat, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Fangohr, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Prabhakar, Absorbing boundary layers for spin wave micromagnetics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 450, 34 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [67] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Lax, Multiple Scattering of Waves, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 23, 287 (1951).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' [68] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Jena, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' G¨obel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Ma, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Saha, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Mertig, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Felser, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Parkin, Elliptical Bloch skyrmion chi- ral twins in an antiskyrmion system, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} +page_content=' 11, 1115 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfewTK/content/2301.03211v1.pdf'} diff --git a/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/2301.04114v1.pdf.txt b/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/2301.04114v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9c5700fff8741efc6ee4bc9529c9c422e3555b12 --- /dev/null +++ b/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/2301.04114v1.pdf.txt @@ -0,0 +1,1154 @@ +Drug design on quantum computers +Raffaele Santagati,1, ∗ Alan Aspuru-Guzik,2 Ryan Babbush,3 Matthias Degroote,1 Leticia Gonz´alez,4 +Elica Kyoseva,1, † Nikolaj Moll,1 Markus Oppel,4 Robert M. Parrish,5 Nicholas C. Rubin,3 Michael +Streif,1 Christofer S. Tautermann,6, 7 Horst Weiss,8 Nathan Wiebe,2 and Clemens Utschig-Utschig1 +1Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany +2Department of Computer Science, University of Toronto, Canada +3Google Quantum AI, Venice, CA 90291, United States +4Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, W¨ahringer Straße 17, 1090 Vienna, Austria +5QC Ware Corp, Palo Alto, CA 94306, United States +6Boehringer Ingelheim Pharma GmbH & Co KG, Birkendorfer Strasse 65, 88397 Biberach, Germany +7Department of General, Inorganic and Theoretical Chemistry, University of Innsbruck, 6020 Innsbruck, Austria +8Next Generation Computing in Global Digitalization, BASF SE, +Carl-Bosch-Strasse 38, 67056 Ludwigshafen am Rhein, Germany +Quantum computers promise to impact industrial applications, for which quantum chemical cal- +culations are required, by virtue of their high accuracy. This perspective explores the challenges and +opportunities of applying quantum computers to drug design, discusses where they could transform +industrial research and elaborates on what is needed to reach this goal. +INTRODUCTION +For over fifty years, the pharmaceutical industry has +seen the cost of developing drugs increase exponentially +from tens of millions in the 1950s to billions of dollars +today, even when the data is adjusted for inflation [1]. +To sustain the progress in treating unmet medical need, +it is essential to look for every source of improvement +in the methodologies employed in drug development. In +the last decades, computational approaches started to +play an increasingly large role in research and devel- +opment [2, 3]. +Many computational methods are em- +ployed from machine learning [4, 5] and molecular dy- +namics [6, 7] to quantum mechanical calculations [8]. +Still, simulating chemical systems, including quantum +mechanical effects, can be computationally intensive and +many of these methods face limited practical applicabil- +ity because of speed and accuracy. +By exploiting their quantum mechanical properties, +quantum computers have been proposed to simulate +quantum systems efficiently [9–13]. +Inspired by this +promise, quantum computing research has proliferated +in recent years, and a community of quantum physics, +chemistry, and information theory experts has brought +improvements in quantum hardware and algorithms [14, +15]. The recent developments also attracted interest be- +yond academia to find practical applications in indus- +try, with investments from private and public sectors. +Often, one of the justifications for those investments is +the promise that quantum computers will enhance quan- +tum chemistry calculations [15–19]. +Most current ef- +forts in quantum computing focus on finding quantum +algorithms for the most challenging electronic structure +∗ raffaele.santagati@boehringer-ingelheim.com +† Present Address: Wellcome Leap Inc., Los Angeles, CA 90069, +United States +problems, for which the largest possible advantage over +classical computations can be expected. However, iden- +tifying such systems with strong electronic correlations +is difficult [20], and there only are a limited number of +indicators, such as those shown in Box I. While solving +the electronic structure problem is an important step for +many chemical applications, if the advantage of quantum +computers is limited to strongly correlated systems, they +might have limited practical significance in drug design. +In this perspective, we discuss the status quo of the ap- +plicability of future quantum computers to problems in +drug discovery; specifically, we focus on quantum chem- +istry calculations because, in our opinion, these will be +the first viable applications to impact drug design. +While we do not give an exhaustive presentation of +the status of quantum computing, we discuss problems in +quantum chemistry for which quantum computers could +offer a speed-up compared to classical computing meth- +ods and compare these problems with the actual compu- +tational needs in computer-aided drug design. Lastly, we +discuss research directions to make quantum computers +an essential tool in the pharmaceutical industry. +I. +STATUS QUO: QUANTUM COMPUTERS +The field of quantum computing has seen rapid devel- +opments in the last decade [13–15]. Still, the way towards +a practical quantum advantage requires major progress +for hardware and algorithms [37, 38]. The most impor- +tant metric for the development of quantum algorithms +is the estimation of their computational cost. These es- +timates define the quantum computing resources (qubits +and run-time) required to solve a problem of interest. +They provide concrete engineering targets for quantum +hardware and shed light on what aspects of the algo- +rithms need improvements. +arXiv:2301.04114v1 [quant-ph] 10 Jan 2023 + +2 +Box I: Some indicators of strong electronic +correlation +Quantum computers are expected to offer an advan- +tage for solving the electronic structure problem of +strongly correlated systems. +Five different indica- +tors with their graphical representations are shown. +There are two regions labelled Classical for cases solv- +able on a classical computer [21–25] and Quantum for +cases where a quantum computer might be required. +Multi-reference: system’s +wavefunction +requiring +many +reference +states +(determinants) with compa- +rable amplitudes [26–28]. +Amplitude +States +Classical +Quantum +Essential spin-symmetry +breaking: +not +fixed +by +adding +dynamical +correla- +tion [29]. +Classical +Quantum +Total spin +Energy +Cluster +expansion have +characteristic failure points +indicating the need for a +multi-reference +model +[30, +31]. +Interaction Strength +Classical +Quantum +CC order +RMS +Amplitude +Near degenerate natural +orbitals +with +non-integer +occupation numbers, e.g. de- +tected from orbital occupa- +tion analysis [21, 32, 33]. +Classical +Quantum +Occupation +Energy +The +number +of +entan- +gled +orbitals grows pro- +portionally to system size, +which +also +needs +to +be +large enough to be classi- +cally hard [34, 35], image +adapted from [36]. +Quantum +correlation +Today, +only +Noisy +Intermediate +Scale +Quantum +(NISQ) computing hardware exists, named after its noisy +nature and the limited number of qubits [39, 40]. Most +NISQ algorithms, e.g., variational quantum eigensolvers +(VQE) [41, 42], heavily rely on classical optimisation +heuristics, and the actual run-time is difficult to esti- +mate. +Also, recent results suggest that in NISQ, the +number of measurements required to achieve a given er- +ror scale exponentially with the depth of the circuit [43]. +For these reasons, we focus our discussion exclusively on +fault-tolerant quantum computers (FTQCs). +FTQCs exploit quantum error correction to exponen- +tially suppress errors [44], at the cost of considerable +additional qubits and run-time. +For example, simu- +lating a classically challenging molecule, such as the +iron-molybdenum complex (FeMoco) [45], would require +roughly 200 logical (error-corrected) qubits which would +be implemented in 2 million physical qubits [46], well +beyond what is achievable with current quantum hard- +ware [40]. +Quantum computers are expected to offer a clear ad- +vantage in finding the ground state energy of a molecular +Hamiltonian (i.e. solving the electronic structure prob- +lem) for strongly correlated systems where all tractable +classical methods fail. To identify those systems, several +conditions need to be satisfied (see Box I), and verify- +ing them can be very demanding and time-consuming +and heavily relies on chemical expertise. Over the past +twenty years, several techniques have been developed for +studying how and when various ab initio methods fail, +delivering indicators of strong correlations [35]. Typical +examples of such situations that require expensive multi- +reference treatment are multi-metal systems, where met- +als are in similar electronic environments and interac- +tions. +A quantum computer can perform such calculations +in polynomial time without making any uncontrolled ap- +proximations if the initial state is close to the ground +state [47–49]. The ground state energy is computed with +a combination of state preparation and quantum phase +estimation (QPE). QPE is a very efficient algorithm to +find the eigenstates and eigenvalues of a Hamiltonian, +and it is at the core of many quantum computing meth- +ods. In Figure 1, we give an example of how these cal- +culations can be performed on quantum computers for +a chemical system. The presented workflow starts on a +classical computer, which helps in refining the geometry +of the chemical system, identifying a good initial state for +the system and synthesising the error-corrected quantum +circuit. The quantum computation starts with internally +preparing this classically-determined initial state. The +next step in the workflow is the application of QPE to the +initial state. The cost of estimating the correct ground +state energy depends directly on the overlap of the initial +state with the ground state, and it becomes progressively +more expensive as the overlap with the correct ground +state decreases [20, 48–50]. Modifications to this work- +flow allow for the calculation of other observables [51], +e.g., molecular forces [52–54]. +Even though FTQC algorithms cannot yet be exe- +cuted, many methods already exist to evaluate their com- +putational cost. For example, for the ground state energy +of the FeMoco [27, 45], through algorithmic improve- +ments, the run-time estimates have been reduced from +years to days [19, 45, 46, 55, 56]. Further improvements +will certainly come, and we will be able to perform such +calculations in the future on an FTQC. In the next sec- +tions, we discuss the state of the art of drug design and +where quantum computers could be employed to solve +the electronic structure part of the problem for relevant +pharmacological systems [19, 28, 57, 58]. + +3 +Accurate +description +of chemical +properties +Quantum algorithm +design +Quantum error + correction +Classical preprocessing +Quantum phase +estimation +Quantum computation +Experimental +structure +determination +Computational geometry +refinement +Generation of +initial state +Initial state +preparation +GND 1st 2nd 3rd 4th 5th +Amplitudes +Eigenstate +QPE +Eigenstate +GND 1st 2nd 3rd 4th 5th +Amplitudes +FIG. 1. +The workflow of electronic structure calculations on quantum computers using the quantum phase estimation (QPE) +algorithm. The first step includes classical preprocessing to optimise the geometry and the Hamiltonian. Afterwards, the +quantum circuits are generated. The calculation on the quantum computer starts with the generation of the initial state, +which is followed by the more expensive calculation of the ground state energy with the QPE. The lower part of the quantum +computation container: The initially prepared state consists of a superposition of many eigenstates but with a high overlap +with the ground state. When the ground state (GND) energy is measured, the initial state is projected into the ground state. +II. +COMPUTER-AIDED DRUG DESIGN +Chemical compounds produced in the pharmaceutical +industry result from a long process of discovery and re- +finement. The steps are summarised in Fig. 2. The drug +discovery process starts with identifying a target protein +involved in the disease pathology. Pharmacological mod- +ulation of this target is assumed beneficial for treating +the disease [59, 60] and is achieved with a molecule bind- +ing to the target. Identifying oral drug candidates, the +most preferred form of drug administration, takes a long +time, starting with very weak binders and taking sev- +eral years of optimisation towards efficacious and safe +molecules [1, 3, 5]. +Millions of compounds are initially screened out of +1060 potential molecules [61]. In the initial stages of the +process, many different properties (e.g., binding affinity) +have to be optimised. Therefore, in the so-called hit-to- +lead and lead-optimisation programs, several thousands +of molecules are synthesised before suitable candidates +for the next steps towards clinical development are identi- +fied [62, 63]. Every synthesised molecule undergoes test- +ing in-vitro (biochemical, biophysical, cellular), and in +case of good properties, also in in-vivo (in an organism) +assays; therefore, the goal is to achieve clinical candi- +dates with the lowest number of optimisation cycles pos- +sible. In this phase of drug discovery, computational ap- +proaches are highly valuable by guiding the design of the +right molecules, and recently several striking successes in +computational design have been reported [2, 5]. +Two major areas where computational chemistry can +support drug design have been identified: (1) the predic- +tion of pharmacokinetic properties (how the compound +is absorbed, distributed, metabolised and excreted from +the body), commonly realised by machine learning mod- +els trained on a wealth of experimental data from the +heritage of projects in a pharma company [4, 64–66]; (2) +the calculation of the binding strength or binding affinity +Registration +Drug candidate +Developement +Lead optimisation +Hit to lead +Hit identification +Discovery research +Target identification +4-5 years +6-8 +years +1-2 +years +1 molecule +5 molecules +200 molecules +10 000 molecules +• Docking +• Virtual screening +• Pharmacohore mapping +• De novo design +• QSAR +• Molecular dynamics +• Quantum mechanics +• Enhanced sampling +1060 of possible +molecules +10s of parameters +to be optimised +1000s of compounds +to be synthesised +FIG. 2. +Workflow in the drug discovery process [3, 63]. +Once the biological target has been identified, the process +starts with the hit finding stage in a potential space of 1060 +molecules [61]. Through a repeated cycle of design, analysis, +synthesis, and in-silico and in-vitro testing, the number of +promising compounds is decreased from 10 000s to a few hun- +dred by designing and selecting those with the best predicted +and measured properties. Only very few highly optimised and +safe molecules proceed into development towards the clinical +trials, and only one is finally selected for approval by the +medicinal agencies [63]. On the right side, the computational +methods employed in the different stages of the drug design +process from [3] are listed. +of a compound to the target, which is one of the most +important properties of a drug candidate [67, 68]. The +binding affinity is equivalent to the binding free energy +between the drug and the target. It directly corresponds +to the required local drug concentration at the target, de- +termining drug efficacy. Therefore, it translates into the +projected therapeutic human dose, the most important +single parameter during drug design. Computations of +the binding strength must be accurate in compound op- +timisation [69]. However, state-of-the-art methods based + +4 +FIG. 3. +Schematic representation of a drug binding event +(pdb ID: 2RGU). The ligand exists as an ensemble of confor- +mations/geometries and orientations (left). Some approaches +of the ligand towards the target result in binding, and some +do not - as indicated by the arrows (right). Eventually, the +sampling of ensembles of unbound and bound structures in so- +lution yield the free energy of drug-target binding [74]. Equiv- +alently, energy differences of ensembles of bound, structurally +similar ligands directly relate to the difference in their binding +strength. +on molecular dynamics simulations with classical force +fields do not perform reliably [70]. The goal is to achieve +high accuracy (within 1.0 kcal/mol to experiment) be- +cause, at physiological temperatures, a 1.5 kcal/mol de- +viation already translates into a dose estimation which +is wrong by one order of magnitude. On an atomistic +scale, a system can be treated on a classical computer +with many different levels of approximations for differ- +ent sizes considered; see BOX II where some common +methods are reported. In contrast to force fields, den- +sity functional theory (DFT) or coupled cluster (CC), +which are methods based on quantum mechanics, lead to +much better descriptions of molecular interactions but at +a much higher computational cost [68]. +Other difficulties in these calculations stem from the +thermodynamic nature of the compounds’ properties [74, +75]. A molecule can bind to a protein in many different +ways [76]. One has to consider different accessible system +geometries and binding pathways. One needs to identify +the configuration with minimal free energy, which is the +statistically most frequently observed one. In Figure 3, +the process of a molecule binding to a protein is picto- +rially depicted. Many different configurations and, thus, +many single-point calculations must be computed. +When evaluating many compounds with similar chem- +ical structures for their binding propensity, it is often +faster to compute the difference in binding strength be- +tween the compounds directly; this task is often accom- +plished with alchemical perturbation methods [67], where +a known compound is gradually morphed into a new one +adapting the electronic structure accordingly [77]. In this +respect, simulating the ensemble properties, by, e.g. nat- +Box II: Common electronic structure methods +employed on classical computers +Commonly used quantum chemistry methods to solve +the electronic structure problem. In the left column, +we zoom in on the Compound I intermediate of Cy- +tochrome c Peroxidase (PDB ID: 1ZBZ [71–73]). As +the method’s accuracy increases from top to bottom, +the molecules that can be calculated with classical +hardware become increasingly smaller. +Cytochrome c in +solution +Binding site +Heme group +Iron cluster +Force Fields/ +Semi-empirical Methods +Methods that cannot fully +describe quantum mechani- +cal effects but can be tuned +with information from quan- +tum methods. +Hartree-Fock/ +Density Functional +Theory (DFT) +Mean-field +methods +treat +electrons in the presence of +the average potential of the +other electrons. +DFT in- +cludes electronic correlation, +while Hartree-Fock does not. +Coupled-Cluster (CC) +Cluster wavefunction meth- +ods that expand around a +single mean-field reference. +Full Configuration +Interaction (FCI) +Method that delivers the ex- +act energy of the electronic +structure problem within a +finite basis set. +ural time-evolution, of the drug-target complex is a key +step from which knowledge about thermodynamic prop- +erties can be directly derived [78, 79]. +The systems, including target, drug, and solvent, are +made of several thousands of atoms (see BOX II), and +free energy calculations require billions of single point +calculations, where energy and force evaluation are per- +formed, see Figure 3. Furthermore, the necessary inclu- +sion of explicit solvent (water) in the model can con- +siderably increase the degrees of freedom and complex- +ity [75, 80], making run-time often impractical. The cal- + +T5 +culation of the binding free energy of a small molecule +to its target protein can take many hours on a classical +computer. Increasing accuracy, e.g. by exploiting DFT, +increases the calculation costs by several orders of mag- +nitude, rendering the full DFT treatment for free energy +calculations elusive. Higher levels of theory treatments, +such as CC, which require even more computational re- +sources, are, therefore, fully out of scope and can only be +applied to small systems. +Other potential use cases for quantum computing in +drug development are the calculation and optimisation +of reaction mechanisms [81] for optimising the drug syn- +thesis conditions and the calculation of molecular spec- +tra for nuclear magnetic resonance (NMR), infra-red (IR) +or vibrational circular dichroism (VCD) spectroscopy to +identify structures [82–84]. However, the impact of quan- +tum computing on these use cases for drug design would +be rather modest if compared to the potential impact +of better and faster calculations at the drug design stage +(lead optimisation). For example, usually, drug synthesis +costs are not the main driver of non-generic drug market +prices. The reason for this is the economic need to bal- +ance out a large amount of failed optimisation programs +and clinical trials, see [63]. Additionally, for the predic- +tion of NMR spectra, lower accuracy methods such as +DFT have been shown to achieve good results in many +cases [83, 85, 86] +In summary, most of the use cases of quantum mechan- +ical calculations in drug design would benefit from speed- +ups to DFT and CC methods, which are still too slow +for broader application in the drug development process +but offer good-enough accuracy for most systems. This +is because most oral drugs are small closed-shell organic +molecules (they need to pass through the gut wall to be +absorbed) which generally lack strong correlation and, +with some rare exceptions, e.g. cytochrome P450 interac- +tions in drug metabolism [28], can be treated with lower +accuracy methods due to their general elemental compo- +sitions [87]. +However, few examples of drug molecules +with metal centres exist, for example, for cancer treat- +ments or contrast-enhanced imaging of tissues [88]. An +open, unexplored question is whether this scarcity of po- +tentially strong-correlated drugs is due to some intrinsic +unwanted features of metal-bearing drugs. This could lie +in their undesired pharmacokinetic behaviour or poten- +tial toxicity, which would make them unfit as drugs. A +different possibility is that they have been avoided due +to the challenges in their computational optimisation. +III. +CHALLENGES AND PROSPECTS +The current limitations of quantum chemistry in drug +design either come from a lack of accuracy (for the few de- +scribed difficult systems) or the large computational costs +of the DFT calculations for ensembles of bio-molecules. +For both limitations, quantum computers do not give +an immediate remedy yet, although promising ideas are +starting to emerge. +Currently, quantum computers are expected to speed +up electronic structure calculations for strongly corre- +lated systems with already-known quantum algorithms +(e.g. QPE). This could be used, for example, to better un- +derstand the physics of cytochrome P450 [28]. However, +the largest impact will come if one can go beyond cal- +culating single-point energies of strongly correlated sys- +tems. +The last 30 years have seen dramatic improvements, +both on the hardware side, as well as on the algorithmic +one [15, 44, 45, 81, 89–95]. Even though these improve- +ments have enabled the impressive quantum computing +capabilities we have today, there is much more needed to +make quantum computing practical for drug discovery. +Concerning the run-time of algorithms, quantum er- +ror correction represents one of the dominant sources +of overhead costs in space and time for executing fault- +tolerant quantum algorithms. Error correction requires +thousands of physical qubits for each logical qubit [91], +resulting in millions of qubits for calculating the FeMoco +ground state energy [45, 46]. To reduce these overheads, +not only better hardware with lower error rates and in- +creased qubit connectivity needs to be developed but also +new further improvements to quantum error correction +should be explored [44, 89, 90]. +On the algorithmic side, one of the central yet unre- +solved challenges is preparing an initial state because the +run-time of QPE directly depends on this state. Even +though the run-time has improved over time [48, 49], the +dependence on the overlap of the initial and target states +cannot be circumvented [50]. Several heuristic solutions +have been proposed [12, 57, 96], while further studies are +required to understand the extent of this problem fully. +For the case of weakly correlated systems, a potential +solution relies on decomposing the system into smaller +sub-systems and applying a series of QPEs on these to +maintain the overall overlap. +Another essential research direction is the reduction of +the overall computational cost by, for example, finding +more compact representations of the systems’ Hamilto- +nian, which directly impacts the run-time of the quantum +algorithms [46, 97, 98]. At the same time, analogously to +classical algorithms, it should be possible to find quan- +tum algorithms for specific cases based on heuristics that +scale much better than general algorithms. Yet the ab- +sence of error-corrected quantum computers prevents the +thorough benchmarking of heuristics today. +However, +there might be more systematic approaches to analyse +the scaling and constant factors of heuristics for specific +input parameters. +Current quantum algorithms focus on delivering speed- +ups at the highest accuracy, which is not always rele- +vant for industrial applications. Substantial run-time im- +provements compared to approximate classical methods +would have a more considerable mid-term impact. How- +ever, speeding up approximate techniques on a quantum +computer seems quite challenging. +DFT and Hartree- + +6 +Fock already have linear scaling implementations on clas- +sical computers, and it will be difficult to outperform +them on a quantum computer. Instead, a quantum com- +puter could provide new insights into the systems’ physics +to improve the classical methods. For example, we could +use quantum computations to design better functionals +for DFT. Alternatively, it might be viable to use quantum +computers to speed up classical calculations in contract- +ing tensor networks [99, 100]. Implementing CC methods +on quantum computers could achieve a quadratic speed- +up for the optimisation phase [101]. Another possibility +is to save computational cost by exploiting perturbation +theory on quantum computers [102]. Recent results have +also shown that quantum computers can outperform clas- +sical mean field methods in simulating electron dynam- +ics [103]. In the future, one could explore new routes in +finding a trade-off between accuracy and costs, for exam- +ple, by tuning the numerical accuracy of the Hamiltonian +simulation [104] or by truncating the amount of informa- +tion in the Hamiltonian. +On the drug design side, while single-point calcula- +tions can give insights into systems’ physics, we typically +require billions of single-point calculations to determine +thermodynamic quantities, e.g. binding affinity. +This +large number of calculations, combined with the quan- +tum computing run-time on the order of days for one +of them [28, 54], makes it impossible to obtain results +in a reasonable time, let alone compete with run-times +of highly optimised experiments. +A potential route to +a more practical calculation of thermodynamic quanti- +ties might come from simultaneously modelling classical +nuclei and electrons in one wave function on the quan- +tum computer. +One can envisage calculating thermo- +dynamic properties, e.g., the free energy, directly on a +quantum computer by generating thermal ensembles of +geometries [105]. Additionally, treating the nuclei quan- +tum mechanically would help interpret molecular spec- +tra [106]. +On a more speculative side, quantum machine learning +algorithms applied to the outcome of quantum computa- +tions have the potential to predict pharmacokinetic prop- +erties [107, 108]. +When large quantum computers be- +come available, we might be able to compute wave func- +tions of many ensembles of molecules and subsequently +run quantum machine learning algorithms on these wave +functions [109–112]. +CONCLUSION +Current classical computing methods fail to describe +quantum systems accurately enough in relevant times +for the pharmaceutical industry, limiting the applicabil- +ity of quantum chemistry to drug design. More accurate +computations could bring significant value to the phar- +maceutical industry by replacing many labour-intensive +experiments with calculations in silico, as long as the +computational cost is lower than the experimental effort. +Quantum computations could enable key, experimentally +inaccessible insights into chemical systems, exploiting +methods that directly derive properties from wave func- +tions [111]. +To have a profound impact on the pharmaceutical in- +dustry, quantum computers need to benefit a broader +set of problems than the small number inaccessible to +classical computers [13, 15]. +Typical relevant systems +have thousands of atoms, e.g. large protein structures +with their surroundings, and rarely require exact accu- +racy. However, in many pharmaceutical use cases, one +must determine thermodynamic properties that rely on +large thermodynamic ensembles, thus requiring many +single-point calculations. Finding new methods that al- +low trade-off accuracy for time on quantum computers or +that avoid sampling could be beneficial. Ideally, quantum +computers should offer accuracy and robustness for both +strongly and weakly correlated systems at a speed that +is currently only accessible by lower-accuracy methods. +By getting rid of some of the current approximations, +quantum calculations in drug design would become truly +predictive and much more widely used. +Major advancements in quantum algorithms for elec- +tronic structure problems brought down computational +costs [46, 81, 113, 114] over the last years, while fur- +ther improvements are required for practical applications +in industry. +Furthermore, fundamental improvements +in hardware, error correction codes and algorithms (e.g. +for state preparation) are necessary to go beyond single- +point energy calculations. +Steps are already being made towards solving some of +these challenges, and several routes exist to achieve these +goals. We are convinced that open research integrating +academia and industry will help make quantum comput- +ing an essential tool to design better drugs faster. +ACKNOWLEDGMENTS +The authors thank Darryl McConnel, Alexander Ren- +ner, Christoph Ehrendorfer, Lorenzo Pautasso, Manuel +M¨oller, and Anika Pflanzer for comments on the various +iterations this perspective went through. The molecules +reported are visualised in Mol* [115]. +[1] J. W. Scannell, A. Blanckley, H. Boldon, and B. War- +rington, Nature Reviews Drug Discovery 11, 191 (2012). +[2] B. +K. +Allen, +M. +M. +Kulkarni, +B. +Chamberlain, +T. Dwight, C. Koh, R. Samant, F. Jernigan, J. Rice, + +7 +D. Tan, S. Li, K. Marino, H. Huang, E. Chiswick, +B. Tesar, S. Sparks, Z. Lin, T. D. McGee, I. Kolossv´ary, +C. Lin, S. Shechter, H. Soutter, C. Bastos, M. Taimi, +S. Lai, A. Petrin, T. Kane, S. Swann, H. Gard- +ner, C. Winter, +and W. Sherman, bioRxiv +(2022), +https://doi.org/10.1101/2022.05.23.493001. +[3] G. Palermo and M. De Vivo, “Computational chemistry +for drug discovery,” in Encyclopedia of Nanotechnology, +edited by B. Bhushan (Springer Netherlands, Dordrecht, +2014) pp. 1–15. +[4] V. G. Maltarollo, J. C. Gertrudes, P. R. Oliveira, and +K. M. Honorio, Expert opinion on drug metabolism & +toxicology 11, 259 (2015). +[5] M. K. Jayatunga, W. Xie, L. Ruder, U. Schulze, +and +C. Meier, Nature Reviews Drug Discovery 21, 175 +(2022). +[6] R. Shukla and T. Tripathi, “Molecular dynamics simu- +lation in drug discovery: Opportunities and challenges,” +in Innovations and Implementations of Computer Aided +Drug Discovery Strategies in Rational Drug Design, +edited by S. K. Singh (Springer Singapore, Singapore, +2021) pp. 295–316. +[7] S. Irle, V. Q. Vuong, M. H. Elayyan, M. R. Talipov, and +S. M. Abel, “Protein molecular dynamics simulations +with approximate qm: What can we learn?” in Quan- +tum Mechanics in Drug Discovery, edited by A. Heifetz +(Springer US, New York, NY, 2020) pp. 149–161. +[8] A. Heifetz, Quantum Mechanics in Drug Discovery, +Methods in Molecular Biology (Springer US, 2020). +[9] R. P. Feynman, International Journal of Theoretical +Physics 21, 467 (1982). +[10] S. Lloyd, Science 273, 1073 (1996). +[11] M. A. Nielsen and I. L. Chuang, Quantum Computa- +tion and Quantum Information (Cambridge University +Press, 2000). +[12] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, +and +M. Head-Gordon, Science 309, 1704 (2005). +[13] Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. +Johnson, M. Kieferov´a, I. D. Kivlichan, T. Menke, +B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, +and +A. Aspuru-Guzik, Chemical Reviews 119, 10856 (2019). +[14] B. Bauer, S. Bravyi, M. Motta, +and G. K.-L. Chan, +Chemical Reviews 120, 12685 (2020). +[15] H. Liu, G. H. Low, D. S. Steiger, T. H¨aner, M. Reiher, +and M. Troyer, Materials Theory 6, 11 (2022). +[16] M. Motta and J. E. Rice, WIREs Computational Molec- +ular Science 12, e1580 (2022). +[17] M. Zinner, F. Dahlhausen, P. Boehme, J. Ehlers, +L. Bieske, +and L. Fehring, Drug Discovery Today 26, +1680 (2021). +[18] A. +Baiardi, +M. +Christandl, +and +M. +Reiher, +arXiv +2212.12220 +(2022), +https://doi.org/10.48550/arXiv.2212.12220. +[19] N. S. Blunt, +J. Camps, +O. Crawford, +R. Izs´ak, +S. Leontica, A. Mirani, A. E. Moylett, S. A. Scivier, +C. S¨underhauf, P. Schopf, J. M. Taylor, and N. Holz- +mann, Journal of Chemical Theory and Computation +18, 7001 (2022). +[20] S. +Lee, +J. +Lee, +H. +Zhai, +Y. +Tong, +A. +M. +Dalzell, +A. +Kumar, +P. +Helms, +J. +Gray, +Z.- +H. +Cui, +W. +Liu, +M. +Kastoryano, +R. +Babbush, +J. +Preskill, +D. +R. +Reichman, +E. +T. +Campbell, +E. F. Valeev, L. Lin, +and G. K.-L. Chan, arXiv +(2022), +https://doi.org/10.48550/arxiv.2208.02199, +2208.02199. +[21] J. M. Bofill and P. Pulay, The Journal of Chemical +Physics 90, 3637 (1989). +[22] A. Khedkar and M. Roemelt, Phys. Chem. Chem. Phys. +23, 17097 (2021). +[23] K. Andersson, P. A. Malmqvist, B. O. Roos, A. J. +Sadlej, and K. Wolinski, The Journal of Physical Chem- +istry 94, 5483 (1990). +[24] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, +and J.-P. Malrieu, The Journal of Chemical Physics +114, 10252 (2001). +[25] K. Pernal, Phys. Rev. Lett. 120, 013001 (2018). +[26] J. P. Coe and M. J. Paterson, Journal of Chemical The- +ory and Computation 11, 4189 (2015). +[27] Z. Li, J. Li, N. S. Dattani, C. J. Umrigar, and G. K.- +L. Chan, The Journal of Chemical Physics 150, 024302 +(2019). +[28] J. J. Goings, A. White, J. Lee, C. S. Tautermann, +M. Degroote, C. Gidney, T. Shiozaki, R. Babbush, +and N. C. Rubin, arXiv , arXiv:2202.01244 (2022), +arXiv:2202.01244 [quant-ph]. +[29] J. Lee and M. Head-Gordon, Physical Chemistry Chem- +ical Physics 21, 4763 (2019). +[30] L. Cheng, J. Gauss, B. Ruscic, P. B. Armentrout, and +J. F. Stanton, Journal of chemical theory and computa- +tion 13, 1044 (2017). +[31] M. Degroote, T. M. Henderson, J. Zhao, J. Dukel- +sky, and G. E. Scuseria, Physical Review B 93, 125124 +(2016). +[32] J. Rissler, R. M. Noack, +and S. R. White, Chemical +Physics 323, 519 (2006). +[33] C. J. Stein and M. Reiher, Journal of chemical theory +and computation 12, 1760 (2016). +[34] G. K.-L. Chan and S. Sharma, Annual review of physical +chemistry 62, 465 (2011). +[35] C. J. Stein and M. Reiher, Molecular Physics 115, 2110 +(2017). +[36] L. Ding, S. Mardazad, S. Das, S. Szalay, U. Schollw¨ock, +Z. Zimbor´as, and C. Schilling, Journal of Chemical The- +ory and Computation 17, 79 (2021). +[37] M. Motta and J. E. Rice, WIREs Computational Molec- +ular Science 12, e1580 (2021). +[38] S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, +and X. Yuan, Reviews of Modern Physics 92, 015003 +(2020). +[39] J. Preskill, Quantum 2, 79 (2018). +[40] K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, +S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, +J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.- +C. Kwek, +and A. Aspuru-Guzik, Reviews of Modern +Physics 94, 015004 (2022). +[41] J. R. McClean, R. Babbush, P. J. Love, and A. Aspuru- +Guzik, The Journal of Physical Chemistry Letters 5, +4368 (2014). +[42] M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, +S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, +L. Cincio, and P. J. Coles, Nature Reviews Physics 3, +625 (2021). +[43] Y. Quek, +D. S. Fran¸ca, +S. Khatri, +J. J. Meyer, +and J. Eisert, arXiv - quant-ph 2210.11505 (2022), +arXiv:2210.11505. +[44] E. T. Campbell, B. M. Terhal, and C. Vuillot, Nature +549, 172 (2017). + +8 +[45] M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, +and +M. Troyer, Proceedings of the National Academy of Sci- +ences 114, 7555 (2017). +[46] J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. +McClean, N. Wiebe, and R. Babbush, PRX Quantum +2, 030305 (2021). +[47] D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, +Communications in Mathematical Physics 270, 359 +(2007). +[48] Y. Ge, J. Tura, and J. I. Cirac, Journal of Mathematical +Physics 60, 022202 (2019). +[49] L. Lin and Y. Tong, Quantum 4, 372 (2020). +[50] A. Y. Kitaev, “Quantum measurements and the Abelian +Stabilizer Problem,” (1995), arXiv:quant-ph/9511026. +[51] E. Knill, G. Ortiz, and R. D. Somma, Physical Review +A 75, 012328 (2007). +[52] T. E. O’Brien, B. Senjean, R. Sagastizabal, X. Bonet- +Monroig, A. Dutkiewicz, F. Buda, L. DiCarlo, +and +L. Visscher, npj Quantum Information 5, 113 (2019). +[53] I. O. Sokolov, P. K. Barkoutsos, L. Moeller, P. Such- +sland, G. Mazzola, +and I. Tavernelli, Phys. Rev. Re- +search 3, 013125 (2021). +[54] T. E. O’Brien, M. Streif, N. C. Rubin, R. Santagati, +Y. Su, W. J. Huggins, J. J. Goings, N. Moll, E. Kyoseva, +M. Degroote, C. S. Tautermann, J. Lee, D. W. Berry, +N. Wiebe, and R. Babbush, arXiv (2021), 2111.12437. +[55] D. Wecker, B. Bauer, B. K. Clark, M. B. Hastings, and +M. Troyer, Phys. Rev. A 90, 022305 (2014). +[56] D. Poulin, A. Kitaev, D. S. Steiger, M. B. Hastings, and +M. Troyer, Phys. Rev. Lett. 121, 010501 (2018). +[57] D. Wecker, M. B. Hastings, N. Wiebe, B. K. Clark, +C. Nayak, +and M. Troyer, Phys. Rev. A 92, 062318 +(2015). +[58] R. N. Tazhigulov, S.-N. Sun, R. Haghshenas, H. Zhai, +A. T. K. Tan, N. C. Rubin, R. Babbush, A. J. Minnich, +and G. K.-L. Chan, arXiv (2022), 2203.15291. +[59] A. B. Hill, Journal of the Royal Society of Medicine 108, +32—37 (2015). +[60] T. P. Kenakin, in Pharmacology in Drug Discovery and +Development (Second Edition), edited by T. P. Kenakin +(Academic Press, 2017) second edition ed., pp. 1–20. +[61] P. G. Polishchuk, T. I. Madzhidov, +and A. Varnek, +Journal of Computer-Aided Molecular Design 27, 675 +(2013). +[62] R. Ferreira de Freitas and M. Schapira, Med. Chem. +Commun. 8, 1970 (2017). +[63] S. M. Paul, D. S. Mytelka, C. T. Dunwiddie, C. C. +Persinger, B. H. Munos, S. R. Lindborg, +and A. L. +Schacht, Nature Reviews Drug Discovery 9, 203 (2010). +[64] A. Talevi and P. A. M. Quiroga, ADME Processes in +Pharmaceutical Sciences, Dosage, Design, and Pharma- +cotherapy Success, edited by {Quiroga, Alan Talevi and +Pablo A. M.} (Springer, 2018). +[65] F. +Miljkovi´c, +A. +Martinsson, +O. +Obrezanova, +B. Williamson, M. Johnson, A. Sykes, A. Bender, +and N. Greene, Molecular Pharmaceutics 18, 4520 +(2021). +[66] J. Jim´enez-Luna, +F. Grisoni, +N. Weskamp, +and +G. Schneider, Expert Opinion on Drug Discovery 16, +949 (2021), pMID: 33779453. +[67] Z. Cournia, B. Allen, +and W. Sherman, Journal of +Chemical Information and Modeling 57, 2911 (2017). +[68] P. Deglmann, A. Sch¨afer, +and C. Lennartz, Interna- +tional Journal of Quantum Chemistry 115, 107 (2015). +[69] C. E. Tinberg, S. D. Khare, J. Dou, L. Doyle, J. W. +Nelson, A. Schena, W. Jankowski, C. G. Kalodimos, +K. Johnsson, B. L. Stoddard, +and D. Baker, Nature +501, 212 (2013). +[70] E. +King, +E. +Aitchison, +H. +Li, +and +R. +Luo, +Frontiers +in +Molecular +Biosciences +8 +(2021), +https://doi.org/10.3389/fmolb.2021.712085. +[71] C. Bonagura, B. Bhaskar, H. Shimizu, H. Li, M. Sun- +daramoorthy, D. E. McRee, D. B. Goodin, +and T. L. +Poulos, “High-resolution crystal structure of compound +i intermediate of cytochrome c peroxidase (ccp),” +(2005). +[72] C. A. Bonagura, B. Bhaskar, H. Shimizu, H. Li, M. Sun- +daramoorthy, D. E. McRee, D. B. Goodin, +and T. L. +Poulos, Biochemistry 42, 5600 (2003). +[73] H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, +T. N. Bhat, H. Weissig, I. N. Shindyalov, +and P. E. +Bourne, Nucleic Acids Research 28, 235 (2000). +[74] N. Heilmann, M. Wolf, M. Kozlowska, E. Sedghamiz, +J. Setzler, M. Brieg, and W. Wenzel, Scientific Reports +10, 18211 (2020). +[75] B. T. Kaynak, J. M. Krieger, B. Dudas, Z. L. Dahmani, +M. G. Costa, E. Balog, A. L. Scott, P. Doruker, D. Per- +ahia, +and I. Bahar, Frontiers in molecular biosciences +9, 832847 (2022). +[76] L. C. James and D. S. Tawfik, Trends in Biochemical +Sciences 28, 361 (2003). +[77] L. F. Song and K. M. Merz Jr., Journal of Chemical +Information and Modeling 60, 5308 (2020). +[78] M. Karplus and J. A. McCammon, Nature Structural +Biology 9, 646 (2002). +[79] W. F. van Gunsteren and A. E. Mark, The Journal of +Chemical Physics 108, 6109 (1998). +[80] P. C. D. Hawkins, Journal of Chemical Information and +Modeling 57, 1747 (2017). +[81] V. von Burg, G. H. Low, T. H¨aner, D. S. Steiger, M. Rei- +her, M. Roetteler, and M. Troyer, Phys. Rev. Research +3, 033055 (2021). +[82] L. A. Joyce, C. C. Nawrat, E. C. Sherer, M. Biba, +A. Brunskill, G. E. Martin, R. D. Cohen, +and I. W. +Davies, Chemical Science 9, 415 (2017). +[83] P. Gao, J. Zhang, Q. Peng, J. Zhang, and V.-A. Gleza- +kou, Journal of Chemical Information and Modeling 60, +3746 (2020). +[84] T. E. O’Brien, L. B. Ioffe, Y. Su, D. Fushman, H. Neven, +R. Babbush, +and V. Smelyanskiy, arXiv +(2021), +2109.02163. +[85] M. B¨uhl, M. Kaupp, O. L. Malkina, and V. G. Malkin, +Journal of computational chemistry 20, 91 (1999). +[86] D. Xin, C. A. Sader, O. Chaudhary, P.-J. Jones, K. Wag- +ner, C. S. Tautermann, Z. Yang, C. A. Busacca, R. A. +Saraceno, K. R. Fandrick, N. C. Gonnella, K. Horspool, +G. Hansen, and C. H. Senanayake, The Journal of Or- +ganic Chemistry 82, 5135 (2017). +[87] B. R. Smith, C. M. Eastman, +and J. T. Njardarson, +Journal of Medicinal Chemistry 57, 9764 (2014). +[88] M. A. Phillips and J. A. Pombeiro, Current Medicinal +Chemistry 26, 7476 (2019). +[89] Y.-C. Lee, C. G. Brell, and S. T. Flammia, Journal of +Statistical Mechanics: Theory and Experiment 2017, +083106 (2017). +[90] I. H. Kim, Y.-H. Liu, S. Pallister, W. Pol, S. Roberts, +and E. Lee, Phys. Rev. Research 4, 023019 (2022). + +9 +[91] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. +Cleland, Phys. Rev. A 86, 032324 (2012). +[92] D. W. Berry, C. Gidney, M. Motta, J. R. McClean, and +R. Babbush, Quantum 3, 208 (2019). +[93] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, +R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. +Buell, et al., Nature 574, 505 (2019). +[94] Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, +X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan, +M. Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, +H.-L. Huang, Y.-H. Huo, L. Li, N. Li, S. Li, Y. Li, +F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong, +H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Xu, K. Yan, +W. Yang, Y. Yang, Y. Ye, J. Yin, C. Ying, J. Yu, C. Zha, +C. Zhang, H. Zhang, K. Zhang, Y. Zhang, H. Zhao, +Y. Zhao, L. Zhou, Q. Zhu, C.-Y. Lu, C.-Z. Peng, X. Zhu, +and J.-W. Pan, Phys. Rev. Lett. 127, 180501 (2021). +[95] L. +S. +Madsen, +F. +Laudenbach, +M. +F. +Askarani, +F. Rortais, T. Vincent, J. F. Bulmer, F. M. Miatto, +L. Neuhaus, L. G. Helt, M. J. Collins, et al., Nature +606, 75 (2022). +[96] N. M. Tubman, +C. Mejuto-Zaera, +J. M. Epstein, +D. Hait, D. S. Levine, W. Huggins, Z. Jiang, J. R. +McClean, R. Babbush, M. Head-Gordon, +and K. B. +Whaley, arXiv (2018), 1809.05523. +[97] G. Barcza, O. Legeza, K. H. Marti, +and M. Reiher, +Phys. Rev. A 83, 012508 (2011). +[98] V. von Burg, G. H. Low, T. H¨aner, D. S. Steiger, M. Rei- +her, M. Roetteler, and M. Troyer, Physical Review Re- +search 3, 033055 (2021). +[99] R. Haghshenas, J. Gray, A. C. Potter, +and G. K.-L. +Chan, Phys. Rev. X 12, 011047 (2022). +[100] I. H. Kim and B. Swingle, arXiv (2017), 1711.07500. +[101] A. Gily´en, S. Arunachalam, and N. Wiebe, “Optimiz- +ing quantum optimization algorithms via faster quan- +tum gradient computation,” in Proceedings of the 2019 +Annual ACM-SIAM Symposium on Discrete Algorithms +(SODA) (Society for Industrial and Applied Mathemat- +ics, 2019) pp. 1425–1444. +[102] K. Mitarai, K. Toyoizumi, +and W. Mizukami, arXiv +2210.00718 (2022). +[103] R. Babbush, W. J. Huggins, D. W. Berry, S. F. Ung, +A. Zhao, D. R. Reichman, H. Neven, A. D. Baczewski, +and J. Lee, arXiv (2023), 2301.01203 [quant-ph]. +[104] D. S. Abrams and S. Lloyd, Physical Review Letters 83, +5162 (1999). +[105] R. D. Somma, C. D. Batista, and G. Ortiz, Phys. Rev. +Lett. 99, 030603 (2007). +[106] D. F. Dinu, M. Podewitz, H. Grothe, K. R. Liedl, and +T. Loerting, The Journal of Physical Chemistry A 123, +8234 (2019). +[107] S. Aleksi´c, D. Seeliger, +and J. B. Brown, Molecular +Informatics 41, 2100113 (2022). +[108] G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, +N. Tishby, L. Vogt-Maranto, +and L. Zdeborov´a, Rev. +Mod. Phys. 91, 045002 (2019). +[109] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, +N. Wiebe, and S. Lloyd, Nature 549, 195 (2017). +[110] H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, +S. Boixo, H. Neven, and J. R. McClean, Nature Com- +munications 12, 2631 (2021). +[111] J. R. McClean, N. C. Rubin, J. Lee, M. P. Harrigan, +T. E. O’Brien, R. Babbush, W. J. Huggins, and H.-Y. +Huang, The Journal of Chemical Physics 155, 150901 +(2021). +[112] H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics +16, 1050 (2020). +[113] M. B. Hastings, D. Wecker, B. Bauer, and M. Troyer, +Quantum Info. Comput. 15, 1–21 (2015). +[114] G. H. Low and I. L. Chuang, Quantum 3, 163 (2019). +[115] D. Sehnal, S. Bittrich, M. Deshpande, R. Svobodov´a, +K. Berka, V. Bazgier, S. Velankar, S. K. Burley, J. Koˇca, +and A. S. Rose, Nucleic Acids Research 49, W431 +(2021). + diff --git a/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/load_file.txt b/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..97fcc8ebc5d3ab022e28a35ea42aa3e103cac443 --- /dev/null +++ b/fdE2T4oBgHgl3EQfxwiK/content/tmp_files/load_file.txt @@ -0,0 +1,1386 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf,len=1385 +page_content='Drug design on quantum computers Raffaele Santagati,1, ∗ Alan Aspuru-Guzik,2 Ryan Babbush,3 Matthias Degroote,1 Leticia Gonz´alez,4 Elica Kyoseva,1, † Nikolaj Moll,1 Markus Oppel,4 Robert M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Parrish,5 Nicholas C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rubin,3 Michael Streif,1 Christofer S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tautermann,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 7 Horst Weiss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='8 Nathan Wiebe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='2 and Clemens Utschig-Utschig1 1Quantum Lab,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Boehringer Ingelheim,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 55218 Ingelheim am Rhein,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Germany 2Department of Computer Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' University of Toronto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Canada 3Google Quantum AI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Venice,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' CA 90291,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' United States 4Institute of Theoretical Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Faculty of Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' University of Vienna,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W¨ahringer Straße 17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 1090 Vienna,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Austria 5QC Ware Corp,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Palo Alto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' CA 94306,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' United States 6Boehringer Ingelheim Pharma GmbH & Co KG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Birkendorfer Strasse 65,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 88397 Biberach,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Germany 7Department of General,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Inorganic and Theoretical Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' University of Innsbruck,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 6020 Innsbruck,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Austria 8Next Generation Computing in Global Digitalization,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' BASF SE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Carl-Bosch-Strasse 38,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 67056 Ludwigshafen am Rhein,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Germany Quantum computers promise to impact industrial applications,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' for which quantum chemical cal- culations are required,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' by virtue of their high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' This perspective explores the challenges and opportunities of applying quantum computers to drug design, discusses where they could transform industrial research and elaborates on what is needed to reach this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' INTRODUCTION For over fifty years, the pharmaceutical industry has seen the cost of developing drugs increase exponentially from tens of millions in the 1950s to billions of dollars today, even when the data is adjusted for inflation [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' To sustain the progress in treating unmet medical need, it is essential to look for every source of improvement in the methodologies employed in drug development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In the last decades, computational approaches started to play an increasingly large role in research and devel- opment [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Many computational methods are em- ployed from machine learning [4, 5] and molecular dy- namics [6, 7] to quantum mechanical calculations [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Still, simulating chemical systems, including quantum mechanical effects, can be computationally intensive and many of these methods face limited practical applicabil- ity because of speed and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' By exploiting their quantum mechanical properties, quantum computers have been proposed to simulate quantum systems efficiently [9–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Inspired by this promise, quantum computing research has proliferated in recent years, and a community of quantum physics, chemistry, and information theory experts has brought improvements in quantum hardware and algorithms [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The recent developments also attracted interest be- yond academia to find practical applications in indus- try, with investments from private and public sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Often, one of the justifications for those investments is the promise that quantum computers will enhance quan- tum chemistry calculations [15–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Most current ef- forts in quantum computing focus on finding quantum algorithms for the most challenging electronic structure ∗ raffaele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='santagati@boehringer-ingelheim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='com † Present Address: Wellcome Leap Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', Los Angeles, CA 90069, United States problems, for which the largest possible advantage over classical computations can be expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, iden- tifying such systems with strong electronic correlations is difficult [20], and there only are a limited number of indicators, such as those shown in Box I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' While solving the electronic structure problem is an important step for many chemical applications, if the advantage of quantum computers is limited to strongly correlated systems, they might have limited practical significance in drug design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In this perspective, we discuss the status quo of the ap- plicability of future quantum computers to problems in drug discovery;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' specifically, we focus on quantum chem- istry calculations because, in our opinion, these will be the first viable applications to impact drug design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' While we do not give an exhaustive presentation of the status of quantum computing, we discuss problems in quantum chemistry for which quantum computers could offer a speed-up compared to classical computing meth- ods and compare these problems with the actual compu- tational needs in computer-aided drug design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lastly, we discuss research directions to make quantum computers an essential tool in the pharmaceutical industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' STATUS QUO: QUANTUM COMPUTERS The field of quantum computing has seen rapid devel- opments in the last decade [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Still, the way towards a practical quantum advantage requires major progress for hardware and algorithms [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The most impor- tant metric for the development of quantum algorithms is the estimation of their computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' These es- timates define the quantum computing resources (qubits and run-time) required to solve a problem of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' They provide concrete engineering targets for quantum hardware and shed light on what aspects of the algo- rithms need improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='04114v1 [quant-ph] 10 Jan 2023 2 Box I: Some indicators of strong electronic correlation Quantum computers are expected to offer an advan- tage for solving the electronic structure problem of strongly correlated systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Five different indica- tors with their graphical representations are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' There are two regions labelled Classical for cases solv- able on a classical computer [21–25] and Quantum for cases where a quantum computer might be required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Multi-reference: system’s wavefunction requiring many reference states (determinants) with compa- rable amplitudes [26–28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Amplitude States Classical Quantum Essential spin-symmetry breaking: not fixed by adding dynamical correla- tion [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Classical Quantum Total spin Energy Cluster expansion have characteristic failure points indicating the need for a multi-reference model [30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Interaction Strength Classical Quantum CC order RMS Amplitude Near degenerate natural orbitals with non-integer occupation numbers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' de- tected from orbital occupa- tion analysis [21, 32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Classical Quantum Occupation Energy The number of entan- gled orbitals grows pro- portionally to system size, which also needs to be large enough to be classi- cally hard [34, 35], image adapted from [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Quantum correlation Today, only Noisy Intermediate Scale Quantum (NISQ) computing hardware exists, named after its noisy nature and the limited number of qubits [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Most NISQ algorithms, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', variational quantum eigensolvers (VQE) [41, 42], heavily rely on classical optimisation heuristics, and the actual run-time is difficult to esti- mate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Also, recent results suggest that in NISQ, the number of measurements required to achieve a given er- ror scale exponentially with the depth of the circuit [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For these reasons, we focus our discussion exclusively on fault-tolerant quantum computers (FTQCs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' FTQCs exploit quantum error correction to exponen- tially suppress errors [44], at the cost of considerable additional qubits and run-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For example, simu- lating a classically challenging molecule, such as the iron-molybdenum complex (FeMoco) [45], would require roughly 200 logical (error-corrected) qubits which would be implemented in 2 million physical qubits [46], well beyond what is achievable with current quantum hard- ware [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Quantum computers are expected to offer a clear ad- vantage in finding the ground state energy of a molecular Hamiltonian (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' solving the electronic structure prob- lem) for strongly correlated systems where all tractable classical methods fail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' To identify those systems, several conditions need to be satisfied (see Box I), and verify- ing them can be very demanding and time-consuming and heavily relies on chemical expertise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Over the past twenty years, several techniques have been developed for studying how and when various ab initio methods fail, delivering indicators of strong correlations [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Typical examples of such situations that require expensive multi- reference treatment are multi-metal systems, where met- als are in similar electronic environments and interac- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A quantum computer can perform such calculations in polynomial time without making any uncontrolled ap- proximations if the initial state is close to the ground state [47–49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The ground state energy is computed with a combination of state preparation and quantum phase estimation (QPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' QPE is a very efficient algorithm to find the eigenstates and eigenvalues of a Hamiltonian, and it is at the core of many quantum computing meth- ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In Figure 1, we give an example of how these cal- culations can be performed on quantum computers for a chemical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The presented workflow starts on a classical computer, which helps in refining the geometry of the chemical system, identifying a good initial state for the system and synthesising the error-corrected quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The quantum computation starts with internally preparing this classically-determined initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The next step in the workflow is the application of QPE to the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The cost of estimating the correct ground state energy depends directly on the overlap of the initial state with the ground state, and it becomes progressively more expensive as the overlap with the correct ground state decreases [20, 48–50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Modifications to this work- flow allow for the calculation of other observables [51], e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', molecular forces [52–54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Even though FTQC algorithms cannot yet be exe- cuted, many methods already exist to evaluate their com- putational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For example, for the ground state energy of the FeMoco [27, 45], through algorithmic improve- ments, the run-time estimates have been reduced from years to days [19, 45, 46, 55, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Further improvements will certainly come, and we will be able to perform such calculations in the future on an FTQC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In the next sec- tions, we discuss the state of the art of drug design and where quantum computers could be employed to solve the electronic structure part of the problem for relevant pharmacological systems [19, 28, 57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 3 Accurate description of chemical properties Quantum algorithm design Quantum error correction Classical preprocessing Quantum phase estimation Quantum computation Experimental structure determination Computational geometry refinement Generation of initial state Initial state preparation GND 1st 2nd 3rd 4th 5th Amplitudes Eigenstate QPE Eigenstate GND 1st 2nd 3rd 4th 5th Amplitudes FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The workflow of electronic structure calculations on quantum computers using the quantum phase estimation (QPE) algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The first step includes classical preprocessing to optimise the geometry and the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Afterwards, the quantum circuits are generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The calculation on the quantum computer starts with the generation of the initial state, which is followed by the more expensive calculation of the ground state energy with the QPE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The lower part of the quantum computation container: The initially prepared state consists of a superposition of many eigenstates but with a high overlap with the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' When the ground state (GND) energy is measured, the initial state is projected into the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' COMPUTER-AIDED DRUG DESIGN Chemical compounds produced in the pharmaceutical industry result from a long process of discovery and re- finement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The steps are summarised in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The drug discovery process starts with identifying a target protein involved in the disease pathology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pharmacological mod- ulation of this target is assumed beneficial for treating the disease [59, 60] and is achieved with a molecule bind- ing to the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Identifying oral drug candidates, the most preferred form of drug administration, takes a long time, starting with very weak binders and taking sev- eral years of optimisation towards efficacious and safe molecules [1, 3, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Millions of compounds are initially screened out of 1060 potential molecules [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In the initial stages of the process, many different properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', binding affinity) have to be optimised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Therefore, in the so-called hit-to- lead and lead-optimisation programs, several thousands of molecules are synthesised before suitable candidates for the next steps towards clinical development are identi- fied [62, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Every synthesised molecule undergoes test- ing in-vitro (biochemical, biophysical, cellular), and in case of good properties, also in in-vivo (in an organism) assays;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' therefore, the goal is to achieve clinical candi- dates with the lowest number of optimisation cycles pos- sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In this phase of drug discovery, computational ap- proaches are highly valuable by guiding the design of the right molecules, and recently several striking successes in computational design have been reported [2, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Two major areas where computational chemistry can support drug design have been identified: (1) the predic- tion of pharmacokinetic properties (how the compound is absorbed, distributed, metabolised and excreted from the body), commonly realised by machine learning mod- els trained on a wealth of experimental data from the heritage of projects in a pharma company [4, 64–66];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' (2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='the calculation of the binding strength or binding affinity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Registration ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Drug candidate ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Developement ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Lead optimisation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Hit to lead ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Hit identification ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Discovery research ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Target identification ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='4-5 years ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='6-8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='years ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='1-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='years ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='1 molecule ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='5 molecules ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='200 molecules ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='10 000 molecules ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Docking ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Virtual screening ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Pharmacohore mapping ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='De novo design ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='QSAR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Molecular dynamics ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Quantum mechanics ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='Enhanced sampling ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='1060 of possible ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='molecules ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='10s of parameters ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='to be optimised ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='1000s of compounds ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='to be synthesised ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Workflow in the drug discovery process [3, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Once the biological target has been identified, the process starts with the hit finding stage in a potential space of 1060 molecules [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Through a repeated cycle of design, analysis, synthesis, and in-silico and in-vitro testing, the number of promising compounds is decreased from 10 000s to a few hun- dred by designing and selecting those with the best predicted and measured properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Only very few highly optimised and safe molecules proceed into development towards the clinical trials, and only one is finally selected for approval by the medicinal agencies [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' On the right side, the computational methods employed in the different stages of the drug design process from [3] are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' of a compound to the target, which is one of the most important properties of a drug candidate [67, 68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The binding affinity is equivalent to the binding free energy between the drug and the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' It directly corresponds to the required local drug concentration at the target, de- termining drug efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Therefore, it translates into the projected therapeutic human dose, the most important single parameter during drug design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Computations of the binding strength must be accurate in compound op- timisation [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, state-of-the-art methods based 4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schematic representation of a drug binding event (pdb ID: 2RGU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The ligand exists as an ensemble of confor- mations/geometries and orientations (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Some approaches of the ligand towards the target result in binding, and some do not - as indicated by the arrows (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Eventually, the sampling of ensembles of unbound and bound structures in so- lution yield the free energy of drug-target binding [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Equiv- alently, energy differences of ensembles of bound, structurally similar ligands directly relate to the difference in their binding strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' on molecular dynamics simulations with classical force fields do not perform reliably [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The goal is to achieve high accuracy (within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='0 kcal/mol to experiment) be- cause, at physiological temperatures, a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='5 kcal/mol de- viation already translates into a dose estimation which is wrong by one order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' On an atomistic scale, a system can be treated on a classical computer with many different levels of approximations for differ- ent sizes considered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' see BOX II where some common methods are reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In contrast to force fields, den- sity functional theory (DFT) or coupled cluster (CC), which are methods based on quantum mechanics, lead to much better descriptions of molecular interactions but at a much higher computational cost [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Other difficulties in these calculations stem from the thermodynamic nature of the compounds’ properties [74, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A molecule can bind to a protein in many different ways [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' One has to consider different accessible system geometries and binding pathways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' One needs to identify the configuration with minimal free energy, which is the statistically most frequently observed one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In Figure 3, the process of a molecule binding to a protein is picto- rially depicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Many different configurations and, thus, many single-point calculations must be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' When evaluating many compounds with similar chem- ical structures for their binding propensity, it is often faster to compute the difference in binding strength be- tween the compounds directly;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' this task is often accom- plished with alchemical perturbation methods [67], where a known compound is gradually morphed into a new one adapting the electronic structure accordingly [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In this respect, simulating the ensemble properties, by, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' nat- Box II: Common electronic structure methods employed on classical computers Commonly used quantum chemistry methods to solve the electronic structure problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In the left column, we zoom in on the Compound I intermediate of Cy- tochrome c Peroxidase (PDB ID: 1ZBZ [71–73]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' As the method’s accuracy increases from top to bottom, the molecules that can be calculated with classical hardware become increasingly smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cytochrome c in solution Binding site Heme group Iron cluster Force Fields/ Semi-empirical Methods Methods that cannot fully describe quantum mechani- cal effects but can be tuned with information from quan- tum methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hartree-Fock/ Density Functional Theory (DFT) Mean-field methods treat electrons in the presence of the average potential of the other electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' DFT in- cludes electronic correlation, while Hartree-Fock does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Coupled-Cluster (CC) Cluster wavefunction meth- ods that expand around a single mean-field reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Full Configuration Interaction (FCI) Method that delivers the ex- act energy of the electronic structure problem within a finite basis set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' ural time-evolution, of the drug-target complex is a key step from which knowledge about thermodynamic prop- erties can be directly derived [78, 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The systems, including target, drug, and solvent, are made of several thousands of atoms (see BOX II), and free energy calculations require billions of single point calculations, where energy and force evaluation are per- formed, see Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Furthermore, the necessary inclu- sion of explicit solvent (water) in the model can con- siderably increase the degrees of freedom and complex- ity [75, 80], making run-time often impractical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The cal- T5 culation of the binding free energy of a small molecule to its target protein can take many hours on a classical computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Increasing accuracy, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' by exploiting DFT, increases the calculation costs by several orders of mag- nitude, rendering the full DFT treatment for free energy calculations elusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Higher levels of theory treatments, such as CC, which require even more computational re- sources, are, therefore, fully out of scope and can only be applied to small systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Other potential use cases for quantum computing in drug development are the calculation and optimisation of reaction mechanisms [81] for optimising the drug syn- thesis conditions and the calculation of molecular spec- tra for nuclear magnetic resonance (NMR), infra-red (IR) or vibrational circular dichroism (VCD) spectroscopy to identify structures [82–84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, the impact of quan- tum computing on these use cases for drug design would be rather modest if compared to the potential impact of better and faster calculations at the drug design stage (lead optimisation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For example, usually, drug synthesis costs are not the main driver of non-generic drug market prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The reason for this is the economic need to bal- ance out a large amount of failed optimisation programs and clinical trials, see [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Additionally, for the predic- tion of NMR spectra, lower accuracy methods such as DFT have been shown to achieve good results in many cases [83, 85, 86] In summary, most of the use cases of quantum mechan- ical calculations in drug design would benefit from speed- ups to DFT and CC methods, which are still too slow for broader application in the drug development process but offer good-enough accuracy for most systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' This is because most oral drugs are small closed-shell organic molecules (they need to pass through the gut wall to be absorbed) which generally lack strong correlation and, with some rare exceptions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' cytochrome P450 interac- tions in drug metabolism [28], can be treated with lower accuracy methods due to their general elemental compo- sitions [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, few examples of drug molecules with metal centres exist, for example, for cancer treat- ments or contrast-enhanced imaging of tissues [88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' An open, unexplored question is whether this scarcity of po- tentially strong-correlated drugs is due to some intrinsic unwanted features of metal-bearing drugs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' This could lie in their undesired pharmacokinetic behaviour or poten- tial toxicity, which would make them unfit as drugs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A different possibility is that they have been avoided due to the challenges in their computational optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' CHALLENGES AND PROSPECTS The current limitations of quantum chemistry in drug design either come from a lack of accuracy (for the few de- scribed difficult systems) or the large computational costs of the DFT calculations for ensembles of bio-molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For both limitations, quantum computers do not give an immediate remedy yet, although promising ideas are starting to emerge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Currently, quantum computers are expected to speed up electronic structure calculations for strongly corre- lated systems with already-known quantum algorithms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' QPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' This could be used, for example, to better un- derstand the physics of cytochrome P450 [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, the largest impact will come if one can go beyond cal- culating single-point energies of strongly correlated sys- tems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The last 30 years have seen dramatic improvements, both on the hardware side, as well as on the algorithmic one [15, 44, 45, 81, 89–95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Even though these improve- ments have enabled the impressive quantum computing capabilities we have today, there is much more needed to make quantum computing practical for drug discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Concerning the run-time of algorithms, quantum er- ror correction represents one of the dominant sources of overhead costs in space and time for executing fault- tolerant quantum algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Error correction requires thousands of physical qubits for each logical qubit [91], resulting in millions of qubits for calculating the FeMoco ground state energy [45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' To reduce these overheads, not only better hardware with lower error rates and in- creased qubit connectivity needs to be developed but also new further improvements to quantum error correction should be explored [44, 89, 90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' On the algorithmic side, one of the central yet unre- solved challenges is preparing an initial state because the run-time of QPE directly depends on this state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Even though the run-time has improved over time [48, 49], the dependence on the overlap of the initial and target states cannot be circumvented [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Several heuristic solutions have been proposed [12, 57, 96], while further studies are required to understand the extent of this problem fully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For the case of weakly correlated systems, a potential solution relies on decomposing the system into smaller sub-systems and applying a series of QPEs on these to maintain the overall overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Another essential research direction is the reduction of the overall computational cost by, for example, finding more compact representations of the systems’ Hamilto- nian, which directly impacts the run-time of the quantum algorithms [46, 97, 98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' At the same time, analogously to classical algorithms, it should be possible to find quan- tum algorithms for specific cases based on heuristics that scale much better than general algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yet the ab- sence of error-corrected quantum computers prevents the thorough benchmarking of heuristics today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, there might be more systematic approaches to analyse the scaling and constant factors of heuristics for specific input parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Current quantum algorithms focus on delivering speed- ups at the highest accuracy, which is not always rele- vant for industrial applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Substantial run-time im- provements compared to approximate classical methods would have a more considerable mid-term impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' How- ever, speeding up approximate techniques on a quantum computer seems quite challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' DFT and Hartree- 6 Fock already have linear scaling implementations on clas- sical computers, and it will be difficult to outperform them on a quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Instead, a quantum com- puter could provide new insights into the systems’ physics to improve the classical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' For example, we could use quantum computations to design better functionals for DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Alternatively, it might be viable to use quantum computers to speed up classical calculations in contract- ing tensor networks [99, 100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Implementing CC methods on quantum computers could achieve a quadratic speed- up for the optimisation phase [101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Another possibility is to save computational cost by exploiting perturbation theory on quantum computers [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Recent results have also shown that quantum computers can outperform clas- sical mean field methods in simulating electron dynam- ics [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' In the future, one could explore new routes in finding a trade-off between accuracy and costs, for exam- ple, by tuning the numerical accuracy of the Hamiltonian simulation [104] or by truncating the amount of informa- tion in the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' On the drug design side, while single-point calcula- tions can give insights into systems’ physics, we typically require billions of single-point calculations to determine thermodynamic quantities, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' binding affinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' This large number of calculations, combined with the quan- tum computing run-time on the order of days for one of them [28, 54], makes it impossible to obtain results in a reasonable time, let alone compete with run-times of highly optimised experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A potential route to a more practical calculation of thermodynamic quanti- ties might come from simultaneously modelling classical nuclei and electrons in one wave function on the quan- tum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' One can envisage calculating thermo- dynamic properties, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', the free energy, directly on a quantum computer by generating thermal ensembles of geometries [105].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Additionally, treating the nuclei quan- tum mechanically would help interpret molecular spec- tra [106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' On a more speculative side, quantum machine learning algorithms applied to the outcome of quantum computa- tions have the potential to predict pharmacokinetic prop- erties [107, 108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' When large quantum computers be- come available, we might be able to compute wave func- tions of many ensembles of molecules and subsequently run quantum machine learning algorithms on these wave functions [109–112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' CONCLUSION Current classical computing methods fail to describe quantum systems accurately enough in relevant times for the pharmaceutical industry, limiting the applicabil- ity of quantum chemistry to drug design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' More accurate computations could bring significant value to the phar- maceutical industry by replacing many labour-intensive experiments with calculations in silico, as long as the computational cost is lower than the experimental effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Quantum computations could enable key, experimentally inaccessible insights into chemical systems, exploiting methods that directly derive properties from wave func- tions [111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' To have a profound impact on the pharmaceutical in- dustry, quantum computers need to benefit a broader set of problems than the small number inaccessible to classical computers [13, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Typical relevant systems have thousands of atoms, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' large protein structures with their surroundings, and rarely require exact accu- racy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' However, in many pharmaceutical use cases, one must determine thermodynamic properties that rely on large thermodynamic ensembles, thus requiring many single-point calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Finding new methods that al- low trade-off accuracy for time on quantum computers or that avoid sampling could be beneficial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ideally, quantum computers should offer accuracy and robustness for both strongly and weakly correlated systems at a speed that is currently only accessible by lower-accuracy methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' By getting rid of some of the current approximations, quantum calculations in drug design would become truly predictive and much more widely used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Major advancements in quantum algorithms for elec- tronic structure problems brought down computational costs [46, 81, 113, 114] over the last years, while fur- ther improvements are required for practical applications in industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Furthermore, fundamental improvements in hardware, error correction codes and algorithms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' for state preparation) are necessary to go beyond single- point energy calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Steps are already being made towards solving some of these challenges, and several routes exist to achieve these goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' We are convinced that open research integrating academia and industry will help make quantum comput- ing an essential tool to design better drugs faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' ACKNOWLEDGMENTS The authors thank Darryl McConnel, Alexander Ren- ner, Christoph Ehrendorfer, Lorenzo Pautasso, Manuel M¨oller, and Anika Pflanzer for comments on the various iterations this perspective went through.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' The molecules reported are visualised in Mol* [115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Scannell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Blanckley, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Boldon, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' War- rington, Nature Reviews Drug Discovery 11, 191 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Allen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kulkarni, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chamberlain, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dwight, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Koh, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Samant, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jernigan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rice, 7 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Marino, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chiswick, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tesar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sparks, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McGee, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kolossv´ary, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shechter, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Soutter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bastos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Taimi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Petrin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kane, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Swann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gard- ner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Winter, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sherman, bioRxiv (2022), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='1101/2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='493001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Palermo and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' De Vivo, “Computational chemistry for drug discovery,” in Encyclopedia of Nanotechnology, edited by B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bhushan (Springer Netherlands, Dordrecht, 2014) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Maltarollo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gertrudes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Oliveira, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Honorio, Expert opinion on drug metabolism & toxicology 11, 259 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jayatunga, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Xie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ruder, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schulze, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Meier, Nature Reviews Drug Discovery 21, 175 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [6] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shukla and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tripathi, “Molecular dynamics simu- lation in drug discovery: Opportunities and challenges,” in Innovations and Implementations of Computer Aided Drug Discovery Strategies in Rational Drug Design, edited by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Singh (Springer Singapore, Singapore, 2021) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 295–316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Irle, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Vuong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Elayyan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Talipov, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Abel, “Protein molecular dynamics simulations with approximate qm: What can we learn?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' in Quan- tum Mechanics in Drug Discovery, edited by A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Heifetz (Springer US, New York, NY, 2020) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 149–161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Heifetz, Quantum Mechanics in Drug Discovery, Methods in Molecular Biology (Springer US, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Feynman, International Journal of Theoretical Physics 21, 467 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lloyd, Science 273, 1073 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Nielsen and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chuang, Quantum Computa- tion and Quantum Information (Cambridge University Press, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aspuru-Guzik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dutoi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Love, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Head-Gordon, Science 309, 1704 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Romero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Olson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Degroote, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Johnson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kieferov´a, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kivlichan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Menke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Peropadre, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sawaya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sim, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Veis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aspuru-Guzik, Chemical Reviews 119, 10856 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [14] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bravyi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Motta, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan, Chemical Reviews 120, 12685 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Low, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Steiger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H¨aner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Materials Theory 6, 11 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Motta and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rice, WIREs Computational Molec- ular Science 12, e1580 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zinner, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dahlhausen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Boehme, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ehlers, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bieske, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fehring, Drug Discovery Today 26, 1680 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Baiardi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Christandl, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, arXiv 2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='12220 (2022), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='12220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [19] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Blunt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Camps, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Crawford, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Izs´ak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Leontica, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mirani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Moylett, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Scivier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S¨underhauf, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schopf, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Taylor, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Holz- mann, Journal of Chemical Theory and Computation 18, 7001 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dalzell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kumar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Helms, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gray, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='- H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cui, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kastoryano, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Preskill, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reichman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Campbell, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Valeev, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan, arXiv (2022), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='48550/arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='02199, 2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='02199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bofill and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pulay, The Journal of Chemical Physics 90, 3637 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Khedkar and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Roemelt, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 23, 17097 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Andersson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Malmqvist, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Roos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sadlej, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wolinski, The Journal of Physical Chem- istry 94, 5483 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [24] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Angeli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cimiraglia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Evangelisti, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Leininger, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Malrieu, The Journal of Chemical Physics 114, 10252 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pernal, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 120, 013001 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Coe and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Paterson, Journal of Chemical The- ory and Computation 11, 4189 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [27] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dattani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Umrigar, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='- L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan, The Journal of Chemical Physics 150, 024302 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Goings, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' White, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tautermann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Degroote, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gidney, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shiozaki, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rubin, arXiv , arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='01244 (2022), arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='01244 [quant-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Head-Gordon, Physical Chemistry Chem- ical Physics 21, 4763 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [30] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gauss, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ruscic, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Armentrout, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Stanton, Journal of chemical theory and computa- tion 13, 1044 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Degroote, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Henderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dukel- sky, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Scuseria, Physical Review B 93, 125124 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rissler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Noack, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' White, Chemical Physics 323, 519 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [33] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Stein and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, Journal of chemical theory and computation 12, 1760 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [34] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sharma, Annual review of physical chemistry 62, 465 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [35] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Stein and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, Molecular Physics 115, 2110 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ding, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mardazad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Das, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Szalay, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schollw¨ock, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zimbor´as, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schilling, Journal of Chemical The- ory and Computation 17, 79 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Motta and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rice, WIREs Computational Molec- ular Science 12, e1580 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McArdle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Endo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aspuru-Guzik, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Benjamin, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yuan, Reviews of Modern Physics 92, 015003 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Preskill, Quantum 2, 79 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [40] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bharti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cervera-Lierta, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kyaw, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Haug, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Alperin-Lea, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Anand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Degroote, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Heimonen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kottmann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Menke, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mok, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sim, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='- C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kwek, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aspuru-Guzik, Reviews of Modern Physics 94, 015004 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Love, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aspuru- Guzik, The Journal of Physical Chemistry Letters 5, 4368 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cerezo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Arrasmith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Benjamin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Endo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fujii, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mitarai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yuan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cincio, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Coles, Nature Reviews Physics 3, 625 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [43] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Quek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fran¸ca, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Khatri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Meyer, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Eisert, arXiv - quant-ph 2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='11505 (2022), arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='11505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [44] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Campbell, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Terhal, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Vuillot, Nature 549, 172 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 8 [45] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Svore, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wecker, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Proceedings of the National Academy of Sci- ences 114, 7555 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gidney, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huggins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, PRX Quantum 2, 030305 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [47] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berry, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ahokas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cleve, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sanders, Communications in Mathematical Physics 270, 359 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [48] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tura, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cirac, Journal of Mathematical Physics 60, 022202 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [49] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tong, Quantum 4, 372 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kitaev, “Quantum measurements and the Abelian Stabilizer Problem,” (1995), arXiv:quant-ph/9511026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [51] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Knill, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ortiz, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Somma, Physical Review A 75, 012328 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O’Brien, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Senjean, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sagastizabal, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bonet- Monroig, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dutkiewicz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Buda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' DiCarlo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Visscher, npj Quantum Information 5, 113 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [53] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sokolov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Barkoutsos, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Moeller, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Such- sland, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mazzola, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tavernelli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Re- search 3, 013125 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [54] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O’Brien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Streif, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rubin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Santagati, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Su, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huggins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Goings, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Moll, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kyoseva, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Degroote, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tautermann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berry, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, arXiv (2021), 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='12437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [55] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wecker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bauer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Clark, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hastings, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A 90, 022305 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [56] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Poulin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kitaev, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Steiger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hastings, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 121, 010501 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [57] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wecker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hastings, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Clark, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Nayak, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A 92, 062318 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [58] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tazhigulov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Haghshenas, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rubin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Minnich, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan, arXiv (2022), 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='15291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hill, Journal of the Royal Society of Medicine 108, 32—37 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [60] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kenakin, in Pharmacology in Drug Discovery and Development (Second Edition), edited by T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kenakin (Academic Press, 2017) second edition ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 1–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [61] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Polishchuk, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Madzhidov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Varnek, Journal of Computer-Aided Molecular Design 27, 675 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [62] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ferreira de Freitas and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schapira, Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 8, 1970 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [63] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Paul, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mytelka, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dunwiddie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Persinger, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Munos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lindborg, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schacht, Nature Reviews Drug Discovery 9, 203 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [64] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Talevi and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Quiroga, ADME Processes in Pharmaceutical Sciences, Dosage, Design, and Pharma- cotherapy Success, edited by {Quiroga, Alan Talevi and Pablo A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='} (Springer, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [65] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Miljkovi´c, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Martinsson, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Obrezanova, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Williamson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Johnson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sykes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bender, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Greene, Molecular Pharmaceutics 18, 4520 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [66] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jim´enez-Luna, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Grisoni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Weskamp, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schneider, Expert Opinion on Drug Discovery 16, 949 (2021), pMID: 33779453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [67] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cournia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Allen, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sherman, Journal of Chemical Information and Modeling 57, 2911 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [68] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Deglmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sch¨afer, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lennartz, Interna- tional Journal of Quantum Chemistry 115, 107 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [69] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tinberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Khare, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Doyle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Nelson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schena, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jankowski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kalodimos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Johnsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Stoddard, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Baker, Nature 501, 212 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [70] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' King, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aitchison, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Luo, Frontiers in Molecular Biosciences 8 (2021), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='3389/fmolb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='712085.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [71] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bonagura, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bhaskar, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shimizu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sun- daramoorthy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McRee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Goodin, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Poulos, “High-resolution crystal structure of compound i intermediate of cytochrome c peroxidase (ccp),” (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [72] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bonagura, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bhaskar, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shimizu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sun- daramoorthy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McRee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Goodin, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Poulos, Biochemistry 42, 5600 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [73] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Westbrook, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Feng, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gilliland, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bhat, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Weissig, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Shindyalov, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bourne, Nucleic Acids Research 28, 235 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [74] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Heilmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wolf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kozlowska, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sedghamiz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Setzler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Brieg, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wenzel, Scientific Reports 10, 18211 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [75] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kaynak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Krieger, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dudas, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dahmani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Costa, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Balog, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Scott, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Doruker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Per- ahia, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bahar, Frontiers in molecular biosciences 9, 832847 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [76] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' James and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tawfik, Trends in Biochemical Sciences 28, 361 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [77] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Song and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Merz Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', Journal of Chemical Information and Modeling 60, 5308 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [78] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Karplus and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McCammon, Nature Structural Biology 9, 646 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [79] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' van Gunsteren and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mark, The Journal of Chemical Physics 108, 6109 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [80] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hawkins, Journal of Chemical Information and Modeling 57, 1747 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [81] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' von Burg, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Low, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H¨aner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Steiger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rei- her, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Roetteler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Research 3, 033055 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [82] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Joyce, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Nawrat, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sherer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Biba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Brunskill, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Martin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cohen, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Davies, Chemical Science 9, 415 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [83] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Peng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gleza- kou, Journal of Chemical Information and Modeling 60, 3746 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [84] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O’Brien, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ioffe, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Su, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fushman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Neven, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Smelyanskiy, arXiv (2021), 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='02163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [85] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B¨uhl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kaupp, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Malkina, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Malkin, Journal of computational chemistry 20, 91 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [86] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Xin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sader, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chaudhary, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jones, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wag- ner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tautermann, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Busacca, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Saraceno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fandrick, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gonnella, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Horspool, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hansen, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Senanayake, The Journal of Or- ganic Chemistry 82, 5135 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [87] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Eastman, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Njardarson, Journal of Medicinal Chemistry 57, 9764 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [88] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Phillips and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pombeiro, Current Medicinal Chemistry 26, 7476 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [89] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Brell, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Flammia, Journal of Statistical Mechanics: Theory and Experiment 2017, 083106 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [90] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pallister, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pol, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Roberts, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Research 4, 023019 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 9 [91] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fowler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mariantoni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Martinis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cleland, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A 86, 032324 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [92] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gidney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Motta, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, Quantum 3, 208 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [93] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Arute, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Arya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bacon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bardin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Barends, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Biswas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Boixo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Brandao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Buell, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', Nature 574, 505 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [94] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Deng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Du, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Fan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Guo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Guo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Guo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Han, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Liang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Qian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Qiao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Xu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ye, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ying, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Yu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Peng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 127, 180501 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [95] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Madsen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Laudenbach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Askarani, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rortais, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Vincent, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bulmer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Miatto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Neuhaus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Helt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Collins, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=', Nature 606, 75 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [96] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tubman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mejuto-Zaera, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Epstein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hait, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Levine, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huggins, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Head-Gordon, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Whaley, arXiv (2018), 1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='05523.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [97] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Barcza, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Legeza, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Marti, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reiher, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' A 83, 012508 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [98] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' von Burg, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Low, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H¨aner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Steiger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rei- her, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Roetteler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Physical Review Re- search 3, 033055 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [99] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Haghshenas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Potter, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' X 12, 011047 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [100] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kim and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Swingle, arXiv (2017), 1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='07500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [101] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Gily´en, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Arunachalam, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, “Optimiz- ing quantum optimization algorithms via faster quan- tum gradient computation,” in Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (Society for Industrial and Applied Mathemat- ics, 2019) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 1425–1444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [102] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mitarai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Toyoizumi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mizukami, arXiv 2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='00718 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [103] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huggins, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berry, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zhao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Reichman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Neven, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Baczewski, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, arXiv (2023), 2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='01203 [quant-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [104] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Abrams and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lloyd, Physical Review Letters 83, 5162 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [105] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Somma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Batista, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Ortiz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 99, 030603 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [106] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Dinu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Podewitz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Grothe, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Liedl, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Loerting, The Journal of Physical Chemistry A 123, 8234 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [107] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Aleksi´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Seeliger, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Brown, Molecular Informatics 41, 2100113 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [108] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Carleo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cirac, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Cranmer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Daudet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Schuld, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Tishby, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Vogt-Maranto, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Zdeborov´a, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 91, 045002 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [109] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Biamonte, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wittek, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Pancotti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rebentrost, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wiebe, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lloyd, Nature 549, 195 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [110] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Broughton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Mohseni, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Boixo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Neven, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, Nature Com- munications 12, 2631 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [111] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' McClean, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rubin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Harrigan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' O’Brien, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Babbush, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huggins, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huang, The Journal of Chemical Physics 155, 150901 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [112] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Huang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Kueng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Preskill, Nature Physics 16, 1050 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [113] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Hastings, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Wecker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bauer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Troyer, Quantum Info.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' 15, 1–21 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [114] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Low and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Chuang, Quantum 3, 163 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' [115] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Sehnal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bittrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Deshpande, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Svobodov´a, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Berka, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Bazgier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Velankar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Burley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Koˇca, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} +page_content=' Rose, Nucleic Acids Research 49, W431 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/fdE2T4oBgHgl3EQfxwiK/content/2301.04114v1.pdf'} diff --git a/fdE_T4oBgHgl3EQf2RwE/content/2301.08339v1.pdf b/fdE_T4oBgHgl3EQf2RwE/content/2301.08339v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..65cb1d762885db7501702a1743ddb73deda69682 --- /dev/null +++ b/fdE_T4oBgHgl3EQf2RwE/content/2301.08339v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:14929dc72f3f521b05b9e30def5cab97c935780cba2f8d64282d0dcc07937571 +size 551439 diff --git a/fdE_T4oBgHgl3EQf2RwE/vector_store/index.pkl b/fdE_T4oBgHgl3EQf2RwE/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..29a9235d0b45157da10f887c4d6b7029db3778c3 --- /dev/null +++ b/fdE_T4oBgHgl3EQf2RwE/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dfb320e5b7375da90f89abb76d59b5e2bfc1d5e91a89dd44acd4dce226331e97 +size 33731 diff --git a/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/2301.05206v1.pdf.txt b/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/2301.05206v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..a766b89521d68b06eb515f476dd99e63b7af4252 --- /dev/null +++ b/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/2301.05206v1.pdf.txt @@ -0,0 +1,2997 @@ +1 +ImMesh: An Immediate LiDAR Localization and Meshing Framework +Jiarong Lin˚, Chongjiang Yuan˚, Yixi Cai, Haotian Li, Yuying Zou, Xiaoping Hong and Fu Zhang +Fig. 1: (a) shows the triangle mesh that is online reconstructed by our proposed work ImMesh, where the white path is our sampling trajectory, +and the yellow frustums are the estimated sensor pose. In (b), we use the estimated camera poses (the yellow frustums) of R3LIVE for +texturing the mesh with the collected images. Based on ImMesh, we developed a lossless texture reconstruction application, with one of our +results shown in (c). Our accompanying video that shows details of this work is available on YouTube: youtu.be/pzT2fMwz428. +Abstract—In this paper, we propose a novel LiDAR(-inertial) +odometry and mapping framework to achieve the goal of si- +multaneous localization and meshing in real-time. This pro- +posed framework termed ImMesh comprises four tightly-coupled +modules: receiver, localization, meshing, and broadcaster. The +localization module utilizes the prepossessed sensor data from +the receiver, estimates the sensor pose online by registering +LiDAR scans to maps, and dynamically grows the map. Then, +our meshing module takes the registered LiDAR scan for in- +crementally reconstructing the triangle mesh on the fly. Finally, +the real-time odometry, map, and mesh are published via our +broadcaster. The key contribution of this work is the meshing +module, which represents a scene by an efficient hierarchical +voxels structure, performs fast finding of voxels observed by +new scans, and reconstructs triangle facets in each voxel in +an incremental manner. This voxel-wise meshing operation is +delicately designed for the purpose of efficiency; it first performs +a dimension reduction by projecting 3D points to a 2D local plane +contained in the voxel, and then executes the meshing operation +˚These two authors contribute equally to this work. +J. Lin, C. Yuan, Y. Cai and F. Zhang are with the Department +of Mechanical Engineering, The University of Hong Kong, Hong Kong +SAR, China. tjiarong.lin, ycj1, yixicai, haotianl, +zyycici, fuzhangu@connect.hku.hk +C. +Yuan +and +X. +Hong +are +with +the +School +of +System +Design +and +Intelligent +Manufacturing, +Southern +University +of +Science +and +Technology, +Shenzhen, +People’s +Republic +of +China.tyuancj2020,hongxpu@sustech.edu.cn +with pull, commit and push steps for incremental reconstruction +of triangle facets. To the best of our knowledge, this is the first +work in literature that can reconstruct online the triangle mesh +of large-scale scenes, just relying on a standard CPU without +GPU acceleration. To share our findings and make contributions +to the community, we make our code publicly available on our +GitHub: github.com/hku-mars/ImMesh. +Index Terms—Mapping, 3D reconstruction, SLAM +I. INTRODUCTION +Recently, the wide emergence of 3D applications such as +metaverse [1, 2], VR/AR [3], video games, and physical sim- +ulator [4] has enriched human lifestyle and boosted productive +efficiency by providing a virtual environment that alike the +real world. These applications are built upon triangle meshes +that represent complex geometry of real-world scenes. Triangle +mesh is the collection of vertices and triangle facets, which +serves as a fundamental tool for objects modeling in most +existing 3D applications. It can not only simplify significantly +the process and boost the speed of rendering [5, 6] and ray- +tracing [7], but also play an irreplaceable role in collision +detection [8, 9], rigid-body dynamics [10, 11], dense mapping +and surveying [12], sensor simulation [13], etc. However, +most existing mesh is manufactured by skillful 3D modelers +with the help of computer-aided design (CAD) software (e.g., +arXiv:2301.05206v1 [cs.RO] 12 Jan 2023 + +(c) +c3) +(c1) +(c1) +(c2) +c22 +Solidworks [14], blender [15], etc.), which limits the mass +production of large-scene meshing. Hence, developing an +efficient mesh method that could reconstruct large scenes in +real-time draws increasing research interests and serves as a +hot topic in the community of 3D reconstruction. +Performing mesh reconstruction in real-time is particularly +important in practical usages. Firstly, online mesh reconstruc- +tion indeed makes data collection effective by providing a +live preview, which is quite important to give a reference for +users. Especially for those non-expert users, a live preview can +serve as a feedback about which parts of the scene have been +reconstructed in good quality already and where additional +data is needed. Secondly, online mesh reconstruction can +immediately output the mesh of scene once data collection +is complete, saving additional post-processing time of offline +mesh reconstruction and hence boosts the productivity of +mass production. Thirdly, it is particularly important for those +real-time applications, especially for fully autonomous robotic +applications, a real-time update of mesh can provide better +maps with denser representation and of higher accuracy, which +can enable the agent to better navigate itself. +Reconstructing the mesh of large scenes from sensor mea- +surements in real-time remains one of the most difficult +problems in the fields of computer graphics, 3D vision, and +robotics, which require reconstructing the surfaces of scenes +with triangle facets that are adjacently connected by edges. +This is a challenging problem that needs to build the geometry +structure with very high accuracy, and the triangle facet should +be reconstructed on surfaces that actually exist in the real +world. Besides, a good mesh reconstruction method should +also suppress the appearance of holes on the reconstructed +surface, and avoid the reconstruction of triangle silver (i.e., the +noodle-like triangles that have a shard acute angle). Real-time +mesh reconstruction in large scenes is even more challenging +as it further requires the reconstruction to operate in an +efficient, incremental manner. +In this work, we propose a real-time mesh reconstruction +framework termed ImMesh to achieve the goal of simultaneous +localization and meshing on the fly. This is a well-engineered +system that is comprised of four tightly-coupled modules +delicately designed for efficiency and accuracy. To the best +of our knowledge, this is the first work in literature that can +reconstruct the triangle mesh of large-scale scenes online and +with a standard CPU. The main contributions of our work are: +‚ We propose a novel system that can estimate the sen- +sor pose and reconstruct the mesh of the surrounding +environment both online. Its localization is built upon +our previous work VoxelMap [16], which can estimate +the sensor pose of better efficiency and higher accuracy +over its counterparts (e.g., FAST-LIO2 [17], SUMA [18], +MULLS [19], Lego-LOAM [20], etc.). Its meshing mod- +ule implements a novel mesh reconstruction approach, +which efficiently reconstructs the mesh in an incremental +manner, and can achieve real-time performance in large- +scale scenarios on a standard desktop CPU. +‚ We implement a novel mesh reconstruction method in +our meshing module, which directly utilizes the registered +LiDAR point as mesh vertices, online reconstructing the +triangle facets (i.e., the indices of three triangle points) in +an incremental manner. Specifically, our meshing module +first utilizes an efficient hierarchical voxel data structure +for fast finding of voxels containing points in new scans. +Then, the voxel-wise 3D meshing problem is converted +into a 2D one by performing dimension reduction. Fi- +nally, the triangle facets are incrementally reconstructed +with the voxel-wise mesh pull, commit and push steps. +‚ We evaluate the runtime performance and meshing ac- +curacy of ImMesh by conducting extensive experiments. +We first verify the overall performance by presenting live +video demonstrations of how the mesh is immediately +reconstructed in the process of data collection. Then +we extensively tested ImMesh with four public datasets +collected with different types of LiDARs in various +scenes. Finally, we evaluate the runtime performance and +meshing accuracy of ImMesh by comparing them against +existing baselines. +‚ We additionally demonstrate how real-time meshing can +be applied in potential applications by presenting two +practical examples. We first show that ImMesh can be +applied for LiDAR point cloud reinforcement, which can +output the reinforced points in regular pattern, and with +higher density and wider FoV compared to raw LiDAR +scan. Then, we combined ImMesh and our previous work +R3LIVE [21, 22] to achieve the goal of losslessly texture +reconstruction of scenes (see Fig. (b)), which is useful +for rapid field surveying. +‚ We make ImMesh publicly available on our GitHub: +github.com/hku-mars/ImMesh1 for sharing our +findings and making contributions to the community, +II. RELATED WORKS +In this section, we discuss the related works of mesh +reconstruction based on 3D point cloud, which are closely +related to this work. Depending on whether the reconstruction +processes can perform online, we categorize existing mesh +reconstruction methods into two classes: offline methods and +online methods. +A. Offline mesh reconstruction +The offline methods usually require a global map in prior, +for example, the full registered point cloud of the scene. +Then, a global mesh reconstruction process is used to build +the mesh. In this category, the most notable works include: +methods based on Poisson surface reconstruction (Poisson- +based), and methods based on Delaunay tetrahedralization +(i.e., 3D Delaunay triangulation) and graph cut (Delaunay- +based). +1) Poisson surface reconstruction (Poisson-based): Given +a set of 3D points with oriented normals that are sampled +on the surface of a 3D model, the basic idea of Poisson +surface reconstruction [23, 24] is to cast the problem of +mesh reconstruction as an optimization problem, which solves +for an approximate indicator function of the inferred solid +1Our codes will be released as this work is accepted. + +3 +whose gradient best matches the input normals. Then, the +continuous isosurface (i.e., the triangle mesh) is extracted +from the indicator function using the method [25, 26] that is +similar to adaptations of the Marching Cubes [27] with octree +representations. +Benefiting from this implicit representation, where the mesh +is extracted from the indicator function instead of being +estimated directly, Poisson surface reconstruction can produce +watertight manifold meshes and is resilient to scanner noise, +misalignment, and missing data. Hence, in the communities of +graphics and vision, these types of methods [23, 24, 28] have +been widely used for reconstructing the mesh from given 3D +scanned data. +2) Delaunay +triangulation +and +graph +cut +(Delaunay- +based): In the category of offline mesh reconstruction meth- +ods, approaches [29]–[31] based on Delaunay tetrahedraliza- +tion and graph cut are also been widely used for generating +the mesh, based on the reconstructed 3D point cloud and the +sensor’s poses. The basic idea of this class of methods is first +to build a tetrahedral decomposition of 3D space by computing +the 3D Delaunay triangulation of the 3D point set. Then, the +Delaunay tetrahedra was labeled as “inside” or “outside” with +the globally optimal label assignment (i.e., the graph cut). +Finally, the triangle mesh can be extracted as the interface +between these classes. +Besides these two classes of methods, there exist other +offline surface mesh reconstruction algorithms such as the +ball-pivoting algorithm [32] that have been proposed in past +decades. However, they are usually not the first choice of +consideration due to the lower precision and worse efficiency +compared to Poisson- and Delaunay-based methods [33]. +Unlike these offline mesh reconstruction methods, our pro- +posed work ImMesh can perform online in an incremental +manner without the whole point cloud of the scene. Besides, +ImMesh also achieves a satisfactory meshing accuracy that is +higher than Poisson-based and slightly lower than Delaunay- +based (see our experimental results in Section VIII-C). +B. Online mesh reconstruction +1) Voxel volume-based methods (TSDF-based): The online +mesh reconstruction method is predominated by TSDF-based +methods, which represent the scene in a voxel volumetric +theme. These methods implicitly reconstruct the mesh in a +two-step pipeline, which first establishes the truncated signed +distance to the closest surface of voxels, then extracts the +continuous triangle mesh by leveraging the Marching Cubes +algorithm [27] from volumes. TSDF-based methods are pop- +ularized by KinectFusion [34], with many follow-up works +focused on scaling this approach to larger scenes [35, 36], +adding multi-resolution capability [37, 38], and improving +efficiency [39]–[41]. Since these classes of methods can be +easily implemented with parallelism, they can achieve real- +time performance with the acceleration of GPUs. +Compared to these methods, our work ImMesh shows +several advantages: Firstly, in ImMesh, the triangle mesh is +directly reconstructed from the point cloud in one step, while +for TSDF-based methods, the mesh is implicitly built in a two- +step pipeline (i.e., SDF update followed by a mesh extraction). +Secondly, ImMesh is able to output the mesh in scan-rate (i.e., +sensor sampling rate), while the mesh extraction of TSDF- +based methods is usually at a lower rate. Thirdly, ImMesh +achieves real-time performance by just running on a standard +CPU, while TSDF-based methods need GPU acceleration for +real-time SDF update. Lastly, TSDF-based methods require +adequate observation for the calculation of SDF of each voxel +w.r.t. the closet surface, which needs the data to be sampled by +a depth sensor of high resolution and moving at a low speed. +On the contrary, our work exploits high-accuracy LiDAR +points for meshing and is robust to points data of low density. +2) Surfel-based mesh reconstruction: Besides TSDF-based +methods, another popular approach is to represent the scene +with a set of points or surfels (e.g., oriented discs). For +example, in work [36, 42, 43], the maps are reconstructed with +point-based representation, and its “surface” is rendered with +the approaches of “point-based rendering” that originated from +the communities of computer graphics [44]–[46]. Besides, +in work [47] , the high-quality map is reconstructed with +surfel-based representations (i.e., use patches), such forms of +mapping representation are popularized in works [48]–[51]. +To reconstruct a dense map, these classes of methods need +a large number of points or tiny patches to represent the +surface of models. This is an inefficient representation that +has high usage of system memory and computation resources. +In contrast, our work reconstructs the surface of models with +triangle mesh, which uses triangle facets of proper size that are +adjacently connected by edges. It is the most efficient solid- +model representation that has been widely adopted in most +modern 3D software. +Compared with works reviewed above, our proposed work +is in a class by itself, which contains the following advantages: +‚ It is an online mesh reconstruction method that recon- +structs the triangle mesh in an incremental manner. It +can achieve real-time performance in large-scale scenes +(e.g., traveling length reaches 7.5 km) by just running on +a standard desktop CPU. +‚ It explicitly reconstructs the triangle mesh by directly +taking the registered LiDAR points as meshing vertices, +performing the voxel-wise meshing operation as each new +LiDAR scan is registered. +‚ It is delicately designed for the purpose of efficiency, and +can achieve satisfactory meshing precision comparable to +existing high-accuracy offline methods. +III. SYSTEM OVERVIEW +Fig. 2 depicts the overview of our proposed system (Im- +Mesh), which consists of a map structure and four modules +that work jointly to achieve the goal of simultaneous localiza- +tion and meshing in real-time. As shown in Fig. 2, from left +to right are: receiver (in red), localization (in orange), map +structure (in green), meshing (in blue) and broadcaster (in +purple). +In the rest sections, we will first introduce our map struc- +tures in Section IV, which will show the detail of the data +structures that will be used in other modules. Next, we will + +4 +Fig. 2: This figure shows the overview of our proposed work ImMesh, which utilizes the raw input sensor data to achieve the goal of +simultaneous localization and meshing. It is constituted by four tightly-coupled modules and a map structure, from left (input) to right +(output) are: receiver (in red), localization (in orange), map structure (in green), meshing (in blue) and broadcaster (in purple). +introduce our receiver and localization module in Section +V. Then, we will present how our meshing modules work +in Section VI. Finally, in Section VII, we will introduce +the broadcaster module, which publishes the localization and +meshing results to other applications. +IV. MAP STRUCTURES +As shown by the map structures (in green) in Fig. 2, we +design four data structures, including a structure of meshing +vertices, a structure of triangle facets, an incremental kd-Tree +(ikd-Tree) for k nearest neighbors (kNN) search and down- +sampling, and a hierarchical-voxels structure representing the +3D space. +A. Mesh vertices +In ImMesh, mesh vertices are the points that constitute +the geometric structure (shape) of mesh. All mesh vertices +are stored in a global list. For the i-th entry of the list that +represents vertex Vi, it contains the following elements: +‚ Its 3D position PospViq P R3 in global frame (i.e., the +first LiDAR frame). +‚ The index(id) of this vertex IdpViq “ i, which is the +unique identification that indicates this point is the i-th +point that appended to map. +‚ The list of pointers to triangles facets T whose vertices +contain Vi: +Tri listpViq “ tPtrpTi1q, PtrpTi2q, ..., PtrpTimqu +(1) +where we use function Ptrp¨q to denote the pointer (i.e., +C++ pointer) of p¨q. +B. Triangle facets +In ImMesh, a triangle facet describes a small surface that +exists in the reconstructed scene. It is maintained online by +our meshing module (see Section VI) and is asynchronously +copied to the broadcaster module for publishing. A triangle +facet T contains the following elements: +‚ The sorted indices Pts idpTq of three points that form +this triangle: +Pts idpTq “ ti, j, ku, +i ă j ă k +(2) +‚ The center CenterpTq and normal NormpTq (both in the +global frame) of this triangle: +CenterpTq “ pPospViq ` PospVjq ` PospVkqq {3 +(3) +NormpTq “ n{p||n||q +(4) +n “ pPospViq ´ PospVjqq ˆ pPospVkq ´ PospVjqq +(5) +C. Incremental kd-Tree (ikd-Tree) +We maintain an incremental kd-tree to enable the fast kNN +search of mesh vertices. The ikd-Tree is proposed in our +previous work [17, 52], which is an efficient dynamic space +partition data structure for fast kNN search. Unlike existing +static kd-tree (e.g., kd-tree implemented in PCL [53] and +FLANN [54]) that require rebuilding the entire tree at each +update, ikd-Tree achieves lower computation time by updating +the tree with newly coming points in an incremental manner. +In ImMesh, we use the ikd-Tree for: +‚ Downsample the point cloud density to keep the min- +imum distance between any of two mesh vertices for +maintaining the triangle mesh at a proper resolution. + +Localization +Odometry +(andn) +LiDAR input +Publish' +LiDARpoints +State +Point cloud +motion +Estimation +registration +Velodyne +Publish +compensation +Point cloud +Broadcaster +IMU input (optional) +code +AcCZ +to +AcCY +a +Gyro Y +Mesh +Probability +Gyro X +Acc X +get +02 +vertices +Trianglemesh +Asynchronous! +Retriving +copy +ikd-Tree +Triangle +Hierachical +facets +voxels +Estimated +Rasterization +Pull +Push +plane +Depth image (optional) +Dimensionality +Voxel-wise mesh +Voxel-wise 3D +1660:9903 +reduction by +pull, commit and +points retrieving +0000 +projection +push +Meshing +ImMesh) framework +26.367 +49.6325 +Hierachical + voxels +Hash +table +L3-Voxel +O3 +Mesh +vertices +etc. +L1-Voxel +O1 +L2-Voxel +O2 +Trianlge +facets +etc. +Octree +Higher level +voxel O4+ +Hierarchical +voxels +Hierachical + voxels +Higher level +Voxel O3+ +Mesh +vertices +etc. +L1-Voxel +O1 +L2-Voxel +O2 +Trianlge +facets +etc. +Octotree +Hash table +World +World +... +Fig. 3: In ImMesh, the world is partitioned by hierarchical voxels. We +compactly store, access, and update the voxels in a spatial hashing +scheme. +‚ Enable the vertex dilation operation in our voxel-wise +meshing operation (see Section VI), which can erode the +gaps between neighbor voxels. +D. Hierarchical voxels +In our map, we partition the 3D space with hierarchical +voxels. As shown in Fig. 3, lower-level voxels contain those +of higher levels. These voxels of different levels are designed +with different sizes and for various purposes: the lowest level +(i.e., L1-Voxel) has the largest voxel size, which partition +the 3D space into small regions by uniform grids. Voxels in +this layer maintain a hash table of pointers that point to the +triangle facet whose center is located inside. This facilitates +the broadcaster for asynchronous copying of these triangle +facets (see Section VII-B). And, the size of the second layer +(i.e., L2-Voxel) is much smaller than the first layer, where the +voxels in this layer store the mesh vertices that constitute the +geometric structure of the mesh. Voxels of this layer allow +the meshing module to fast retrieve all in-voxel mesh vertices +for voxel-wise meshing operations (see Section VI). Lastly, as +shown in Fig. 3, the L2-Voxel and its sub-voxels form a typical +octree data structure, which is used in our localization module +for a further split of non-planar point clusters to achieve better +pose estimation (see Section V). +1) L1-Voxel O1: As illustrated in Fig. 3, we uniformly +partition the 3D world into many small regions with L1-Voxel. +To avoid large memory consumption in allocating regular +volumetric grids (e.g., in kinectFusion [34]), we compactly +store, access, and update the voxels with a spatial hashing +scheme alike [36]. We map the 3D world space into the hash +table via a hash function Hashp¨q, where the hash function +allows an efficient look-up of voxel blocks with the integer- +rounded world coordinates. The array of pointers to Voxel is +stored in the hash table. +Hashpx, y, zq “ Int Hashpxi, yi, ziq +(6) +“ Modppxi ¨ p1q ‘ pyi ¨ p1q ‘ pzi ¨ p3q, nq +(7) +xi “ Roundpx ˚ 100{rxq, +yi “ Roundpy ˚ 100{ryq +zi “ Roundpz ˚ 100{rzq +(8) +where x, y, z are coordinates of 3D space, xi, yi, zi are spec- +ified integer rounded world coordinates, rx, ry, rz are the +voxel size in three dimensions, ‘ is the XOR operation, and +function Modpa, bq is the calculation of integer a modulus +another integer b. p1, p2, p3 are three large prime numbers for +reducing the collision probability [36, 55], n is the hash table +size. In our work, we set the value of p1, p2, p3 and n as +116101, 37199, 93911 and 201326611, respectively. +Notice that the hash table is unstructured, indicating that +the neighboring voxels are not stored spatially but in different +parts of the buckets (shown in Fig. 3). Besides, for resolving +the possible hash collision (i.e., two pieces of data in a hash +table share the same hash value), we adopt the technique in +[36], using the implementation of unordered map container +in C++ standard library (std) [56]. In this work, we access a +L1-voxel with a given 3D vector p “ rx, y, zsT P R3 by: +O1 “ Get L1 voxelpHashppqq +(9) +Shown in Fig. 3, each L1-Voxel contains the voxels of the +higher hierarchical layer. To identify the work stage of L1- +Voxel, we use a flag to mark the status as either Sync-required +or Synced. These two statuses indicate the update flag related +to the data synchronization of triangle facets, as we will use +in Section VI-E and Section VII-B. +For each L1-Voxel, it stores and maintains a hash table of +pointers pointing to a triangle facet whose center is located +in the voxel. These pointers can be efficiently looked up via +Int Hashpi, j, kq in (6), where i, j, k are the sorted indices +(i.e., i ă j ă k) of three mesh vertices. These in-voxel triangle +facets are maintained (i.e., added or erased) by the meshing +module, and are asynchronously copied to broadcaster module +for publishing to other applications. +2) L2-Voxel O2 and voxels of higher layer: L2-Voxel is the +second biggest container, which stores an array of points that +point to all in-voxel mesh vertex, and contains the voxels of +higher layer. It is used in both of our localization and meshing +modules; in localization module, L2-Voxel stores the in-voxel +registered LiDAR points used to constitute planar features +for estimating the sensor pose; in meshing module, L2-Voxel +enables fast retrieval of all in-voxel mesh vertices and provides +the local estimated planar norm for projecting the 3D points +into the 2D plane. +For a L2-Voxel O2, it has a status flag indicating whether +it has new points appended. To be detailed, O2 is marked as +Activated if this voxel has new mesh vertices registered from +the latest LiDAR scan (see Section V-C). And the Activated +flag is reset as deactivated after the voxel-wise meshing +operation is performed on this voxel (see Section VI-G). +Similar to (9), we achieve fast access to a L2-Voxel with a +given 3D vector p “ rx, y, zsT P R3 through hash tables: +O2 “ Get L2 voxelpHashppqq +(10) +where the hash function Hashp¨q in (10) and (9) are distin- +guished with different voxel size rx, ry, rz in (8). +For voxels of higher layer, e.g., voxel O3 of the third layer +and higher O3`, they are designed to partition the non-planer +points (in voxels of the higher layer) with a smaller spatial size +(higher resolution), which make them more likely to construct +a planar feature for localization, as introduced in the coming +section. +Notice that the voxels of L2- and higher levels construct an +Octree. We access the voxels of the third layer and higher in +a way similar to Octree [57]. + +pJock2 +AOXGI +blhow6 +V. RECEIVER AND LOCALIZATION +The receiver module is designed for processing and packag- +ing the input sensor data. As shown in the red box of Fig. 2, +our receiver module receives the streaming of LiDAR data +from live or offline recorded files, processes the data to a uni- +fied data format (i.e., customized point cloud data) that make +ImMesh compatible with LiDARs of different manufacturers, +scanning mechanisms (i.e., mechanical spinning, solid-state) +and point cloud density (e.g., 64-, 32-, 16-lines, etc.). Besides, +if the IMU source is available, our input module will also +package the IMU measurements within a LiDAR frame by +referring to the sampling time. +The localization module utilizes the input data stream of +receiver module, real-time estimating the sensor poses of +6 DoF and registering the points to map. Our localization +module is built upon our previous work VoxelMap [16], which +represents the surrounding environment with the probabilistic +representation, estimating pose with an iterated Kalman filter +by maximum a posterior. +In designing our localization module, we have noticed that +a number of works appeared in the literature recently, which +utilize the reconstructed mesh for improving the localization +accuracy of both visual-slam (e.g., [58]) and LiDAR-slam +system (e.g., [59]–[61]). However, in ImMesh, the online +reconstructed mesh is not used in our localization module +because: 1) our mesh is reconstructed with points that are +registered by the localization module, re-using mesh in lo- +calization will take more computation efforts and bring extra +latency in publishing the estimated pose. 2) the accuracy of our +localization module is indeed enough for most of the robotics +and surveying applications, which achieve the localization +results of better efficiency and higher accuracy compared to its +counterparts like FAST-LIO2 [17], SUMA [18], MULLS [19], +Lego-LOAM [20], etc. Despite this, we hold a positive attitude +toward seeking the possibility of improving the localization +accuracy with our online reconstructed mesh in future work. +A. Voxel map construction +Our localization is built by representing the surrounding en- +vironment with the probabilistic representation, which counts +both LiDAR measurement noises and sensor pose estimation +errors, and constructs the voxel-volumetric maps in a coarse- +to-fine adaptive resolution manner. But, in this work, we +mainly focus our attention on how to real-time reconstruct the +triangle mesh of the scene, and avoid introducing too many +complicated noise analyses that might confuse the reader. We +only discuss those processes in localization module that are +closely related to our meshing module in this paper. For the de- +tailed modeling and analysis of LiDAR’s measurement noise, +we recommend our readers to our previous work VoxelMap +[16]. +For a LiDAR sampling point, we first compensate the in- +frame motion distortion with an IMU backward propagation +introduced in [17]. Let us use Lpi denote i-th LiDAR sampling +point after motion compensation, it is registered to world frame +as W pi with the estimated sensor pose pW +L R, W +L tq P SEp3q: +Wpi “ W +L RLpi ` W +L t +(11) +The register LiDAR points are stored inside the voxels (e.g., +L2-Voxel), let us consider the distribution of points Wpi pi “ +1, ..., Nq that are located inside the L2-Voxel. We have the +points covariance matrix A calculated as: +¯p “ 1 +N +N +ÿ +i“1 +Wpi, +A “ 1 +N +N +ÿ +i“1 +`Wpi ´ ¯p +˘ `Wpi ´ ¯p +˘T (12) +where the symmetric matrix A depicted the distribution of +points. Let us perform the eigendecomposition of matrix A: +AU “ +» +– +λ1 +λ2 +λ3 +fi +fl “ +u1 +u2 +u3 +‰ +, +λ1 ě λ2 ě λ3 (13) +where λ1, λ2, λ3 are the eigenvalues and u1, u2, u3 are the +correspondent eigenvectors. +If the minimum eigenvalue λ3 is less than a specified +threshold, which indicates that the points inside this voxel are +distributed on a thin planar surface, we regard all points Wpi +pi “ 1, ..., Nq as a planar feature. Otherwise, this voxel will +be further subdivided into voxels of higher level with smaller +size (i.e., L3-, L4-,..., voxel) until: 1) the tiers of layer reach +bound (set as tier-5 for our work) 2) the minimum eigenvalue +of points covariance matrix A of a voxel smaller than a given +threshold. +If points Wpi pi “ 1, ..., Nq inside the voxel indeed forming +a planar feature, whose minimum eigenvalue λ3 of its points +covariance matrix A less than a specified threshold. We +represent this planar feature by using its normal vector n and +a point q that lies in this plane. The normal vector is well +known as the eigenvector w.r.t. associated with the minimum +eigenvalus λ3, i.e., n “ u3 in (13). And point q “ ¯p is +calculated in (12). +B. State Estimation +1) Point-to-plane residual: +In our localization module, +we solve the sensor pose by minimizing the Point-to-plane +residual. Given a LiDAR point Wpi predicted in the world +frame with the pose prior, we first find which voxel it lies +in by hashing with (10). Then, all the contained voxels of +higher layers are polled for a possible match with the point. +Specifically, let a sub-voxel contains a plane with normal ni +and center qi, we calculate the point-to-plane distance: +di “ nT +i pWpi ´ qiq +(14) +If point pi lies on the candidate plane with this point-to- +plane distance di falling within the 3-σ bound of the plane +measurement noise, we treat this point-to-plane pair as an +effective match and add it to the residuals for estimating the +sensor pose. +2) LiDAR pose estimation by maximum a posterior (MAP): +We build a LiDAR(-inertial) odometry system based on an +iterated error-state extended Kalman filter (IESKF) similar to +that derived in our previous works [17, 62]. Assume that +we are given a state estimation prior, which is provided +from a constant velocity assumption for LiDAR-only odom- +etry (e.g., Kitti dataset in our Experiment-1), or from IMU +propagation for LiDAR-inertial odometry (e.g., NCLT-dataset, + +7 +NTU-dataset, R3LIVE-dataset our self-collected data in Sec- +tion VIII). This will be fused with the point-to-plane distance +matched in Section V-B1 to form a maximum a posteriori +(MAP) estimation. Then, we solve this MAP problem by +leveraging an IESKF, which leads an optimal state estimation +of sensor pose pW +L R, W +L tq that is used for registering the +LiDAR point with (11). +C. Point cloud registration +After the state estimation, we perform the point cloud +registration for transforming each measurement point +Lpi +from LiDAR frame to global frame (i.e., the first LiDAR +frame) with (11). This registered point cloud is then used +for: 1) Published to other applications with our broadcaster. 2) +Use for updating the probabilistic voxel map. 3) Appended to +map structure that serves as the mesh vertices for shaping the +geometry structure of our online reconstructed triangle mesh. +1) Update of voxel map: The registered LiDAR points are +used for constructing the probabilistic voxel map by updating +the point distributions (i.e, A in (12)), planar parameters +(i.e., n, q) and the correspondent uncertainties of all possible +hierarchical voxels. For the details of this voxel map update, +we refer the reader to our previous work [16]. Besides, if a +new register point does not lie on an existing L2 (or L1) voxel, +a new L2 (or L1) voxel will be created and added to the hash +table, after, this point will be added to the newly constructed +voxel. +2) Append of mesh vertices: The registered LiDAR points +are also used for forming the meshing vertices in map struc- +tures. To be detailed, we first leverage a voxel-grid filter for +downsampling register LiDAR point cloud. Then, to avoid +the appearance of tiny triangles in reconstructing the mesh, +we leverage the ikd-Tree (see Section IV-C) for keeping the +minimum distance between any of two meshing points. That +is, for each register LiDAR point W pi in global frame, we +search for the nearest mesh vertex in map structure with ikd- +Tree, if the euclidean distance this point and the searhed vertex +smaller than a given threshold, we will discard this point. +Otherwise, this point will be used for: 1) Constructing a new +mesh vertex Vi, where i is the unique index that indicates Vi +is the i-th appended vertex. 2) Appending the pointer of Vi +to the ikd-Tree. 3) Pushing back the pointer PtrpViq to the +point array of the L2-Voxel O2 +j that Vi located in. After, the +status flag of O2 +j is set as activated for notifying the meshing +module for performing the voxel-wise re-meshing operation +(see Section VI). +VI. MESHING +In ImMesh, our meshing module takes the registered LiDAR +scan for incrementally reconstructing the triangle mesh on the +fly. We explicitly reconstruct the triangle mesh by directly +utilizing 3D registered LiDAR points as mesh vertex with +two considerations: 1) The points sampled by LiDAR and +registered via the ICP-based methods [63, 64] have very high +positional accuracy. Hence, they are capable of shaping the +geometric structure of the mesh. 2) A LiDAR measurement +point naturally lies on the surface of the detected object. That +is, a laser pulse is emitted from the infrared transmitter and +reflected by the surface of the detected object. The returned +pulse is captured by the receiver, and the ranging distance of +the sensor from the surface is finally calculated by counting +the time of flight (ToF). +A. Goals and requirements +With the accurate mesh vertices appended from the point +cloud registration in Section V-C, the problem of online mesh +reconstruction is converted to another goal, which is to seek a +proper way for real-time reconstructing the triangle facets with +a growing 3D point set. However, to the best of our knowledge, +this is a new area in the community that has not been explored +yet. Given a set of growing 3D points, our meshing module +is designed to incrementally reconstruct the triangle facets +considering the following four major requirements: +Firstly, precision is our prior consideration. For each recon- +structed triangle facet that represents the surface of the scene, +we require it to lie on an existing plane. +Secondly, the reconstructed mesh should be hole-less. In +the dense reconstruction of the surface triangle mesh, the +appearance of holes is unacceptable. To be detailed, these +holes lead to the wrong results in the rasterization of the depth +image, which wrongly rasterizes the surfaces behind a real +object to the front. Consequently, robotic applications based +on our meshing result might lead to severe accidents (e.g., +crashing into a wall). Besides, the holes on surfaces make the +whole reconstructed map unsightly and chaotically. +Thirdly, the reconstruction of triangle mesh should avoid +constructing sliver triangles. The sliver triangle (i.e., the +noodle-like triangle), as defined in the communities of com- +puter graphic [65]: whose area is so thin that its interior does +not contain a distinct span for each scan line, has some unde- +sired properties in the field of computer graphics. For example, +these noodle-like triangles would cause some errors in the +numerical analysis on them [66]. Besides, these unfavorable +properties cause troubles in the pipelines of rendering (e.g., +rasterization, texturing, and anti-aliasing [5, 6, 67]), Which +leads to the loss of accuracy in calculating (e.g., depth testing, +interpolation, etc.) the pixel values distributed near the sharp +angle [6, 68, 69]. +Lastly, the complexity of triangle mesh reconstruction +should be computationally efficient to meet the requirement of +real-time applications. The time consumption of each meshing +process should not exceed the sampling duration of two +consecutive LiDAR frames. +B. Challenges and approaches +To achieve our goals of dense incremental meshing with +the four requirements listed above, our system is proposed +based on a deep analysis of the challenges. The challenges +and corresponding scientific approaches are briefed below: +The first challenge is that the global map is continuously +grown by the newly registered LiDAR points, with each update +of a LiDAR scan only affecting part of the scene. Hence, +for an incremental mesh reconstruction method, it should +be able to process only those parts of the scene with new + +8 +points appended in. In our work, we incrementally perform +the mesh reconstruction with a mechanism similar to git +[70]. For each incremental mesh update, we first retrieve +the data of the voxels with new mesh vertices appended via +the pull step (detailed in Section VI-E1). Then, an efficient +voxel-wise meshing algorithm is executed to reconstruct the +mesh with these data. The incremental modifications of newly +reconstructed results w.r.t. pulled results are calculated in +our commit step (detailed in Section VI-E2). Finally, these +incremental modifications are merged to the global map via +our push step (detailed in Section VI-E3). +Given a set of 3D vertices, the second challenge is how to +correctly and efficiently reconstruct the triangle facets repre- +senting the surfaces of the scene. Since it is hard to directly +reconstruct mesh from these mesh vertices in 3D space, our +work performs the meshing operation in 2D. To be detailed, for +vertices located in a small region (i.e., in L2-Voxel), we first +project them into a proper plane (i.e., the estimated plane given +by the localization module). The mesh of these 2D points is +constructed using the 2D meshing algorithms and is recovered +back to 3D (detailed in Section VI-D2). +C. Voxel-wise vertex retrieval +1) Retrieval of in-voxel vertices: To reconstruct the triangle +mesh in an incremental manner, the first step is to retrieve +the vertices that need to mesh with the newly added points. +In ImMesh, we use the hierarchical voxels (see Section IV-D) +for subdividing the 3D space into many regions. The flags that +indicate the status of each L1-Voxel are used for identifying +whether a L2-Voxel has newly appended mesh vertices (see +Section V-C). +Take an activated L2-Voxel O2 +i as an example. We perform +a voxel-wise meshing operation to reconstruct the triangle +facets with all in-voxel vertices. Since the pointers of these +vertices are stored in a pointer array attached to O2 +i , we +address these pointers to retrieve all in-voxel vertices, denoted +as VIn +i “ tVj1, Vj2, ..., Vjmu. +2) Vertex dilation: In practice, if we perform the meshing +operation with only the in-voxel mesh vertices, the gaps +between neighborhood voxels will appear due to the absence of +triangles facets across voxels, as shown in Fig. 4(b). Motivated +by morphological operations (e.g., dilation and erosion) in +digital image processing [71], we perform the 3D point cloud +dilation for adding neighborhood points of VIn +i +to erode the +gaps between voxels, as shown in Fig. 4(a). +For vertex Vij +P +VIn +i , we perform the radius-search +operation by leveraging the ikd-Tree (see Section IV-C) for +searching the nearest vertices of Vij with their euclidean +distance smaller than a given value dr (usually set as 1{4 +of the size of L2-Voxel). Using ˜Vij to denote the searched +neighbor vertices and Vi to denote the dilated vertices, we +have: +@V P ˜Vij, +ˇˇ|PospVq ´ PospVijq +ˇˇ | ď dj +(15) +If V P Vij is not included in Vi, we add V by Vi “ +Vi Y V. +Fig. 4: The comparisons of mesh reconstruction with (a) and without +(b) the vertex dilation. +The full algorithm of our voxel-wise vertex retrieval is +shown in Algorithm 1. +Algorithm 1: Voxel-wise vertex retrieval of O2 +i +Input : The activated voxel O2 +i +Output: The retrieved vertex set Vi +Start +: Copy all in-voxel pointer list to VIn +i . +Vi “ VIn +i +. +1 foreach Vij P VIn +i +do +2 +˜Vij = RadiusSearch(Vij,dr) +3 +foreach V P ˜Vij do +4 +if V R Vi then +5 +Vi “ Vi Y V +Return: The retrived vertex set Vi after dilation +D. Dimensional reduction by projection +With the mesh vertices Vi retrieved from Algorithm 1, we +introduce the voxel-wise mesh reconstruction. +1) Projection 3D vertices on a 2D plane: Since it is hard to +directly mesh with Vi distributed in 3D space in real-time, we +simplify the 3D meshing problem to a 2D one by projecting Vi +on a suitable plane. Based on the analysis of the characteristics +of Vi, we provide two reasons to perform the dimensional +reduction by projection, listed as follows: 1) For a 3D point +sampled by LiDAR, it is distributed on a surface. Hence, for +vertices Vi retrieved from Algorithm 1 that distributed in a +small region (i.e., in a L2-Voxel O2 +i ), they tend to form a +planar-like point cluster. 2) For these planar-like point clusters, +we can approximately mesh them in a 2D view on their lying +surface. Imagine a 2D ant climbing on 3D surfaces solving +this 3D problem in a 2D view, as shown in Fig. 5. + +A +区区 +? +A +K +A +区 +发 +AA9 +3D meshing +Fig. 5: In ImMesh, we reduce the 3D meshing problem to a 2D one +by projecting the 3D points onto an estimated surface plane. Imagine +a 2D ant climbing on 3D surfaces solving this 3D problem in a 2D +view. +The plane pn, qq suitable for projection has already been +calculated in our localization module in Section V-A. The +norm n of the plane is the eigenvector u3 that corresponds +to the minimum eigenvalue λ3 in (13), which is the eigende- +composition of point covariance matrix A in voxel O2 +i . q is +the center points inside O2 +i . +Remark: Even though O2 +i might be further divided into +voxel of lower layer by the localization module, the norm +n and q of O2 +i is being updated at each new LiDAR frame. +For each vertex Vij P Vi, we project it to plane pn, qq. +The resultant 2D point uij is calculated as: +pij “ rφ, ρsT P R2 +(16) +φ “ +` +PospVijq ´ q +˘T u1, +ρ “ +` +PospVijq ´ q +˘T u2 (17) +where u1, u2 are the other two eigenvectors in (13). We use +Pi “ tpi1, pi2, ..., pimu to denote the 2D point set after +projected from Vi. +2) Two-dimensional Delaunay triangulation: After the pro- +jection, the dimension of 3D meshing problem is reduced to +a 2D one, which can be solved by 2D Delaunay triangulation. +Given a set of 2D point P, the two-dimensional triangula- +tion problem is well known as introduced in [72, 73], which +is to find T of triangular facets s.t.: 1) Any of two facets are +either disjoint or share a lower dimensional face (i.e., edge or +point). 2) The set of facets in T is connected with adjacency +relation. 3) The domain PT , which is the union of facets +in T, has no singularity2. With these three useful properties, +the 2D Delaunay triangulation has been widely applied for +reconstructing dense facets with a given 2D point set (e.g., +[74]). +As defined in [75, 76], the Delaunay triangulation DelpPq +of a 2D point set P “ tp1, p2, ..., pmu is the geometric dual +of the Voronoi diagram: there is an edge between two points +ui and uj in the Delaunay triangulation if and only if their +Voronoi cell Vpuiq and Vpujq have a non-empty intersection. +DelpPq yields a triangulation of P, which is a partition of the +2The union UT of all simplices in T is called the domain of T . A +point in the domain of T is said to be singular if its surrounding in PT +is neither a topological ball nor a topological disc (view https://doc.cgal.org/ +latest/Triangulation 2/index.html of [72] for detail). +convex hull of P into d-dimensional simplices (e.g., triangle +in 2D, tetrahedra in 3D), as shown in Fig. 5. +Remark: The Voronoi cell Vpuiq associated with the point +pi is the region of space that is closer to ui than to all other +points in P: +Vppiq “ tp P Rd : @j ‰ i, ||p ´ pi|| ď ||p ´ pj||u +(18) +Considering our requirements in Section VI-A, we chose +Delaunay triangulation to reconstruct the mesh for its remark- +able properties as follows. Firstly, it is a 2D triangulation +providing mesh with no hole leaf in the convex hull of P, +which satisfies our first requirement. Secondly, it naturally +avoids sliver triangles by maximizing the minimum angles +of the triangles in triangulation, which meets our second +requirement. Finally, it is a fast algorithm suitable for real- +time requirements. The algorithm complexity of n points is +Ωpnlogpnqq in 2D (p.s. Ωpn2q in 3D) [77]. +Let us use T i “ DelpPiq “ tTi1, Ti2, ..., Tinu to denote +the triangle facets after the Delaunay triangulation DelpPiq. +For each triangle facets Tij P T i, we retrive the indices with +(2): tα, β, γu “ Pts idpTijq, indicating that this triangle +is formed with 2D points tpiα, piβ, piγu. Returning back to +3D space, we constitute a triangle facet Tij with vertices +tViα, Viβ, Viγu, as shown in Fig. 5. +E. Voxel-wise meshing with pull, commit and push +With the triangle facets T i constructed by the voxel-wise +meshing operation, we incrementally merge T i to the existing +triangle facets +GT +in the map structure. This update is +designed with a mechanism similar to git [70] (a version +control software) that includes pull, commit, and push steps. +1) Pull: Given the vertices Vi obtained from Algorithm 1, +we retrieve the triangle facets T Pull +i +from the map structure. +The algorithm of pull step is shown in Algorithm 2. +Algorithm 2: Voxel-wise mesh pull. +Input : The retrieved vertex set Vi from Algorithm 1 +Output: The pulled triangle facets T Pull +i +Start +: T Pull +i +“ tnullu +1 foreach Vj P Vi do +2 +Get all vertices related triangle set T Vj “ TripVjq +foreach Tk P T Vj do +3 +Get triangle vertex index tα, β, γu “ Pts idpTkq +4 +if pVα P Viq and pVβ P Viq and pVγ P Viq then +5 +T Pull +i +“ T Pull +i +Y Tk +Return: The pulled triangle facets T Pull +i +2) Commit: In this step, we find out the incremental modi- +fications of the reconstructed triangle facets T i (in Section +VI-D2) w.r.t. the pulled facets T Pull +i +(from Algorithm 2). +These incremental modifications are summarized into an array +of mesh facets to be added T Add +i +and an array of mesh facets +to be erased T Erase +i +. The detailed processes of this commit +step are shown in Algorithm 3. + +10 +Algorithm 3: Voxel-wise mesh commit. +Input : The pulled triangle facets T Pull +i +from Algorithm 2 +The reconstructed triangle facets T i +Output: The triangle facets to be added T Add +i +. +The triangle facets to be erased T Erase +i +. +Start +: T Add +i +“ tnullu, +T Erase +i +“ tnullu +1 foreach Tj P T i do +2 +if Tj R T Pull +i +then +3 +T Add +i +“ T Add +i +Y Tj +4 foreach Tj P T Pull +i +do +5 +if Tj R T i then +6 +T Erase +i +“ T Erase +i +Y Tj +Return: The triangle facets to be added T Add +i +and erased +T Erase +i +. +Algorithm 4: Voxel-wise mesh push. +Input : The triangle facets that need to erased T Erase +i +. +The triangle facets that need to added T Add +i +. +1 Function Add_triangle(Tj): +2 +Get point indices tα, β, γu “ IdpTjq +3 +Construct triangle TG +j “ Tripα, β, γq in global map. +4 +Calculate the center of TG +j : +5 +CenterpTG +j q “ pVα ` Vβ ` Vγq {3 +6 +Find the L1-Voxel V1 that CenterpTG +j q located in: +V1 “ Get L1 voxelpHashpCenterpTG +jqqq +7 +Set the status flag of V1 to Sync-required (Section +IV-D2). +8 +Add PtrpTG +j q to triangle list of L1-Voxel V1. +9 +Add PtrpTG +j q to triangle list of points Vα, Vβ, Vγ. +10 Function Erase_triangle(Tj): +11 +Get point indices tα, β, γu “ IdpTjq +12 +Remove PtrpTG +j q in triangle list of points Vα, Vβ, Vγ. +13 +Find the L1-Voxel V1 with CenterpTG +j q via (9): +V1 “ Get L1 voxelpHashpCenterpTG +jqqq +14 +Set the status flag of V1 to Sync-required (Section +IV-D2). +15 +Remove PtrpTG +j q from triangle list of L1-Voxel V1. +16 +Delete triangle TG +j from memory. +17 foreach Tj P T Add +i +do +18 +Add_triangle(Tj) +19 foreach Tj P T Erase +i +do +20 +Erase_triangle(Tj) +3) Push: With the incremental modification T Erase +i +and +T Add +i +from the previous commit step, we perform the erasion +and addition operations of global triangle mesh facets respec- +tively. The detailed processes of our push step is shown in +Algorithm 4. +F. Parallelism +To further improve the real-time performance, we imple- +ment our algorithms with parallelism for better utilization of +the computation power of a multi-core CPU. In ImMesh, we +have two major parallelisms as follows: +The first parallelism is implemented between the local- +ization module and the meshing module. Except for the +point cloud registration in localization module, which needs +to operate the mesh vertices as the meshing operation, the +remaining processes of localization module are parallelized +with the meshing module. More specifically, once our meshing +processes start, the localization module is allowed to process +the new coming LiDAR scan for estimation of the pose of +LiDAR. However, the point cloud registration step is only +allowed to be executed after the end of the meshing process. +The second parallelism is implemented among the voxel- +wise meshing operation of each activated voxel. The voxel- +wise meshing operations of different voxels are standalone +thus, no conflicted operations exist on the same set of data. +G. The full meshing algorithm +To sum up, our full meshing processes are shown in +Algorithm 5. +Algorithm 5: The full meshing process of each update +of LiDAR scan +Input : The set of L2-Voxels V2 “ tO2 +1, O2 +2, ..., O2 +mu that +activated in Section V-C +Start +: The triangle facets that need to added +T Add “ tnullu, and to be erased in this update +T Erase “ tnullu. +1 foreach O2 +i P V2 do in parallel +2 +Retrieve vertices Vi with Algorithm 1. +3 +Reconstruct the triangle facets T i with Vi (Section +VI-D2), +4 +Performing voxel-wise mesh pull (Algorithm 2) to get +T Pull +i +. +Ź // Mesh pull +5 +Performing voxel-wise mesh commit (Algorithm 3) to +get the triangle facets that need to be added T Add +i +and +erased T Erase +i +. +Ź // Mesh commit +6 +T Add “ T Add Ť T Add +i +, +T Erase “ T Erase Ť T Erase +i +/* === Mesh push start === +*/ +7 foreach Tj P T Add do +8 +Add_triangle(Tj) +Ź // In Algorithm 4 +9 foreach Tj P T Erase do +10 +Erase_triangle(Tj) +Ź // In Algorithm 4 +/* === Mesh push end === +*/ +11 foreach O2 +i P V2 do +12 +Reset status of O2 +i as deactived. +/* Remark 1: Line 1„6 are done in parallel for better +real-time performance (as mentioned in Section +VI-F). +*/ +/* Remark 2: The mesh push step Line 7„10 is +different with the voxel-wise operations in +Algorithm 4. The T Add and T Erase are processed after +the parallelism to avoid possible conflicts when +operating the same data (i.e., triangle facets in +our mapping module) (Line 1„6). +*/ +VII. BROADCASTER +In ImMesh, the broadcaster module publishes our state +estimating results (i.e., odometry) and mapping results (i.e., +new registered point cloud and triangle mesh) to other ap- +plications. In addition, if the depth image is required, the +broadcaster module will also rasterize the triangle meshes +into a customized depth image (e.g., user-defined resolution +and FoV). +A. Broadcast of odometry +The real-time 6-dof sensor pose from localization module +(Section V-B) is published with the LiDAR frame starting + +11 +timestamp at a frequency of the LiDAR sampling rate. Besides, +if the IMU source is available, the broadcaster module pub- +lishes the odometry propagated from the IMU preintegration +[78] at the frequency of the IMU sampling rate. +B. Broadcast of triangle facets +Since the triangle facets are stored in an unstructured hash +table of L1-Voxels in map structure, they can not be directly +applied for broadcast. To resolve this problem, our broadcaster +module maintains a background thread that asynchronously +copies the triangle facets from the hash table of each sync- +required L1-Voxels (set as sync-required in Algorithm 4) to +a structured array for broadcasting. Then, these sync-required +voxels are marked as synced after the copying. Finally, The +broadcaster module publishes the refreshed triangle facets to +other applications. +C. Rasterization of depth image +Some robotic applications, such as autonomous navigation +[79] and exploration [80] tasks, require dense accurate depth +images for obstacle avoidance. To meet the requirements of +these scenarios, the broadcaster module utilizes the triangle +facets from Section VII-B to rasterize a depth image at any +customized resolution and FoV, based on the fast implemen- +tation of OpenGL [67]. +1) Reinforcement of LiDAR point cloud: With the depth +image from rasterization, LiDAR point cloud reinforcement is +enabled by unprojecting the 3D points from the depth image. +In detail, with the projection matrix and estimated pose used +for rasterizing the depth image, the 3D points are obtained (i.e., +unproject) w.r.t. each depth value on the depth image. As a +result, the 3D point cloud is enhanced with higher resolution +and larger FoV than the raw LiDAR measurement scan (see +our Application-1 in Section VIII-D). +VIII. EXPERIMENTS AND RESULTS +In this section, we extensively evaluate the performance of +ImMesh. Notice that our localization module is built upon our +previous work VoxelMap [16] with no modification that rela- +tive to the state estimation. Hence, the localization precision +of this work performs as well as [16]. We recommend our +readers get more details about our localization accuracy by +referring to the results reported in our previous work. +In this paper, we lead the experiments by evaluating our +meshing ability, especially on the runtime performance and +accuracy in reconstructing the triangle mesh. +A. Experiment-1: ImMesh for immediate mesh reconstruction +In this experiment, we verify the overall performance of +ImMesh toward real-time simultaneous localization and mesh- +ing with live video demonstrations. As shown in Fig. 6(b), +we record the full process of our data sampling at the cam- +pus of the University of Hong Kong (HKU), deploying the +ImMesh for simultaneously estimating the sensor pose and +reconstructing the triangle mesh on the fly. The full video +demonstration of this experiment is available on YouTube: +youtu.be/pzT2fMwz428?t=9. +Fig. 6: (a) shows our handheld device for data collection and online +mesh reconstruction. (b) shows a snapshot of our accompanying video +(on YouTube: youtu.be/pzT2fMwz428?t=9) of Experiment-1, +with three time-aligned views of different sources including a screen- +recorded view (in red), a camera preview (in yellow), and a third- +person view (in blue). +1) Experiment setup: Our handheld device for data collec- +tion is shown in Fig. 6(a), which includes a mini-computer +(equipped with an Intel i9-10900 CPU and 64 GB RAM), +a Livox avia 3D LiDAR (FoV: 70.4 °ˆ77.2°), and a preview +only RGB camera. In this experiment video, three time-aligned +views of different sources are presented, including: 1) a screen- +recorded view that shows the estimated posed and online +reconstructed triangles mesh of ImMesh. 2) a camera preview +that records the video stream of the front-facing camera. 3) +a third-person view that records the whole process of this +experiment. +2) Result and analysis: As presented in the video, benefits +from the accurate uncertainty models of the LiDAR point and +plane that counting both LiDAR measurement noise and sensor +pose estimation errors in our localization module, ImMesh +is able to provide the 6-DoF pose estimation of very high +accuracy in real-time. What is worth mentioning is, without +any additional processing (i.e., loop detection), all of these +two trials can close the loop itself after traveling 957 m +and 391 m. In addition, with the efficient architecture design +and our careful engineering implementation on our meshing +module, the triangle mesh of the surrounding environment is +incrementally reconstructed on the fly. With the live preview +of real-time meshing as a reference, it is quite useful to let +users know whether the data sampling is sufficient enough for +any part of the scene, especially for those non-expert users. At +the end of the data sampling, the dense accurate triangle mesh +of this scene is already reconstructed. This is why we name +our system the Immediately Meshing (ImMesh) framework. +B. Experiment-2: Extensive evaluation of ImMesh on public +datasets with various types of LiDAR in different scenes +With all the modules delicately designed for efficiency and +careful engineering implementations, both the localization and +meshing modules easily achieve real-time performances on a +standard multi-core CPU. In this experiment, we statics the +average time consumption on four public datasets with the +computation platform listed in Section VIII-A1. +The four datasets we chose are: the Kitti dataset [81], +the NCTL dataset [82], the NTU VIRAL dataset [83] and +the R3LIVE dataset [22]. They are collected in different +scenarios ranging from urban structured buildings to field- +cluttered complex environments (see Table II), using various +types of LiDARs that include mechanical spinning LiDAR + +Screen +Camera +LiDAR +Mini-PC +a)12 +TABLE I: The specifications of LiDARs in four datasets +Dataset +Kitti +NCLT +NTU VIRAL +R3LIVE +LiDAR +Velodyne HDL-64E +Velodyne HDL-32E +Ouster OS1-16 Gen1 +Livox Avia +Scanning +mechanism +Mechanical, +spinning 64-line +Mechanical, +spinning 32-line +Mechanical, +spinning 16-line +Solid-state, +Risley’s prism +Field of View +(Horizontal˝ ˆ Vertical˝) +360.0˝ ˆ 26.8˝ +360.0˝ ˆ 41.3˝ +360.0˝ ˆ 33.2˝ +70.4˝ ˆ 77.2˝ +Points per secondr1s +1,333,312 +695,000 +327,680 +240,000 +Price +$ 75,000 +$ 8,800 +$ 3,500 +$ 1,599 +1 Only show the point rate of single-return mode. +TABLE II: This table shows the detailed information (e.g., length, duration, scenarios) of each testing sequence, the time consumption of +ImMesh in processing a LiDAR scan, and the number of vertices and facets of each reconstructed mesh in Experiment-2. +Sequece +Traveling +length (m) +Durations +(s) +LiDAR +frames +Meshing +mean/Std (ms) +Localization +mean/Std (ms) +Number of +vertices (k) +Number of +facets(k) +Scenarios +Kitti 00 +3,724.2 +456 +4,541 +32.1 / 12.0 +49.0 / 11.7 +3,339.4 +7,692.7 +Urban city +Kitti 01 +2,453.2 +146 +1,101 +34.5 / 10.5 +51.1 / 18.5 +2,033.0 +4,046.8 +High way +Kitti 02 +5,058.9 +509 +4,661 +33.5 / 7.0 +36.2 / 9.5 +4,390.3 +10,028.1 +Residential +Kitti 03 +560.9 +88 +801 +28 / 7.1 +49.0 / 12.2 +730.0 +1,550.8 +Countryside; Road +Kitti 04 +393.6 +27 +271 +30.1 / 9.4 +42.4 / 12.9 +411.7 +850.6 +Urban city; Road +Kitti 05 +2,205.6 +303 +2,761 +29.6 / 8.2 +38.7 / 11.5 +2,167.4 +4,950.3 +Residential +Kitti 06 +1,232.9 +123 +1,101 +23.1 / 5.6 +56.9 / 9.7 +886.1 +1,889.4 +Urban city +Kitti 07 +2,453.2 +114 +1,101 +20.7 / 7.4 +31.3 / 8.6 +764.4 +1,710.5 +Urban city +Kitti 08 +3,222.8 +441 +4,071 +32.4 / 7.8 +45.7 / 17.7 +3,559.1 +7,936.3 +Urban city +Kitti 09 +1,705.1 +171 +1,591 +34.5 / 7.5 +43.1 / 19.2 +1,827.4 +4,127.5 +Countryside; Road +Kitti 10 +919.5 +132 +1,201 +23.4 / 6.9 +30.9 / 11.9 +939.6 +2,096.5 +Residential +NCLT 2012-01-15 +7,499.8 +6739 +66,889 +26.3 / 14.1 +21.3 / 9.8 +9,659.7 +26,608.3 +Campus; Indoor +NCLT 2012-04-29 +3,183.1 +2598 +25,819 +25.4 / 13.9 +19.1 / 5.4 +4,820.9 +13,483.9 +Campus +NCLT 2012-06-15 +4,085.9 +3310 +32,954 +24.5 / 14.4 +22.3 / 7.7 +6,361.0 +17,473.5 +Campus +NCLT 2013-01-10 +1,132.3 +1024 +10,212 +20.2 / 12.5 +19.3 / 6.5 +2,020.6 +5,495.8 +Campus +NCLT 2013-04-05 +4,523.6 +4167 +41,651 +20.6 / 13.8 +26.8 / 11.7 +9,582.3 +23,982.4 +Campus +NTU VIRAL eee 01 +265.3 +398 +3,987 +11.2 / 6.7 +14.5 / 3.4 +597.6 +1,380.3 +Aerial; Outdoor +NTU VIRAL nya 01 +200.6 +396 +3,949 +9.4 / 5.3 +10.2 / 1.7 +536.8 +1,247.6 +Aerial; Indoor +NTU VIRAL rtp 01 +449.6 +482 +4,615 +12.1 / 8.5 +10.9 / 2.6 +719.2 +2,030.5 +Aerial; Outdoor +NTU VIRAL sbs 01 +222.1 +354 +3,542 +11.4 / 8.0 +17.2 / 3.2 +472.5 +1,150.4 +Aerial; Outdoor +NTU VIRAL tnp 01 +319.4 +583 +5,795 +6.3 / 3.7 +8.8 / 1.2 +155.5 +414.0 +Aerial; Indoor +R3LIVE hku campus 00 +190.6 +202 +2,022 +12.0 / 7.3 +11.5 / 3.2 +587.1 +1,236.9 +Campus +R3LIVE hku campus 01 +374.6 +304 +3,043 +20.4 / 12.6 +17.2 / 6.9 +1,323.4 +2,862.9 +Campus +R3LIVE hku campus 02 +354.3 +323 +3,236 +13.5 / 6.4 +11.9 / 2.8 +867.9 +1,913.6 +Campus +R3LIVE hku campus 03 +181.2 +173 +1,737 +12.2 / 5.7 +11.3 / 2.9 +550.0 +1,130.6 +Campus +R3LIVE hku main building +1,036.9 +1170 +11,703 +16.9 / 14.3 +12.5 / 8.0 +3,031.2 +6,803.6 +Indoor; Outdoor +R3LIVE hku park 00 +247.3 +228 +2,285 +30.1 / 15.9 +12.6 / 3.7 +919.5 +2,380.2 +Cluttered field +R3LIVE hku park 01 +401.8 +351 +3,520 +31.5 / 12.2 +12.6 / 3.9 +1,673.0 +3,964.8 +Cluttered field +R3LIVE hkust campus 00 +1,317.2 +1073 +10,732 +26.0 / 12.8 +18.0 / 7.6 +4,916.7 +11,246.8 +Campus +R3LIVE hkust campus 01 +1,524.3 +1162 +11,629 +27.1 / 13.9 +16.8 / 6.7 +5,353.1 +12,638.1 +Campus +R3LIVE hkust campus 02 +2,112.2 +1618 +4,787 +26.7 / 14.5 +20.3 / 6.1 +1,991.6 +4,653.5 +Campus +R3LIVE hkust campus 03 +503.8 +478 +16,181 +33.6 / 13.3 +21.0 / 5.3 +7,673.8 +18,247.3 +Campus +TABLE III: Two ImMesh configurations for two types of LiDARs +(i.e., mechanical and solid-state LiDAR). +Minimum point L1-voxel O1 +L2-voxel O2 +distance (m) +size (m) +size (m) +Mechanical LiDAR +0.15 +15.0 +0.60 +Solid-state LiDAR +0.10 +10.0 +0.40 +TABLE IV: The average/maximum time of meshing and localization +module for processing each LiDAR scan in four datasets. +Kitti +NCLT +NTU VIRAL +R3LIVE +mean/max mean/max +mean/max +mean/max +Meshing (ms) +31.3 / 34.5 24.2 / 25.4 +9.8 / 17.2 +25.3 / 33.6 +Localization (ms) 42.2 / 56.9 22.3 / 26.8 +11.9 / 17.2 +16.6 / 21.0 +of different channels and solid-state LiDAR of small FoV +(see the specifications in Table I). Hence, the adaptability of +ImMesh is sufficiently validated by extensive tests on these +four distinguished datasets. +1) Experiment setup: Thanks to the parameter insensitivity +of ImMesh, we are able to benchmark ImMesh in four datasets +with only two sets of configurations. The two configurations +are reasonably required for adapting two classes of LiDARs +(i.e., mechanical and solid-state LiDAR), as shown in Table III. +Since the 3D points sampled by a solid-state LiDAR are +distributed in a small sensor FoV, the accumulated point cloud +of solid-state LiDAR usually has a higher density. Therefore, +we set the minimum point distance and voxel size for solid- + +LIVOX +AVIAVelodyne13 +Fig. 7: In Experiment-3, we use CAD software to design a solid model to generate a ground truth triangle mesh as a reference, which +contains four zones simulating different scenarios, as the white entity shown in this figure. To simulate the data collecting process with +different vehicles, we generate the LiDAR point cloud data by traveling along three distinguished trajectories, whose sampling poses are +colored in different colors (i.e., red, yellow, and blue). +state LiDAR 1.5 times smaller than those for mechanical +LiDAR, as shown in Table III. For the other setups, we +maintained the same configuration except for some necessary +adjustments to match the hardware setup. +2) Result and analysis: Table II shows the detailed infor- +mation (e.g., length, duration, scene) of each sequence, the +average time consumption of our localization and meshing +module in processing a LiDAR scan, and the number vertices +and facets of each reconstructed mesh. From Table II, it +is seen that the average cost-time of both localization and +meshing modules are closely related to the density of the +input LiDAR scan. To be detailed, the LiDAR of a higher +channel has a much higher point sampling rate (see Table I) +which causes more data to be processed in each update of a +LiDAR frame (e.g., more points in a voxel and more voxels +activated in each frame). Besides, for the same set of datasets, +the processing time also varies among different scenarios. The +sequences sampled in a high-way or field environment (e.g., +Kitti 01, Kitti 09) usually have a longer LiDAR sampling +range and hence leading to more points per frame to be +processed. Thanks to the efficient data structure (e.g., ikd-Tree, +hashed hierarchical voxel) and parallelism strategy, which +allows us to perform the state estimation and incremental mesh +reconstruction simultaneously, the time consumption of large- +scale datasets is bounded in an acceptable value (ď35 ms for +meshing, ď49 ms for localization). +The average and maximum time consumption of ImMesh in +four datasets are shown in Table IV, reflecting that our system +satisfies the real-time requirement even with different types +of LiDAR and in various scenarios. Notice that the LiDAR +sample rate are 10 Hz for all datasets, and our meshing and +localization are run in parallel (see Section VI-F). +C. Experiment-3: Quantitative evaluation of meshing accu- +racy +In this experiment, we horizontally evaluate the runtime +performance and meshing accuracy of ImMesh by comparing +it with existing state-of-the-art mesh reconstruction methods. + +The coordinate +The ground-truth +The samplingposes +Thesamplingposes +The sampling poses +axes +model +oftrajectory-1 +oftrajectory-2 +oftrajectory-3 +> +四 +Z +Zone-A +Zone-B +Zone-C +Zone-D +(Side view) +A +AV +AT +四 +Z +Zone-A +Zone-B +Zone-C +N +Zone-D +A +0 +(Bird view) +N +V14 +Fig. 8: This figure shows the qualitative results of Experiment-3, with all “positive” facets (correctly reconstructed) colored in white and +“negative” facets (wrongly reconstructed) colored in red. (a) and (b) present a set of qualitative results of four candidates under Trajectory- +3@640 ˆ 480. (c) shows the reconstructed mesh of TSDF feeding with depth images of different resolutions. +TABLE V: The average time consumption of candidates in reconstructing the triangle mesh in Experiment-3. +Time consumption (Unit: second(s)) +Method +Trajectory-1 +@640x480 +Trajectory-1 +@320x240 +Trajectory-1 +@160x120 +Trajectory-2 +@640x480 +Trajectory-2 +@320x240 +Trajectory-2 +@160x120 +Trajectory-3 +@640x480 +Trajectory-3 +@320x240 +Trajectory-3 +@160x120 +ImMesh (ours) +6.877 +6.451 +5.522 +15.649 +14.066 +13.206 +24.536 +18.617 +15.055 +Del +371.632 +132.181 +30.366 +696.641 +353.304 +56.765 +960.613 +323.224 +85.008 +TSDF +6.064 +5.522 +5.513 +16.191 +16.146 +16.028 +20.544 +20.391 +20.309 +Poi +141.848 +78.605 +29.610 +635.079 +198.028 +45.280 +957.743 +310.080 +137.976 +TABLE VI: The meshing accuracy of four candidates evaluated with Criteria-1 in Experiment-3. +Criteria-1:Meshing precision +������ +in Zone-A / in Zone-B +in Zone-C / in Zone-D +in all zones (average) +������ +(Unit: percentage(%)) +Method +Trajectory-1 +@640x480 +Trajectory-1 +@320x240 +Trajectory-1 +@160x120 +Trajectory-2 +@640x480 +Trajectory-2 +@320x240 +Trajectory-2 +@160x120 +Trajectory-3 +@640x480 +Trajectory-3 +@320x240 +Trajectory-3 +@160x120 +ImMesh +(ours) +99.96 / 99.43 +98.06 / 98.98 +99.01 +99.72 / 97.93 +96.06 / 97.15 +97.48 +98.65 / 93.82 +91.47 / 92.50 +93.47 +99.60 / 99.48 +98.38 / 99.49 +99.20 +98.91 / 98.76 +96.51 / 98.09 +98.09 +95.98 / 96.27 +90.58 / 94.07 +94.29 +98.97 / 98.97 +98.00 / 99.05 +98.72 +96.30 / 96.33 +95.24 / 97.53 +96.31 +85.21 / 82.84 +84.88 / 89.59 +85.53 +Del +97.62 / 97.38 +92.95 / 97.54 +96.39 +98.38 / 98.98 +96.20 / 98.86 +98.15 +97.04 / 97.56 +95.09 / 97.68 +96.90 +98.49 / 99.27 +94.39 / 99.09 +97.83 +98.24 / 99.24 +95.31 / 98.96 +98.03 +97.49 / 98.38 +93.94 / 98.14 +97.16 +96.28 / 97.27 +94.30 / 98.14 +96.47 +94.20 / 94.77 +92.75 / 96.31 +94.49 +92.41 / 91.61 +93.60 / 96.59 +93.47 +TSDF +98.93 / 99.88 +93.38 / 99.10 +97.56 +99.83 / 97.57 +92.78 / 96.30 +96.35 +94.18 / 90.42 +74.31 / 80.64 +83.55 +97.96 / 99.53 +90.53 / 98.13 +96.21 +96.30 / 96.48 +86.02 / 96.24 +93.36 +92.60 / 84.98 +75.82 / 87.48 +84.97 +99.54 / 99.62 +92.74 / 99.43 +97.67 +99.12 / 99.11 +96.60 / 99.21 +98.43 +85.88 / 85.45 +83.08 / 89.48 +85.76 +Poi +96.95 / 97.07 +91.14 / 92.11 +93.62 +97.04 / 97.30 +91.02 / 92.30 +93.67 +97.27 / 96.92 +88.43 / 91.87 +92.38 +96.13 / 97.00 +92.27 / 92.00 +94.10 +96.31 / 97.10 +91.70 / 91.26 +94.25 +95.77 / 96.90 +91.83 / 92.25 +94.35 +95.86 / 96.94 +91.72 / 92.44 +94.25 +95.78 / 96.23 +91.91 / 92.23 +93.98 +89.13 / 84.11 +86.43 / 89.06 +87.06 +1) Prepare of simulated data: Since the ground truth trian- +gle mesh of the real-world data can not be directly obtained, +we use CAD software SolidWorks [14] to design a ground truth +solid model for reference, as shown in Fig. 7. This solid model +we made is constituted of four distinguished zones for an +extensive evaluation of the meshing results in different scenes, +which include the simple planar zone (Zone-A), simple curvy +(bending) zone (Zone-B), complex planar zone (Zone-C), and +complex curvy Zone (Zone-D). Each zone has an equal size +of lengthˆwidthˆheight as 10.0 mˆ10.0 mˆ6.5 m. +To simulate point clouds collected by a real LiDAR, we +built a simulator to unproject the “LiDAR” points from the +depth images generated from the rasterization of the ground +truth models with given poses. In this experiment, we ras- +terized the depth image with a pinhole projection model of +horizontalˆvertical FoV as 80˝ ˆ 60˝. Besides, to simulate +the LiDAR of different point cloud densities, we rasterized +the depth image with three sets of resolutions (see Table V) +including 640 ˆ 480, 320 ˆ 240, and 160 ˆ 120. Finally, we +designed three distinguished sampling trajectories as shown in +Fig. 7. Each trajectory contained a number of manually placed +poses for simulating different vehicles in collecting the data. + +148 +@640x480 +(a3) +(a4) Poi trajectory-3 +@640x480 +@640x480 +(a) (c) +(b1) ImMesh trajectory-3 +(b2) Del trajectory-3 +(b3) TSDF trajectory-3 +(b4) Poi trajectory +(b) +@640x480 +@640x480 +@640x480 +@640x48015 +0 +5 +10 +15 +20 +25 +0 +5 +10 +15 +20 +25 +30 +Trajectory-1@640X480 +0 +10 +20 +30 +40 +50 +60 +70 +80 +0 +10 +20 +30 +40 +Trajectory-2@640X480 +0 +20 +40 +60 +80 +100 +0 +5 +10 +15 +20 +25 +Trajectory-3@640X480 +0 +5 +10 +15 +20 +25 +0 +10 +20 +30 +40 +50 +Trajectory-1@320X240 +0 +10 +20 +30 +40 +50 +60 +70 +80 +0 +10 +20 +30 +40 +Trajectory-2@320X240 +0 +20 +40 +60 +80 +100 +5 +10 +15 +20 +25 +Trajectory-3@320X240 +0 +5 +10 +15 +20 +25 +Index of sampling poses + of Trajectory-1 +0 +20 +40 +60 +80 +Trajectory-1@160X120 +0 +10 +20 +30 +40 +50 +60 +70 +80 +Index of sampling poses + of Trajectory-2 +0 +20 +40 +60 +Trajectory-2@160X120 +0 +20 +40 +60 +80 +100 +Index of sampling poses + of Trajectory-3 +5 +10 +15 +20 +25 +30 +Trajectory-3@160X120 +Average depth error (cm) in each frame +TSDF +Del +Poi +ImMesh (Ours) +Fig. 10: Re-rendering depth error in each frame of four candidates in Experiment-3. +TABLE VII: The meshing accuracy of four candidates evaluated by Criteria-2 in Experiment-3. +Criteria-2: Re-rendering depth error (Unit: centimeter (cm)) +Method +Trajectory-1 +@640x480 +Trajectory-1 +@320x240 +Trajectory-1 +@160x120 +Trajectory-2 +@640x480 +Trajectory-2 +@320x240 +Trajectory-2 +@160x120 +Trajectory-3 +@640x480 +Trajectory-3 +@320x240 +Trajectory-3 +@160x120 +ImMesh (ours) +2.146 +3.678 +6.67 +1.686 +3.115 +5.838 +2.076 +3.943 +7.592 +Del +2.216 +3.37 +6.176 +1.832 +2.807 +5.358 +1.674 +3.205 +6.327 +TSDF +5.068 +15.643 +30.421 +4.231 +5.652 +19.352 +3.724 +9.167 +17.288 +Poi +9.844 +9.611 +10.594 +6.546 +6.377 +10.466 +8.21 +8.848 +12.142 +The details of these three trajectories are shown below: +‚ The trajectory-1 (in red) contains 28 sampling poses, +simulating the LiDAR mounted on a car with a height of 1.5 m +away from the ground (i.e., z “ 0 plane). The LiDAR data is +collected by moving from Zone-A to Zone-D. +‚ The trajectory-2 (in yellow) contains 81 sampling poses. +It simulates a handheld LiDAR collecting data at the height +fixed as 1.5 m. The LiDAR data is collected by traveling in +an “8”-like pattern which sufficiently captures the model’s +surface from different views. +‚ The trajectory-3 (in blue) contains 102 sampling poses, +imitating a LiDAR mounted on a drone flying at the height +of 8.5 m. The LiDAR data is collected from a tilted bird view +by flying in an “S”-like pattern. +Due to the limitation of height in sampling the data, LiDAR +in trajectory-1 and trajectory-2 did not capture the ceiling sur- +face of the model. Conversely, LiDAR in trajectory-3 captured +the ceiling surfaces but failed to capture the bottom surfaces +of the models. Besides, LiDAR in trajectory-1 traveled in one +direction; hence only the surfaces facing against the positive +Y -axis were captured. +2) Experiment setup: In this experiment, we conducted a +fair evaluation of meshing ability among our work and existing +mesh reconstruction baselines, which includes a TSDF-based +method implemented by Point cloud library (PCL) [53] with +GPU acceleration, Delaunay triangulation and graph cut based +method implemented by OpenMVS [84], and the official +implementation of Poisson surface reconstruction [23, 24]. +We conducted the evaluation of candidates on a desktop +PC that equips with an Intel i7-9700K CPU, 64Gb RAM, +and a Nvidia 2080 Ti GPU with 12Gb graphics memory. +We feed our ImMesh and TSDF-based (TSDF) method with +LiDAR points frame by frame. To avoid the pose estimation +error that affects the result of meshing, we disable the pose +estimation module and feed ImMesh and TSDF with the +ground truth poses. For offline mesh reconstruction methods: +Delaunay triangulation and graph cut (Del) based method and +Poisson surface reconstruction (Poi), we feed them with the +accumulated point cloud of all frames. To avoid the uneven +point cloud density which leads to errors in calculating the +norm for Poi, and to avoid Del reconstructing the tiny facets +that lead to a biased calculation of accuracy, we leverage a +voxel grid filter with a leaf size of 1.0 cm ˆ 1.0 cm ˆ 1.0 cm +to downsample the accumulated point cloud before feeding to +Poi and Del. +Due to and limitation of graphics memory (12Gb for Nvidia +2080 Ti), we set the TSDF cell size as 0.2 m such that TSDF +can utilize the GPU acceleration while preserving satisfying + +16 +Fig. 11: The first row of images shows the comparisons between a raw LiDAR scan (colored in white) and our reinforced points (colored +in cyan) under different sets of rasterizing FoV. The second and third rows of images show the comparisons of raw and reinforced points +after projection on the current sensor frame. For more detailed visualizations of this process, please refer to our accompanying video on +YouTube: youtu.be/pzT2fMwz428?t=499. +precision in the mesh reconstruction. For our ImMesh, the +parameter configuration for solid-state LiDAR is used, as +shown in Table III. For Poi, we set the octree level as 12 and +removed large hulls by deleting facets with one of their edges +longer than 15.0 cm. For other configurations of all candidates, +we set them as their default configuration. +In this experiment, we horizontally evaluated the meshing +accuracy of candidates by comparing their reconstructed mesh +with the ground truth models. A set of qualitative results of +four candidates under Trajectory-3@640 ˆ 480 are shown in +Fig. 8(a and b). To sufficiently and fairly calculate the accuracy +by comparing the mesh of the candidate’s and ground truth, +two criteria are adopted for counting the difference, shown +below: +‚ Criteria-1: For a triangle facet Tcan +i +of a candidate’s +reconstructed mesh, we first find out a triangle facet Tgt +j +of +the ground truth model, whose point-to-plane distance from +this facet to the center of Tcan +i +is minimum.Tcan +i +is regarded +as “positive” if it satisfies both of the following conditions: 1) +The point-to-plane distance between Tgt +i +and CenterpTcan +i +q +smaller than 5.0 cm; 2) The angular distance between the norm +vector of Tcan +i +and the norm vector of Tgt +j +smaller than 15˝. +Otherwise, this triangle facet Tcan +i +is treated as “negative”. +The ratios of “positive” over the total number of facets in each +zone (and the entire simulated scene) served as Criteria-1 for +evaluating the meshing accuracy, as the results are shown in +Table VI. +‚ Criteria-2: For each candidate’s reconstructed mesh, it is +rasterized into a depth image in the same way as rasterizing +the ground truth model to a depth image (for generating +the simulation data, see Section VIII-C1). The average depth +error of each pixel depth value is calculated between each +depth image pair of the candidate and ground truth (i.e., +re-rendering error), serving as Criteria-2 for evaluating the +meshing accuracy, with the results shown in Figure. 10 and +Table VII. +While Criteria-1 reflects the correctness of candidates in +reconstructing the mesh and reflects different performances in +different zones, it is unable to count the holes of the mesh. +On the contrary, Criteria-2 reflects the errors caused by holes +but can not count the facets out of view (e.g., the facets +hide behind other facets). Referring to the results calculated +according to Criteria-1 (i.e., Table VI) and Criteria-2 (i.e., +Figure. 10 and Table VII), we conducted the evaluation and +analysis on the meshing accuracy of four candidates. +3) Results and analysis of runtime performance: The aver- +age time consumption of four candidates is listed in Table V. +The online methods ImMesh and TSDF show a comparative +runtime performance, while the offline methods Del and Poi +consume about two orders of magnitude larger than the online +methods. Notice that TSDF achieves the comparative runtime +performance as ours with the acceleration of an Nivdia 2080 +Ti GPU, which indicates the highest computation efficiency of +our ImMesh among the four candidates. +4) Result and analysis of meshing accuracy: The results +evaluated by Criteria-1 are shown in Table VI. All candidates +show satisfying accuracy in reconstructing the mesh of the +simple planar models in Zone-A, followed by the simple +curvy model in Zone-B. In complex scenes, all candidates +show lower accuracy and achieve worse results in Zone-C, +where many square cylinders cross each other, making it hard +to reconstruct well. In addition, as the point cloud (i.e., the +resolution of depth images) becomes sparser, the accuracy +drops responsibly, especially for TSDF-based method. Lastly, +Poi shows a bad accuracy in complex scenes due to the +unwanted facets appearing at the sharp edge of the models, + +Comparison of input and +reinforced LiDAR points +Depth FoV=30.0°×22.7 +0epth FoV=50.0°x38.6 +Depth +FoV=77.4°×62.0 +current LiDAR scan +Projection of +inforced LiDAR Points +Projection of re- +Depth +meter +Depth +neter +Depth (meter +Depth (meter +50.0006.125 +150.000 +50.00017 +as the facets colored in red shown in Fig. 8(b4 and c4). +The results evaluated by Criteria-2 are shown in Figure. 10 +and Table VII. Del achieves the best precision by showing the +lowest depth error. Our proposed algorithm ImMesh performs +closely to Del, followed by Poi and TSDF. As the graphs +shown in each column of Figure. 10, the average depth error of +the TSDF increases sharply as the resolution of depth images +goes down, due to the appearance of the holes on the mesh +(as shown in Fig. 8(c)). This unwanted phenomenon that uses +TSDF-based methods for constructing mesh with depth image +of low resolution is also reported in other work [59]. +5) Summary: We lead the conclusions of Experiment-3 +based on the results and analysis discussed in Section VIII-C3 +and Section VIII-C4: For offline applications, which only care +about quality and neglect time consumption, Del is the best +choice, and our ImMesh is the second best one. Poi shows +satisfying results in simple scenes, but it is incapable of +reconstructing complex scenes with many sharp edges. For +real-time applications, our work ImMesh is the best choice. +Even though TSDF with GPU implementation can meet the +runtime requirement of real-time scenarios, its performance is +unsatisfying due to the low meshing accuracy compared to +ImMesh. +D. Application-1: ImMesh for LiDAR point cloud reinforce- +ment +Benefiting from ImMesh’s real-time ability to reconstruct +the triangle mesh on the fly, depth images can be rasterized +from the reconstructed facets online in the current sensor +frame. By unprojecting the 3D points from the depth image, +point clouds of a regular pattern can be retrieved with wider +FoV and denser distribution compared to the original input +LiDAR scan. We termed this process as LiDAR point rein- +forcement. +In this experiment, we demonstrate the LiDAR point cloud +reinforcement with a solid-state LiDAR Livox Avia with FoV +of 70.4˝ˆ77.2˝. The comparisons between the original points +of a LiDAR frame (colored in white) and after our reinforce- +ment (colored in cyan) with different sets of rasterization FoV +are shown in Fig. 11. As the white points shown in the first row +of Fig. 11, the input LiDAR scan is sparse with an irregular +scanning pattern. After the reinforcement, the resultant 3D +points colored in cyan are distributed in a regular pattern, +with denser density and wider FoV (as the rasterization FoV +is bigger than LiDAR’s). To have a better sense of their +differences, we present the comparisons of depth images after +projection, as shown in the second and third rows of Fig. 11. +In this manner, the LiDAR points after reinforcement can +benefit the applications in these scenarios: 1) the reinforced +points of denser density and wider FoV enable navigation +algorithms to achieve better planning performance and make +smarter decisions. 2) it provides unified point cloud outputs +neglecting scanning patterns of different LiDARs. Compared +to the use of original LiDAR points with specific scanning +patterns, using these points of regular patterns potentially +benefits learning-based algorithms for better generalization. +E. Application-2: ImMesh for rapid, lossless texture recon- +struction +In this application, we show how ImMesh can be applied +in applications of losslessly texture reconstruction for rapid +field surveying. As shown in Fig. 12(b1„b3), we mounted +a Livox avia LiDAR and a Hikvision CA-050-11UC global +shutter RGB camera on a DJI M300 drone platform. +We collected the data in a mountain field by taking off +from Zone-A (see Fig. 12(a)), and flying in a “s”-like pattern +trajectory with a traveling distance of 975 m. We leveraged +ImMesh for reconstructing the mesh from collected LiDAR +data and used R3LIVE++ [21, 22] for estimating the camera’s +poses (as the yellow frustum shown in Fig. 12(a, c1 and +c2)). We textured each facet of the reconstructed mesh by the +RGB image captured by the nearest camera with the estimated +camera pose from R3LIVE++. Benefit from the high efficiency +of ImMesh and R3LIVE++, the total time of reconstructing the +RGB textured mesh from this sequence of duration 325 s cost +only 686 s, with 328 s for ImMesh, with 330 s for R3LIVE++ +and 28 s for texturing. Fig. 12(a) shows a bird view of our +mesh after texturing, with the close-up views of textured mesh +in Zone-A, B, and C are shown in Fig. 12(e1, e2, and e3), +respectively. In Fig. 12(c1 and c2), we show the altitude of +this map by coloring the facets in their height w.r.t. the take-off +point (i.e., the ground plane in Zone-A). +As the close-up views shown in the bottom three rows of +Fig. 12, the reconstructed mesh (d1„d3) from our ImMesh +after texturing (e1„e3) successfully preserves the textures of +maps when comparing with the RGB colored point cloud +reconstructed by R3LIVE++ (f1„f3). Since the density of +the point cloud is not infinite, R3LIVE++ is unable to loss- +lessly reconstruct the scene’s radiance by storing radiance +information in points with limited density. On the contrary, +reconstructing the maps with mesh reconstructed by ImMesh, +and texturing the facets with collected images and the camera +poses of R3LIVE++. The raw color images photoed by the +camera are losslessly preserved on the facets of the mesh. +Hence this is a lossless manner for reconstructing the texture +of the scene. Compared to existing counterparts (e.g., structure +from motion (SFM) [12, 30]), this manner shows significant +advantages on: 1) It is a reliable solution that does not require +GPS measurement. 2) It is a rapid reconstruction method that +costs just 2„3 times of data sampling time for reconstructing a +scene. 3) It is a lossless texture reconstruction method, while +preserving geometry structure of very high accuracy that is +constructed from LiDAR’s measurement. +The accompanying video that records the full process of this +lossless texture reconstruction is available on our YouTube: +youtu.be/pzT2fMwz428?t=622, and an additional trial +is shown in our Supplementary Material3. +IX. CONCLUSIONS AND FUTURE WORK +A. Conclusions +In this work, we proposed a novel meshing framework +termed ImMesh for achieving the goal of simultaneous local- +3https://github.com/hku-mars/ImMesh/blob/main/supply/Supplementary +material.pdf + +18 +Fig. 12: (b1„b3) show our UAV platform for data collection. (a) show the bird view of our lossless texture reconstruction result. (c1 and c2) +show the altitude of this map by coloring the facets in their height w.r.t. the take-off point (i.e., the ground plane in Zone-A). The qualitative +comparison of mapping results in Zone-A, B, and C of ImMesh, ImMesh after textured, and R3LIVE are shown in (d„f). To see the detailed +reconstruction process of the scene, please refer to our video on YouTube: youtu.be/pzT2fMwz428?t=622. +ization and meshing framework in real-time. To the best of our +knowledge, it is the first work in literature to reconstruct the +triangle mesh of a large-scale scene in an incremental manner +in real-time. In ImMesh, the localization module represents +the surrounding environment in a probabilistic representation, +estimating the sensor pose in real-time by leveraging an +iterated Kalman filter to maximize a posterior. The meshing +module directly utilizes the registered LiDAR point as mesh +vertices, real-time reconstructing the triangle facets in a novel +incremental manner. To be detailed, our meshing module first +utilizes an efficient hierarchical voxel data structure for fast +finding of voxels containing newly appended vertices. Then, +the voxel-wise 3D meshing problem is converted into a 2D +one by performing dimension reduction. Finally, the triangle +facets are incrementally reconstructed with pull, commit, and +push steps. +In our experiments, we first verified the overall performance +by presenting live video demonstrations of how the mesh +is immediately reconstructed in the process of data collec- +tion. Then we extensively tested ImMesh with four public +datasets collected by four distinguished LiDAR in various +scenes, which confirmed the real-time ability in all sequences +we evaluated. Lastly, we horizontally evaluated the meshing +performance of ImMesh in Experiment-3 by comparing it +against existing meshing baselines. The results show that +ImMesh achieves high meshing accuracy while keeping the +best runtime performance among all candidates. +In our applications, we first show how ImMesh can be +applied for LiDAR point cloud reinforcement, which generates +reinforced points in a regular pattern with denser density and +wider FoV compared to raw LiDAR scan. In Application-2, +we combined our works ImMesh and R3LIVE++ to achieve + +(b1) +Mini PC +40 +长区区区区区区区区 +LiDAR +Camera +区区区区区区区区 +Height +Zone-B +Camera +(c1) +LiDAR +(c2) +b62 +Height +40m +(b3 +a +ImMesh +ImMeshwith +texture +R'LIVE++ +(f1) +(f2 +(f3) +Zone-A +Zone-B +Zone-019 +the goal of losslessly texture reconstruction of scenes. Finally, +to share our findings and make contributions to the commu- +nity, we make our code publicly available on our GitHub: +github.com/hku-mars/ImMesh. +B. Future work +In ImMesh, we propose a novel framework that can simul- +taneously localization and meshing in real-time. Further, to +realize the goal of lossless texture reconstruction of scenes, our +current solution is combining ImMesh and R3LIVE at a system +level as presented in our Application-2 (in Section VIII-E), +which is indeed a solution but not the elegant one. Hence, our +future work would trend to make ImMesh and R3LIVE work +in a more tightly combined style. Besides, since our system +does not implement any loop correction yet, it drifts gradually +due to accumulated localization errors. Our future work will +integrate our recent works [85, 86] on loop detection based +on LiDAR point cloud, which is able to online detecting the +possible loop and then reduce the drift by leveraging the loop +correction. +X. ACKNOWLEDGEMENTS +The authors would like to thank DJI Co., Ltd4 for providing +devices and research found. +REFERENCES +[1] S. Mystakidis, “Metaverse,” Encyclopedia, vol. 2, no. 1, pp. 486–497, +2022. +[2] Y. Wang, Z. Su, N. Zhang, R. Xing, D. Liu, T. H. Luan, and X. Shen, +“A survey on metaverse: Fundamentals, security, and privacy,” IEEE +Communications Surveys & Tutorials, 2022. +[3] P. Cipresso, I. A. C. Giglioli, M. A. Raya, and G. Riva, “The past, +present, and future of virtual and augmented reality research: a network +and cluster analysis of the literature,” Frontiers in psychology, p. 2086, +2018. +[4] S. Shah, D. Dey, C. Lovett, and A. Kapoor, “Airsim: High-fidelity visual +and physical simulation for autonomous vehicles,” in Field and service +robotics. +Springer, 2018, pp. 621–635. +[5] S. Laine and T. Karras, “High-performance software rasterization on +gpus,” in Proceedings of the ACM SIGGRAPH Symposium on High +Performance Graphics, 2011, pp. 79–88. +[6] T. Akenine-Moller, E. Haines, and N. Hoffman, Real-time rendering. +AK Peters/crc Press, 2019. +[7] J. Arvo, Graphics gems II. +Elsevier, 2013. +[8] P. Jim´enez, F. Thomas, and C. Torras, “3d collision detection: a survey,” +Computers & Graphics, vol. 25, no. 2, pp. 269–285, 2001. +[9] C. Ericson, Real-time collision detection. +Crc Press, 2004. +[10] R. Featherstone, Rigid body dynamics algorithms. +Springer, 2014. +[11] D. Baraff, “An introduction to physically based modeling: rigid body +simulation i—unconstrained rigid body dynamics,” SIGGRAPH course +notes, vol. 82, 1997. +[12] J. L. Schonberger and J.-M. Frahm, “Structure-from-motion revisited,” +in Proceedings of the IEEE conference on computer vision and pattern +recognition, 2016, pp. 4104–4113. +[13] F. Kong, X. Liu, B. Tang, J. Lin, Y. Ren, Y. Cai, F. Zhu, N. Chen, and +F. Zhang, “Marsim: A light-weight point-realistic simulator for lidar- +based uavs,” arXiv preprint arXiv:2211.10716, 2022. +[14] D. S. SolidWorks, “Solidworks®,” Version Solidworks, vol. 1, 2005. +[15] B. O. Community, “Blender—a 3d modelling and rendering package,” +Blender Foundation, 2018. +[16] C. Yuan, W. Xu, X. Liu, X. Hong, and F. Zhang, “Efficient and +probabilistic adaptive voxel mapping for accurate online lidar odometry,” +IEEE Robotics and Automation Letters, vol. 7, no. 3, pp. 8518–8525, +2022. +4https://www.dji.com +[17] W. Xu, Y. Cai, D. He, J. Lin, and F. Zhang, “Fast-lio2: Fast direct +lidar-inertial odometry,” IEEE Transactions on Robotics, 2022. +[18] J. Behley and C. Stachniss, “Efficient surfel-based slam using 3d laser +range data in urban environments.” in Robotics: Science and Systems, +vol. 2018, 2018, p. 59. +[19] Y. Pan, P. Xiao, Y. He, Z. Shao, and Z. Li, “Mulls: Versatile lidar +slam via multi-metric linear least square,” in 2021 IEEE International +Conference on Robotics and Automation (ICRA). +IEEE, 2021, pp. +11 633–11 640. +[20] T. Shan and B. Englot, “Lego-loam: Lightweight and ground-optimized +lidar odometry and mapping on variable terrain,” in 2018 IEEE/RSJ +International Conference on Intelligent Robots and Systems (IROS). +IEEE, 2018, pp. 4758–4765. +[21] J. Lin and F. Zhang, “R3live: A robust, real-time, rgb-colored, lidar- +inertial-visual tightly-coupled state estimation and mapping package,” +in 2022 International Conference on Robotics and Automation (ICRA). +IEEE, 2022, pp. 10 672–10 678. +[22] ——, “R3live++: A robust, real-time, radiance reconstruction pack- +age with a tightly-coupled lidar-inertial-visual state estimator,” arXiv +preprint arXiv:2209.03666, 2022. +[23] M. Kazhdan, M. Bolitho, and H. Hoppe, “Poisson surface recon- +struction,” in Proceedings of the fourth Eurographics symposium on +Geometry processing, vol. 7, 2006. +[24] M. Kazhdan and H. Hoppe, “Screened poisson surface reconstruction,” +ACM Transactions on Graphics (ToG), vol. 32, no. 3, pp. 1–13, 2013. +[25] J. Wilhelms and A. Van Gelder, “Octrees for faster isosurface genera- +tion,” ACM Transactions on Graphics (TOG), vol. 11, no. 3, pp. 201– +227, 1992. +[26] R. Shekhar, E. Fayyad, R. Yagel, and J. F. Cornhill, “Octree-based +decimation of marching cubes surfaces,” in Proceedings of Seventh +Annual IEEE Visualization’96. +IEEE, 1996, pp. 335–342. +[27] W. E. Lorensen and H. E. Cline, “Marching cubes: A high resolution +3d surface construction algorithm,” ACM siggraph computer graphics, +vol. 21, no. 4, pp. 163–169, 1987. +[28] M. Kazhdan, M. Chuang, S. Rusinkiewicz, and H. Hoppe, “Poisson +surface reconstruction with envelope constraints,” in Computer graphics +forum, vol. 39, no. 5. +Wiley Online Library, 2020, pp. 173–182. +[29] P. Labatut, J.-P. Pons, and R. Keriven, “Efficient multi-view reconstruc- +tion of large-scale scenes using interest points, delaunay triangulation +and graph cuts,” in 2007 IEEE 11th international conference on com- +puter vision. +IEEE, 2007, pp. 1–8. +[30] V. Litvinov and M. Lhuillier, “Incremental solid modeling from sparse +and omnidirectional structure-from-motion data,” in British Machine +Vision Conference, 2013. +[31] M. Jancosek and T. Pajdla, “Exploiting visibility information in surface +reconstruction to preserve weakly supported surfaces,” International +scholarly research notices, vol. 2014, 2014. +[32] F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva, and G. Taubin, “The +ball-pivoting algorithm for surface reconstruction,” IEEE transactions on +visualization and computer graphics, vol. 5, no. 4, pp. 349–359, 1999. +[33] R. Wang, J. Peethambaran, and D. Chen, “Lidar point clouds to 3-d +urban models : a review,” IEEE Journal of Selected Topics in Applied +Earth Observations and Remote Sensing, vol. 11, no. 2, pp. 606–627, +2018. +[34] R. A. Newcombe, S. Izadi, O. Hilliges, D. Molyneaux, D. Kim, +A. J. Davison, P. Kohi, J. Shotton, S. Hodges, and A. Fitzgibbon, +“Kinectfusion: Real-time dense surface mapping and tracking,” in 2011 +10th IEEE international symposium on mixed and augmented reality. +Ieee, 2011, pp. 127–136. +[35] J. Chen, D. Bautembach, and S. Izadi, “Scalable real-time volumetric +surface reconstruction,” ACM Transactions on Graphics (ToG), vol. 32, +no. 4, pp. 1–16, 2013. +[36] M. Nießner, M. Zollh¨ofer, S. Izadi, and M. Stamminger, “Real-time +3d reconstruction at scale using voxel hashing,” ACM Transactions on +Graphics (ToG), vol. 32, no. 6, pp. 1–11, 2013. +[37] O. K¨ahler, V. Prisacariu, J. Valentin, and D. Murray, “Hierarchical voxel +block hashing for efficient integration of depth images,” IEEE Robotics +and Automation Letters, vol. 1, no. 1, pp. 192–197, 2015. +[38] E. Vespa, N. Nikolov, M. Grimm, L. Nardi, P. H. J. Kelly, and +S. Leutenegger, “Efficient octree-based volumetric SLAM supporting +signed-distance and occupancy mapping,” IEEE Robotics and Automa- +tion Letters, vol. 3, no. 2, pp. 1144–1151, Apr. 2018. +[39] O. K¨ahler, V. A. Prisacariu, C. Y. Ren, X. Sun, P. Torr, and D. Murray, +“Very high frame rate volumetric integration of depth images on mobile +devices,” IEEE transactions on visualization and computer graphics, +vol. 21, no. 11, pp. 1241–1250, 2015. + +20 +[40] M. Klingensmith, I. Dryanovski, S. S. Srinivasa, and J. Xiao, “Chisel: +Real time large scale 3d reconstruction onboard a mobile device us- +ing spatially hashed signed distance fields.” in Robotics: science and +systems, vol. 4, no. 1. +Citeseer, 2015. +[41] H. Oleynikova, Z. Taylor, M. Fehr, R. Siegwart, and J. Nieto, “Voxblox: +Incremental 3d euclidean signed distance fields for on-board mav +planning,” in 2017 IEEE/RSJ International Conference on Intelligent +Robots and Systems (IROS). +IEEE, 2017, pp. 1366–1373. +[42] D. Lefloch, M. Kluge, H. Sarbolandi, T. Weyrich, and A. Kolb, “Com- +prehensive use of curvature for robust and accurate online surface +reconstruction,” IEEE transactions on pattern analysis and machine +intelligence, vol. 39, no. 12, pp. 2349–2365, 2017. +[43] D. Lefloch, T. Weyrich, and A. Kolb, “Anisotropic point-based fusion,” +in 2015 18th International Conference on Information Fusion (Fusion). +IEEE, 2015, pp. 2121–2128. +[44] T. Weise, T. Wismer, B. Leibe, and L. Van Gool, “In-hand scanning +with online loop closure,” in 2009 IEEE 12th International Conference +on Computer Vision Workshops, ICCV Workshops. +IEEE, 2009, pp. +1630–1637. +[45] S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3d model +acquisition,” ACM Transactions on Graphics (TOG), vol. 21, no. 3, pp. +438–446, 2002. +[46] M. Habbecke and L. Kobbelt, “A surface-growing approach to multi- +view stereo reconstruction,” in 2007 IEEE Conference on Computer +Vision and Pattern Recognition. +IEEE, 2007, pp. 1–8. +[47] T. Bodenmueller, “Streaming surface reconstruction from real time 3d +measurements,” Ph.D. dissertation, Technische Universit¨at M¨unchen, +2009. +[48] T. Whelan, S. Leutenegger, R. Salas-Moreno, B. Glocker, and A. Davi- +son, “Elasticfusion: Dense slam without a pose graph.” +Robotics: +Science and Systems, 2015. +[49] T. Whelan, R. F. Salas-Moreno, B. Glocker, A. J. Davison, and +S. Leutenegger, “Elasticfusion: Real-time dense slam and light source +estimation,” The International Journal of Robotics Research, vol. 35, +no. 14, pp. 1697–1716, 2016. +[50] W. Gao and R. Tedrake, “Surfelwarp: Efficient non-volumetric single +view dynamic reconstruction,” arXiv preprint arXiv:1904.13073, 2019. +[51] T. Sch¨ops, T. Sattler, and M. Pollefeys, “Surfelmeshing: Online surfel- +based mesh reconstruction,” IEEE transactions on pattern analysis and +machine intelligence, vol. 42, no. 10, pp. 2494–2507, 2019. +[52] Y. Cai, W. Xu, and F. Zhang, “ikd-tree: An incremental kd tree for +robotic applications,” arXiv preprint arXiv:2102.10808, 2021. +[53] R. B. Rusu and S. Cousins, “3d is here: Point cloud library (pcl),” in +2011 IEEE international conference on robotics and automation. IEEE, +2011, pp. 1–4. +[54] M. Muja and D. G. Lowe, “Fast approximate nearest neighbors with +automatic algorithm configuration.” VISAPP (1), vol. 2, no. 331-340, +p. 2, 2009. +[55] M. Teschner, B. Heidelberger, M. M¨uller, D. Pomerantes, and M. H. +Gross, “Optimized spatial hashing for collision detection of deformable +objects.” in Vmv, vol. 3, 2003, pp. 47–54. +[56] ISO, ISO/IEC 14882:1998: Programming languages – C++, Sep. 1998. +[57] A. Hornung, K. M. Wurm, M. Bennewitz, C. Stachniss, and W. Burgard, +“Octomap: An efficient probabilistic 3d mapping framework based on +octrees,” Autonomous robots, vol. 34, no. 3, pp. 189–206, 2013. +[58] V. Panek, Z. Kukelova, and T. Sattler, “Meshloc: Mesh-based visual +localization,” in European Conference on Computer Vision. +Springer, +2022, pp. 589–609. +[59] I. Vizzo, X. Chen, N. Chebrolu, J. Behley, and C. Stachniss, “Poisson +surface reconstruction for lidar odometry and mapping,” in 2021 IEEE +International Conference on Robotics and Automation (ICRA). +IEEE, +2021, pp. 5624–5630. +[60] M. Dreher, H. Blum, R. Siegwart, and A. Gawel, “Global localization +in meshes,” in ISARC. Proceedings of the International Symposium on +Automation and Robotics in Construction, vol. 38. IAARC Publications, +2021, pp. 747–754. +[61] M. Oelsch, M. Karimi, and E. Steinbach, “R-loam: Improving lidar +odometry and mapping with point-to-mesh features of a known 3d +reference object,” IEEE Robotics and Automation Letters, vol. 6, no. 2, +pp. 2068–2075, 2021. +[62] J. Lin, C. Zheng, W. Xu, and F. Zhang, “R2live: A robust, real-time, +lidar-inertial-visual tightly-coupled state estimator and mapping,” IEEE +Robotics and Automation Letters, vol. 6, no. 4, pp. 7469–7476, 2021. +[63] J. Zhang and S. Singh, “Loam: Lidar odometry and mapping in real- +time.” in Robotics: Science and Systems, vol. 2, no. 9. +Berkeley, CA, +2014, pp. 1–9. +[64] J. Lin and F. Zhang, “Loam livox: A fast, robust, high-precision lidar +odometry and mapping package for lidars of small fov,” in 2020 IEEE +International Conference on Robotics and Automation (ICRA). +IEEE, +2020, pp. 3126–3131. +[65] R. Stevens, Computer Graphics Dictionary, ser. ADVANCES IN +COMPUTER GRAPHICS AND GAME DEVELOPMENT SERIES. +Charles River Media, 2002. [Online]. Available: https://books.google. +com.hk/books?id=XqlJcMi1Pi0C +[66] W. Kahan, “Miscalculating area and angles of a needle-like triangle,” +University of California, Berkeley, vol. 94720, 1776. +[67] M. Woo, J. Neider, T. Davis, and D. Shreiner, OpenGL programming +guide: the official guide to learning OpenGL. +Addison-Wesley Long- +man Publishing Co., Inc., 1999. +[68] F. Evans, S. Skiena, and A. Varshney, “Optimizing triangle strips for fast +rendering,” in Proceedings of Seventh Annual IEEE Visualization’96. +IEEE, 1996, pp. 319–326. +[69] D. Hearn, M. P. Baker, and M. P. Baker, Computer graphics with +OpenGL. +Pearson Prentice Hall Upper Saddle River, NJ:, 2004, vol. 3. +[70] J. Loeliger and M. McCullough, Version Control with Git: Powerful +tools and techniques for collaborative software development. ” O’Reilly +Media, Inc.”, 2012. +[71] K. R. Castleman, Digital image processing. +Prentice Hall Press, 1996. +[72] A. Fabri and S. Pion, “Cgal: The computational geometry algorithms +library,” in Proceedings of the 17th ACM SIGSPATIAL international +conference on advances in geographic information systems, 2009, pp. +538–539. +[73] C. D. Toth, J. O’Rourke, and J. E. Goodman, Handbook of discrete and +computational geometry. +CRC press, 2017. +[74] A. Rosinol, M. Abate, Y. Chang, and L. Carlone, “Kimera: an open- +source library for real-time metric-semantic localization and mapping,” +in 2020 IEEE International Conference on Robotics and Automation +(ICRA). +IEEE, 2020, pp. 1689–1696. +[75] S. Fortune, “Voronoi diagrams and delaunay triangulations,” Computing +in Euclidean geometry, pp. 225–265, 1995. +[76] J.-D. Boissonnat and M. Yvinec, Algorithmic geometry. +Cambridge +university press, 1998. +[77] D. Attali, J.-D. Boissonnat, and A. Lieutier, “Complexity of the delaunay +triangulation of points on surfaces the smooth case,” in Proceedings of +the nineteenth annual symposium on Computational Geometry, 2003, +pp. 201–210. +[78] C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold +preintegration for real-time visual–inertial odometry,” IEEE Transactions +on Robotics, vol. 33, no. 1, pp. 1–21, 2016. +[79] B. Zhou, J. Pan, F. Gao, and S. Shen, “Raptor: Robust and perception- +aware trajectory replanning for quadrotor fast flight,” IEEE Transactions +on Robotics, vol. 37, no. 6, pp. 1992–2009, 2021. +[80] B. Zhou, Y. Zhang, X. Chen, and S. Shen, “Fuel: Fast uav exploration +using incremental frontier structure and hierarchical planning,” IEEE +Robotics and Automation Letters, vol. 6, no. 2, pp. 779–786, 2021. +[81] A. Geiger, P. Lenz, and R. Urtasun, “Are we ready for autonomous +driving? the kitti vision benchmark suite,” in 2012 IEEE conference on +computer vision and pattern recognition. +IEEE, 2012, pp. 3354–3361. +[82] N. Carlevaris-Bianco, A. K. Ushani, and R. M. Eustice, “University +of michigan north campus long-term vision and lidar dataset,” The +International Journal of Robotics Research, vol. 35, no. 9, pp. 1023– +1035, 2016. +[83] T.-M. Nguyen, S. Yuan, M. Cao, Y. Lyu, T. H. Nguyen, and L. Xie, +“Ntu viral: A visual-inertial-ranging-lidar dataset, from an aerial vehicle +viewpoint,” The International Journal of Robotics Research, vol. 41, +no. 3, pp. 270–280, 2022. +[84] D. Cernea, “OpenMVS: Multi-view stereo reconstruction library,” 2020. +[Online]. Available: https://cdcseacave.github.io/openMVS +[85] C. Yuan, J. Lin, Z. Zou, X. Hong, and F. Zhang, “Std: Stable triangle +descriptor for 3d place recognition,” arXiv preprint arXiv:2209.12435, +2022. +[86] J. Lin and F. Zhang, “A fast, complete, point cloud based loop closure for +lidar odometry and mapping,” arXiv preprint arXiv:1909.11811, 2019. + +1 +Supplementary Material: An additional trial of our lossless texture reconstruction based on ImMesh +Fig. 1: In this trial, we collected the data by flying over islands in an “B”-like trajectory, as the blue path shown in (a). (b1) and (b2) show the side view and bird view of our reconstructed +triangle mesh, where the mesh is colored by their altitude w.r.t. the sea level. (a) show the overview of our lossless texture reconstruction result, where we use the estimated camera poses (the +yellow frustums) of R3LIVE++ for texturing the mesh with the collected images. The entire texture reconstruction of this 578 s sequence only costs 1210 s (on Intel i9-10900), with 583 s for +ImMesh, 587 s for R3LIVE++, and 40 s for texturing. To see the detailed reconstruction process of the scene, please refer to our video on YouTube: youtu.be/pzT2fMwz428?t=892. + +(a) +Height +Height +(b1) +(b2) +15 m +15 m +30 m +45 \ No newline at end of file diff --git a/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/load_file.txt b/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e9a0ecf41e4a02bb697334acafe8dfa6b3a8a594 --- /dev/null +++ b/g9E4T4oBgHgl3EQfrQ0j/content/tmp_files/load_file.txt @@ -0,0 +1,2087 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf,len=2086 +page_content='1 ImMesh: An Immediate LiDAR Localization and Meshing Framework Jiarong Lin˚, Chongjiang Yuan˚, Yixi Cai, Haotian Li, Yuying Zou, Xiaoping Hong and Fu Zhang Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1: (a) shows the triangle mesh that is online reconstructed by our proposed work ImMesh, where the white path is our sampling trajectory, and the yellow frustums are the estimated sensor pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In (b), we use the estimated camera poses (the yellow frustums) of R3LIVE for texturing the mesh with the collected images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Based on ImMesh, we developed a lossless texture reconstruction application, with one of our results shown in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Our accompanying video that shows details of this work is available on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Abstract—In this paper, we propose a novel LiDAR(-inertial) odometry and mapping framework to achieve the goal of si- multaneous localization and meshing in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This pro- posed framework termed ImMesh comprises four tightly-coupled modules: receiver, localization, meshing, and broadcaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The localization module utilizes the prepossessed sensor data from the receiver, estimates the sensor pose online by registering LiDAR scans to maps, and dynamically grows the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, our meshing module takes the registered LiDAR scan for in- crementally reconstructing the triangle mesh on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, the real-time odometry, map, and mesh are published via our broadcaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The key contribution of this work is the meshing module, which represents a scene by an efficient hierarchical voxels structure, performs fast finding of voxels observed by new scans, and reconstructs triangle facets in each voxel in an incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This voxel-wise meshing operation is delicately designed for the purpose of efficiency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' it first performs a dimension reduction by projecting 3D points to a 2D local plane contained in the voxel, and then executes the meshing operation ˚These two authors contribute equally to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cai and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang are with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong SAR, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' tjiarong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='lin, ycj1, yixicai, haotianl, zyycici, fuzhangu@connect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='hku.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='hk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yuan and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hong are with the School of System Design and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, People’s Republic of China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='tyuancj2020,hongxpu@sustech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='cn with pull, commit and push steps for incremental reconstruction of triangle facets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To the best of our knowledge, this is the first work in literature that can reconstruct online the triangle mesh of large-scale scenes, just relying on a standard CPU without GPU acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To share our findings and make contributions to the community, we make our code publicly available on our GitHub: github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='com/hku-mars/ImMesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Index Terms—Mapping, 3D reconstruction, SLAM I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' INTRODUCTION Recently, the wide emergence of 3D applications such as metaverse [1, 2], VR/AR [3], video games, and physical sim- ulator [4] has enriched human lifestyle and boosted productive efficiency by providing a virtual environment that alike the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These applications are built upon triangle meshes that represent complex geometry of real-world scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Triangle mesh is the collection of vertices and triangle facets, which serves as a fundamental tool for objects modeling in most existing 3D applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It can not only simplify significantly the process and boost the speed of rendering [5, 6] and ray- tracing [7], but also play an irreplaceable role in collision detection [8, 9], rigid-body dynamics [10, 11], dense mapping and surveying [12], sensor simulation [13], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' However, most existing mesh is manufactured by skillful 3D modelers with the help of computer-aided design (CAD) software (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='05206v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='RO] 12 Jan 2023 (c) c3) (c1) (c1) (c2) c22 Solidworks [14], blender [15], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ), which limits the mass production of large-scene meshing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, developing an efficient mesh method that could reconstruct large scenes in real-time draws increasing research interests and serves as a hot topic in the community of 3D reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Performing mesh reconstruction in real-time is particularly important in practical usages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Firstly, online mesh reconstruc- tion indeed makes data collection effective by providing a live preview, which is quite important to give a reference for users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Especially for those non-expert users, a live preview can serve as a feedback about which parts of the scene have been reconstructed in good quality already and where additional data is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Secondly, online mesh reconstruction can immediately output the mesh of scene once data collection is complete, saving additional post-processing time of offline mesh reconstruction and hence boosts the productivity of mass production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Thirdly, it is particularly important for those real-time applications, especially for fully autonomous robotic applications, a real-time update of mesh can provide better maps with denser representation and of higher accuracy, which can enable the agent to better navigate itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Reconstructing the mesh of large scenes from sensor mea- surements in real-time remains one of the most difficult problems in the fields of computer graphics, 3D vision, and robotics, which require reconstructing the surfaces of scenes with triangle facets that are adjacently connected by edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This is a challenging problem that needs to build the geometry structure with very high accuracy, and the triangle facet should be reconstructed on surfaces that actually exist in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, a good mesh reconstruction method should also suppress the appearance of holes on the reconstructed surface, and avoid the reconstruction of triangle silver (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the noodle-like triangles that have a shard acute angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Real-time mesh reconstruction in large scenes is even more challenging as it further requires the reconstruction to operate in an efficient, incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this work, we propose a real-time mesh reconstruction framework termed ImMesh to achieve the goal of simultaneous localization and meshing on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This is a well-engineered system that is comprised of four tightly-coupled modules delicately designed for efficiency and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To the best of our knowledge, this is the first work in literature that can reconstruct the triangle mesh of large-scale scenes online and with a standard CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The main contributions of our work are: ‚ We propose a novel system that can estimate the sen- sor pose and reconstruct the mesh of the surrounding environment both online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Its localization is built upon our previous work VoxelMap [16], which can estimate the sensor pose of better efficiency and higher accuracy over its counterparts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', FAST-LIO2 [17], SUMA [18], MULLS [19], Lego-LOAM [20], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Its meshing mod- ule implements a novel mesh reconstruction approach, which efficiently reconstructs the mesh in an incremental manner, and can achieve real-time performance in large- scale scenarios on a standard desktop CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ We implement a novel mesh reconstruction method in our meshing module, which directly utilizes the registered LiDAR point as mesh vertices, online reconstructing the triangle facets (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the indices of three triangle points) in an incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Specifically, our meshing module first utilizes an efficient hierarchical voxel data structure for fast finding of voxels containing points in new scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, the voxel-wise 3D meshing problem is converted into a 2D one by performing dimension reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fi- nally, the triangle facets are incrementally reconstructed with the voxel-wise mesh pull, commit and push steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ We evaluate the runtime performance and meshing ac- curacy of ImMesh by conducting extensive experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We first verify the overall performance by presenting live video demonstrations of how the mesh is immediately reconstructed in the process of data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then we extensively tested ImMesh with four public datasets collected with different types of LiDARs in various scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, we evaluate the runtime performance and meshing accuracy of ImMesh by comparing them against existing baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ We additionally demonstrate how real-time meshing can be applied in potential applications by presenting two practical examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We first show that ImMesh can be applied for LiDAR point cloud reinforcement, which can output the reinforced points in regular pattern, and with higher density and wider FoV compared to raw LiDAR scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, we combined ImMesh and our previous work R3LIVE [21, 22] to achieve the goal of losslessly texture reconstruction of scenes (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (b)), which is useful for rapid field surveying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ We make ImMesh publicly available on our GitHub: github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='com/hku-mars/ImMesh1 for sharing our findings and making contributions to the community, II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' RELATED WORKS In this section, we discuss the related works of mesh reconstruction based on 3D point cloud, which are closely related to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Depending on whether the reconstruction processes can perform online, we categorize existing mesh reconstruction methods into two classes: offline methods and online methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Offline mesh reconstruction The offline methods usually require a global map in prior, for example, the full registered point cloud of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, a global mesh reconstruction process is used to build the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this category, the most notable works include: methods based on Poisson surface reconstruction (Poisson- based), and methods based on Delaunay tetrahedralization (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', 3D Delaunay triangulation) and graph cut (Delaunay- based).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Poisson surface reconstruction (Poisson-based): Given a set of 3D points with oriented normals that are sampled on the surface of a 3D model, the basic idea of Poisson surface reconstruction [23, 24] is to cast the problem of mesh reconstruction as an optimization problem, which solves for an approximate indicator function of the inferred solid 1Our codes will be released as this work is accepted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3 whose gradient best matches the input normals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, the continuous isosurface (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the triangle mesh) is extracted from the indicator function using the method [25, 26] that is similar to adaptations of the Marching Cubes [27] with octree representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Benefiting from this implicit representation, where the mesh is extracted from the indicator function instead of being estimated directly, Poisson surface reconstruction can produce watertight manifold meshes and is resilient to scanner noise, misalignment, and missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, in the communities of graphics and vision, these types of methods [23, 24, 28] have been widely used for reconstructing the mesh from given 3D scanned data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Delaunay triangulation and graph cut (Delaunay- based): In the category of offline mesh reconstruction meth- ods, approaches [29]–[31] based on Delaunay tetrahedraliza- tion and graph cut are also been widely used for generating the mesh, based on the reconstructed 3D point cloud and the sensor’s poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The basic idea of this class of methods is first to build a tetrahedral decomposition of 3D space by computing the 3D Delaunay triangulation of the 3D point set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, the Delaunay tetrahedra was labeled as “inside” or “outside” with the globally optimal label assignment (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the graph cut).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, the triangle mesh can be extracted as the interface between these classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides these two classes of methods, there exist other offline surface mesh reconstruction algorithms such as the ball-pivoting algorithm [32] that have been proposed in past decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' However, they are usually not the first choice of consideration due to the lower precision and worse efficiency compared to Poisson- and Delaunay-based methods [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Unlike these offline mesh reconstruction methods, our pro- posed work ImMesh can perform online in an incremental manner without the whole point cloud of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, ImMesh also achieves a satisfactory meshing accuracy that is higher than Poisson-based and slightly lower than Delaunay- based (see our experimental results in Section VIII-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Online mesh reconstruction 1) Voxel volume-based methods (TSDF-based): The online mesh reconstruction method is predominated by TSDF-based methods, which represent the scene in a voxel volumetric theme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These methods implicitly reconstruct the mesh in a two-step pipeline, which first establishes the truncated signed distance to the closest surface of voxels, then extracts the continuous triangle mesh by leveraging the Marching Cubes algorithm [27] from volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' TSDF-based methods are pop- ularized by KinectFusion [34], with many follow-up works focused on scaling this approach to larger scenes [35, 36], adding multi-resolution capability [37, 38], and improving efficiency [39]–[41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Since these classes of methods can be easily implemented with parallelism, they can achieve real- time performance with the acceleration of GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Compared to these methods, our work ImMesh shows several advantages: Firstly, in ImMesh, the triangle mesh is directly reconstructed from the point cloud in one step, while for TSDF-based methods, the mesh is implicitly built in a two- step pipeline (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', SDF update followed by a mesh extraction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Secondly, ImMesh is able to output the mesh in scan-rate (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', sensor sampling rate), while the mesh extraction of TSDF- based methods is usually at a lower rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Thirdly, ImMesh achieves real-time performance by just running on a standard CPU, while TSDF-based methods need GPU acceleration for real-time SDF update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lastly, TSDF-based methods require adequate observation for the calculation of SDF of each voxel w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the closet surface, which needs the data to be sampled by a depth sensor of high resolution and moving at a low speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' On the contrary, our work exploits high-accuracy LiDAR points for meshing and is robust to points data of low density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Surfel-based mesh reconstruction: Besides TSDF-based methods, another popular approach is to represent the scene with a set of points or surfels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', oriented discs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For example, in work [36, 42, 43], the maps are reconstructed with point-based representation, and its “surface” is rendered with the approaches of “point-based rendering” that originated from the communities of computer graphics [44]–[46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, in work [47] , the high-quality map is reconstructed with surfel-based representations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', use patches), such forms of mapping representation are popularized in works [48]–[51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To reconstruct a dense map, these classes of methods need a large number of points or tiny patches to represent the surface of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This is an inefficient representation that has high usage of system memory and computation resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In contrast, our work reconstructs the surface of models with triangle mesh, which uses triangle facets of proper size that are adjacently connected by edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It is the most efficient solid- model representation that has been widely adopted in most modern 3D software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Compared with works reviewed above, our proposed work is in a class by itself, which contains the following advantages: ‚ It is an online mesh reconstruction method that recon- structs the triangle mesh in an incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It can achieve real-time performance in large-scale scenes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', traveling length reaches 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 km) by just running on a standard desktop CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ It explicitly reconstructs the triangle mesh by directly taking the registered LiDAR points as meshing vertices, performing the voxel-wise meshing operation as each new LiDAR scan is registered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ It is delicately designed for the purpose of efficiency, and can achieve satisfactory meshing precision comparable to existing high-accuracy offline methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' SYSTEM OVERVIEW Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2 depicts the overview of our proposed system (Im- Mesh), which consists of a map structure and four modules that work jointly to achieve the goal of simultaneous localiza- tion and meshing in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, from left to right are: receiver (in red), localization (in orange), map structure (in green), meshing (in blue) and broadcaster (in purple).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In the rest sections, we will first introduce our map struc- tures in Section IV, which will show the detail of the data structures that will be used in other modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Next, we will 4 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2: This figure shows the overview of our proposed work ImMesh, which utilizes the raw input sensor data to achieve the goal of simultaneous localization and meshing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It is constituted by four tightly-coupled modules and a map structure, from left (input) to right (output) are: receiver (in red), localization (in orange), map structure (in green), meshing (in blue) and broadcaster (in purple).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' introduce our receiver and localization module in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, we will present how our meshing modules work in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, in Section VII, we will introduce the broadcaster module, which publishes the localization and meshing results to other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' MAP STRUCTURES As shown by the map structures (in green) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, we design four data structures, including a structure of meshing vertices, a structure of triangle facets, an incremental kd-Tree (ikd-Tree) for k nearest neighbors (kNN) search and down- sampling, and a hierarchical-voxels structure representing the 3D space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Mesh vertices In ImMesh, mesh vertices are the points that constitute the geometric structure (shape) of mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' All mesh vertices are stored in a global list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For the i-th entry of the list that represents vertex Vi, it contains the following elements: ‚ Its 3D position PospViq P R3 in global frame (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the first LiDAR frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ The index(id) of this vertex IdpViq “ i, which is the unique identification that indicates this point is the i-th point that appended to map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ The list of pointers to triangles facets T whose vertices contain Vi: Tri listpViq “ tPtrpTi1q, PtrpTi2q, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', PtrpTimqu (1) where we use function Ptrp¨q to denote the pointer (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', C++ pointer) of p¨q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Triangle facets In ImMesh, a triangle facet describes a small surface that exists in the reconstructed scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It is maintained online by our meshing module (see Section VI) and is asynchronously copied to the broadcaster module for publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A triangle facet T contains the following elements: ‚ The sorted indices Pts idpTq of three points that form this triangle: Pts idpTq “ ti, j, ku, i ă j ă k (2) ‚ The center CenterpTq and normal NormpTq (both in the global frame) of this triangle: CenterpTq “ pPospViq ` PospVjq ` PospVkqq {3 (3) NormpTq “ n{p||n||q (4) n “ pPospViq ´ PospVjqq ˆ pPospVkq ´ PospVjqq (5) C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Incremental kd-Tree (ikd-Tree) We maintain an incremental kd-tree to enable the fast kNN search of mesh vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The ikd-Tree is proposed in our previous work [17, 52], which is an efficient dynamic space partition data structure for fast kNN search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Unlike existing static kd-tree (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', kd-tree implemented in PCL [53] and FLANN [54]) that require rebuilding the entire tree at each update, ikd-Tree achieves lower computation time by updating the tree with newly coming points in an incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In ImMesh, we use the ikd-Tree for: ‚ Downsample the point cloud density to keep the min- imum distance between any of two mesh vertices for maintaining the triangle mesh at a proper resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=" Localization Odometry (andn) LiDAR input Publish' LiDARpoints State Point cloud motion Estimation registration Velodyne Publish compensation Point cloud Broadcaster IMU input (optional) code AcCZ to AcCY a Gyro Y Mesh Probability Gyro X Acc X get 02 vertices Trianglemesh Asynchronous!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Retriving copy ikd-Tree Triangle Hierachical facets voxels Estimated Rasterization Pull Push plane Depth image (optional) Dimensionality Voxel-wise mesh Voxel-wise 3D 1660:9903 reduction by pull, commit and points retrieving 0000 projection push Meshing ImMesh) framework 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='367 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6325 Hierachical voxels Hash table L3-Voxel O3 Mesh vertices etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' L1-Voxel O1 L2-Voxel O2 Trianlge facets etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Octree Higher level voxel O4+ Hierarchical voxels Hierachical voxels Higher level Voxel O3+ Mesh vertices etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' L1-Voxel O1 L2-Voxel O2 Trianlge facets etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Octotree Hash table World World .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3: In ImMesh, the world is partitioned by hierarchical voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We compactly store, access, and update the voxels in a spatial hashing scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ Enable the vertex dilation operation in our voxel-wise meshing operation (see Section VI), which can erode the gaps between neighbor voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hierarchical voxels In our map, we partition the 3D space with hierarchical voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, lower-level voxels contain those of higher levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These voxels of different levels are designed with different sizes and for various purposes: the lowest level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', L1-Voxel) has the largest voxel size, which partition the 3D space into small regions by uniform grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Voxels in this layer maintain a hash table of pointers that point to the triangle facet whose center is located inside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This facilitates the broadcaster for asynchronous copying of these triangle facets (see Section VII-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' And, the size of the second layer (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', L2-Voxel) is much smaller than the first layer, where the voxels in this layer store the mesh vertices that constitute the geometric structure of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Voxels of this layer allow the meshing module to fast retrieve all in-voxel mesh vertices for voxel-wise meshing operations (see Section VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lastly, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, the L2-Voxel and its sub-voxels form a typical octree data structure, which is used in our localization module for a further split of non-planar point clusters to achieve better pose estimation (see Section V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) L1-Voxel O1: As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, we uniformly partition the 3D world into many small regions with L1-Voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To avoid large memory consumption in allocating regular volumetric grids (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', in kinectFusion [34]), we compactly store, access, and update the voxels with a spatial hashing scheme alike [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We map the 3D world space into the hash table via a hash function Hashp¨q, where the hash function allows an efficient look-up of voxel blocks with the integer- rounded world coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The array of pointers to Voxel is stored in the hash table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hashpx, y, zq “ Int Hashpxi, yi, ziq (6) “ Modppxi ¨ p1q ‘ pyi ¨ p1q ‘ pzi ¨ p3q, nq (7) xi “ Roundpx ˚ 100{rxq, yi “ Roundpy ˚ 100{ryq zi “ Roundpz ˚ 100{rzq (8) where x, y, z are coordinates of 3D space, xi, yi, zi are spec- ified integer rounded world coordinates, rx, ry, rz are the voxel size in three dimensions, ‘ is the XOR operation, and function Modpa, bq is the calculation of integer a modulus another integer b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' p1, p2, p3 are three large prime numbers for reducing the collision probability [36, 55], n is the hash table size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In our work, we set the value of p1, p2, p3 and n as 116101, 37199, 93911 and 201326611, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Notice that the hash table is unstructured, indicating that the neighboring voxels are not stored spatially but in different parts of the buckets (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, for resolving the possible hash collision (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', two pieces of data in a hash table share the same hash value), we adopt the technique in [36], using the implementation of unordered map container in C++ standard library (std) [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this work, we access a L1-voxel with a given 3D vector p “ rx, y, zsT P R3 by: O1 “ Get L1 voxelpHashppqq (9) Shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, each L1-Voxel contains the voxels of the higher hierarchical layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To identify the work stage of L1- Voxel, we use a flag to mark the status as either Sync-required or Synced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These two statuses indicate the update flag related to the data synchronization of triangle facets, as we will use in Section VI-E and Section VII-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For each L1-Voxel, it stores and maintains a hash table of pointers pointing to a triangle facet whose center is located in the voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These pointers can be efficiently looked up via Int Hashpi, j, kq in (6), where i, j, k are the sorted indices (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', i ă j ă k) of three mesh vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These in-voxel triangle facets are maintained (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', added or erased) by the meshing module, and are asynchronously copied to broadcaster module for publishing to other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) L2-Voxel O2 and voxels of higher layer: L2-Voxel is the second biggest container, which stores an array of points that point to all in-voxel mesh vertex, and contains the voxels of higher layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It is used in both of our localization and meshing modules;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' in localization module, L2-Voxel stores the in-voxel registered LiDAR points used to constitute planar features for estimating the sensor pose;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' in meshing module, L2-Voxel enables fast retrieval of all in-voxel mesh vertices and provides the local estimated planar norm for projecting the 3D points into the 2D plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For a L2-Voxel O2, it has a status flag indicating whether it has new points appended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, O2 is marked as Activated if this voxel has new mesh vertices registered from the latest LiDAR scan (see Section V-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' And the Activated flag is reset as deactivated after the voxel-wise meshing operation is performed on this voxel (see Section VI-G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Similar to (9), we achieve fast access to a L2-Voxel with a given 3D vector p “ rx, y, zsT P R3 through hash tables: O2 “ Get L2 voxelpHashppqq (10) where the hash function Hashp¨q in (10) and (9) are distin- guished with different voxel size rx, ry, rz in (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For voxels of higher layer, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', voxel O3 of the third layer and higher O3`, they are designed to partition the non-planer points (in voxels of the higher layer) with a smaller spatial size (higher resolution), which make them more likely to construct a planar feature for localization, as introduced in the coming section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Notice that the voxels of L2- and higher levels construct an Octree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We access the voxels of the third layer and higher in a way similar to Octree [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' pJock2 AOXGI blhow6 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' RECEIVER AND LOCALIZATION The receiver module is designed for processing and packag- ing the input sensor data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As shown in the red box of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, our receiver module receives the streaming of LiDAR data from live or offline recorded files, processes the data to a uni- fied data format (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', customized point cloud data) that make ImMesh compatible with LiDARs of different manufacturers, scanning mechanisms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', mechanical spinning, solid-state) and point cloud density (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', 64-, 32-, 16-lines, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, if the IMU source is available, our input module will also package the IMU measurements within a LiDAR frame by referring to the sampling time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The localization module utilizes the input data stream of receiver module, real-time estimating the sensor poses of 6 DoF and registering the points to map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Our localization module is built upon our previous work VoxelMap [16], which represents the surrounding environment with the probabilistic representation, estimating pose with an iterated Kalman filter by maximum a posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In designing our localization module, we have noticed that a number of works appeared in the literature recently, which utilize the reconstructed mesh for improving the localization accuracy of both visual-slam (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', [58]) and LiDAR-slam system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', [59]–[61]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' However, in ImMesh, the online reconstructed mesh is not used in our localization module because: 1) our mesh is reconstructed with points that are registered by the localization module, re-using mesh in lo- calization will take more computation efforts and bring extra latency in publishing the estimated pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) the accuracy of our localization module is indeed enough for most of the robotics and surveying applications, which achieve the localization results of better efficiency and higher accuracy compared to its counterparts like FAST-LIO2 [17], SUMA [18], MULLS [19], Lego-LOAM [20], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Despite this, we hold a positive attitude toward seeking the possibility of improving the localization accuracy with our online reconstructed mesh in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Voxel map construction Our localization is built by representing the surrounding en- vironment with the probabilistic representation, which counts both LiDAR measurement noises and sensor pose estimation errors, and constructs the voxel-volumetric maps in a coarse- to-fine adaptive resolution manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' But, in this work, we mainly focus our attention on how to real-time reconstruct the triangle mesh of the scene, and avoid introducing too many complicated noise analyses that might confuse the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We only discuss those processes in localization module that are closely related to our meshing module in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For the de- tailed modeling and analysis of LiDAR’s measurement noise, we recommend our readers to our previous work VoxelMap [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For a LiDAR sampling point, we first compensate the in- frame motion distortion with an IMU backward propagation introduced in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Let us use Lpi denote i-th LiDAR sampling point after motion compensation, it is registered to world frame as W pi with the estimated sensor pose pW L R, W L tq P SEp3q: Wpi “ W L RLpi ` W L t (11) The register LiDAR points are stored inside the voxels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', L2-Voxel), let us consider the distribution of points Wpi pi “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Nq that are located inside the L2-Voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We have the points covariance matrix A calculated as: ¯p “ 1 N N ÿ i“1 Wpi, A “ 1 N N ÿ i“1 `Wpi ´ ¯p ˘ `Wpi ´ ¯p ˘T (12) where the symmetric matrix A depicted the distribution of points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Let us perform the eigendecomposition of matrix A: AU “ » – λ1 λ2 λ3 fi fl “ u1 u2 u3 ‰ , λ1 ě λ2 ě λ3 (13) where λ1, λ2, λ3 are the eigenvalues and u1, u2, u3 are the correspondent eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' If the minimum eigenvalue λ3 is less than a specified threshold, which indicates that the points inside this voxel are distributed on a thin planar surface, we regard all points Wpi pi “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Nq as a planar feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Otherwise, this voxel will be further subdivided into voxels of higher level with smaller size (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', L3-, L4-,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', voxel) until: 1) the tiers of layer reach bound (set as tier-5 for our work) 2) the minimum eigenvalue of points covariance matrix A of a voxel smaller than a given threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' If points Wpi pi “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Nq inside the voxel indeed forming a planar feature, whose minimum eigenvalue λ3 of its points covariance matrix A less than a specified threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We represent this planar feature by using its normal vector n and a point q that lies in this plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The normal vector is well known as the eigenvector w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' associated with the minimum eigenvalus λ3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', n “ u3 in (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' And point q “ ¯p is calculated in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' State Estimation 1) Point-to-plane residual: In our localization module, we solve the sensor pose by minimizing the Point-to-plane residual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Given a LiDAR point Wpi predicted in the world frame with the pose prior, we first find which voxel it lies in by hashing with (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, all the contained voxels of higher layers are polled for a possible match with the point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Specifically, let a sub-voxel contains a plane with normal ni and center qi, we calculate the point-to-plane distance: di “ nT i pWpi ´ qiq (14) If point pi lies on the candidate plane with this point-to- plane distance di falling within the 3-σ bound of the plane measurement noise, we treat this point-to-plane pair as an effective match and add it to the residuals for estimating the sensor pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) LiDAR pose estimation by maximum a posterior (MAP): We build a LiDAR(-inertial) odometry system based on an iterated error-state extended Kalman filter (IESKF) similar to that derived in our previous works [17, 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Assume that we are given a state estimation prior, which is provided from a constant velocity assumption for LiDAR-only odom- etry (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Kitti dataset in our Experiment-1), or from IMU propagation for LiDAR-inertial odometry (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', NCLT-dataset, 7 NTU-dataset, R3LIVE-dataset our self-collected data in Sec- tion VIII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This will be fused with the point-to-plane distance matched in Section V-B1 to form a maximum a posteriori (MAP) estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, we solve this MAP problem by leveraging an IESKF, which leads an optimal state estimation of sensor pose pW L R, W L tq that is used for registering the LiDAR point with (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Point cloud registration After the state estimation, we perform the point cloud registration for transforming each measurement point Lpi from LiDAR frame to global frame (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the first LiDAR frame) with (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This registered point cloud is then used for: 1) Published to other applications with our broadcaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Use for updating the probabilistic voxel map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) Appended to map structure that serves as the mesh vertices for shaping the geometry structure of our online reconstructed triangle mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Update of voxel map: The registered LiDAR points are used for constructing the probabilistic voxel map by updating the point distributions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e, A in (12)), planar parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', n, q) and the correspondent uncertainties of all possible hierarchical voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For the details of this voxel map update, we refer the reader to our previous work [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, if a new register point does not lie on an existing L2 (or L1) voxel, a new L2 (or L1) voxel will be created and added to the hash table, after, this point will be added to the newly constructed voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Append of mesh vertices: The registered LiDAR points are also used for forming the meshing vertices in map struc- tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, we first leverage a voxel-grid filter for downsampling register LiDAR point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, to avoid the appearance of tiny triangles in reconstructing the mesh, we leverage the ikd-Tree (see Section IV-C) for keeping the minimum distance between any of two meshing points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' That is, for each register LiDAR point W pi in global frame, we search for the nearest mesh vertex in map structure with ikd- Tree, if the euclidean distance this point and the searhed vertex smaller than a given threshold, we will discard this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Otherwise, this point will be used for: 1) Constructing a new mesh vertex Vi, where i is the unique index that indicates Vi is the i-th appended vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Appending the pointer of Vi to the ikd-Tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) Pushing back the pointer PtrpViq to the point array of the L2-Voxel O2 j that Vi located in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' After, the status flag of O2 j is set as activated for notifying the meshing module for performing the voxel-wise re-meshing operation (see Section VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' MESHING In ImMesh, our meshing module takes the registered LiDAR scan for incrementally reconstructing the triangle mesh on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We explicitly reconstruct the triangle mesh by directly utilizing 3D registered LiDAR points as mesh vertex with two considerations: 1) The points sampled by LiDAR and registered via the ICP-based methods [63, 64] have very high positional accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, they are capable of shaping the geometric structure of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) A LiDAR measurement point naturally lies on the surface of the detected object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' That is, a laser pulse is emitted from the infrared transmitter and reflected by the surface of the detected object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The returned pulse is captured by the receiver, and the ranging distance of the sensor from the surface is finally calculated by counting the time of flight (ToF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Goals and requirements With the accurate mesh vertices appended from the point cloud registration in Section V-C, the problem of online mesh reconstruction is converted to another goal, which is to seek a proper way for real-time reconstructing the triangle facets with a growing 3D point set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' However, to the best of our knowledge, this is a new area in the community that has not been explored yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Given a set of growing 3D points, our meshing module is designed to incrementally reconstruct the triangle facets considering the following four major requirements: Firstly, precision is our prior consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For each recon- structed triangle facet that represents the surface of the scene, we require it to lie on an existing plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Secondly, the reconstructed mesh should be hole-less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In the dense reconstruction of the surface triangle mesh, the appearance of holes is unacceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, these holes lead to the wrong results in the rasterization of the depth image, which wrongly rasterizes the surfaces behind a real object to the front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Consequently, robotic applications based on our meshing result might lead to severe accidents (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', crashing into a wall).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, the holes on surfaces make the whole reconstructed map unsightly and chaotically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Thirdly, the reconstruction of triangle mesh should avoid constructing sliver triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The sliver triangle (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the noodle-like triangle), as defined in the communities of com- puter graphic [65]: whose area is so thin that its interior does not contain a distinct span for each scan line, has some unde- sired properties in the field of computer graphics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For example, these noodle-like triangles would cause some errors in the numerical analysis on them [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, these unfavorable properties cause troubles in the pipelines of rendering (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', rasterization, texturing, and anti-aliasing [5, 6, 67]), Which leads to the loss of accuracy in calculating (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', depth testing, interpolation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=') the pixel values distributed near the sharp angle [6, 68, 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lastly, the complexity of triangle mesh reconstruction should be computationally efficient to meet the requirement of real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The time consumption of each meshing process should not exceed the sampling duration of two consecutive LiDAR frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Challenges and approaches To achieve our goals of dense incremental meshing with the four requirements listed above, our system is proposed based on a deep analysis of the challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The challenges and corresponding scientific approaches are briefed below: The first challenge is that the global map is continuously grown by the newly registered LiDAR points, with each update of a LiDAR scan only affecting part of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, for an incremental mesh reconstruction method, it should be able to process only those parts of the scene with new 8 points appended in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In our work, we incrementally perform the mesh reconstruction with a mechanism similar to git [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For each incremental mesh update, we first retrieve the data of the voxels with new mesh vertices appended via the pull step (detailed in Section VI-E1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, an efficient voxel-wise meshing algorithm is executed to reconstruct the mesh with these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The incremental modifications of newly reconstructed results w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' pulled results are calculated in our commit step (detailed in Section VI-E2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, these incremental modifications are merged to the global map via our push step (detailed in Section VI-E3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Given a set of 3D vertices, the second challenge is how to correctly and efficiently reconstruct the triangle facets repre- senting the surfaces of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Since it is hard to directly reconstruct mesh from these mesh vertices in 3D space, our work performs the meshing operation in 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, for vertices located in a small region (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', in L2-Voxel), we first project them into a proper plane (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the estimated plane given by the localization module).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The mesh of these 2D points is constructed using the 2D meshing algorithms and is recovered back to 3D (detailed in Section VI-D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Voxel-wise vertex retrieval 1) Retrieval of in-voxel vertices: To reconstruct the triangle mesh in an incremental manner, the first step is to retrieve the vertices that need to mesh with the newly added points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In ImMesh, we use the hierarchical voxels (see Section IV-D) for subdividing the 3D space into many regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The flags that indicate the status of each L1-Voxel are used for identifying whether a L2-Voxel has newly appended mesh vertices (see Section V-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Take an activated L2-Voxel O2 i as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We perform a voxel-wise meshing operation to reconstruct the triangle facets with all in-voxel vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Since the pointers of these vertices are stored in a pointer array attached to O2 i , we address these pointers to retrieve all in-voxel vertices, denoted as VIn i “ tVj1, Vj2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Vjmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Vertex dilation: In practice, if we perform the meshing operation with only the in-voxel mesh vertices, the gaps between neighborhood voxels will appear due to the absence of triangles facets across voxels, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Motivated by morphological operations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', dilation and erosion) in digital image processing [71], we perform the 3D point cloud dilation for adding neighborhood points of VIn i to erode the gaps between voxels, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For vertex Vij P VIn i , we perform the radius-search operation by leveraging the ikd-Tree (see Section IV-C) for searching the nearest vertices of Vij with their euclidean distance smaller than a given value dr (usually set as 1{4 of the size of L2-Voxel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Using ˜Vij to denote the searched neighbor vertices and Vi to denote the dilated vertices, we have: @V P ˜Vij, ˇˇ|PospVq ´ PospVijq ˇˇ | ď dj (15) If V P Vij is not included in Vi, we add V by Vi “ Vi Y V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4: The comparisons of mesh reconstruction with (a) and without (b) the vertex dilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The full algorithm of our voxel-wise vertex retrieval is shown in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Algorithm 1: Voxel-wise vertex retrieval of O2 i Input : The activated voxel O2 i Output: The retrieved vertex set Vi Start : Copy all in-voxel pointer list to VIn i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Vi “ VIn i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1 foreach Vij P VIn i do 2 ˜Vij = RadiusSearch(Vij,dr) 3 foreach V P ˜Vij do 4 if V R Vi then 5 Vi “ Vi Y V Return: The retrived vertex set Vi after dilation D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Dimensional reduction by projection With the mesh vertices Vi retrieved from Algorithm 1, we introduce the voxel-wise mesh reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Projection 3D vertices on a 2D plane: Since it is hard to directly mesh with Vi distributed in 3D space in real-time, we simplify the 3D meshing problem to a 2D one by projecting Vi on a suitable plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Based on the analysis of the characteristics of Vi, we provide two reasons to perform the dimensional reduction by projection, listed as follows: 1) For a 3D point sampled by LiDAR, it is distributed on a surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, for vertices Vi retrieved from Algorithm 1 that distributed in a small region (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', in a L2-Voxel O2 i ), they tend to form a planar-like point cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) For these planar-like point clusters, we can approximately mesh them in a 2D view on their lying surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Imagine a 2D ant climbing on 3D surfaces solving this 3D problem in a 2D view, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A 区区 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A K A 区 发 AA9 3D meshing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5: In ImMesh, we reduce the 3D meshing problem to a 2D one by projecting the 3D points onto an estimated surface plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Imagine a 2D ant climbing on 3D surfaces solving this 3D problem in a 2D view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The plane pn, qq suitable for projection has already been calculated in our localization module in Section V-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The norm n of the plane is the eigenvector u3 that corresponds to the minimum eigenvalue λ3 in (13), which is the eigende- composition of point covariance matrix A in voxel O2 i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' q is the center points inside O2 i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Remark: Even though O2 i might be further divided into voxel of lower layer by the localization module, the norm n and q of O2 i is being updated at each new LiDAR frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For each vertex Vij P Vi, we project it to plane pn, qq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The resultant 2D point uij is calculated as: pij “ rφ, ρsT P R2 (16) φ “ ` PospVijq ´ q ˘T u1, ρ “ ` PospVijq ´ q ˘T u2 (17) where u1, u2 are the other two eigenvectors in (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We use Pi “ tpi1, pi2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', pimu to denote the 2D point set after projected from Vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Two-dimensional Delaunay triangulation: After the pro- jection, the dimension of 3D meshing problem is reduced to a 2D one, which can be solved by 2D Delaunay triangulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Given a set of 2D point P, the two-dimensional triangula- tion problem is well known as introduced in [72, 73], which is to find T of triangular facets s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' : 1) Any of two facets are either disjoint or share a lower dimensional face (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', edge or point).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) The set of facets in T is connected with adjacency relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) The domain PT , which is the union of facets in T, has no singularity2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' With these three useful properties, the 2D Delaunay triangulation has been widely applied for reconstructing dense facets with a given 2D point set (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', [74]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As defined in [75, 76], the Delaunay triangulation DelpPq of a 2D point set P “ tp1, p2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', pmu is the geometric dual of the Voronoi diagram: there is an edge between two points ui and uj in the Delaunay triangulation if and only if their Voronoi cell Vpuiq and Vpujq have a non-empty intersection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' DelpPq yields a triangulation of P, which is a partition of the 2The union UT of all simplices in T is called the domain of T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A point in the domain of T is said to be singular if its surrounding in PT is neither a topological ball nor a topological disc (view https://doc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='cgal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='org/ latest/Triangulation 2/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='html of [72] for detail).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' convex hull of P into d-dimensional simplices (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', triangle in 2D, tetrahedra in 3D), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Remark: The Voronoi cell Vpuiq associated with the point pi is the region of space that is closer to ui than to all other points in P: Vppiq “ tp P Rd : @j ‰ i, ||p ´ pi|| ď ||p ´ pj||u (18) Considering our requirements in Section VI-A, we chose Delaunay triangulation to reconstruct the mesh for its remark- able properties as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Firstly, it is a 2D triangulation providing mesh with no hole leaf in the convex hull of P, which satisfies our first requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Secondly, it naturally avoids sliver triangles by maximizing the minimum angles of the triangles in triangulation, which meets our second requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, it is a fast algorithm suitable for real- time requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The algorithm complexity of n points is Ωpnlogpnqq in 2D (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ωpn2q in 3D) [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Let us use T i “ DelpPiq “ tTi1, Ti2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Tinu to denote the triangle facets after the Delaunay triangulation DelpPiq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For each triangle facets Tij P T i, we retrive the indices with (2): tα, β, γu “ Pts idpTijq, indicating that this triangle is formed with 2D points tpiα, piβ, piγu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Returning back to 3D space, we constitute a triangle facet Tij with vertices tViα, Viβ, Viγu, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Voxel-wise meshing with pull, commit and push With the triangle facets T i constructed by the voxel-wise meshing operation, we incrementally merge T i to the existing triangle facets GT in the map structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This update is designed with a mechanism similar to git [70] (a version control software) that includes pull, commit, and push steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Pull: Given the vertices Vi obtained from Algorithm 1, we retrieve the triangle facets T Pull i from the map structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The algorithm of pull step is shown in Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Algorithm 2: Voxel-wise mesh pull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Input : The retrieved vertex set Vi from Algorithm 1 Output: The pulled triangle facets T Pull i Start : T Pull i “ tnullu 1 foreach Vj P Vi do 2 Get all vertices related triangle set T Vj “ TripVjq foreach Tk P T Vj do 3 Get triangle vertex index tα,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' γu “ Pts idpTkq 4 if pVα P Viq and pVβ P Viq and pVγ P Viq then 5 T Pull i “ T Pull i Y Tk Return: The pulled triangle facets T Pull i 2) Commit: In this step,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' we find out the incremental modi- fications of the reconstructed triangle facets T i (in Section VI-D2) w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the pulled facets T Pull i (from Algorithm 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' These incremental modifications are summarized into an array of mesh facets to be added T Add i and an array of mesh facets to be erased T Erase i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The detailed processes of this commit step are shown in Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 Algorithm 3: Voxel-wise mesh commit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Input : The pulled triangle facets T Pull i from Algorithm 2 The reconstructed triangle facets T i Output: The triangle facets to be added T Add i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The triangle facets to be erased T Erase i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Start : T Add i “ tnullu, T Erase i “ tnullu 1 foreach Tj P T i do 2 if Tj R T Pull i then 3 T Add i “ T Add i Y Tj 4 foreach Tj P T Pull i do 5 if Tj R T i then 6 T Erase i “ T Erase i Y Tj Return: The triangle facets to be added T Add i and erased T Erase i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Algorithm 4: Voxel-wise mesh push.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Input : The triangle facets that need to erased T Erase i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The triangle facets that need to added T Add i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1 Function Add_triangle(Tj): 2 Get point indices tα, β, γu “ IdpTjq 3 Construct triangle TG j “ Tripα, β, γq in global map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4 Calculate the center of TG j : 5 CenterpTG j q “ pVα ` Vβ ` Vγq {3 6 Find the L1-Voxel V1 that CenterpTG j q located in: V1 “ Get L1 voxelpHashpCenterpTG jqqq 7 Set the status flag of V1 to Sync-required (Section IV-D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8 Add PtrpTG j q to triangle list of L1-Voxel V1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 9 Add PtrpTG j q to triangle list of points Vα, Vβ, Vγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 Function Erase_triangle(Tj): 11 Get point indices tα, β, γu “ IdpTjq 12 Remove PtrpTG j q in triangle list of points Vα, Vβ, Vγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 13 Find the L1-Voxel V1 with CenterpTG j q via (9): V1 “ Get L1 voxelpHashpCenterpTG jqqq 14 Set the status flag of V1 to Sync-required (Section IV-D2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 15 Remove PtrpTG j q from triangle list of L1-Voxel V1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 16 Delete triangle TG j from memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 17 foreach Tj P T Add i do 18 Add_triangle(Tj) 19 foreach Tj P T Erase i do 20 Erase_triangle(Tj) 3) Push: With the incremental modification T Erase i and T Add i from the previous commit step, we perform the erasion and addition operations of global triangle mesh facets respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The detailed processes of our push step is shown in Algorithm 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Parallelism To further improve the real-time performance, we imple- ment our algorithms with parallelism for better utilization of the computation power of a multi-core CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In ImMesh, we have two major parallelisms as follows: The first parallelism is implemented between the local- ization module and the meshing module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Except for the point cloud registration in localization module, which needs to operate the mesh vertices as the meshing operation, the remaining processes of localization module are parallelized with the meshing module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' More specifically, once our meshing processes start, the localization module is allowed to process the new coming LiDAR scan for estimation of the pose of LiDAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' However, the point cloud registration step is only allowed to be executed after the end of the meshing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The second parallelism is implemented among the voxel- wise meshing operation of each activated voxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The voxel- wise meshing operations of different voxels are standalone thus, no conflicted operations exist on the same set of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The full meshing algorithm To sum up, our full meshing processes are shown in Algorithm 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Algorithm 5: The full meshing process of each update of LiDAR scan Input : The set of L2-Voxels V2 “ tO2 1, O2 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', O2 mu that activated in Section V-C Start : The triangle facets that need to added T Add “ tnullu, and to be erased in this update T Erase “ tnullu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1 foreach O2 i P V2 do in parallel 2 Retrieve vertices Vi with Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3 Reconstruct the triangle facets T i with Vi (Section VI-D2), 4 Performing voxel-wise mesh pull (Algorithm 2) to get T Pull i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ź // Mesh pull 5 Performing voxel-wise mesh commit (Algorithm 3) to get the triangle facets that need to be added T Add i and erased T Erase i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ź // Mesh commit 6 T Add “ T Add Ť T Add i , T Erase “ T Erase Ť T Erase i /* === Mesh push start === / 7 foreach Tj P T Add do 8 Add_triangle(Tj) Ź // In Algorithm 4 9 foreach Tj P T Erase do 10 Erase_triangle(Tj) Ź // In Algorithm 4 /* === Mesh push end === / 11 foreach O2 i P V2 do 12 Reset status of O2 i as deactived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' /* Remark 1: Line 1„6 are done in parallel for better real-time performance (as mentioned in Section VI-F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' / /* Remark 2: The mesh push step Line 7„10 is different with the voxel-wise operations in Algorithm 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The T Add and T Erase are processed after the parallelism to avoid possible conflicts when operating the same data (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', triangle facets in our mapping module) (Line 1„6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' / VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' BROADCASTER In ImMesh, the broadcaster module publishes our state estimating results (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', odometry) and mapping results (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', new registered point cloud and triangle mesh) to other ap- plications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In addition, if the depth image is required, the broadcaster module will also rasterize the triangle meshes into a customized depth image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', user-defined resolution and FoV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Broadcast of odometry The real-time 6-dof sensor pose from localization module (Section V-B) is published with the LiDAR frame starting 11 timestamp at a frequency of the LiDAR sampling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, if the IMU source is available, the broadcaster module pub- lishes the odometry propagated from the IMU preintegration [78] at the frequency of the IMU sampling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Broadcast of triangle facets Since the triangle facets are stored in an unstructured hash table of L1-Voxels in map structure, they can not be directly applied for broadcast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To resolve this problem, our broadcaster module maintains a background thread that asynchronously copies the triangle facets from the hash table of each sync- required L1-Voxels (set as sync-required in Algorithm 4) to a structured array for broadcasting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, these sync-required voxels are marked as synced after the copying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, The broadcaster module publishes the refreshed triangle facets to other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rasterization of depth image Some robotic applications, such as autonomous navigation [79] and exploration [80] tasks, require dense accurate depth images for obstacle avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To meet the requirements of these scenarios, the broadcaster module utilizes the triangle facets from Section VII-B to rasterize a depth image at any customized resolution and FoV, based on the fast implemen- tation of OpenGL [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Reinforcement of LiDAR point cloud: With the depth image from rasterization, LiDAR point cloud reinforcement is enabled by unprojecting the 3D points from the depth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In detail, with the projection matrix and estimated pose used for rasterizing the depth image, the 3D points are obtained (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', unproject) w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' each depth value on the depth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As a result, the 3D point cloud is enhanced with higher resolution and larger FoV than the raw LiDAR measurement scan (see our Application-1 in Section VIII-D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' EXPERIMENTS AND RESULTS In this section, we extensively evaluate the performance of ImMesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Notice that our localization module is built upon our previous work VoxelMap [16] with no modification that rela- tive to the state estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, the localization precision of this work performs as well as [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We recommend our readers get more details about our localization accuracy by referring to the results reported in our previous work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this paper, we lead the experiments by evaluating our meshing ability, especially on the runtime performance and accuracy in reconstructing the triangle mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Experiment-1: ImMesh for immediate mesh reconstruction In this experiment, we verify the overall performance of ImMesh toward real-time simultaneous localization and mesh- ing with live video demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6(b), we record the full process of our data sampling at the cam- pus of the University of Hong Kong (HKU), deploying the ImMesh for simultaneously estimating the sensor pose and reconstructing the triangle mesh on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The full video demonstration of this experiment is available on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6: (a) shows our handheld device for data collection and online mesh reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (b) shows a snapshot of our accompanying video (on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=9) of Experiment-1, with three time-aligned views of different sources including a screen- recorded view (in red), a camera preview (in yellow), and a third- person view (in blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Experiment setup: Our handheld device for data collec- tion is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6(a), which includes a mini-computer (equipped with an Intel i9-10900 CPU and 64 GB RAM), a Livox avia 3D LiDAR (FoV: 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 °ˆ77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2°), and a preview only RGB camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this experiment video, three time-aligned views of different sources are presented, including: 1) a screen- recorded view that shows the estimated posed and online reconstructed triangles mesh of ImMesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) a camera preview that records the video stream of the front-facing camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) a third-person view that records the whole process of this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Result and analysis: As presented in the video, benefits from the accurate uncertainty models of the LiDAR point and plane that counting both LiDAR measurement noise and sensor pose estimation errors in our localization module, ImMesh is able to provide the 6-DoF pose estimation of very high accuracy in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' What is worth mentioning is, without any additional processing (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', loop detection), all of these two trials can close the loop itself after traveling 957 m and 391 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In addition, with the efficient architecture design and our careful engineering implementation on our meshing module, the triangle mesh of the surrounding environment is incrementally reconstructed on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' With the live preview of real-time meshing as a reference, it is quite useful to let users know whether the data sampling is sufficient enough for any part of the scene, especially for those non-expert users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' At the end of the data sampling, the dense accurate triangle mesh of this scene is already reconstructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This is why we name our system the Immediately Meshing (ImMesh) framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Experiment-2: Extensive evaluation of ImMesh on public datasets with various types of LiDAR in different scenes With all the modules delicately designed for efficiency and careful engineering implementations, both the localization and meshing modules easily achieve real-time performances on a standard multi-core CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this experiment, we statics the average time consumption on four public datasets with the computation platform listed in Section VIII-A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The four datasets we chose are: the Kitti dataset [81], the NCTL dataset [82], the NTU VIRAL dataset [83] and the R3LIVE dataset [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' They are collected in different scenarios ranging from urban structured buildings to field- cluttered complex environments (see Table II),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' using various types of LiDARs that include mechanical spinning LiDAR Screen Camera LiDAR Mini-PC a)12 TABLE I: The specifications of LiDARs in four datasets Dataset Kitti NCLT NTU VIRAL R3LIVE LiDAR Velodyne HDL-64E Velodyne HDL-32E Ouster OS1-16 Gen1 Livox Avia Scanning mechanism Mechanical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' spinning 64-line Mechanical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' spinning 32-line Mechanical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' spinning 16-line Solid-state,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Risley’s prism Field of View (Horizontal˝ ˆ Vertical˝) 360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0˝ ˆ 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8˝ 360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0˝ ˆ 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3˝ 360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0˝ ˆ 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2˝ 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4˝ ˆ 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2˝ Points per secondr1s 1,333,312 695,000 327,680 240,000 Price $ 75,000 $ 8,800 $ 3,500 $ 1,599 1 Only show the point rate of single-return mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' TABLE II: This table shows the detailed information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', length, duration, scenarios) of each testing sequence, the time consumption of ImMesh in processing a LiDAR scan, and the number of vertices and facets of each reconstructed mesh in Experiment-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sequece Traveling length (m) Durations (s) LiDAR frames Meshing mean/Std (ms) Localization mean/Std (ms) Number of vertices (k) Number of facets(k) Scenarios Kitti 00 3,724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 456 4,541 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 3,339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 7,692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 Urban city Kitti 01 2,453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 146 1,101 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 2,033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 4,046.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 High way Kitti 02 5,058.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 509 4,661 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 4,390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 10,028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 Residential Kitti 03 560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 88 801 28 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 730.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 1,550.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 Countryside;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Road Kitti 04 393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 27 271 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 850.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Urban city;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Road Kitti 05 2,205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 303 2,761 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 / 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 2,167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 4,950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 Residential Kitti 06 1,232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 123 1,101 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 886.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 1,889.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 Urban city Kitti 07 2,453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 114 1,101 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 1,710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Urban city Kitti 08 3,222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 441 4,071 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 / 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 3,559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 7,936.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 Urban city Kitti 09 1,705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 171 1,591 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 1,827.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 4,127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Countryside;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Road Kitti 10 919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 132 1,201 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 939.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 2,096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Residential NCLT 2012-01-15 7,499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 6739 66,889 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 9,659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 26,608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 Campus;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Indoor NCLT 2012-04-29 3,183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 2598 25,819 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 4,820.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 13,483.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 Campus NCLT 2012-06-15 4,085.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 3310 32,954 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 6,361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 17,473.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Campus NCLT 2013-01-10 1,132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 1024 10,212 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 2,020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 5,495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 Campus NCLT 2013-04-05 4,523.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 4167 41,651 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 / 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 9,582.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 23,982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 Campus NTU VIRAL eee 01 265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 398 3,987 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 597.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 1,380.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 Aerial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Outdoor NTU VIRAL nya 01 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 396 3,949 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 1,247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Aerial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Indoor NTU VIRAL rtp 01 449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 482 4,615 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 2,030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Aerial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Outdoor NTU VIRAL sbs 01 222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 354 3,542 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 1,150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 Aerial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Outdoor NTU VIRAL tnp 01 319.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 583 5,795 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 / 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 Aerial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Indoor R3LIVE hku campus 00 190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 202 2,022 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 1,236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 Campus R3LIVE hku campus 01 374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 304 3,043 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 1,323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 2,862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 Campus R3LIVE hku campus 02 354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 323 3,236 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 867.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 1,913.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Campus R3LIVE hku campus 03 181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 173 1,737 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 550.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 1,130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Campus R3LIVE hku main building 1,036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 1170 11,703 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 3,031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 6,803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Indoor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Outdoor R3LIVE hku park 00 247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 228 2,285 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 2,380.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 Cluttered field R3LIVE hku park 01 401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 351 3,520 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 1,673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 3,964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 Cluttered field R3LIVE hkust campus 00 1,317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 1073 10,732 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 4,916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 11,246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 Campus R3LIVE hkust campus 01 1,524.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 1162 11,629 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 / 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 5,353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 12,638.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 Campus R3LIVE hkust campus 02 2,112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 1618 4,787 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 / 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='1 1,991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 4,653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 Campus R3LIVE hkust campus 03 503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 478 16,181 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 / 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 7,673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 18,247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 Campus TABLE III: Two ImMesh configurations for two types of LiDARs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', mechanical and solid-state LiDAR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Minimum point L1-voxel O1 L2-voxel O2 distance (m) size (m) size (m) Mechanical LiDAR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 Solid-state LiDAR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 TABLE IV: The average/maximum time of meshing and localization module for processing each LiDAR scan in four datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kitti NCLT NTU VIRAL R3LIVE mean/max mean/max mean/max mean/max Meshing (ms) 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 / 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Localization (ms) 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 / 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='3 / 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='8 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='9 / 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 / 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 of different channels and solid-state LiDAR of small FoV (see the specifications in Table I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, the adaptability of ImMesh is sufficiently validated by extensive tests on these four distinguished datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1) Experiment setup: Thanks to the parameter insensitivity of ImMesh, we are able to benchmark ImMesh in four datasets with only two sets of configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The two configurations are reasonably required for adapting two classes of LiDARs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', mechanical and solid-state LiDAR), as shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Since the 3D points sampled by a solid-state LiDAR are distributed in a small sensor FoV, the accumulated point cloud of solid-state LiDAR usually has a higher density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Therefore, we set the minimum point distance and voxel size for solid- LIVOX AVIAVelodyne13 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7: In Experiment-3, we use CAD software to design a solid model to generate a ground truth triangle mesh as a reference, which contains four zones simulating different scenarios, as the white entity shown in this figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To simulate the data collecting process with different vehicles, we generate the LiDAR point cloud data by traveling along three distinguished trajectories, whose sampling poses are colored in different colors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', red, yellow, and blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' state LiDAR 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 times smaller than those for mechanical LiDAR, as shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For the other setups, we maintained the same configuration except for some necessary adjustments to match the hardware setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Result and analysis: Table II shows the detailed infor- mation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', length, duration, scene) of each sequence, the average time consumption of our localization and meshing module in processing a LiDAR scan, and the number vertices and facets of each reconstructed mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' From Table II, it is seen that the average cost-time of both localization and meshing modules are closely related to the density of the input LiDAR scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, the LiDAR of a higher channel has a much higher point sampling rate (see Table I) which causes more data to be processed in each update of a LiDAR frame (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', more points in a voxel and more voxels activated in each frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, for the same set of datasets, the processing time also varies among different scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The sequences sampled in a high-way or field environment (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Kitti 01, Kitti 09) usually have a longer LiDAR sampling range and hence leading to more points per frame to be processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Thanks to the efficient data structure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', ikd-Tree, hashed hierarchical voxel) and parallelism strategy, which allows us to perform the state estimation and incremental mesh reconstruction simultaneously, the time consumption of large- scale datasets is bounded in an acceptable value (ď35 ms for meshing, ď49 ms for localization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The average and maximum time consumption of ImMesh in four datasets are shown in Table IV, reflecting that our system satisfies the real-time requirement even with different types of LiDAR and in various scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Notice that the LiDAR sample rate are 10 Hz for all datasets, and our meshing and localization are run in parallel (see Section VI-F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Experiment-3: Quantitative evaluation of meshing accu- racy In this experiment, we horizontally evaluate the runtime performance and meshing accuracy of ImMesh by comparing it with existing state-of-the-art mesh reconstruction methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The coordinate The ground-truth The samplingposes Thesamplingposes The sampling poses axes model oftrajectory-1 oftrajectory-2 oftrajectory-3 > 四 Z Zone-A Zone-B Zone-C Zone-D (Side view) A AV AT 四 Z Zone-A Zone-B Zone-C N Zone-D A 0 (Bird view) N V14 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8: This figure shows the qualitative results of Experiment-3, with all “positive” facets (correctly reconstructed) colored in white and “negative” facets (wrongly reconstructed) colored in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (a) and (b) present a set of qualitative results of four candidates under Trajectory- 3@640 ˆ 480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (c) shows the reconstructed mesh of TSDF feeding with depth images of different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' TABLE V: The average time consumption of candidates in reconstructing the triangle mesh in Experiment-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Time consumption (Unit: second(s)) Method Trajectory-1 @640x480 Trajectory-1 @320x240 Trajectory-1 @160x120 Trajectory-2 @640x480 Trajectory-2 @320x240 Trajectory-2 @160x120 Trajectory-3 @640x480 Trajectory-3 @320x240 Trajectory-3 @160x120 ImMesh (ours) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='877 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='451 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='522 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='649 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='066 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='206 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='536 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='617 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='055 Del 371.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='632 132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='181 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='366 696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='641 353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='304 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='765 960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='613 323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='224 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='008 TSDF 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='064 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='522 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='513 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='191 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='146 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='028 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='544 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='391 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='309 Poi 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='848 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='605 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='610 635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='079 198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='028 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='280 957.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='743 310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='080 137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='976 TABLE VI: The meshing accuracy of four candidates evaluated with Criteria-1 in Experiment-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Criteria-1:Meshing precision ������ in Zone-A / in Zone-B in Zone-C / in Zone-D in all zones (average) ������ (Unit: percentage(%)) Method Trajectory-1 @640x480 Trajectory-1 @320x240 Trajectory-1 @160x120 Trajectory-2 @640x480 Trajectory-2 @320x240 Trajectory-2 @160x120 Trajectory-3 @640x480 Trajectory-3 @320x240 Trajectory-3 @160x120 ImMesh (ours) 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='96 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='43 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='06 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='98 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='01 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='72 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='93 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='06 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='48 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='65 / 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='82 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='47 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='50 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='47 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='48 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='49 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='91 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='76 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='51 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='09 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='09 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='98 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='27 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='58 / 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='07 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='29 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='97 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='97 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='00 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='05 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='72 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='33 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='24 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='53 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='31 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='21 / 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='84 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='88 / 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='59 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='53 Del 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='62 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='95 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='54 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='39 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='98 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='86 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='04 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='56 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='09 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='68 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='90 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='49 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='27 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='39 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='09 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='83 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='24 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='24 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='31 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='96 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='03 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='49 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='94 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='14 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='16 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='28 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='27 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='14 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='47 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 / 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='77 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='75 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='31 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='49 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='41 / 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='61 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='59 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='47 TSDF 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='93 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='88 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='56 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='83 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='57 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='78 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='35 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='18 / 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='42 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='31 / 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='64 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='55 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='96 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='53 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='53 / 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='13 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='21 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='48 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='02 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='24 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='36 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 / 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='98 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='82 / 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='48 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='97 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='54 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='62 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='74 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='43 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='67 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='12 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='11 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 / 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='21 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='43 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='88 / 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='45 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='08 / 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='48 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='76 Poi 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='95 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='07 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='14 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='11 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='62 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='04 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='02 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='67 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='27 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='92 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='43 / 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='87 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='38 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='13 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='00 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='27 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='00 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='31 / 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='70 / 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='26 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='77 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='90 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='83 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='35 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='86 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='94 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='72 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='44 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='78 / 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='23 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='91 / 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='23 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='98 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='13 / 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='11 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='43 / 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='06 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='06 1) Prepare of simulated data: Since the ground truth trian- gle mesh of the real-world data can not be directly obtained, we use CAD software SolidWorks [14] to design a ground truth solid model for reference, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This solid model we made is constituted of four distinguished zones for an extensive evaluation of the meshing results in different scenes, which include the simple planar zone (Zone-A), simple curvy (bending) zone (Zone-B), complex planar zone (Zone-C), and complex curvy Zone (Zone-D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Each zone has an equal size of lengthˆwidthˆheight as 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 mˆ10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 mˆ6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To simulate point clouds collected by a real LiDAR, we built a simulator to unproject the “LiDAR” points from the depth images generated from the rasterization of the ground truth models with given poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this experiment, we ras- terized the depth image with a pinhole projection model of horizontalˆvertical FoV as 80˝ ˆ 60˝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, to simulate the LiDAR of different point cloud densities, we rasterized the depth image with three sets of resolutions (see Table V) including 640 ˆ 480, 320 ˆ 240, and 160 ˆ 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, we designed three distinguished sampling trajectories as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Each trajectory contained a number of manually placed poses for simulating different vehicles in collecting the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='148 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(a3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(a4) Poi trajectory-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(a) (c) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(b1) ImMesh trajectory-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(b2) Del trajectory-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(b3) TSDF trajectory-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(b4) Poi trajectory ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='(b) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='@640x48015 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-1@640X480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='70 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-2@640X480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-3@640X480 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-1@320X240 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='70 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-2@320X240 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-3@320X240 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Index of sampling poses ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='of Trajectory-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-1@160X120 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='70 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Index of sampling poses ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='of Trajectory-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-2@160X120 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Index of sampling poses ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='of Trajectory-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Trajectory-3@160X120 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Average depth error (cm) in each frame ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='TSDF ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Del ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Poi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='ImMesh (Ours) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10: Re-rendering depth error in each frame of four candidates in Experiment-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' TABLE VII: The meshing accuracy of four candidates evaluated by Criteria-2 in Experiment-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Criteria-2: Re-rendering depth error (Unit: centimeter (cm)) Method Trajectory-1 @640x480 Trajectory-1 @320x240 Trajectory-1 @160x120 Trajectory-2 @640x480 Trajectory-2 @320x240 Trajectory-2 @160x120 Trajectory-3 @640x480 Trajectory-3 @320x240 Trajectory-3 @160x120 ImMesh (ours) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='146 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='678 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='67 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='686 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='115 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='838 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='076 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='943 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='592 Del 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='216 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='37 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='176 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='832 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='807 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='358 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='674 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='205 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='327 TSDF 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='068 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='643 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='421 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='231 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='652 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='352 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='724 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='167 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='288 Poi 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='844 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='611 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='594 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='546 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='377 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='466 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='21 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='848 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='142 The details of these three trajectories are shown below: ‚ The trajectory-1 (in red) contains 28 sampling poses, simulating the LiDAR mounted on a car with a height of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 m away from the ground (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', z “ 0 plane).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The LiDAR data is collected by moving from Zone-A to Zone-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ The trajectory-2 (in yellow) contains 81 sampling poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' It simulates a handheld LiDAR collecting data at the height fixed as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The LiDAR data is collected by traveling in an “8”-like pattern which sufficiently captures the model’s surface from different views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ The trajectory-3 (in blue) contains 102 sampling poses, imitating a LiDAR mounted on a drone flying at the height of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The LiDAR data is collected from a tilted bird view by flying in an “S”-like pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Due to the limitation of height in sampling the data, LiDAR in trajectory-1 and trajectory-2 did not capture the ceiling sur- face of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Conversely, LiDAR in trajectory-3 captured the ceiling surfaces but failed to capture the bottom surfaces of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, LiDAR in trajectory-1 traveled in one direction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' hence only the surfaces facing against the positive Y -axis were captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) Experiment setup: In this experiment, we conducted a fair evaluation of meshing ability among our work and existing mesh reconstruction baselines, which includes a TSDF-based method implemented by Point cloud library (PCL) [53] with GPU acceleration, Delaunay triangulation and graph cut based method implemented by OpenMVS [84], and the official implementation of Poisson surface reconstruction [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We conducted the evaluation of candidates on a desktop PC that equips with an Intel i7-9700K CPU, 64Gb RAM, and a Nvidia 2080 Ti GPU with 12Gb graphics memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We feed our ImMesh and TSDF-based (TSDF) method with LiDAR points frame by frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To avoid the pose estimation error that affects the result of meshing, we disable the pose estimation module and feed ImMesh and TSDF with the ground truth poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For offline mesh reconstruction methods: Delaunay triangulation and graph cut (Del) based method and Poisson surface reconstruction (Poi), we feed them with the accumulated point cloud of all frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To avoid the uneven point cloud density which leads to errors in calculating the norm for Poi, and to avoid Del reconstructing the tiny facets that lead to a biased calculation of accuracy, we leverage a voxel grid filter with a leaf size of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 cm ˆ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 cm ˆ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 cm to downsample the accumulated point cloud before feeding to Poi and Del.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Due to and limitation of graphics memory (12Gb for Nvidia 2080 Ti), we set the TSDF cell size as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2 m such that TSDF can utilize the GPU acceleration while preserving satisfying 16 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11: The first row of images shows the comparisons between a raw LiDAR scan (colored in white) and our reinforced points (colored in cyan) under different sets of rasterizing FoV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The second and third rows of images show the comparisons of raw and reinforced points after projection on the current sensor frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For more detailed visualizations of this process, please refer to our accompanying video on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' precision in the mesh reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For our ImMesh, the parameter configuration for solid-state LiDAR is used, as shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For Poi, we set the octree level as 12 and removed large hulls by deleting facets with one of their edges longer than 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For other configurations of all candidates, we set them as their default configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this experiment, we horizontally evaluated the meshing accuracy of candidates by comparing their reconstructed mesh with the ground truth models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A set of qualitative results of four candidates under Trajectory-3@640 ˆ 480 are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8(a and b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To sufficiently and fairly calculate the accuracy by comparing the mesh of the candidate’s and ground truth, two criteria are adopted for counting the difference, shown below: ‚ Criteria-1: For a triangle facet Tcan i of a candidate’s reconstructed mesh, we first find out a triangle facet Tgt j of the ground truth model, whose point-to-plane distance from this facet to the center of Tcan i is minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='Tcan i is regarded as “positive” if it satisfies both of the following conditions: 1) The point-to-plane distance between Tgt i and CenterpTcan i q smaller than 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 cm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) The angular distance between the norm vector of Tcan i and the norm vector of Tgt j smaller than 15˝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Otherwise, this triangle facet Tcan i is treated as “negative”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The ratios of “positive” over the total number of facets in each zone (and the entire simulated scene) served as Criteria-1 for evaluating the meshing accuracy, as the results are shown in Table VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ‚ Criteria-2: For each candidate’s reconstructed mesh, it is rasterized into a depth image in the same way as rasterizing the ground truth model to a depth image (for generating the simulation data, see Section VIII-C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The average depth error of each pixel depth value is calculated between each depth image pair of the candidate and ground truth (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', re-rendering error), serving as Criteria-2 for evaluating the meshing accuracy, with the results shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 and Table VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' While Criteria-1 reflects the correctness of candidates in reconstructing the mesh and reflects different performances in different zones, it is unable to count the holes of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' On the contrary, Criteria-2 reflects the errors caused by holes but can not count the facets out of view (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the facets hide behind other facets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Referring to the results calculated according to Criteria-1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Table VI) and Criteria-2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 and Table VII), we conducted the evaluation and analysis on the meshing accuracy of four candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) Results and analysis of runtime performance: The aver- age time consumption of four candidates is listed in Table V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The online methods ImMesh and TSDF show a comparative runtime performance, while the offline methods Del and Poi consume about two orders of magnitude larger than the online methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Notice that TSDF achieves the comparative runtime performance as ours with the acceleration of an Nivdia 2080 Ti GPU, which indicates the highest computation efficiency of our ImMesh among the four candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4) Result and analysis of meshing accuracy: The results evaluated by Criteria-1 are shown in Table VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' All candidates show satisfying accuracy in reconstructing the mesh of the simple planar models in Zone-A, followed by the simple curvy model in Zone-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In complex scenes, all candidates show lower accuracy and achieve worse results in Zone-C, where many square cylinders cross each other, making it hard to reconstruct well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In addition, as the point cloud (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the resolution of depth images) becomes sparser, the accuracy drops responsibly, especially for TSDF-based method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lastly, Poi shows a bad accuracy in complex scenes due to the unwanted facets appearing at the sharp edge of the models, Comparison of input and reinforced LiDAR points Depth FoV=30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0°×22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='7 0epth FoV=50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0°x38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='6 Depth FoV=77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4°×62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0 current LiDAR scan Projection of inforced LiDAR Points Projection of re- Depth meter Depth neter Depth (meter Depth (meter 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='0006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='125 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='000 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='00017 as the facets colored in red shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8(b4 and c4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The results evaluated by Criteria-2 are shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 and Table VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Del achieves the best precision by showing the lowest depth error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Our proposed algorithm ImMesh performs closely to Del, followed by Poi and TSDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As the graphs shown in each column of Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10, the average depth error of the TSDF increases sharply as the resolution of depth images goes down, due to the appearance of the holes on the mesh (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' This unwanted phenomenon that uses TSDF-based methods for constructing mesh with depth image of low resolution is also reported in other work [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5) Summary: We lead the conclusions of Experiment-3 based on the results and analysis discussed in Section VIII-C3 and Section VIII-C4: For offline applications, which only care about quality and neglect time consumption, Del is the best choice, and our ImMesh is the second best one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Poi shows satisfying results in simple scenes, but it is incapable of reconstructing complex scenes with many sharp edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' For real-time applications, our work ImMesh is the best choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Even though TSDF with GPU implementation can meet the runtime requirement of real-time scenarios, its performance is unsatisfying due to the low meshing accuracy compared to ImMesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Application-1: ImMesh for LiDAR point cloud reinforce- ment Benefiting from ImMesh’s real-time ability to reconstruct the triangle mesh on the fly, depth images can be rasterized from the reconstructed facets online in the current sensor frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' By unprojecting the 3D points from the depth image, point clouds of a regular pattern can be retrieved with wider FoV and denser distribution compared to the original input LiDAR scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We termed this process as LiDAR point rein- forcement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this experiment, we demonstrate the LiDAR point cloud reinforcement with a solid-state LiDAR Livox Avia with FoV of 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='4˝ˆ77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='2˝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The comparisons between the original points of a LiDAR frame (colored in white) and after our reinforce- ment (colored in cyan) with different sets of rasterization FoV are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As the white points shown in the first row of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11, the input LiDAR scan is sparse with an irregular scanning pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' After the reinforcement, the resultant 3D points colored in cyan are distributed in a regular pattern, with denser density and wider FoV (as the rasterization FoV is bigger than LiDAR’s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To have a better sense of their differences, we present the comparisons of depth images after projection, as shown in the second and third rows of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In this manner, the LiDAR points after reinforcement can benefit the applications in these scenarios: 1) the reinforced points of denser density and wider FoV enable navigation algorithms to achieve better planning performance and make smarter decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) it provides unified point cloud outputs neglecting scanning patterns of different LiDARs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Compared to the use of original LiDAR points with specific scanning patterns, using these points of regular patterns potentially benefits learning-based algorithms for better generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Application-2: ImMesh for rapid, lossless texture recon- struction In this application, we show how ImMesh can be applied in applications of losslessly texture reconstruction for rapid field surveying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(b1„b3), we mounted a Livox avia LiDAR and a Hikvision CA-050-11UC global shutter RGB camera on a DJI M300 drone platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We collected the data in a mountain field by taking off from Zone-A (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(a)), and flying in a “s”-like pattern trajectory with a traveling distance of 975 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We leveraged ImMesh for reconstructing the mesh from collected LiDAR data and used R3LIVE++ [21, 22] for estimating the camera’s poses (as the yellow frustum shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(a, c1 and c2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' We textured each facet of the reconstructed mesh by the RGB image captured by the nearest camera with the estimated camera pose from R3LIVE++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Benefit from the high efficiency of ImMesh and R3LIVE++, the total time of reconstructing the RGB textured mesh from this sequence of duration 325 s cost only 686 s, with 328 s for ImMesh, with 330 s for R3LIVE++ and 28 s for texturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(a) shows a bird view of our mesh after texturing, with the close-up views of textured mesh in Zone-A, B, and C are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(e1, e2, and e3), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12(c1 and c2), we show the altitude of this map by coloring the facets in their height w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the take-off point (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the ground plane in Zone-A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' As the close-up views shown in the bottom three rows of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12, the reconstructed mesh (d1„d3) from our ImMesh after texturing (e1„e3) successfully preserves the textures of maps when comparing with the RGB colored point cloud reconstructed by R3LIVE++ (f1„f3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Since the density of the point cloud is not infinite, R3LIVE++ is unable to loss- lessly reconstruct the scene’s radiance by storing radiance information in points with limited density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' On the contrary, reconstructing the maps with mesh reconstructed by ImMesh, and texturing the facets with collected images and the camera poses of R3LIVE++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The raw color images photoed by the camera are losslessly preserved on the facets of the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence this is a lossless manner for reconstructing the texture of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Compared to existing counterparts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', structure from motion (SFM) [12, 30]), this manner shows significant advantages on: 1) It is a reliable solution that does not require GPS measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2) It is a rapid reconstruction method that costs just 2„3 times of data sampling time for reconstructing a scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3) It is a lossless texture reconstruction method, while preserving geometry structure of very high accuracy that is constructed from LiDAR’s measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The accompanying video that records the full process of this lossless texture reconstruction is available on our YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=622, and an additional trial is shown in our Supplementary Material3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' CONCLUSIONS AND FUTURE WORK A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Conclusions In this work, we proposed a novel meshing framework termed ImMesh for achieving the goal of simultaneous local- 3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='com/hku-mars/ImMesh/blob/main/supply/Supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='pdf 18 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12: (b1„b3) show our UAV platform for data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (a) show the bird view of our lossless texture reconstruction result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (c1 and c2) show the altitude of this map by coloring the facets in their height w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the take-off point (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', the ground plane in Zone-A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The qualitative comparison of mapping results in Zone-A, B, and C of ImMesh, ImMesh after textured, and R3LIVE are shown in (d„f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To see the detailed reconstruction process of the scene, please refer to our video on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ization and meshing framework in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To the best of our knowledge, it is the first work in literature to reconstruct the triangle mesh of a large-scale scene in an incremental manner in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In ImMesh, the localization module represents the surrounding environment in a probabilistic representation, estimating the sensor pose in real-time by leveraging an iterated Kalman filter to maximize a posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The meshing module directly utilizes the registered LiDAR point as mesh vertices, real-time reconstructing the triangle facets in a novel incremental manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To be detailed, our meshing module first utilizes an efficient hierarchical voxel data structure for fast finding of voxels containing newly appended vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then, the voxel-wise 3D meshing problem is converted into a 2D one by performing dimension reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, the triangle facets are incrementally reconstructed with pull, commit, and push steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In our experiments, we first verified the overall performance by presenting live video demonstrations of how the mesh is immediately reconstructed in the process of data collec- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Then we extensively tested ImMesh with four public datasets collected by four distinguished LiDAR in various scenes, which confirmed the real-time ability in all sequences we evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lastly, we horizontally evaluated the meshing performance of ImMesh in Experiment-3 by comparing it against existing meshing baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The results show that ImMesh achieves high meshing accuracy while keeping the best runtime performance among all candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' In our applications, we first show how ImMesh can be applied for LiDAR point cloud reinforcement, which generates reinforced points in a regular pattern with denser density and wider FoV compared to raw LiDAR scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=" In Application-2, we combined our works ImMesh and R3LIVE++ to achieve (b1) Mini PC 40 长区区区区区区区区 LiDAR Camera 区区区区区区区区 Height Zone-B Camera (c1) LiDAR (c2) b62 Height 40m (b3 a ImMesh ImMeshwith texture R'LIVE++ (f1) (f2 (f3) Zone-A Zone-B Zone-019 the goal of losslessly texture reconstruction of scenes." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Finally, to share our findings and make contributions to the commu- nity, we make our code publicly available on our GitHub: github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='com/hku-mars/ImMesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Future work In ImMesh, we propose a novel framework that can simul- taneously localization and meshing in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Further, to realize the goal of lossless texture reconstruction of scenes, our current solution is combining ImMesh and R3LIVE at a system level as presented in our Application-2 (in Section VIII-E), which is indeed a solution but not the elegant one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hence, our future work would trend to make ImMesh and R3LIVE work in a more tightly combined style.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Besides, since our system does not implement any loop correction yet, it drifts gradually due to accumulated localization errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Our future work will integrate our recent works [85, 86] on loop detection based on LiDAR point cloud, which is able to online detecting the possible loop and then reduce the drift by leveraging the loop correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ACKNOWLEDGEMENTS The authors would like to thank DJI Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Ltd4 for providing devices and research found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' REFERENCES [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Mystakidis, “Metaverse,” Encyclopedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 486–497, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [2] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Su, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Luan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shen, “A survey on metaverse: Fundamentals, security, and privacy,” IEEE Communications Surveys & Tutorials, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cipresso, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Giglioli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Raya, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Riva, “The past, present, and future of virtual and augmented reality research: a network and cluster analysis of the literature,” Frontiers in psychology, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2086, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Dey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lovett, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kapoor, “Airsim: High-fidelity visual and physical simulation for autonomous vehicles,” in Field and service robotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Springer, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 621–635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Laine and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Karras, “High-performance software rasterization on gpus,” in Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 79–88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Akenine-Moller, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Haines, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hoffman, Real-time rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' AK Peters/crc Press, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Arvo, Graphics gems II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Elsevier, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Jim´enez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Thomas, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Torras, “3d collision detection: a survey,” Computers & Graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 269–285, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ericson, Real-time collision detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Crc Press, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [10] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Featherstone, Rigid body dynamics algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Springer, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Baraff, “An introduction to physically based modeling: rigid body simulation i—unconstrained rigid body dynamics,” SIGGRAPH course notes, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 82, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Schonberger and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Frahm, “Structure-from-motion revisited,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4104–4113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [13] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cai, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chen, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “Marsim: A light-weight point-realistic simulator for lidar- based uavs,” arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10716, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' SolidWorks, “Solidworks®,” Version Solidworks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [15] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Community, “Blender—a 3d modelling and rendering package,” Blender Foundation, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yuan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hong, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “Efficient and probabilistic adaptive voxel mapping for accurate online lidar odometry,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 8518–8525, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='dji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='com [17] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “Fast-lio2: Fast direct lidar-inertial odometry,” IEEE Transactions on Robotics, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Behley and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Stachniss, “Efficient surfel-based slam using 3d laser range data in urban environments.” in Robotics: Science and Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2018, 2018, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [19] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shao, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Li, “Mulls: Versatile lidar slam via multi-metric linear least square,” in 2021 IEEE International Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11 633–11 640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [20] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shan and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Englot, “Lego-loam: Lightweight and ground-optimized lidar odometry and mapping on variable terrain,” in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4758–4765.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “R3live: A robust, real-time, rgb-colored, lidar- inertial-visual tightly-coupled state estimation and mapping package,” in 2022 International Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10 672–10 678.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [22] ——, “R3live++: A robust, real-time, radiance reconstruction pack- age with a tightly-coupled lidar-inertial-visual state estimator,” arXiv preprint arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='03666, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kazhdan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Bolitho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hoppe, “Poisson surface recon- struction,” in Proceedings of the fourth Eurographics symposium on Geometry processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kazhdan and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hoppe, “Screened poisson surface reconstruction,” ACM Transactions on Graphics (ToG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–13, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wilhelms and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Van Gelder, “Octrees for faster isosurface genera- tion,” ACM Transactions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 201– 227, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shekhar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fayyad, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yagel, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cornhill, “Octree-based decimation of marching cubes surfaces,” in Proceedings of Seventh Annual IEEE Visualization’96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 1996, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 335–342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [27] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lorensen and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cline, “Marching cubes: A high resolution 3d surface construction algorithm,” ACM siggraph computer graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 163–169, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kazhdan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chuang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rusinkiewicz, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hoppe, “Poisson surface reconstruction with envelope constraints,” in Computer graphics forum, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wiley Online Library, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 173–182.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Labatut, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pons, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Keriven, “Efficient multi-view reconstruc- tion of large-scale scenes using interest points, delaunay triangulation and graph cuts,” in 2007 IEEE 11th international conference on com- puter vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2007, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [30] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Litvinov and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lhuillier, “Incremental solid modeling from sparse and omnidirectional structure-from-motion data,” in British Machine Vision Conference, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Jancosek and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pajdla, “Exploiting visibility information in surface reconstruction to preserve weakly supported surfaces,” International scholarly research notices, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2014, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Bernardini, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Mittleman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rushmeier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Silva, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Taubin, “The ball-pivoting algorithm for surface reconstruction,” IEEE transactions on visualization and computer graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 349–359, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [33] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Peethambaran, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chen, “Lidar point clouds to 3-d urban models : a review,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 606–627, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [34] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Newcombe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Izadi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hilliges, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Molyneaux, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Davison, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kohi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shotton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hodges, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fitzgibbon, “Kinectfusion: Real-time dense surface mapping and tracking,” in 2011 10th IEEE international symposium on mixed and augmented reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ieee, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 127–136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Bautembach, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Izadi, “Scalable real-time volumetric surface reconstruction,” ACM Transactions on Graphics (ToG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–16, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nießner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zollh¨ofer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Izadi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Transactions on Graphics (ToG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–11, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [37] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' K¨ahler, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Prisacariu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Valentin, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Murray, “Hierarchical voxel block hashing for efficient integration of depth images,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 192–197, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [38] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Vespa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nikolov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Grimm, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nardi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kelly, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Leutenegger, “Efficient octree-based volumetric SLAM supporting signed-distance and occupancy mapping,” IEEE Robotics and Automa- tion Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1144–1151, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [39] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' K¨ahler, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Prisacariu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ren, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sun, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Torr, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Murray, “Very high frame rate volumetric integration of depth images on mobile devices,” IEEE transactions on visualization and computer graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1241–1250, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 20 [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Klingensmith, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Dryanovski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Srinivasa, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xiao, “Chisel: Real time large scale 3d reconstruction onboard a mobile device us- ing spatially hashed signed distance fields.” in Robotics: science and systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Citeseer, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [41] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Oleynikova, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Taylor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fehr, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Siegwart, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nieto, “Voxblox: Incremental 3d euclidean signed distance fields for on-board mav planning,” in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1366–1373.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lefloch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kluge, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sarbolandi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Weyrich, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kolb, “Com- prehensive use of curvature for robust and accurate online surface reconstruction,” IEEE transactions on pattern analysis and machine intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2349–2365, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [43] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lefloch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Weyrich, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kolb, “Anisotropic point-based fusion,” in 2015 18th International Conference on Information Fusion (Fusion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2121–2128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [44] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Weise, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wismer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Leibe, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Van Gool, “In-hand scanning with online loop closure,” in 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1630–1637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rusinkiewicz, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hall-Holt, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Levoy, “Real-time 3d model acquisition,” ACM Transactions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 438–446, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [46] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Habbecke and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kobbelt, “A surface-growing approach to multi- view stereo reconstruction,” in 2007 IEEE Conference on Computer Vision and Pattern Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2007, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [47] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Bodenmueller, “Streaming surface reconstruction from real time 3d measurements,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' dissertation, Technische Universit¨at M¨unchen, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [48] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Whelan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Leutenegger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Salas-Moreno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Glocker, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Davi- son, “Elasticfusion: Dense slam without a pose graph.” Robotics: Science and Systems, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [49] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Whelan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Salas-Moreno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Glocker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Davison, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Leutenegger, “Elasticfusion: Real-time dense slam and light source estimation,” The International Journal of Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 14, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1697–1716, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [50] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Gao and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Tedrake, “Surfelwarp: Efficient non-volumetric single view dynamic reconstruction,” arXiv preprint arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='13073, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [51] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sch¨ops, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sattler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pollefeys, “Surfelmeshing: Online surfel- based mesh reconstruction,” IEEE transactions on pattern analysis and machine intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2494–2507, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [52] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cai, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “ikd-tree: An incremental kd tree for robotic applications,” arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='10808, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [53] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rusu and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cousins, “3d is here: Point cloud library (pcl),” in 2011 IEEE international conference on robotics and automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [54] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Muja and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lowe, “Fast approximate nearest neighbors with automatic algorithm configuration.” VISAPP (1), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 331-340, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Teschner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Heidelberger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' M¨uller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pomerantes, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Gross, “Optimized spatial hashing for collision detection of deformable objects.” in Vmv, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 47–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [56] ISO, ISO/IEC 14882:1998: Programming languages – C++, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [57] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hornung, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Wurm, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Bennewitz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Stachniss, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Burgard, “Octomap: An efficient probabilistic 3d mapping framework based on octrees,” Autonomous robots, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 189–206, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [58] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Panek, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kukelova, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Sattler, “Meshloc: Mesh-based visual localization,” in European Conference on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Springer, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 589–609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [59] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Vizzo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chebrolu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Behley, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Stachniss, “Poisson surface reconstruction for lidar odometry and mapping,” in 2021 IEEE International Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 5624–5630.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [60] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Dreher, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Blum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Siegwart, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Gawel, “Global localization in meshes,” in ISARC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Proceedings of the International Symposium on Automation and Robotics in Construction, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IAARC Publications, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 747–754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [61] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Oelsch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Karimi, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Steinbach, “R-loam: Improving lidar odometry and mapping with point-to-mesh features of a known 3d reference object,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2068–2075, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [62] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zheng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “R2live: A robust, real-time, lidar-inertial-visual tightly-coupled state estimator and mapping,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 7469–7476, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [63] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Singh, “Loam: Lidar odometry and mapping in real- time.” in Robotics: Science and Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Berkeley, CA, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [64] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “Loam livox: A fast, robust, high-precision lidar odometry and mapping package for lidars of small fov,” in 2020 IEEE International Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3126–3131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [65] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Stevens, Computer Graphics Dictionary, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ADVANCES IN COMPUTER GRAPHICS AND GAME DEVELOPMENT SERIES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Charles River Media, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Available: https://books.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='hk/books?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='id=XqlJcMi1Pi0C [66] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Kahan, “Miscalculating area and angles of a needle-like triangle,” University of California, Berkeley, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 94720, 1776.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [67] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Woo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Neider, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Davis, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shreiner, OpenGL programming guide: the official guide to learning OpenGL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Addison-Wesley Long- man Publishing Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=', 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [68] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Evans, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Skiena, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Varshney, “Optimizing triangle strips for fast rendering,” in Proceedings of Seventh Annual IEEE Visualization’96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 1996, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 319–326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [69] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hearn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Baker, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Baker, Computer graphics with OpenGL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pearson Prentice Hall Upper Saddle River, NJ:, 2004, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [70] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Loeliger and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' McCullough, Version Control with Git: Powerful tools and techniques for collaborative software development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' ” O’Reilly Media, Inc.”, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [71] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Castleman, Digital image processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Prentice Hall Press, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [72] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fabri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pion, “Cgal: The computational geometry algorithms library,” in Proceedings of the 17th ACM SIGSPATIAL international conference on advances in geographic information systems, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 538–539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [73] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Toth, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' O’Rourke, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Goodman, Handbook of discrete and computational geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' CRC press, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [74] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Rosinol, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Abate, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Carlone, “Kimera: an open- source library for real-time metric-semantic localization and mapping,” in 2020 IEEE International Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1689–1696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [75] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Fortune, “Voronoi diagrams and delaunay triangulations,” Computing in Euclidean geometry, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 225–265, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [76] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Boissonnat and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yvinec, Algorithmic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cambridge university press, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [77] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Attali, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Boissonnat, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lieutier, “Complexity of the delaunay triangulation of points on surfaces the smooth case,” in Proceedings of the nineteenth annual symposium on Computational Geometry, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 201–210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [78] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Forster, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Carlone, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Dellaert, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Scaramuzza, “On-manifold preintegration for real-time visual–inertial odometry,” IEEE Transactions on Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1–21, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [79] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Pan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Gao, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shen, “Raptor: Robust and perception- aware trajectory replanning for quadrotor fast flight,” IEEE Transactions on Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1992–2009, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [80] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Chen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Shen, “Fuel: Fast uav exploration using incremental frontier structure and hierarchical planning,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 779–786, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [81] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Geiger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lenz, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Urtasun, “Are we ready for autonomous driving?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the kitti vision benchmark suite,” in 2012 IEEE conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' IEEE, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3354–3361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [82] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Carlevaris-Bianco, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Ushani, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Eustice, “University of michigan north campus long-term vision and lidar dataset,” The International Journal of Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1023– 1035, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [83] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nguyen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yuan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lyu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Nguyen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Xie, “Ntu viral: A visual-inertial-ranging-lidar dataset, from an aerial vehicle viewpoint,” The International Journal of Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 41, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 270–280, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [84] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Cernea, “OpenMVS: Multi-view stereo reconstruction library,” 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Available: https://cdcseacave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='io/openMVS [85] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Yuan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Hong, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “Std: Stable triangle descriptor for 3d place recognition,” arXiv preprint arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='12435, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' [86] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Lin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' Zhang, “A fast, complete, point cloud based loop closure for lidar odometry and mapping,” arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='11811, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1 Supplementary Material: An additional trial of our lossless texture reconstruction based on ImMesh Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' 1: In this trial, we collected the data by flying over islands in an “B”-like trajectory, as the blue path shown in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (b1) and (b2) show the side view and bird view of our reconstructed triangle mesh, where the mesh is colored by their altitude w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' the sea level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (a) show the overview of our lossless texture reconstruction result, where we use the estimated camera poses (the yellow frustums) of R3LIVE++ for texturing the mesh with the collected images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' The entire texture reconstruction of this 578 s sequence only costs 1210 s (on Intel i9-10900), with 583 s for ImMesh, 587 s for R3LIVE++, and 40 s for texturing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' To see the detailed reconstruction process of the scene, please refer to our video on YouTube: youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='be/pzT2fMwz428?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content='t=892.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} +page_content=' (a) Height Height (b1) (b2) 15 m 15 m 30 m 45' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/g9E4T4oBgHgl3EQfrQ0j/content/2301.05206v1.pdf'} diff --git a/jNAzT4oBgHgl3EQf4_5S/content/2301.01852v1.pdf b/jNAzT4oBgHgl3EQf4_5S/content/2301.01852v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..756e318e77b301baf18cf8b5e005fddd2a8f36ee --- /dev/null +++ b/jNAzT4oBgHgl3EQf4_5S/content/2301.01852v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8b9aaa0c2980face28b66f5b4cdfd5d41ffe73cdc2b0b7cde33d45a6e62a0790 +size 2021772 diff --git a/lNFAT4oBgHgl3EQfbh0y/vector_store/index.pkl b/lNFAT4oBgHgl3EQfbh0y/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..eeef020d44e98fe0c4a279a5218c5c3de8cb8d2b --- /dev/null +++ b/lNFAT4oBgHgl3EQfbh0y/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5364aa0f6e700f5efa24c2c28b6604dfc6f5d43d2cf350df2fafc6fd135166f5 +size 65874 diff --git a/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/2301.00686v1.pdf.txt b/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/2301.00686v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..50448042c919a77b988928ca56d83c0d89afae9a --- /dev/null +++ b/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/2301.00686v1.pdf.txt @@ -0,0 +1,1420 @@ +Supersymmetric algebra of the massive supermembrane +M.P. Garcia del Moral∗ +´Area de F´ısica, Departamento de Qu´ımica, +Universidad de la Rioja, La Rioja 26006, Spain +and +Departamento de F´ısica, +Universidad de Antofagasta, Aptdo 02800, Chile. +P. Le´on† and A. Restuccia‡ +Departamento de F´ısica, Universidad de Antofagasta, Aptdo 02800, Chile. +In this paper, we obtain the explicit expression of the supersymmetric algebra associated with the +recently proposed massive supermembrane including all surface terms. We formulate the theory as +the limit of a supermembrane on a genus-two compact Riemann surface when one of the handles +becomes a string attached to a torus. The formulation reduces to a supermembrane on a punctured +torus with a ”string spike” (in the sense of [1]), attached to it. In this limit, we identify all surface +terms of the algebra and give the explicit expression of the Hamiltonian in agreement with the +previous formulation of it. The symmetry under area preserving diffeomorphisms, connected and +nonconnected to the identity, is also discussed. +Only parabolic Sl(2, Z) discrete symmetries are +preserved. +Keywords: Supermembrane, Supersymmetric algebra, singularities +I. +INTRODUCTION +Recently, new aspects of M2-brane theory in D=11 di- +mensions have been developed. In [2] using the Nicolai +map a perturbative quantization approach have been pro- +posed. In [3] the existence and uniqueness of the ground +state of the theory on the valleys of the theory have been +obtained, In [4–7] new sectors of the theory formulated on +different backgrounds characterized by topological condi- +tions have been analyzed. In distinction to the formula- +tions on a Minkowski target space these supersymmetric +sectors of the M2-brane have discrete spectrum. They +correspond to supermembranes with a topological con- +dition associated with the presence of 2-form worldvol- +ume fluxes induced by either the presence of a topological +central charge condition [4], the presence of supergravity +constant and quantized three-form [6], or either on a tar- +get space with G4 content, as the supermembrane on a +pp-wave [5] whose matrix model corresponds to [8], or +more recently the formulation of a massive supermem- +brane [7].This massive supermembrane corresponds to a +supermembrane theory formulated on a M9 ×LCD back- +ground, where M9 is a nine dimensional Minkowski space +and LCD is a Light Cone Diagram, a two dimensional flat +strip with identifications and with prescribed segments +whose curvature becomes infinite at some points. This, +surface only has one (non-trivial) compact dimension and +therefore the supermembrane in this background exhibit +ten non-compact dimensions. Moreover, the theory has +nontrivial mass terms not present on the supermembrane +theory compactified on a circle that, together with the +rest of the structure of the potential render the spectrum +of the regularized theory to be discrete. The goal of this +paper is to characterize the susy algebra including all +the boundary terms. This may give light on the role of +∗ m-pilar.garciam@unirioja.es; maria.garciadelmoral@uantof.cl +† pablo.leon@ua.cl +‡ alvaro.restuccia@uantof.cl +the singularities in the structure of the constraints that +will be useful to obtain the string theory associated with +this sector. Furthermore, the analysis of the singulari- +ties allows to characterize the dimensions of the sources +coupled to the M2 -brane, as for the example the M9- +brane discussed in [9]. The supermembrane only admits +backgrounds that allow a consistent coupling to the 11D +supergravity and its reductions. Hence, the algebra may +give light to the supergravity background to which this +massive supermembrane couples. The study of algebras +and their deformations, and consequently their symme- +tries, have also been used in the literature to obtain ki- +netic terms of their associated supergravity Lagrangian +densities. Although we will no proceed in this direction, +this is another possible application of the results of this +work. +The paper is structured as follows: In section 2, we re- +call basic aspects of the supermembrane theory formula- +tion and its Hamiltonian in the case of a supermembrane +with a topological central charge condition. In section +3, we summarize the main properties of the Light Cone +Diagram formulation that will be needed for the compu- +tations. In section 3, we present a new formulation of the +massive supermembrane obtained in [7] which directly in- +corporates all the boundary terms of the formulation. In +section 5, we obtain the supersymmetric transformation +and in section 6, we get the supersymmetric algebra of +supercharges. In section 7, we discuss other fundamental +symmetry , that is the area preserving diffeomorphisms, +in order to characterize completely the symmetries of the +theory. In section 8, we present ours conclusions. +II. +THE SUPERMEMBRANE ACTION IN THE +LIGHT CONE GAUGE +The supermembrane was originally introduced in [10]. +Its formulation in the Light Cone Gauge (LCG) on a +Minkowski target space was obtained [11]. In this section +we will briefly review some of those results in [11] and we +will present the supermembrane action in the light cone +arXiv:2301.00686v1 [hep-th] 2 Jan 2023 + +2 +gauge on M9 × T 2. The action of the supermembrane in +a Minkowski space-time is given by +S = −TM2 +� +R×Σ +dξ3 +�√−g + εuvw ¯˜ΨΓµν∂w ˜Ψ +× +�1 +2∂u ˜Xµ(∂v ˜Xν + ¯˜ΨΓν∂v ˜Ψ) + 1 +6 +¯˜ΨΓµ∂u ˜Ψ¯˜ΨΓν∂v ˜Ψ +�� +, +(1) +where TM2 is the M2-brane tension, Γµ are the gamma +matrix in eleven dimensions, ˜Xµ (µ, ν = 0, .., 10) are the +embedding maps of the supermembrane, θ is a 32 com- +ponent Majorana spinor and Σ is a compact Riemann +surface. All the fields are functions of the world-volume +coordinates ξu (u, v, w = 0, 1, 2) and guv are the compo- +nents of the world-volume induced metric, this is +guv = (∂u ˜Xµ + ¯˜ΨΓµ∂u ˜Ψ)(∂v ˜Xν + ¯˜ΨΓν∂v ˜Ψ)ηµν. (2) +Now we can use the light cone coordinates +˜Xµ = +(X+, X−, ˜XM) with M, N = 1, .., 9 +X± = +1 +√ +2( ˜X10 ± ˜X0), +Γ± = +1 +√ +2(Γ10 ± Γ0), +(3) +and, decomposing ξu = (t, σr) with r = 1, 2, one can fix +the LCG as follows, +X+ = t, +Γ+ ˜Ψ = 0. +(4) +Thus, we can write the Lagrangian density can be written +as 1 +L = −TM2( +� +¯g∆ + ϵrs∂r ˜XM ¯˜ΨΓ−ΓM∂s ˜Ψ), +(5) +where +¯grs = ∂r ˜XM∂s ˜XM, +ur = g0r = ∂r ˜X− + ∂t ˜XM∂r ˜XM, +g00 = 2∂t ˜XM∂t ˜XM + 2¯˜ΨΓ−∂0 ˜Ψ, +and ¯g = det(¯grs), ∆ = −g00 + ur¯grsus. Then, the conju- +gate momenta can be written as +˜P− = TM2 +� +¯g +∆, +˜P M = ˜P−(∂0 ˜XM − urgrs∂s ˜XM), +˜S = − ˜P−Γ− ˜Ψ. +Thus, the Hamiltonian density is given by +H = +˜P +2 + T 2 +M2¯g +2 ˜P− +− TM2ϵrs∂r ˜XM ¯˜ΨΓ−ΓM∂s ˜Ψ, +(6) +1 We are using ε0rs = −ϵrs +subject to the following constraints +˜P∂r ˜X + ˜P−∂r ˜X− + ¯˜SΓ− ˜Ψ = 0, +˜S + TM2 +� +¯g +∆Γ− ˜Ψ = 0. +(7) +Now, we can use the area preserving diffeomorphims to +set the gauge ˜P− = P 0 +− +√ +W, where +� +˜W is a scalar den- +sity satisfying +� +Σ +� +˜W = 1. +(8) +This allows to introduce the Lie bracket +{·, ·} = +ϵrs +� +˜W +∂r · ∂s · . +(9) +The supermembrane Lagrangian density can be writ- +ten in a way that is explicitly invariant under area pre- +serving diffeomorphims (see [11]). This requires the in- +troduction of a gauge field ω related to time-dependent +reparametrizations of the world-volume. This will be +L +P + +0 +� +˜W += 1 +2(D0 ˜XM)2 + ¯˜ΨΓ− ˜Ψ − T 2 +M2 +4P + +0 +{ ˜XM, ˜XN}2 ++ TM2 +P + +0 +¯˜ΨΓ−Γa{ ˜XM, ˜Ψ} + D0 ˜X−, +(10) +where +D0• = ∂t • −{ω, •}, +{•, •} = ϵrs +√ +W +∂r • ∂s • . (11) +Furthermore, we can now solve (7) for ˜X−, this is +∂r ˜X− = − +1 +P 0 +− +� +˜W +(˜P∂r ˜X + ¯˜SΓ−∂r ˜Ψ). +(12) +In order to ensure the existence of a solution for ˜X−, one +must impose +φ = d(d ˜X−) = d +� +1 +� +˜W +(˜Pd ˜X + ¯˜SΓ−d˜Ψ) +� += 0 (13) +ϕk = +� +Ck +d ˜X− = +� +Ck +1 +� +˜W +(˜Pd ˜X + ¯˜SΓ−d˜Ψ) = 0,(14) +where Ck (k = 1, .., 2g for g > 1)are the homology basis +of one-cycles over Σ. They correspond to the local and +global first class constraints associated with the residual +symmetry of Area Preserving Diffeomorphisms (APD). +Now it is possible to write the Hamiltonian of the the- +ory as, +H = +1 +2P 0 +− +� +Σ +d2σ +� +˜W +� � +˜P +� +˜W +�2 ++ T 2 +M2 +2 +{ ˜XM, ˜XN}2 +− 2TM2P 0 +− ¯˜ΨΓ−ΓM{ ˜XM, ˜Ψ} +� +. +(15) + +3 +Now one can compactify the M2-brane Hamiltonian +on M9 × T 2 and take as a base manifold a regular genus- +two Riemann surface Σ2. Thus, due to the compact di- +mensions, the embedding maps can be decomposed as +˜XM = ( ˜Xm, ˜Xr), with m = 1, ..., 7 labelling the noncom- +pact dimensions and r = 1, 2 the compact ones associated +with the 2-torus. The ˜Xm maps Σ2 to the transverse sub- +space of M9 while ˜Xr maps Σ2 to the target T2. +Hence, the Hamiltonian of the supermembrane can be +written as +H = +1 +2P 0 +− +� +Σ2 +d2σ +� +˜W +� � ˜Pm +� +˜W +�2 ++ +� +˜Pr +� +˜W +�2 ++ T 2 +M2 +2 +{ ˜Xm, ˜Xn}2 + T 2 +M2{ ˜Xm, ˜Xr}2 + T 2 +M2 +2 +{ ˜Xr, ˜Xs}2 +− 2TM2P 0 +− ¯˜ΨΓ−Γm{ ˜Xm, ˜Ψ} − 2TM2P 0 +− ¯˜ΨΓ−Γr{ ˜Xr, ˜Ψ} +� +, +(16) +subject now to the following five APD constraints +φ = d +� +1 +� +˜W +( ˜Pmd ˜Xm + ˜Prd ˜Xr + ¯˜SΓ−d˜Ψ) +� += 0, +(17) +ϕk = +� +Ck +1 +� +˜W +( ˜Pmd ˜Xm + ˜Prd ˜Xr + ¯˜SΓ−d˜Ψ) = 0, (18) +where k = 1, ..., 4. +We will use these expressions in the subsequent sections +of the paper. +III. +PARAMETRIZATION OF THE TWICE +PUNCTURED TORUS +In this section we recall some useful results about the +relation between the Light Cone diagram (LCD) and the +torus with two punctures Σ1,2 (see figure (1)) needed to +describe the massive supermembrane formulation. The +Light Cone diagram is a two dimensional flat strip with +identifications and with prescribed segments whose cur- +vature becomes infinite at some points. This results are +the base of the massive supermembrane formulation [7] +and they will be useful in the next sections. The relation +between these two surfaces is given by the Mandelstam +map (see [12, 13]) +F(z) = α ln +�Θ1(z − Z1|τ) +Θ1(z − Z2|τ) +� +− 2πiαIm(Z1 − Z2) +Imτ +(z − z0), +(19) +where Θ1(z, τ) are the Jacobi functions and Zr with +r = 1, 2 are the positions of the punctures in a complex +coordinates over the torus. The set of parameters neces- +sary to characterize the torus with two punctures are the +Teichm¨uller parameter, τ, and the positions of the Punc- +tures, Zr. On the twice punctured torus the coordinate +system z is defined in terms of the holomorphic one-form +dz satisfying +Thus, we can decompose dz as +dz = d ˆX1 + τd ˆX2, +with +� +Ck +d ˆXr = δr +k, +(20) +where d ˆXr is a set of real normalized forms over the reg- +ular torus. +On the other hand, the set of parameters that describe +the LCD are the external momenta α, the internal mo- +menta βr, the interaction time T, with and the twist +angles θr. +Then in order to complete the equivalence +between the two surfaces, (see figure 1.), the following +relation between both sets of parameter is required +2πi(Z1 − Z2) = (θ1 + θ2)β1 − αθ2 − 2πiβ1τ. +(21) +It is useful to decompose the Mandelstam map in terms +of its real and imaginary parts, that is F = G + iH. The +function G is single valued, but dG is harmonic, since it +has poles at the punctures. The function H is multivalued +and dH is harmonic.The behavior of each function near +the punctures is given by +G ∼ (−1)r+1α ln |z − Zr|, +(22) +H ∼ (−1)r+1αϕ, +with +ϕ ∈ (0, 2π) (r = 1, 2).(23) +On the other hand, near the zeros of dF,denoted as Pa, +the functions G and H can be written as +G(z) − G(Pa) ∼ 1 +2Re(D(Pa)(z − Pa)2), +(24) +H(z) − H(Pa) ∼ 1 +2Im(D(Pa)(z − Pa)2), +(25) +where +D(Pa) = +2 +� +r=1 +(−1)r+1 +�∂2 +zΘ1(Pa − zr, τ) +Θ1(Pa − zr, τ) +− +�∂zΘ1(Pa − zr, τ) +Θ1(Pa − zr, τ) +�2 � +. +Finally, we recall some properties of the functions K and +H that will be useful in the next section, +G(z + 1) − G(z) = G(z + τ) − G(z) = 0 +(26) +H(z + 1) − H(z) = 2παIm(Z2 − Z1) +Im(τ) +, +(27) +H(z + τ) − H(z) = 2παIm((Z2 − Z1)¯τ) +Im(τ) +. +(28) +IV. +MASSIVE SUPERMEMBRANE +In this section, we present a new formulation of the +massive supermembrane and its connection with the for- +mulation found in [7]. +Specifically, in order to make +clearer the surface terms that appear in the supersym- +metric algebra, we use a different approach than +[7]. +Instead of considering the supermembrane formulated in +M9 × LCD on a twice punctured torus as the base mani- +fold, we will start with the M2-brane on a compact genus- +two Riemann surface Σ2 as the base manifold in M9 ×T 2 + +4 +FIG. 1. The torus with two punctures and the one loop interaction string diagram with one incoming/outgoing string. The +Mandelstam map send the punctures over the torus to ±∞ in the LCD. +FIG. 2. (a) The genus two regular Riemann surface Σ2. (b) A deformation of Σ2. (c) The surface ˜Σ1,2 obtained by taking one +of the radii of Σ2 tending to zero. This correspond to a singular T 2 with a string attached to it. +as the target space. +In order to establish a connection +with the formulation of the massive supermembrane [7], +we will take a specific limit to deform Σ2 as described +in the figure (2). +That is, we will assume that one of +the radii of the handles of the genus two surface tends to +zero. As a result, we can expand the maps Xm, Xr and +Ψ in a Fourier series and keep only the order zero of the +variable associated with the small radius. Thus, under +these considerations, the supermembrane maps will de- +pend only on the coordinate along the handle (see figure +(2)-(b)). In this way, we get a string-like configuration +like the ones described in [14]. Thus, we will end up with +a surface, that we will denote ˜Σ1,2, which is a twice punc- +tured torus Σ1,2 with a string attached to the punctures +(see figure (2)-(c)). Then we will also deform the target +T 2 to a LCD surface. Thus, the metric that we shall +define over the LCD on the target is given by +ds2 = l2d ˆG2 + dH2 = dK2 + α2d ˆH2, +(29) +where ˆH = H/α, +ˆG = G/α and l is constant with +length units. +Now we can describe the dependence of the M2-brane +fields in two regions. The first one is the definition of the +maps on Σ1,2 and the second one is the string attached +to it that we shall denote as γ2. Then, given a coordinate +system, z (given in the previous section), over Σ1,2 and +defining as u the coordinate associated to γ2 we can write +( ˜Xm, ˜Ψ) = +� +(Xm(t, z, ¯z), Ψ(t, z, ¯z)) over +Σ1,2 +(Y m(t, u), Θ(t, u)) +over +γ2 +,(30) +and +˜Xr = +� +XK(t, z, ¯z)δr +1 + XH(t, z, ¯z)δr +2 over +Σ1,2 +Y r(t, u) +over +γ2 +.(31) +The maps XK and XH are defined as in [7], i.e, +XK = K + AK, +XH = H + AH, +(32) +where m is an integer and the 1-forms dAK, dAH are +exact over Σ1,2 +Under all this consideration, as discussed in [1, 14], the +string we are considering does not change the superme- +mbrane energy and therefore we can write +H = +� +Σ2→˜Σ1,2 +H = +� +Σ1,2 +H. +(33) +The string-like configuration that we are considering +here has no M2-brane dynamics associated with it. This +is so, because it does not have any contribution to the +Hamiltonian of the theory. Thus, without losing general- +ity, we can impose +Y m +s (u, t) = const, +Y r +s (u, t) = const, +Θs(u, t) = const, +(34) +which implies +Xm +���� +Z2 +Z1 += Ψ +���� +Z2 +Z1 += 0. +(35) +On the other hand, since the Y r +s (u, t) are single value +functions, it is reasonable to consider that AK and AH +are continuous functions of Y r. Consequently, + +(a) +(b) +(c)5 +AK +���� +Z2 +Z1 += AH +���� +Z2 +Z1 += 0. +(36) +At this point we can follow the same steps presented +in [7] to analyse the Hamiltonian over Σ1,2. Specifically, +we shall define the world-volume metric, over Σ1,2, as +√ +W = 1 +4π ϵrs∂r ˆK∂s ˆH, +(37) +where K ≡ tanh ˆG. Then we can fix the gauge +{K, AK} + m{H, AH} = 0. +(38) +In order to deal with the singular behavior of the metric +at the punctures and zeros we shall cut the fundamental +region of Σ1,2, that we will call Σ1,2, through a closed +curve that circumvents the two punctures, and the zeros +with a radius ϵ and touch a point O ∈ ∂Σ1,2, see figure +3 (see [15]). We shall denote as Cr the curves around +the punctures, Dr the curves around the zeros, and as Ij, +with j = 1, .., 4, to all the curves in between. Following +the discussion presented in [7], it is clear that the curves +Ij can be chosen as curves H = cte. The we will denote +as Σ′ the resulting region after cutting Σ1,2. +Under all these considerations, the Hamiltonian of the +theory can be written as (see [7] for more details) +H = (lαTM2m)2 +2P + +0 ++ +1 +2P + +0 +lim +ϵ→0 +� +Σ′ dσ2√ +W +�� Pm +√ +W +�2 ++ +� PK +√ +W +�2 ++ +� PH +√ +W +�2 ++ T 2 +M2 +�1 +2{Xm, Xn}2 ++ 2{Xm, K}{Xm, AK} + m2{Xm, H}2 + {Xm, K}2 ++ {Xm, AK}2 + {Xm, AH}2 + m2{H, AK}2 ++ 2m{Xm, H}{Xm, AH} + 2m{H, AK}{AH, AK} ++ {K, AK}2 + 2{AH, K}{AH, AK} + {AH, AK}2 ++ {K, AH}2 + {H, AH}2 +� +− 2P + +0 TM2(¯ΨΓ−Γm{Xm, Ψ} ++ ¯ΨΓ−ΓK{AK, Ψ} + ¯ΨΓ−ΓH{AH, Ψ} + ¯ΨΓ−ΓK{K, Ψ} ++ ¯ΨΓ−ΓH{H, Ψ}) +� +. +(39) +By defining +f ≡ +� PK +√ +W +dXK + PH +√ +W +dXH + Pm +√ +W +dXm + ¯ΨΓ−dΨ +� +, let’s now us discuss the constraints after deforming Σ2. +First, we have the local APD constraint given by +df = 0. +(40) +On the other hand we have also four global constraints, +the first two are the associated with the homology basis of +cycles defined over the regular torus (see figure (4-(a))), +i.e +ζ1 ≡ +� +a +f = 0, +and, +ζ2 ≡ +� +b +f = 0 +(41) +We have another constraint associated to the singularities +ζ3 ≡ +� +C1 +f = 0. +(42) +This constraint arises from the homology curve of Σ2 +around the handle, whose radius was send to zero to +get the string-like configuration. The final constraint is +the one associated with the homology curve along the +deformed handle of σ2, shown in figure 4, which is still +present after deforming Σ2 into ˜Σ1,2. +ζ4 ≡ +� +y +f = 0. +(43) +Notice, that we could not write ζ4 directly in terms of +K, H. +This is because the curve γ is defined in both, +Σ1,2 and in the string attached in the punctures. Thus, +it is convenient to separate the curve γ into two pieces +((see figure (4-(b))) and we will denoted as γ1 and γ2. +The curve γ1 is the part of γ defined over Σ1,2 and γ2 +corresponds to the string with end points at the punc- +tures. Now, because of (34), we can write +ζ4 = +� +γ1 +f = 0. +(44) +In the following we will list some of the features of the +massive supermembrane Hamiltonian. From Eq. (39) it +can be seen that it is very different from a standard com- +pactification of the M2-brane on a S1. Firstly,it contains +a mass term associated with the nontrivial topology of +the LCD on the target space given by +lim +ϵ→0 +� +Σ′ dK ∧ d ˆH α m2 +4 +{K, ˆH}2 = 2παl m2 +(45) +This term can be interpreted as a as the uplift to ten non +compact dimensions of the central charge condition pro- +posed in [16]. In second place, it possesses non vanishing +mass terms associated with the dynamics fields Xm,AK +and AH, these are +(∂KXm)2 + ( ∂ ˆ +HXm)2 ̸= 0, +(∂KAK)2 + (∂ ˆ +HAK)2 ̸= 0, +(∂KAH)2 + (∂ ˆ +HAH)2 ̸= 0. +Thus, the fermionic potential is dominated by the bosonic +potential due to these non-vanishing quadratic contribu- +tion to the Hamiltonian. This fact, and together with +the structure of the rest of the potential, ensure that the +Hamiltonian satisfy the discreteness sufficient condition +found in [17], as formerly shown in [7]. +Finally, we would to mention that taking as a starting +point a compact Riemann surface of genus two, is the +simplest case, but it is not the only possibility to find +massive terms in the Hamiltonian of the theory. + +6 +FIG. 3. The region Σ′ obtained by cutting Σ1,2 through the curves C1,C2 and I. The path obtained by the union of the curves +C1,I,C2 and I−1 is denoted by c +FIG. 4. (a) Nontrivial cycles over ˜Σ1,2. (b) The curve γ and his decomposition into the curves γ1 and γ2. +V. +SUPERSYMMETRIC TRANSFORMATIONS +In this section, we will analyze the supersymmetry of +our formulation of the massive supermembrane. Thus, we +shall follow the same procedure presented in the previous +section, that is, we will begin with the M2-brane over +a regular compact genus two Riemann surface. In gen- +eral, the supermembrane action (in the light cone gauge) +is invariant under the following supersymmetric transfor- +mations originally found in [11], +δ ˜XM = −2¯ηΓMΨ, +(46) +δΨ = 1 +2Γ+(D0 ˜XMΓM + Γ−)η + TM2 +4P + +0 +{ ˜XM, XN}Γ+ΓMNη +(47) +δω = −2TM2 +P + +0 +¯ηΨ, +(48) +provided the following boundary terms are equal to zero +P + +0 δL +TM2 += − +� +R +dt +� +Σ +d +� +¯ΨΓ−ΓMd ˜XMδΨ + 2¯ΨΓMΓ−η ++ 2¯ΨΓMNη∂t ˜XMdXN − 2 +3(¯ΨΓ−dΨ¯ηΨ +− ¯ηΓMΨ¯ΨΓ−ΓMdΨ) +� ++ lim +ϵ→0 +� +Σ′ d2σ +� +R +dt∂t +�√ +W ¯ΨΓ−∂Ψ − 2 +√ +W ¯ΨΓ−η ++ +√ +W ¯ΨΓMNη{ ˜XM, XN} +� += 0, +(49) +where η is a constant spinor. +Notice that, in this surface term, only the derivatives of +the maps X are displayed, which are single-valued. Thus, +since Ψ is also a single-valued and we are considering a +compact regular Riemann surface as a base manifold, this +surface term is identical to zero. Moreover, this allows +to conclude that, at least from this surface term, there +are not restrictions to the supersymmetric parameter, η, +when we take the limit Σ2 → ˜Σ1,2. +On the other hand, in [7], it was shown that in order +to preserve the topological term given in equation (45) +and the mass terms in the Hamiltonian that leads to the +good spectral properties of the Hamiltonian, we need to +impose the following condition +Γ+ +� +Γ− + 1 +2ΓKH +� +η = 0, +(50) +which implies that half of the supersymmetry is broken, +in distinction with the case of a supermembrane on a +torus. +VI. +SUPERSYMMETRIC ALGEBRA +Following with our analysis of the supersymmetric +properties of the massive supermembrane, in this section +we shall present the supersymmetric algebra of the mas- +sive supermembrane. Specifically, we will compute the +supersymmetric charges and their Dirac brackets. As be- +fore, we will begin with the formation of the M2-brane +over Σ2. From (15) we can derive the supercharge density +associated with the transformations (46-48) + +[_b +3 +Z2 +14 +P2 +D2 +b-1 +b +D1 +C1 +P1 +b +Z1 +0 +12 +5 +a +(a) +(b) +(c)Y2 +a +b +(a) +(b)7 +J0 = P + +0 +� +˜W +� +2(∂0 ˜XMΓM + Γ−) ++ TM2 +P + +0 +{ ˜XM, ˜XN}ΓMN +� +Ψ. +(51) +Thus the supersymmetric charges, defined as +Q± = 1 +2Γ±Γ∓Q, +Q = +� +Σ2 +dσ2J0, +(52) +can be written as +Q+ = +� +Σ2 +dσ2[2 ˜PMΓM + TM2 +� +˜W{ ˜XM, ˜XN}ΓMN]˜Ψ, +(53) +Q− = 2P + +0 Γ− +� +Σ2 +dσ2� +˜W ˜Ψ. +(54) +The only non trivial Dirac’s brackets in our case are given +by +{ ˜XM(σ), PN(σ′)}D.B = δM +N δ2(σ − σ′), +(55) +{Ψα(σ), Ψβ(σ′)}D.B = +1 +4 +� +˜WP + +0 +(Γ+)α +βδ2(σ − σ′), (56) +where we are considering that σ and σ′ are the coordi- +nates of two points inside Σ2. With these expressions and +using the Gamma matrices properties we get +{Q− +α , Q− +β }D.B = −2P + +0 (Γ+)αβ, +(57) +{Q+ +α, Q− +β }D.B = −(ΓMΓ+Γ−)αβP M +0 +− TM2 +2 +(ΓMNΓ+Γ−)αβ +� +Σ2 +dσ2� +˜W{ ˜XM, ˜XN}, +(58) +{Q+ +α, Q+ +β }D.B = 2(Γ+)αβH +− 2TM2(Γ+ΓM)αβ +� +Σ2 +dσ2� +˜W{ ˜X−, ˜XM}. +(59) +Notice that this is the most general form of the supersym- +metric algebra for the supermembrane found in [18, 19]. +Now, we can analyse the surface terms in detail. How- +ever, since we are considering the limit Σ2 → ˜Σ1,2, the +surface term in the last two terms leads to several dif- +ferences. This is due to the two singular points resulting +from the deformation of Σ2. From the general superal- +gebra in eleven dimensions (see for example [20, 21]) it +can be seem that the surface terms can be interpreted in +terms of tensorial charges. Specifically, the surface term +in (58) and (59) are related with the charges ZMN and +Z+M, respectively. +As is discussed in [22], the 2-form +ZMN gives a 2-brane charge and it has been conjectured +that the dual of the from Z+M gives a 9-brane charge. +Now, let us analyse in detail the surface terms begin- +ning with the one in (58). In the limit Σ2 → ˜Σ1,2 it can +be shown that +� +Σ2 +dσ2� +˜W{ ˜XM, ˜XN} → +� +˜Σ1,2 +dσ2√ +W{XM, XN}. +(60) +Thus, following the same arguments of section IV , we +can also write +� +˜Σ1,2 +dσ2√ +W{XM, XN} = +� +Σ1,2 +dσ2√ +W{XM, XN} += lim +ϵ→0 +� +Σ′ dσ2√ +W{XM, XN}. +The only non-trivial contributions of this term are given +by +lim +ϵ→0 +� +Σ′ dσ2√ +W{XM, XN} = lα +4π lim +ϵ→0 +� +Σ′[δM +K (1 +2d ˆK ∧ d ˆH ++ d ˆ +AK ∧ d ˆH) + δM +m d ˆ +Xm ∧ d ˆH]δN +H − (M → N). +This can be simplified to obtain +lim +ϵ→0 +� +Σ′ dσ2√ +W{XM, XN} += lα +�1 +2δM +K + +� +δM +m +� +γ1 +dXm + δM +K +� +γ1 +dAK +�� +δN +H − (M → N). +(61) +Now, we can a analyse the surface term in (59). Fol- +lowing the same idea of the previous case, we can write +(in the limit Σ2 → ˜Σ1,2) +� +˜Σ1,2 +dσ2√ +W{X−, XM} = +� +Σ1,2 +dσ2√ +W{X−, XM}, +which leads to +� +Σ′ dσ2√ +W{X−, XM} = +� +lim +ϵ→0 +� +Σ′ XMφ ++ ζ2 +� +a +dXM − ζ1 +� +b +dXM + lα +4π lim +ϵ→0 +� � +r +� � +Cr ++ +� +Dr +� ++ +� +u +� � +Iu ++ +� +Iu−1 +�� +XMdX− +� +. +(62) +Since XMdX− is well defined at Pr, the limit ϵ → 0 of the +integral over Dr are equal to zero. The integral around +the punctures leads to +lim +ϵ→0 +� +r +� +Cr +XMdX− = − +� +γ1 +dXM +� +C1 +dX− = − +� +γ1 +dXMζ3. +Moreover, it can be proved that +� +u +� � +Iu ++ +� +Iu−1 +�� +XMdX− = −2παδM +H +� +γ1 +dX−. +Thus, the final form of the massive supermembrane +algebra is given by + +8 +{Q− +α , Q− +β }D.B = −2P + +0 (Γ+)αβ, +(63) +{Q+ +α, Q− +β }D.B = −(ΓMΓ+Γ−)αβP M +0 +− Tαl +2 (ΓMHΓ+Γ−)αβδM +K , +(64) +{Q+ +α, Q+ +β }D.B = 2(Γ+)αβH − 2T(Γ+ΓM)αβ +� +lim +ϵ→0 +� +Σ′ XMφ1 ++ 2παδM +H +Im(τ) +� +Im(Z2 − Z1)ζ2 − Im((Z2 − Z1)¯τ)ζ1 +� +− 2 +� +lδM +K ζ3 + παδM +H ζ4 +�� +. +(65) +At this point, the following comments are in order: +• In [7], the massive supermembrane is interpreted as +the uplift to ten non compact dimensions of the su- +permembrane with C± fluxes and parabolic mon- +odromy. Then, we can interpret (63)-(65) as the +generalisation of the M2-brane super algebra when +the world volume of the theory is a twice punctured +torus. +• In (64), we get a constant term which is analo- +gous to the fluxes/central charge contribution to +the super algebra presented in [23]. +However, in +the present case, this term is not proportional to +an integer. +• We showed that the surface term in (65), can be +written in terms of the constraints of the theory. +The terms related with the constraints are analo- +gous to the case without punctures (see [23]). How- +ever, in our case, we have two extra global con- +straints related with the punctures. Moreover, the +multiplicative factors of each are related to the +moduli of the twice punctured torus, while in [23] +are the winding numbers of the theory. +VII. +AREA PRESERVING DIFFEOMORPHISMS +Another relevant symmetry of the supermembrane the- +ory is the invariance under APD. In this section, we will +discuss the realization of this symmetry in the massive +supermembrane formulation. +As discussed in previous +sections, the Hamiltonian of the supermembrane on ˜Σ1,2 +is the same as in Σ1,2. Thus we will restrict ourselves to +the analysis of the APD for the Hamiltonian given by (39) +. Under APD connected to the identity, any functional +O of the canonical variables transform as +δξO = +� +O, < dξ ∧ +� PM +√ +W +dXM + ¯ΨΓ−dΨ +� +> +� +P.B. +, +(66) +where, in this case corresponds to +< dξ ∧ +� PM +√ +W +dXM + ¯ΨΓ−dΨ +� +> += lim +ϵ→0 +� +Σ′ +� PM +√ +W +dXM + ¯ΨΓ−dΨ +� +. +(67) +In these expressions, ξ, is the infinitesimal parameter of +the transformation. +This parameter defines globally a +closed 1-form dξ. +Thus, ξ is globally defined over Σ′, +that is, the dξ is an exact form. If ξ is not globally de- +fined, then dξ is a closed but not exact form. It can be +verified that the following APD transformations holds for +the massive supermembrane +δξXM = {ξ, XM}, +δξPM = +√ +W +� +ξ, PM +√ +W +� +, +δξΨ = {ξ, Ψ}. +(68) +They are the same as the ones found in [11] and [24] +describing the the case of the supermembrane on a flat +Minkowski spacetime. They also hold for the supermem- +brane with central charge [4]. Now, in order to determine +the symmetries of the massive supermembrane under area +preserving diffeomorphims non connected to the identity, +we shall start by recalling the non punctured case. For +these transformations, the homology basis defined a two +torus without punctures transform as +d ˆXi → Si +jd ˆXj, +S ∈ Sl(2, Z), +(69) +while +τ → aτ + b +cτ + d, +� +a b +c d +� +∈ Sl(2, Z). +(70) +Thus, from (19), it can be found that, under this trans- +formations, the Mandelstam map transforms as +F +� +z +cτ + d, +Z1 +cτ + d, +Z2 +cτ + d, aτ + b +cτ + d +� += F(z, Z1, Z2, τ) + +iπc +cτ + d(Z1 +1 − Z2 +2), (71) +implying that dF (and therefore dG and dH) is invariant +under APD conected and non connected to the identity. +However, the 1-form dK is invariant under the APD con- +nected to the identity but it may not be invariant under +the not connected to the identity transformations. Indeed +we get +dK → +1 − K2 +0 +(1 + K0K)2 dK, +(72) +where +K0 = tanh +� +Re +� iπc +cτ + d(Z1 +1 − Z2 +2) +�� +. +(73) +It is clear that the massive supermembrane action will +be invariant under APD non connected to the identity as +long as dK is invariant under this transformations. Thus, +the only possible transformation in Sl(2, Z) that satisfy +this requirement is when c = 0. In other words, the mas- +sive supermembrane is invariant under APD connected to +the identity, but it is only invariant under the parabolic +subgroup of Sl(2, Z), transforming isotopy classes of not +connected to the identity APD. The massive supermem- +brane discussed in this work (see also [7]), represents an +explicit realization of Hull’s conjecture about the origin, + +9 +in M-theory, of Roman’s supergravity in terms oftorus +bundles with parabolic Sl(2, Z) monodromy. +In [7], it was presented the relation between the mon- +odromies defined over a twice punctured torus and the +nontrivial (1,1)-Knots. This relation is based on an epi- +morphism Ω between the mapping class group of the +twice punctured torus (MCG(Σ1,2)) and the mapping +class group of the regular torus (MCG(Σ)) +Ω : MCG(Σ1,2) → MCG(Σ) ∼= Sl(2, Z). +(74) +Now, since our M2-brane formulation is only invariant +under the Sl(2, Z) parabolic subgroup, the monodromies +are also restricted to this subgroup as shown in [7]. Fur- +thermore, this could classified all the non trivial (1,1)- +Knots that, under Ω, are mapped into the parabolic sub- +group of Sl(2, Z). +VIII. +CONCLUSIONS +We obtained the supersymmetric algebra of the mas- +sive Supermembrane with target space M9XLCD and +base manifold a punctured torus. The LCD is taken to be +conformally equivalent to a punctured torus. The target +space has ten non-compactified dimension and a nontriv- +ial compactification on the 11th one. The compactified +dimension is not homeomorphic to a circle. The worldvol- +ume considered corresponds to a 2-genus Riemann surface +where a zero limit radius has been imposed on one homol- +ogy cycle. The Hamiltonian of this construction shows in +an explicit way the role of surface terms generated by the +singularities. The surface terms are expressed in terms of +the the local and four global APD constraints. The con- +struction can be generalized to more punctures although +the explicit construction will become more cumbersome. +We also discuss the invariance of the massive M2-brane +under APD. We also show, using a different argument +than the one in [7], that only parabolic Sl(2, Z) symme- +try among isotopy classes is preserved , in agreement with +Hull’s conjecture about M-theory origin of 10D massive +Romans supergravity. +IX. +ACKNOWLEDGEMENTS +P.L. has been supported by the projects MINEDUC- +UA ANT1956, MINEDUC-UA ANT2156 of the U. de +Antofagasta. P.L and A.R have been supported by the +MINEDUC-UA ANT2255 of the U. de Antofagasta. The +authors also thank to Semillero funding project SEM18- +02 from U. Antofagasta. +[1] B. De Wit, M. L¨uscher, and H. Nicolai. The supermem- +brane is unstable. Nuclear Physics B, 320(1):135 – 159, +1989. +[2] Olaf Lechtenfeld and Hermann Nicolai. A perturbative +expansion scheme for supermembrane and matrix theory. +JHEP, 02:114, 2022. +[3] L. Boulton, M.P. Garcia del Moral, and A. Restuccia. +Existence of a supersymmetric massless ground state of +the SU(N) matrix model globally on its valleys. JHEP, +05:281, 2021. +[4] M. P. Garcia del Moral and A. Restuccia. Spectrum of +a noncommutative formulation of the D = 11 supermem- +brane with winding. Phys. Rev., D66:045023, 2002. +[5] K. Dasgupta, M. M. Sheikh-Jabbari, and M. Van Raams- +donk. Matrix perturbation theory for M theory on a PP +wave. JHEP, 05:056, 2002. +[6] M. P. Garcia Del Moral, C. Las Heras, P. Leon, J. M. +Pena, and A. Restuccia. M2-branes on a constant flux +background. Phys. Lett., B797:134924, 2019. +[7] M.P. Garcia del Moral, P. Leon, and A. Restuccia. The +massive supermembrane on a knot. JHEP, 10:212, 2021. +[8] David Eliecer Berenstein, Juan Martin Maldacena, and +Horatiu Stefan Nastase. Strings in flat space and pp waves +from N=4 superYang-Mills. JHEP, 04:013, 2002. +[9] Eric Bergshoeff and Jan Pieter van der Schaar. On M +nine-branes. Class. Quant. Grav., 16:23–39, 1999. +[10] E. Bergshoeff, E. Sezgin, and P.K. Townsend. Supermem- +branes and eleven-dimensional supergravity. Phys. Lett. +B, 189(1):75 – 78, 1987. +[11] B. de Wit, J. Hoppe, and H. Nicolai. On the quantum +mechanics of supermembranes. Nucl. Phys. B, 305(4):545 +– 581, 1988. +[12] S. Mandelstam. +Interacting-string picture of dual- +resonance models. Nuclear Physics B, 64:205 – 235, 1973. +[13] Steven B. Giddings and Scott A. Wolpert. A triangula- +tion of moduli space from light-cone string theory. Comm. +Math. Phys., 109(2):177–190, 1987. +[14] Hermann Nicolai and Robert Helling. Supermembranes +and M(atrix) theory. +In Nonperturbative aspects of +strings, branes and supersymmetry. Proceedings, Spring +School on nonperturbative aspects of string theory and +supersymmetric gauge theories and Conference on super- +five-branes and physics in 5 + 1 dimensions, Trieste, +Italy, March 23-April 3, 1998, pages 29–74, 1998. +[15] H.M. Farkas and I. Kra. Riemann Surfaces. Graduate +Texts in Mathematics. Springer New York, 2012. +[16] I. Martin, A. Restuccia and R. S. Torrealba, +On the +stability of compactified D = 11 supermembranes. Nucl. +Phys. B, 521, 117-128, 1998. +[17] Lyonell Boulton, M.P. Garcia del Moral, and Alvaro +Restuccia. Spectral properties in supersymmetric matrix +models. Nucl. Phys. B, 856:716–747, 2012. +[18] B. de Wit, J. Hoppe, and H. Nicolai. On the Quantum +Mechanics of Supermembranes. Nucl. Phys., B305:545, +1988. [,73(1988)]. +[19] Bernard de Wit, Kasper Peeters, and Jan C. Plefka. Open +and closed supermembranes with winding. Nucl. Phys. B +Proc. Suppl., 68:206–215, 1998. +[20] J W van Holten and A van Proeyen. N=1 supersymme- +try algebras in d=2,3,4 mod 8. +Journal of Physics A: +Mathematical and General, 15(12):3763–3783, dec 1982. +[21] P. K. Townsend. P-brane democracy. In PASCOS / HOP- +KINS 1995 (Joint Meeting of the International Sympo- +sium on Particles, Strings and Cosmology and the 19th +Johns Hopkins Workshop on Current Problems in Parti- +cle Theory), pages 375–389, 7 1995. +[22] C. M. Hull. Gravitational duality, branes and charges. +Nucl. Phys. B, 509:216–251, 1998. + +10 +[23] M.P. Garcia del Moral, C. Las Heras, P. Leon, J.M. Pena, +and A. Restuccia. Fluxes, twisted tori, monodromy and +U(1) supermembranes. JHEP, 09:097, 2020. +[24] B. de Wit, U. Marquard, and H. Nicolai. Area Preserv- +ing Diffeomorphisms and Supermembrane Lorentz Invari- +ance. Commun. Math. Phys., 128:39, 1990. + diff --git a/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/load_file.txt b/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..0913e7eab254bd6381057c688a2be06f477f4305 --- /dev/null +++ b/ltAyT4oBgHgl3EQfyfm4/content/tmp_files/load_file.txt @@ -0,0 +1,456 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf,len=455 +page_content='Supersymmetric algebra of the massive supermembrane M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral∗ ´Area de F´ısica, Departamento de Qu´ımica, Universidad de la Rioja, La Rioja 26006, Spain and Departamento de F´ısica, Universidad de Antofagasta, Aptdo 02800, Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Le´on† and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia‡ Departamento de F´ısica, Universidad de Antofagasta, Aptdo 02800, Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In this paper, we obtain the explicit expression of the supersymmetric algebra associated with the recently proposed massive supermembrane including all surface terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We formulate the theory as the limit of a supermembrane on a genus-two compact Riemann surface when one of the handles becomes a string attached to a torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The formulation reduces to a supermembrane on a punctured torus with a ”string spike” (in the sense of [1]), attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In this limit, we identify all surface terms of the algebra and give the explicit expression of the Hamiltonian in agreement with the previous formulation of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The symmetry under area preserving diffeomorphisms, connected and nonconnected to the identity, is also discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Only parabolic Sl(2, Z) discrete symmetries are preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Keywords: Supermembrane, Supersymmetric algebra, singularities I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' INTRODUCTION Recently, new aspects of M2-brane theory in D=11 di- mensions have been developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In [2] using the Nicolai map a perturbative quantization approach have been pro- posed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In [3] the existence and uniqueness of the ground state of the theory on the valleys of the theory have been obtained, In [4–7] new sectors of the theory formulated on different backgrounds characterized by topological condi- tions have been analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In distinction to the formula- tions on a Minkowski target space these supersymmetric sectors of the M2-brane have discrete spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' They correspond to supermembranes with a topological con- dition associated with the presence of 2-form worldvol- ume fluxes induced by either the presence of a topological central charge condition [4], the presence of supergravity constant and quantized three-form [6], or either on a tar- get space with G4 content, as the supermembrane on a pp-wave [5] whose matrix model corresponds to [8], or more recently the formulation of a massive supermem- brane [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='This massive supermembrane corresponds to a supermembrane theory formulated on a M9 ×LCD back- ground, where M9 is a nine dimensional Minkowski space and LCD is a Light Cone Diagram, a two dimensional flat strip with identifications and with prescribed segments whose curvature becomes infinite at some points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This, surface only has one (non-trivial) compact dimension and therefore the supermembrane in this background exhibit ten non-compact dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Moreover, the theory has nontrivial mass terms not present on the supermembrane theory compactified on a circle that, together with the rest of the structure of the potential render the spectrum of the regularized theory to be discrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The goal of this paper is to characterize the susy algebra including all the boundary terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This may give light on the role of ∗ m-pilar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='garciam@unirioja.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='es;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' maria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='garciadelmoral@uantof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='cl † pablo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='leon@ua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='cl ‡ alvaro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='restuccia@uantof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='cl the singularities in the structure of the constraints that will be useful to obtain the string theory associated with this sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Furthermore, the analysis of the singulari- ties allows to characterize the dimensions of the sources coupled to the M2 -brane, as for the example the M9- brane discussed in [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The supermembrane only admits backgrounds that allow a consistent coupling to the 11D supergravity and its reductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Hence, the algebra may give light to the supergravity background to which this massive supermembrane couples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The study of algebras and their deformations, and consequently their symme- tries, have also been used in the literature to obtain ki- netic terms of their associated supergravity Lagrangian densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Although we will no proceed in this direction, this is another possible application of the results of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The paper is structured as follows: In section 2, we re- call basic aspects of the supermembrane theory formula- tion and its Hamiltonian in the case of a supermembrane with a topological central charge condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In section 3, we summarize the main properties of the Light Cone Diagram formulation that will be needed for the compu- tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In section 3, we present a new formulation of the massive supermembrane obtained in [7] which directly in- corporates all the boundary terms of the formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In section 5, we obtain the supersymmetric transformation and in section 6, we get the supersymmetric algebra of supercharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In section 7, we discuss other fundamental symmetry , that is the area preserving diffeomorphisms, in order to characterize completely the symmetries of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In section 8, we present ours conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' THE SUPERMEMBRANE ACTION IN THE LIGHT CONE GAUGE The supermembrane was originally introduced in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Its formulation in the Light Cone Gauge (LCG) on a Minkowski target space was obtained [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In this section we will briefly review some of those results in [11] and we will present the supermembrane action in the light cone arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='00686v1 [hep-th] 2 Jan 2023 2 gauge on M9 × T 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The action of the supermembrane in a Minkowski space-time is given by S = −TM2 � R×Σ dξ3 �√−g + εuvw ¯˜ΨΓµν∂w ˜Ψ × �1 2∂u ˜Xµ(∂v ˜Xν + ¯˜ΨΓν∂v ˜Ψ) + 1 6 ¯˜ΨΓµ∂u ˜Ψ¯˜ΨΓν∂v ˜Ψ �� , (1) where TM2 is the M2-brane tension, Γµ are the gamma matrix in eleven dimensions, ˜Xµ (µ, ν = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='., 10) are the embedding maps of the supermembrane, θ is a 32 com- ponent Majorana spinor and Σ is a compact Riemann surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' All the fields are functions of the world-volume coordinates ξu (u, v, w = 0, 1, 2) and guv are the compo- nents of the world-volume induced metric, this is guv = (∂u ˜Xµ + ¯˜ΨΓµ∂u ˜Ψ)(∂v ˜Xν + ¯˜ΨΓν∂v ˜Ψ)ηµν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (2) Now we can use the light cone coordinates ˜Xµ = (X+, X−, ˜XM) with M, N = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='., 9 X± = 1 √ 2( ˜X10 ± ˜X0), Γ± = 1 √ 2(Γ10 ± Γ0), (3) and, decomposing ξu = (t, σr) with r = 1, 2, one can fix the LCG as follows, X+ = t, Γ+ ˜Ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (4) Thus, we can write the Lagrangian density can be written as 1 L = −TM2( � ¯g∆ + ϵrs∂r ˜XM ¯˜ΨΓ−ΓM∂s ˜Ψ), (5) where ¯grs = ∂r ˜XM∂s ˜XM, ur = g0r = ∂r ˜X− + ∂t ˜XM∂r ˜XM, g00 = 2∂t ˜XM∂t ˜XM + 2¯˜ΨΓ−∂0 ˜Ψ, and ¯g = det(¯grs), ∆ = −g00 + ur¯grsus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then, the conju- gate momenta can be written as ˜P− = TM2 � ¯g ∆, ˜P M = ˜P−(∂0 ˜XM − urgrs∂s ˜XM), ˜S = − ˜P−Γ− ˜Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, the Hamiltonian density is given by H = ˜P 2 + T 2 M2¯g 2 ˜P− − TM2ϵrs∂r ˜XM ¯˜ΨΓ−ΓM∂s ˜Ψ, (6) 1 We are using ε0rs = −ϵrs subject to the following constraints ˜P∂r ˜X + ˜P−∂r ˜X− + ¯˜SΓ− ˜Ψ = 0, ˜S + TM2 � ¯g ∆Γ− ˜Ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (7) Now, we can use the area preserving diffeomorphims to set the gauge ˜P− = P 0 − √ W, where � ˜W is a scalar den- sity satisfying � Σ � ˜W = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (8) This allows to introduce the Lie bracket {·, ·} = ϵrs � ˜W ∂r · ∂s · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (9) The supermembrane Lagrangian density can be writ- ten in a way that is explicitly invariant under area pre- serving diffeomorphims (see [11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This requires the in- troduction of a gauge field ω related to time-dependent reparametrizations of the world-volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This will be L P + 0 � ˜W = 1 2(D0 ˜XM)2 + ¯˜ΨΓ− ˜Ψ − T 2 M2 4P + 0 { ˜XM, ˜XN}2 + TM2 P + 0 ¯˜ΨΓ−Γa{ ˜XM, ˜Ψ} + D0 ˜X−, (10) where D0• = ∂t • −{ω, •}, {•, •} = ϵrs √ W ∂r • ∂s • .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (11) Furthermore, we can now solve (7) for ˜X−, this is ∂r ˜X− = − 1 P 0 − � ˜W (˜P∂r ˜X + ¯˜SΓ−∂r ˜Ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (12) In order to ensure the existence of a solution for ˜X−, one must impose φ = d(d ˜X−) = d � 1 � ˜W (˜Pd ˜X + ¯˜SΓ−d˜Ψ) � = 0 (13) ϕk = � Ck d ˜X− = � Ck 1 � ˜W (˜Pd ˜X + ¯˜SΓ−d˜Ψ) = 0,(14) where Ck (k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='., 2g for g > 1)are the homology basis of one-cycles over Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' They correspond to the local and global first class constraints associated with the residual symmetry of Area Preserving Diffeomorphisms (APD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now it is possible to write the Hamiltonian of the the- ory as, H = 1 2P 0 − � Σ d2σ � ˜W � � ˜P � ˜W �2 + T 2 M2 2 { ˜XM, ˜XN}2 − 2TM2P 0 − ¯˜ΨΓ−ΓM{ ˜XM, ˜Ψ} � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (15) 3 Now one can compactify the M2-brane Hamiltonian on M9 × T 2 and take as a base manifold a regular genus- two Riemann surface Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, due to the compact di- mensions, the embedding maps can be decomposed as ˜XM = ( ˜Xm, ˜Xr), with m = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 7 labelling the noncom- pact dimensions and r = 1, 2 the compact ones associated with the 2-torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The ˜Xm maps Σ2 to the transverse sub- space of M9 while ˜Xr maps Σ2 to the target T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Hence, the Hamiltonian of the supermembrane can be written as H = 1 2P 0 − � Σ2 d2σ � ˜W � � ˜Pm � ˜W �2 + � ˜Pr � ˜W �2 + T 2 M2 2 { ˜Xm, ˜Xn}2 + T 2 M2{ ˜Xm, ˜Xr}2 + T 2 M2 2 { ˜Xr, ˜Xs}2 − 2TM2P 0 − ¯˜ΨΓ−Γm{ ˜Xm, ˜Ψ} − 2TM2P 0 − ¯˜ΨΓ−Γr{ ˜Xr, ˜Ψ} � , (16) subject now to the following five APD constraints φ = d � 1 � ˜W ( ˜Pmd ˜Xm + ˜Prd ˜Xr + ¯˜SΓ−d˜Ψ) � = 0, (17) ϕk = � Ck 1 � ˜W ( ˜Pmd ˜Xm + ˜Prd ˜Xr + ¯˜SΓ−d˜Ψ) = 0, (18) where k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We will use these expressions in the subsequent sections of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' PARAMETRIZATION OF THE TWICE PUNCTURED TORUS In this section we recall some useful results about the relation between the Light Cone diagram (LCD) and the torus with two punctures Σ1,2 (see figure (1)) needed to describe the massive supermembrane formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The Light Cone diagram is a two dimensional flat strip with identifications and with prescribed segments whose cur- vature becomes infinite at some points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This results are the base of the massive supermembrane formulation [7] and they will be useful in the next sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The relation between these two surfaces is given by the Mandelstam map (see [12, 13]) F(z) = α ln �Θ1(z − Z1|τ) Θ1(z − Z2|τ) � − 2πiαIm(Z1 − Z2) Imτ (z − z0), (19) where Θ1(z, τ) are the Jacobi functions and Zr with r = 1, 2 are the positions of the punctures in a complex coordinates over the torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The set of parameters neces- sary to characterize the torus with two punctures are the Teichm¨uller parameter, τ, and the positions of the Punc- tures, Zr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On the twice punctured torus the coordinate system z is defined in terms of the holomorphic one-form dz satisfying Thus, we can decompose dz as dz = d ˆX1 + τd ˆX2, with � Ck d ˆXr = δr k, (20) where d ˆXr is a set of real normalized forms over the reg- ular torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On the other hand, the set of parameters that describe the LCD are the external momenta α, the internal mo- menta βr, the interaction time T, with and the twist angles θr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then in order to complete the equivalence between the two surfaces, (see figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' ), the following relation between both sets of parameter is required 2πi(Z1 − Z2) = (θ1 + θ2)β1 − αθ2 − 2πiβ1τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (21) It is useful to decompose the Mandelstam map in terms of its real and imaginary parts, that is F = G + iH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The function G is single valued, but dG is harmonic, since it has poles at the punctures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The function H is multivalued and dH is harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='The behavior of each function near the punctures is given by G ∼ (−1)r+1α ln |z − Zr|, (22) H ∼ (−1)r+1αϕ, with ϕ ∈ (0, 2π) (r = 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (23) On the other hand, near the zeros of dF,denoted as Pa, the functions G and H can be written as G(z) − G(Pa) ∼ 1 2Re(D(Pa)(z − Pa)2), (24) H(z) − H(Pa) ∼ 1 2Im(D(Pa)(z − Pa)2), (25) where D(Pa) = 2 � r=1 (−1)r+1 �∂2 zΘ1(Pa − zr, τ) Θ1(Pa − zr, τ) − �∂zΘ1(Pa − zr, τ) Θ1(Pa − zr, τ) �2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Finally, we recall some properties of the functions K and H that will be useful in the next section, G(z + 1) − G(z) = G(z + τ) − G(z) = 0 (26) H(z + 1) − H(z) = 2παIm(Z2 − Z1) Im(τ) , (27) H(z + τ) − H(z) = 2παIm((Z2 − Z1)¯τ) Im(τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (28) IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' MASSIVE SUPERMEMBRANE In this section, we present a new formulation of the massive supermembrane and its connection with the for- mulation found in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Specifically, in order to make clearer the surface terms that appear in the supersym- metric algebra, we use a different approach than [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Instead of considering the supermembrane formulated in M9 × LCD on a twice punctured torus as the base mani- fold, we will start with the M2-brane on a compact genus- two Riemann surface Σ2 as the base manifold in M9 ×T 2 4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The torus with two punctures and the one loop interaction string diagram with one incoming/outgoing string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The Mandelstam map send the punctures over the torus to ±∞ in the LCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (a) The genus two regular Riemann surface Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (b) A deformation of Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (c) The surface ˜Σ1,2 obtained by taking one of the radii of Σ2 tending to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This correspond to a singular T 2 with a string attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' as the target space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In order to establish a connection with the formulation of the massive supermembrane [7], we will take a specific limit to deform Σ2 as described in the figure (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' That is, we will assume that one of the radii of the handles of the genus two surface tends to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' As a result, we can expand the maps Xm, Xr and Ψ in a Fourier series and keep only the order zero of the variable associated with the small radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, under these considerations, the supermembrane maps will de- pend only on the coordinate along the handle (see figure (2)-(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In this way, we get a string-like configuration like the ones described in [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, we will end up with a surface, that we will denote ˜Σ1,2, which is a twice punc- tured torus Σ1,2 with a string attached to the punctures (see figure (2)-(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then we will also deform the target T 2 to a LCD surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, the metric that we shall define over the LCD on the target is given by ds2 = l2d ˆG2 + dH2 = dK2 + α2d ˆH2, (29) where ˆH = H/α, ˆG = G/α and l is constant with length units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now we can describe the dependence of the M2-brane fields in two regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The first one is the definition of the maps on Σ1,2 and the second one is the string attached to it that we shall denote as γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then, given a coordinate system, z (given in the previous section), over Σ1,2 and defining as u the coordinate associated to γ2 we can write ( ˜Xm, ˜Ψ) = � (Xm(t, z, ¯z), Ψ(t, z, ¯z)) over Σ1,2 (Y m(t, u), Θ(t, u)) over γ2 ,(30) and ˜Xr = � XK(t, z, ¯z)δr 1 + XH(t, z, ¯z)δr 2 over Σ1,2 Y r(t, u) over γ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (31) The maps XK and XH are defined as in [7], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='e, XK = K + AK, XH = H + AH, (32) where m is an integer and the 1-forms dAK, dAH are exact over Σ1,2 Under all this consideration, as discussed in [1, 14], the string we are considering does not change the superme- mbrane energy and therefore we can write H = � Σ2→˜Σ1,2 H = � Σ1,2 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (33) The string-like configuration that we are considering here has no M2-brane dynamics associated with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This is so, because it does not have any contribution to the Hamiltonian of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, without losing general- ity, we can impose Y m s (u, t) = const, Y r s (u, t) = const, Θs(u, t) = const, (34) which implies Xm ���� Z2 Z1 = Ψ ���� Z2 Z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (35) On the other hand, since the Y r s (u, t) are single value functions, it is reasonable to consider that AK and AH are continuous functions of Y r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Consequently, (a) (b) (c)5 AK ���� Z2 Z1 = AH ���� Z2 Z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (36) At this point we can follow the same steps presented in [7] to analyse the Hamiltonian over Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Specifically, we shall define the world-volume metric, over Σ1,2, as √ W = 1 4π ϵrs∂r ˆK∂s ˆH, (37) where K ≡ tanh ˆG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then we can fix the gauge {K, AK} + m{H, AH} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (38) In order to deal with the singular behavior of the metric at the punctures and zeros we shall cut the fundamental region of Σ1,2, that we will call Σ1,2, through a closed curve that circumvents the two punctures, and the zeros with a radius ϵ and touch a point O ∈ ∂Σ1,2, see figure 3 (see [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We shall denote as Cr the curves around the punctures, Dr the curves around the zeros, and as Ij, with j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='., 4, to all the curves in between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Following the discussion presented in [7], it is clear that the curves Ij can be chosen as curves H = cte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The we will denote as Σ′ the resulting region after cutting Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Under all these considerations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' the Hamiltonian of the theory can be written as (see [7] for more details) H = (lαTM2m)2 2P + 0 + 1 2P + 0 lim ϵ→0 � Σ′ dσ2√ W �� Pm √ W �2 + � PK √ W �2 + � PH √ W �2 + T 2 M2 �1 2{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Xn}2 + 2{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' K}{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK} + m2{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' H}2 + {Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' K}2 + {Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK}2 + {Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AH}2 + m2{H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK}2 + 2m{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' H}{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AH} + 2m{H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK}{AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK} + {K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK}2 + 2{AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' K}{AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK} + {AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AK}2 + {K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AH}2 + {H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AH}2 � − 2P + 0 TM2(¯ΨΓ−Γm{Xm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Ψ} + ¯ΨΓ−ΓK{AK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Ψ} + ¯ΨΓ−ΓH{AH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Ψ} + ¯ΨΓ−ΓK{K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Ψ} + ¯ΨΓ−ΓH{H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Ψ}) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (39) By defining f ≡ � PK √ W dXK + PH √ W dXH + Pm √ W dXm + ¯ΨΓ−dΨ � , let’s now us discuss the constraints after deforming Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' First, we have the local APD constraint given by df = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (40) On the other hand we have also four global constraints, the first two are the associated with the homology basis of cycles defined over the regular torus (see figure (4-(a))), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='e ζ1 ≡ � a f = 0, and, ζ2 ≡ � b f = 0 (41) We have another constraint associated to the singularities ζ3 ≡ � C1 f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (42) This constraint arises from the homology curve of Σ2 around the handle, whose radius was send to zero to get the string-like configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The final constraint is the one associated with the homology curve along the deformed handle of σ2, shown in figure 4, which is still present after deforming Σ2 into ˜Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' ζ4 ≡ � y f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (43) Notice, that we could not write ζ4 directly in terms of K, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This is because the curve γ is defined in both, Σ1,2 and in the string attached in the punctures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, it is convenient to separate the curve γ into two pieces ((see figure (4-(b))) and we will denoted as γ1 and γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The curve γ1 is the part of γ defined over Σ1,2 and γ2 corresponds to the string with end points at the punc- tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now, because of (34), we can write ζ4 = � γ1 f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (44) In the following we will list some of the features of the massive supermembrane Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (39) it can be seen that it is very different from a standard com- pactification of the M2-brane on a S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Firstly,it contains a mass term associated with the nontrivial topology of the LCD on the target space given by lim ϵ→0 � Σ′ dK ∧ d ˆH α m2 4 {K, ˆH}2 = 2παl m2 (45) This term can be interpreted as a as the uplift to ten non compact dimensions of the central charge condition pro- posed in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In second place, it possesses non vanishing mass terms associated with the dynamics fields Xm,AK and AH, these are (∂KXm)2 + ( ∂ ˆ HXm)2 ̸= 0, (∂KAK)2 + (∂ ˆ HAK)2 ̸= 0, (∂KAH)2 + (∂ ˆ HAH)2 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, the fermionic potential is dominated by the bosonic potential due to these non-vanishing quadratic contribu- tion to the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This fact, and together with the structure of the rest of the potential, ensure that the Hamiltonian satisfy the discreteness sufficient condition found in [17], as formerly shown in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Finally, we would to mention that taking as a starting point a compact Riemann surface of genus two, is the simplest case, but it is not the only possibility to find massive terms in the Hamiltonian of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The region Σ′ obtained by cutting Σ1,2 through the curves C1,C2 and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The path obtained by the union of the curves C1,I,C2 and I−1 is denoted by c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (a) Nontrivial cycles over ˜Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (b) The curve γ and his decomposition into the curves γ1 and γ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' SUPERSYMMETRIC TRANSFORMATIONS In this section, we will analyze the supersymmetry of our formulation of the massive supermembrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, we shall follow the same procedure presented in the previous section, that is, we will begin with the M2-brane over a regular compact genus two Riemann surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In gen- eral,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' the supermembrane action (in the light cone gauge) is invariant under the following supersymmetric transfor- mations originally found in [11],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' δ ˜XM = −2¯ηΓMΨ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (46) δΨ = 1 2Γ+(D0 ˜XMΓM + Γ−)η + TM2 4P + 0 { ˜XM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' XN}Γ+ΓMNη (47) δω = −2TM2 P + 0 ¯ηΨ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (48) provided the following boundary terms are equal to zero P + 0 δL TM2 = − � R dt � Σ d � ¯ΨΓ−ΓMd ˜XMδΨ + 2¯ΨΓMΓ−η + 2¯ΨΓMNη∂t ˜XMdXN − 2 3(¯ΨΓ−dΨ¯ηΨ − ¯ηΓMΨ¯ΨΓ−ΓMdΨ) � + lim ϵ→0 � Σ′ d2σ � R dt∂t �√ W ¯ΨΓ−∂Ψ − 2 √ W ¯ΨΓ−η + √ W ¯ΨΓMNη{ ˜XM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' XN} � = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (49) where η is a constant spinor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Notice that, in this surface term, only the derivatives of the maps X are displayed, which are single-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, since Ψ is also a single-valued and we are considering a compact regular Riemann surface as a base manifold, this surface term is identical to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Moreover, this allows to conclude that, at least from this surface term, there are not restrictions to the supersymmetric parameter, η, when we take the limit Σ2 → ˜Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On the other hand, in [7], it was shown that in order to preserve the topological term given in equation (45) and the mass terms in the Hamiltonian that leads to the good spectral properties of the Hamiltonian, we need to impose the following condition Γ+ � Γ− + 1 2ΓKH � η = 0, (50) which implies that half of the supersymmetry is broken, in distinction with the case of a supermembrane on a torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' SUPERSYMMETRIC ALGEBRA Following with our analysis of the supersymmetric properties of the massive supermembrane, in this section we shall present the supersymmetric algebra of the mas- sive supermembrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Specifically, we will compute the supersymmetric charges and their Dirac brackets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' As be- fore, we will begin with the formation of the M2-brane over Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' From (15) we can derive the supercharge density associated with the transformations (46-48) [_b 3 Z2 14 P2 D2 b-1 b D1 C1 P1 b Z1 0 12 5 a (a) (b) (c)Y2 a b (a) (b)7 J0 = P + 0 � ˜W � 2(∂0 ˜XMΓM + Γ−) + TM2 P + 0 { ˜XM, ˜XN}ΓMN � Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (51) Thus the supersymmetric charges, defined as Q± = 1 2Γ±Γ∓Q, Q = � Σ2 dσ2J0, (52) can be written as Q+ = � Σ2 dσ2[2 ˜PMΓM + TM2 � ˜W{ ˜XM, ˜XN}ΓMN]˜Ψ, (53) Q− = 2P + 0 Γ− � Σ2 dσ2� ˜W ˜Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (54) The only non trivial Dirac’s brackets in our case are given by { ˜XM(σ), PN(σ′)}D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = δM N δ2(σ − σ′), (55) {Ψα(σ), Ψβ(σ′)}D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = 1 4 � ˜WP + 0 (Γ+)α βδ2(σ − σ′), (56) where we are considering that σ and σ′ are the coordi- nates of two points inside Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' With these expressions and using the Gamma matrices properties we get {Q− α , Q− β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = −2P + 0 (Γ+)αβ, (57) {Q+ α, Q− β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = −(ΓMΓ+Γ−)αβP M 0 − TM2 2 (ΓMNΓ+Γ−)αβ � Σ2 dσ2� ˜W{ ˜XM, ˜XN}, (58) {Q+ α, Q+ β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = 2(Γ+)αβH − 2TM2(Γ+ΓM)αβ � Σ2 dσ2� ˜W{ ˜X−, ˜XM}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (59) Notice that this is the most general form of the supersym- metric algebra for the supermembrane found in [18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now, we can analyse the surface terms in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' How- ever, since we are considering the limit Σ2 → ˜Σ1,2, the surface term in the last two terms leads to several dif- ferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This is due to the two singular points resulting from the deformation of Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' From the general superal- gebra in eleven dimensions (see for example [20, 21]) it can be seem that the surface terms can be interpreted in terms of tensorial charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Specifically, the surface term in (58) and (59) are related with the charges ZMN and Z+M, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' As is discussed in [22], the 2-form ZMN gives a 2-brane charge and it has been conjectured that the dual of the from Z+M gives a 9-brane charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now, let us analyse in detail the surface terms begin- ning with the one in (58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In the limit Σ2 → ˜Σ1,2 it can be shown that � Σ2 dσ2� ˜W{ ˜XM, ˜XN} → � ˜Σ1,2 dσ2√ W{XM, XN}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (60) Thus, following the same arguments of section IV , we can also write � ˜Σ1,2 dσ2√ W{XM, XN} = � Σ1,2 dσ2√ W{XM, XN} = lim ϵ→0 � Σ′ dσ2√ W{XM, XN}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The only non-trivial contributions of this term are given by lim ϵ→0 � Σ′ dσ2√ W{XM, XN} = lα 4π lim ϵ→0 � Σ′[δM K (1 2d ˆK ∧ d ˆH + d ˆ AK ∧ d ˆH) + δM m d ˆ Xm ∧ d ˆH]δN H − (M → N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This can be simplified to obtain lim ϵ→0 � Σ′ dσ2√ W{XM, XN} = lα �1 2δM K + � δM m � γ1 dXm + δM K � γ1 dAK �� δN H − (M → N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (61) Now, we can a analyse the surface term in (59).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Fol- lowing the same idea of the previous case, we can write (in the limit Σ2 → ˜Σ1,2) � ˜Σ1,2 dσ2√ W{X−, XM} = � Σ1,2 dσ2√ W{X−, XM}, which leads to � Σ′ dσ2√ W{X−, XM} = � lim ϵ→0 � Σ′ XMφ + ζ2 � a dXM − ζ1 � b dXM + lα 4π lim ϵ→0 � � r � � Cr + � Dr � + � u � � Iu + � Iu−1 �� XMdX− � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (62) Since XMdX− is well defined at Pr, the limit ϵ → 0 of the integral over Dr are equal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The integral around the punctures leads to lim ϵ→0 � r � Cr XMdX− = − � γ1 dXM � C1 dX− = − � γ1 dXMζ3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Moreover, it can be proved that � u � � Iu + � Iu−1 �� XMdX− = −2παδM H � γ1 dX−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, the final form of the massive supermembrane algebra is given by 8 {Q− α , Q− β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = −2P + 0 (Γ+)αβ, (63) {Q+ α, Q− β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = −(ΓMΓ+Γ−)αβP M 0 − Tαl 2 (ΓMHΓ+Γ−)αβδM K , (64) {Q+ α, Q+ β }D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B = 2(Γ+)αβH − 2T(Γ+ΓM)αβ � lim ϵ→0 � Σ′ XMφ1 + 2παδM H Im(τ) � Im(Z2 − Z1)ζ2 − Im((Z2 − Z1)¯τ)ζ1 � − 2 � lδM K ζ3 + παδM H ζ4 �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (65) At this point, the following comments are in order: In [7], the massive supermembrane is interpreted as the uplift to ten non compact dimensions of the su- permembrane with C± fluxes and parabolic mon- odromy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Then, we can interpret (63)-(65) as the generalisation of the M2-brane super algebra when the world volume of the theory is a twice punctured torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In (64), we get a constant term which is analo- gous to the fluxes/central charge contribution to the super algebra presented in [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' However, in the present case, this term is not proportional to an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We showed that the surface term in (65), can be written in terms of the constraints of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The terms related with the constraints are analo- gous to the case without punctures (see [23]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' How- ever, in our case, we have two extra global con- straints related with the punctures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Moreover, the multiplicative factors of each are related to the moduli of the twice punctured torus, while in [23] are the winding numbers of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' AREA PRESERVING DIFFEOMORPHISMS Another relevant symmetry of the supermembrane the- ory is the invariance under APD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In this section, we will discuss the realization of this symmetry in the massive supermembrane formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' As discussed in previous sections, the Hamiltonian of the supermembrane on ˜Σ1,2 is the same as in Σ1,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus we will restrict ourselves to the analysis of the APD for the Hamiltonian given by (39) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Under APD connected to the identity, any functional O of the canonical variables transform as δξO = � O, < dξ ∧ � PM √ W dXM + ¯ΨΓ−dΨ � > � P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' , (66) where, in this case corresponds to < dξ ∧ � PM √ W dXM + ¯ΨΓ−dΨ � > = lim ϵ→0 � Σ′ � PM √ W dXM + ¯ΨΓ−dΨ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (67) In these expressions, ξ, is the infinitesimal parameter of the transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This parameter defines globally a closed 1-form dξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, ξ is globally defined over Σ′, that is, the dξ is an exact form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' If ξ is not globally de- fined, then dξ is a closed but not exact form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' It can be verified that the following APD transformations holds for the massive supermembrane δξXM = {ξ, XM}, δξPM = √ W � ξ, PM √ W � , δξΨ = {ξ, Ψ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (68) They are the same as the ones found in [11] and [24] describing the the case of the supermembrane on a flat Minkowski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' They also hold for the supermem- brane with central charge [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Now, in order to determine the symmetries of the massive supermembrane under area preserving diffeomorphims non connected to the identity, we shall start by recalling the non punctured case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' For these transformations, the homology basis defined a two torus without punctures transform as d ˆXi → Si jd ˆXj, S ∈ Sl(2, Z), (69) while τ → aτ + b cτ + d, � a b c d � ∈ Sl(2, Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (70) Thus, from (19), it can be found that, under this trans- formations, the Mandelstam map transforms as F � z cτ + d, Z1 cτ + d, Z2 cτ + d, aτ + b cτ + d � = F(z, Z1, Z2, τ) + iπc cτ + d(Z1 1 − Z2 2), (71) implying that dF (and therefore dG and dH) is invariant under APD conected and non connected to the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' However, the 1-form dK is invariant under the APD con- nected to the identity but it may not be invariant under the not connected to the identity transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Indeed we get dK → 1 − K2 0 (1 + K0K)2 dK, (72) where K0 = tanh � Re � iπc cτ + d(Z1 1 − Z2 2) �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (73) It is clear that the massive supermembrane action will be invariant under APD non connected to the identity as long as dK is invariant under this transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Thus, the only possible transformation in Sl(2, Z) that satisfy this requirement is when c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In other words, the mas- sive supermembrane is invariant under APD connected to the identity, but it is only invariant under the parabolic subgroup of Sl(2, Z), transforming isotopy classes of not connected to the identity APD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The massive supermem- brane discussed in this work (see also [7]), represents an explicit realization of Hull’s conjecture about the origin, 9 in M-theory, of Roman’s supergravity in terms oftorus bundles with parabolic Sl(2, Z) monodromy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In [7], it was presented the relation between the mon- odromies defined over a twice punctured torus and the nontrivial (1,1)-Knots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' This relation is based on an epi- morphism Ω between the mapping class group of the twice punctured torus (MCG(Σ1,2)) and the mapping class group of the regular torus (MCG(Σ)) Ω : MCG(Σ1,2) → MCG(Σ) ∼= Sl(2, Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' (74) Now, since our M2-brane formulation is only invariant under the Sl(2, Z) parabolic subgroup, the monodromies are also restricted to this subgroup as shown in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Fur- thermore, this could classified all the non trivial (1,1)- Knots that, under Ω, are mapped into the parabolic sub- group of Sl(2, Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' CONCLUSIONS We obtained the supersymmetric algebra of the mas- sive Supermembrane with target space M9XLCD and base manifold a punctured torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The LCD is taken to be conformally equivalent to a punctured torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The target space has ten non-compactified dimension and a nontriv- ial compactification on the 11th one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The compactified dimension is not homeomorphic to a circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The worldvol- ume considered corresponds to a 2-genus Riemann surface where a zero limit radius has been imposed on one homol- ogy cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The Hamiltonian of this construction shows in an explicit way the role of surface terms generated by the singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The surface terms are expressed in terms of the the local and four global APD constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The con- struction can be generalized to more punctures although the explicit construction will become more cumbersome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We also discuss the invariance of the massive M2-brane under APD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' We also show, using a different argument than the one in [7], that only parabolic Sl(2, Z) symme- try among isotopy classes is preserved , in agreement with Hull’s conjecture about M-theory origin of 10D massive Romans supergravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' ACKNOWLEDGEMENTS P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' has been supported by the projects MINEDUC- UA ANT1956, MINEDUC-UA ANT2156 of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' de Antofagasta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='L and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='R have been supported by the MINEDUC-UA ANT2255 of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' de Antofagasta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The authors also thank to Semillero funding project SEM18- 02 from U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Antofagasta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' De Wit, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' L¨uscher, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nicolai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The supermem- brane is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nuclear Physics B, 320(1):135 – 159, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [2] Olaf Lechtenfeld and Hermann Nicolai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' A perturbative expansion scheme for supermembrane and matrix theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 02:114, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Boulton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Existence of a supersymmetric massless ground state of the SU(N) matrix model globally on its valleys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 05:281, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Spectrum of a noncommutative formulation of the D = 11 supermem- brane with winding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', D66:045023, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Dasgupta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Sheikh-Jabbari, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Van Raams- donk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Matrix perturbation theory for M theory on a PP wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 05:056, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia Del Moral, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Las Heras, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Leon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Pena, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' M2-branes on a constant flux background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', B797:134924, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Leon, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' The massive supermembrane on a knot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 10:212, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [8] David Eliecer Berenstein, Juan Martin Maldacena, and Horatiu Stefan Nastase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Strings in flat space and pp waves from N=4 superYang-Mills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 04:013, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [9] Eric Bergshoeff and Jan Pieter van der Schaar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On M nine-branes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 16:23–39, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [10] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Bergshoeff, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Sezgin, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Townsend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Supermem- branes and eleven-dimensional supergravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B, 189(1):75 – 78, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [11] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' de Wit, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Hoppe, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nicolai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On the quantum mechanics of supermembranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B, 305(4):545 – 581, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Mandelstam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Interacting-string picture of dual- resonance models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nuclear Physics B, 64:205 – 235, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [13] Steven B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Giddings and Scott A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Wolpert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' A triangula- tion of moduli space from light-cone string theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 109(2):177–190, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [14] Hermann Nicolai and Robert Helling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Supermembranes and M(atrix) theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In Nonperturbative aspects of strings, branes and supersymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Proceedings, Spring School on nonperturbative aspects of string theory and supersymmetric gauge theories and Conference on super- five-branes and physics in 5 + 1 dimensions, Trieste, Italy, March 23-April 3, 1998, pages 29–74, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Farkas and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Kra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Riemann Surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Graduate Texts in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Springer New York, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [16] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Martin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Torrealba, On the stability of compactified D = 11 supermembranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B, 521, 117-128, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [17] Lyonell Boulton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral, and Alvaro Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Spectral properties in supersymmetric matrix models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B, 856:716–747, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' de Wit, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Hoppe, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nicolai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' On the Quantum Mechanics of Supermembranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', B305:545, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [,73(1988)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [19] Bernard de Wit, Kasper Peeters, and Jan C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Plefka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Open and closed supermembranes with winding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 68:206–215, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [20] J W van Holten and A van Proeyen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' N=1 supersymme- try algebras in d=2,3,4 mod 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Journal of Physics A: Mathematical and General, 15(12):3763–3783, dec 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Townsend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' P-brane democracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' In PASCOS / HOP- KINS 1995 (Joint Meeting of the International Sympo- sium on Particles, Strings and Cosmology and the 19th Johns Hopkins Workshop on Current Problems in Parti- cle Theory), pages 375–389, 7 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [22] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Hull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Gravitational duality, branes and charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' B, 509:216–251, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' 10 [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Garcia del Moral, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Las Heras, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Leon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Pena, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Restuccia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Fluxes, twisted tori, monodromy and U(1) supermembranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' JHEP, 09:097, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' [24] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' de Wit, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Marquard, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Nicolai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Area Preserv- ing Diffeomorphisms and Supermembrane Lorentz Invari- ance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} +page_content=', 128:39, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltAyT4oBgHgl3EQfyfm4/content/2301.00686v1.pdf'} diff --git a/m9E3T4oBgHgl3EQfigrM/content/tmp_files/2301.04581v1.pdf.txt b/m9E3T4oBgHgl3EQfigrM/content/tmp_files/2301.04581v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..76031b6ca1ab91e6f9c04610b9fbe7ee2f266999 --- /dev/null +++ b/m9E3T4oBgHgl3EQfigrM/content/tmp_files/2301.04581v1.pdf.txt @@ -0,0 +1,1790 @@ +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +1 +Elevation Estimation-Driven Building 3D +Reconstruction from Single-View Remote Sensing +Imagery +Yongqiang Mao, Kaiqiang Chen, Liangjin Zhao, Wei Chen, +Deke Tang, Wenjie Liu, Zhirui Wang, Wenhui Diao, Xian Sun, Kun Fu +Abstract—Building 3D reconstruction from remote sensing +images has a wide range of applications in smart cities, pho- +togrammetry and other fields. Methods for automatic 3D urban +building modeling typically employ multi-view images as input to +algorithms to recover point clouds and 3D models of buildings. +However, such models rely heavily on multi-view images of +buildings, which are time-intensive and limit the applicability +and practicality of the models. To solve these issues, we focus +on designing an efficient DSM estimation-driven reconstruction +framework (Building3D), which aims to reconstruct 3D building +models from the input single-view remote sensing image. Existing +DSM estimation networks suffer from the imbalance between +local features and global features, which leads to over-smooth +DSM estimates at instance boundaries. To address this issue, we +propose a Semantic Flow Field-guided DSM Estimation (SFFDE) +network, which utilizes the proposed concept of elevation seman- +tic flow to achieve the registration of local and global features. +First, in order to make the network semantics globally aware, +we propose an Elevation Semantic Globalization (ESG) module +to realize the semantic globalization of instances. Further, in +order to alleviate the semantic span of global features and +original local features, we propose a Local-to-Global Elevation +Semantic Registration (L2G-ESR) module based on elevation +semantic flow. Our Building3D is rooted in the SFFDE network +for building elevation prediction, synchronized with a building +extraction network for building masks, and then sequentially +performs point cloud reconstruction, surface reconstruction (or +CityGML model reconstruction). On this basis, our Building3D +can optionally generate CityGML models or surface mesh models +of the buildings. Extensive experiments on ISPRS Vaihingen and +DFC2019 datasets on the DSM estimation task show that our +SFFDE significantly improves upon state-of-the-arts and δ1, δ2 +and δ3 metrics of our SFFDE are improved to 0.595, 0.897 and +0.970. Furthermore, our Building3D achieves impressive results +This work was supported by National Key R&D Program of China under +Grant No. 2021YFB3900504. (Corresponding author: Kaiqiang Chen.) +Yongqiang Mao, Wenjie Liu, Xian Sun, and Kun Fu are with the +Aerospace Information Research Institute, Chinese Academy of Sciences, Bei- +jing 100190, China, the Key Laboratory of Network Information System Tech- +nology (NIST), Aerospace Information Research Institute, Chinese Academy +of Sciences, Beijing 100190, China, the University of Chinese Academy of +Sciences and the School of Electronic, Electrical and Communication Engi- +neering, University of Chinese Academy of Sciences, Beijing 100190, China +(e-mail: maoyongqiang19@mails.ucas.ac.cn; liuwenjie18@mails.ucas.ac.cn; +sunxian@aircas.ac.cn; kunfuiecas@gmail.com). +Kaiqiang Chen, Liangjin Zhao, Zhirui Wang, and Wenhui Diao are +with the Aerospace Information Research Institute, Chinese Academy of +Sciences, Beijing 100190, China and the Key Laboratory of Network +Information System Technology (NIST), Aerospace Information Research +Institute, Chinese Academy of Sciences, Beijing 100190, China (e-mail: +chenkaiqiang14@mails.ucas.ac.cn;). +Wei Chen and Deke Tang are with the Geovis Technology Co., Ltd. (e-mail: +chenwei@geovis.com.cn; tangdk@geovis.com.cn) +in the 3D point cloud and 3D model reconstruction process. +Index Terms—DSM Estimation, 3D Building Reconstruction, +Remote Sensing Images, Elevation Semantic Flow +I. INTRODUCTION +T +HANKS to the increasing development of various sen- +sors, various remote sensing data have been applied in +different fields [7], [8], including semantic segmentation [39], +[41] and object detection [35], [42], [43] of 2D remote sensing +image, and 3D point cloud classification [36]–[38]. Among +them, the interpretation of interactive information between +two-dimensional data and three-dimensional data gradually +enters researchers’ field of vision. 3D reconstruction of urban +buildings is a significant constituent of remote sensing image +interpretation, where the goal is to parse image or point cloud +data to generate 3D model representations [32]–[34], [44]–[46] +of urban buildings. In recent years, large-scale geospatial mesh +models of urban buildings have been introduced widespreadly +in many fields, such as navigation and urban planning [63], +urban 3D maps [62], etc. +Among the existing 3D model acquisition methods, there +are mainly four approaches: airborne lidars, Geiger-mode +lidars, reconstruction based on multi-view UAV images, and +reconstruction based on single-view remote sensing images. +Although airborne lidar can obtain accurate 3D point clouds +[31], [47], [49]–[52] of buildings in the target area, it is limited +by high acquisition cost and low acquisition efficiency and +difficult to apply to large-scale tasks. Recent Geiger-mode +lidars [48] can acquire data efficiently, they suffer from high +noise and low penetration. Building reconstruction based on +multi-view UAV images +[32], [34] can acquire 2D image +data for 3D model reconstruction at low cost, but it has a +very high time cost for large-scale regional reconstruction and +requires a high degree of overlap between images. Unlike +airborne lidar and drone images, single-view remote sensing +imagery can cover a larger area with high stability and low +cost. Therefore, we focus on the 3D reconstruction of buildings +based on single-view remote sensing imagery (Fig. 1), aiming +to utilize low-cost large-scale remote sensing imagery for fast +urban building reconstruction. +For single-view-based building 3D reconstruction methods, +some methods [29] derive 3D building models (e.g., CityGML) +and only focus on the restoration of roof structure topology. +The researchers aim to reconstruct the roof topology using +arXiv:2301.04581v1 [cs.CV] 11 Jan 2023 + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +2 +SFFDE Network +Patch +Fusion +Building Extraction Network +a. DSM Estimation +b. Building Extraction +Input: Single-view +Remote Sensing Image +c. Point Cloud Reconstruction +Elevation Map +Building Mask +Surface +Reconstruction +e. Surface Reconstruction +Output: 3D Mesh Model +Point Cloud +Reconstruction +Building Edge +Detection +Point Cloud +3dfier +Output: CityGML Model +d. CityGML Reconstruction +Fig. 1. Flowchart of the proposed Building3D framework for 3D reconstruction of buildings. The input of Building3D is a single-view remote sensing image, +the outputs are the corresponding elevation maps, building masks, point cloud, and 3D building model. The blue dotted line represents optional follow-up +operations (CityGML models or Mesh models). +traditional methods, and then obtain 3D data in the form of +CityGML based on the building height information. Some +researchers use pre-labeled roof structure types to train the +network and then extract the roof topology. However, these +methods are limited to the extraction of topology structure, +which brings unnecessary extraction of artificial prior knowl- +edge for building reconstruction, resulting in cumbersome and +redundant reconstruction process, which is not conducive to +building reconstruction in large-scale areas. In order to solve +this problem, based on the prediction of building elevation +information, we perform 3D mapping of building elevation +to obtain building point cloud data, and then selectively +reconstruct the subsequent CityGML model or mesh model +of the buildings. Based on this, our reconstruction framework +(Fig. +1) can simultaneously reconstruct more realistic mesh +models of buildings and virtual models like CityGML. +For single-view remote sensing images, the elevation in- +formation of buildings is a key factor in constructing the 3D +building models. Although substantial progress has been made +in existing elevation prediction methods [1]–[6] from remote +sensing images, the problem of low prediction accuracy occurs +when both regular and irregular textured objects are present. +Through our investigation, we realize that the low prediction +accuracy of textured regular and irregular objects is caused +by the inability of the receptive field to achieve a local-global +trade-off. The imbalance between global and local features will +cause the network to suffer from insufficient receptive field in +the learning process, and it cannot take into account the ex- +traction of regular texture and irregular texture object features +at the same time. Since the features extracted by CNN have +local perception, to solve this problem, we introduce elevation +semantic globalization to obtain global feature perception. +However, the network at this time does not have the ability to +take into account and trade off local and global features at the +same time. To address this issue, we introduce the concept of +elevation semantic flow embedded in a local-to-global feature +registration module to explicitly model the changing trend +between global and local features to trade off local and global +features. Based on this, we propose an Elevation Semantic +Flow Field-guided DSM Estimation (SFFDE) network (Fig. +1) to obtain accurate elevation predictions for various textured +objects. +In this paper, we propose a single-view remote sensing +image-based building reconstruction framework (Building3D) +based on the SFFDE network, as illustrated in Fig. 1. Unlike +previous research schemes targeting roof topology, our Build- +ing3D aims to recover both the CityGML model as well as the +real mesh model of the buildings. Our Building3D framework +consists of four parts: Semantic Flow Field-guided DSM +Estimation (SFFDE) network, building extraction network, +point cloud reconstruction process, and building reconstruc- +tion process. Given a single-view remote sensing image, the +elevation information of the image is first predicted through +our SFFDE network, which is mainly composed of two parts: +Elevation Semantic Globalization (ESG) and Local-to-Global +Elevation Semantic Registration (L2G-ESR), which realize the +purpose of feature globalization and local and global feature +registration, respectively. At the same time, the building mask +is extracted from the image through the building extraction +network. Next, the building elevation is extracted using the +building mask, and the elevations of other uninteresting objects +are filtered out. Based on this, the building elevation is used to +reconstruct the point cloud data to obtain the 3D point cloud +of the building. Finally, CityGML reconstruction or surface +reconstruction is performed using the point cloud to obtain +the final CityGML or 3D mesh model. +The contributions of this study are summarized as follows: +• We introduce a Semantic Flow Field-guided DSM Esti- +mation (SFFDE) network based on the proposed elevation +semantic flow field for the local-to-global registration +of elevation semantics. Specifically, Elevation Semantic +Globalization (ESG) and Local-to-Global Elevation Se- +mantic Registration (L2G-ESR) are designed to achieve +the globalization and local-to-global registration of fea- +tures, respectively. +• We propose a single-view image based building 3D + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +3 +reconstruction framework (Building3D) rooted in the +proposed SFFDE network and extract building masks ac- +cording to the building extraction network for subsequent +3D point cloud and building reconstruction. +• Experiments on ISPRS Vaihingen [64] and DFC2019 [31] +datasets show that our SFFDE network significantly out- +performs the baseline model, achieving new state-of-the- +art. What’s more, our Building3D achieves impressive +results in the 3D point cloud and building reconstruction +process. +The remainder of this article is organized as follows: In +Section II, we give a brief review of the related works on +DSM estimation, building extraction, and building reconstruc- +tion. The details of our proposed framework Building3D and +semantic flow field-guided DSM estimation (SFFDE) network +are given in Section III. In Section IV, extensive experiments +are conducted on ISPRS Vaihingen dataset and DFC2019 +dataset to demonstrate the effectiveness of our SFFDE net- +work. Also, the 3D reconstruction experiments of buildings are +given in Section IV. Finally, Section V concludes this article. +II. RELATED WORK +A. DSM Estimation +The existing methods [1]–[4] for DSM elevation estimation +in the remote sensing field are mainly divided into three types: +random field-based methods, CNN-based methods, and some +hybrid methods. In random field-based methods, researchers +[5], [6] utilize conditional random field (CRF) and Markov +random field (MRF) to model the local and global structure of +an image. Considering that local features cannot provide suffi- +cient features for predicting depth values, Batra and Saxena [5] +model the relationship between adjacent regions. Furthermore, +in order to obtain global features beyond the local ones, Saxena +et al. [6], [10] first compute the features of the four nearest +neighbors of the specified patch, and then use the MRF and +Laplacian models to estimate the depth of each patch. In +recent years, CNN has been widely used in the fields of object +classification, semantic segmentation, and object detection. In- +spired by this, some researchers [11] propose a ResNet-based +convolutional network to predict DSM elevation information. +In IMG2DSM [15], an adversarial loss function is introduced +to improve the possibility of synthesizing DSM. It also em- +ploys a conditional generative adversarial network to build +image-to-DSM elevation translation. Zhang and Chen [18] +improve the learning ability of abstract features of objects +of different scales by means of multi-scale feature extraction +through a multi-path fusion network. Li et al. [14] divided +the height values into intervals with increasing spacing, and +transformed the regression problem into an ordinal regression +problem, using an ordinal loss for network training. After +that, a post-processing technique is designed to convert the +predicted height map of each patch into a seamless height +map. Carvalho et al. [16] have studied various loss functions of +depth regression in depth, and combined the encoder-decoder +architecture with adversarial loss, and then proposed a new +depth estimation network D3-Net. In the hybrid methods, +Wang et al. [19] propose a joint framework incorporating +hierarchical conditional random fields, aiming to predict depth +and segmentation outcomes from a single-view remote sensing +image. Srivastava et al. [17] use a method for supervised +network training via a multi-task loss and introduce a unified +framework for elevation estimation and semantic segmentation +of single-view remote sensing image. +However, none of these methods take into account the need +for accurate elevation prediction to simultaneously guarantee +the extraction of representative features for both regular and +irregular textured objects, which is caused by the imbalance +between global and local features. To address this issue, we +propose a semantic flow field-guided DSM estimation network +to trade off local and global features. +B. Building Extraction +Many researchers +[20]–[22] have devoted themselves to +designing efficient methods for automatically extracting build- +ings, which mainly consists of methods based on hand- +crafted features and methods based on deep learning. In the +handcrafted feature-based methods, geometric, spectral, and +contextual information of buildings are used to design rep- +resentative features for accurate building extraction. Lin and +Nevatia [20] first apply edge detection to building extraction +for the detection of roofs, walls and shadows. Later, the fractal +network algorithm is proposed by Baatz [21] to segment the +image at multiple scales and extract the target building by +combining the texture and other features of the image. Wang +and Liu [22] achieve the purpose of pixel-by-pixel classifica- +tion of images by using machine learning methods to receive +input from feature vectors constructed from image texture, +shape, and structural features. However, methods based on +handcrafted features often only utilize the shallow features of +objects, ignoring the semantics of deep features. Therefore, +methods based on deep learning gradually enter the field +of vision of researchers. Minh [23] applies an image patch- +based building block extraction method to building extraction, +an early work on convolutional neural networks applied to +building extraction. On this basis, Minh also uses CRF or +post-processing to refine the results of the network. Later, +Huang et al. [24] introduce an improved DeconvNet that adds +upsampling and cheat connection operations to deconvolution +layers to achieve building extraction. Wu et al. [25] propose a +multi-constraint FCN to perform feature learning on remote +sensing images for the purpose of automatically extracting +buildings. +In this paper, we apply the popular segmentation network +DeeplabV3+ [55] to generate binary masks for buildings. +C. Building Reconstruction +The existing methods for 3D building reconstruction mainly +focus on the roof topology restoration. Researchers [26]– +[28], [30] extract roof vertices, eave lines, or segmented +planes as primitives from an image or DSM through image +segmentation, edge detection, plane patch detection, etc. After +that, the combination, segmentation, topologically analysis of +the individual geometric primitives are executed in sequence +to generate the 3D shapes of the buildings. Bulatov et al. [26] + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +4 +Elevation Semantic Globalization +L2G-ESR +PPM +L2G-ESR +L2G-ESR +L2G-ESR +Conv +Sigmoid +Linear +Linear +Linear +Query +Key +Value +Flatten +HW×C +T +C×HW +HW×HW +HW×C +HW×C +berHu Loss +Proj +Proj +L2G-ESR +Project Operation +Local-to-Global Elevation Semantic Registration +PPM +Pyramid Pooling Module +Encoder +Decoder +Fig. 2. Flowchart of the proposed Semantic Flow Field-guided DSM Estimation (SFFDE) network for DSM estimation. The proposed elevation semantic +globalization (ESG) is responsible for the global semantic representation. Furthermore, local-to-global elevation semantic registration (L2G-ESR) is introduced +to achieve the trade-off of local and global features. +extract building regions by performing vegetation and outlier +filtering on a normalized DSM (nDSM), and then combine +the extracted building pixels with operations such as graph- +based orthophoto segmentation, dominant direction extraction, +polygonization, and generalization to extract buildings contour. +Finally, they construct the building model by topologically +analyzing the roof details. Li et al. [28] classify MVS point +clouds through graph-cut based Markov random fields (MRF), +followed by RANSAC and regularized MRF for optimization +and roof structure extraction, respectively. +However, these methods suffer from the limitations of multi- +view image input or surfel geometric topology, thus bringing +great difficulties to building reconstruction in large scenes. +To address this issue, we propose a DSM estimation-driven +framework for building 3D reconstruction with single-view +remote sensing image as input. +III. OUR APPROACH +A. Overview +The flowchart of our proposed building 3D reconstruction +framework (Building3D) is illustrated in Fig. 1. As a single- +view image-based building 3D reconstruction approach, our +framework consists of four stages: DSM estimation branch, +building extraction branch, point cloud reconstruction branch +and building reconstruction branch (surface reconstruction +or CityGML reconstruction). Given an input remote sensing +image, the DSM estimation branch and the building extraction +branch first come into play to estimate the elevation informa- +tion and extract the buildings, respectively. On this basis, the +information obtained by the building extraction branch is used +to filter the information from the elevation results predicted +in the DSM estimation branch to obtain only the elevation +information of buildings. Next, the point cloud data corre- +sponding to the building is recovered according to the input +image and the predicted elevation information. Finally, surface +reconstruction or CityGML reconstruction is performed on +the point cloud of buildings obtained by the point cloud +reconstruction branch to obtain the final mesh or CityGML +model. In the following, we first introduce the semantic flow +field-driven DSM estimation (SFFDE) network, and then intro- +duce the framework’s building extraction process, point cloud +reconstruction process, and building reconstruction process. +B. Semantic Flow Field-guided DSM Estimation Network +Considering generating fine 3D point clouds, the accurate +DSM information is necessary. To address this issue, we design +a Semantic Flow Field-guided DSM Estimation (SFFDE) net- +work, as shown in Fig. 2. Our SFFDE selects PSPNet [60] as +the baseline and consists of three stages: First, a single remote +sensing image is sent into a feature extraction network (such as +resnet101) and a PPM (Pyramid Pooling Module) [60] module +to obtain high-level representations of features. Second, an +Elevation Semantic Globalization (ESG) module is introduced +for the globalization of semantic features to obtain high- +level global semantic representation. Finally, we propose a +Local-to-Global Elevation Semantic Registration (L2G-ESR) +module to achieve the registration of low-level local semantics +and high-level global semantics of features between different +resolutions. Furthermore, our SFFDE network is driven by the +berHuLoss [56] during training. +1) Elevation Semantic Globalization: The stacking of con- +volutional layers and pooling layers can increase the receptive +field, but the receptive field of the convolution kernel of +a specific layer on the original image is limited, which is +unavoidable in local operations. However, elevation estimation +based on single view remote sensing image requires more +information on the original image. If the global information +can be introduced in some layers, the problem that the local +operation of the convolution cannot capture the global infor- +mation can be well solved, and it can bring richer information +to the subsequent layers. Inspired by the transformer [40] ar- +chitecture, we introduce the Elevation Semantic Globalization +(ESG) module (Fig. 2) for the global semantic representation. + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +5 +Given feature maps F ∈ RH×W ×C(H, W, C stand for +height, width, and number of channels, respectively.), after +the feature extraction of the backbone, these feature maps +are high-level semantic features with local perception. Before +being sent to the ESG module, the feature map F is stretched +from a 2D raster image into a 1D vector (regardless of the +channel dimension), which can be formulated as: +F = flatten (F) +(1) +where F ∈ RN×C(N = H × W). The stretched feature +F goes through three fully connected layers in parallel for +feature transformation, so that the 2D raster image features are +mapped to the same space as the 1D vector features, which is +formulated as: +� +Q, K, V +� += +� +FC1(F), FC2(F), FC3(F) +� += +� +WqF, WkF, WvF +� +(2) +where Q, K, V ∈ RN×D. D is the number of channels of +the output features. Given query embeddings Query to be +enhanced and feature maps Key, Value to be fused, the ESG +operation is defined as +Fesg = ESG +� +Q, K, V +� += Softmax +� +WqF(WkF)⊤� +WvF +(3) +where Fesg ∈ RN×D is the query feature after ESG operation. +After this, we set up a multi-head ESG operation module +based on ESG operation and transformer architecture, the +formula is as follows: +Fout = MHE(WqF, WkF, WvF) +(4) +where Fout is the output features of MHE. MHE is the multi- +head ESG operation which is similar to multi-head attention +(MHA) operation [40]. Specifically, each ESG head can be +expressed as: +Headi = ESG(Q, K, V ) +(5) +where Q, K, V represents the Query, Key, and Value matrix, +respectively. Then, based on this, multi-head ESG can be +expressed mathematically as: +MultiHead(Q, K, V ) = Cat(Head1, . . . , Head8)W +(6) +where Cat is the concatenate operation and W represent the +weight of the final full connection operation. Different ESG +heads represent different subspaces, and the results of all ESG +heads are spliced together to obtain the final result through full +connection. +Next, a feature projection operation is adopted to perform +feature mapping between spatial one-dimensional features +and spatial two-dimensional features. Formally, the obtained +projection feature Fproj can be defined as: +Fproj = Relu +� +LN +� +FC(Fout) +�� +(7) +where LN is the LayerNorm [58] operation. Finally, the +projection feature Fproj ∈ RN×D is reshaped to the same +resolution as F. +2) Elevation Semantic Flow: To register features at differ- +ent resolutions, inspired by Optical Flow, we introduce the +concept of Elevation Semantic Flow (ESF). The Optical Flow +is the method that employs the changes of pixels in the image +sequence in the time domain and the correlation between +adjacent frames to find the corresponding relationship between +the previous frame and the current frame, so as to calculate +the motion of objects between adjacent frames. Analogous +to the instantaneous gray change rate of pixels at the same +location between video frames in a short period of time, we +define a semantic change rate of elevation, that is, the semantic +displacement of pixels between adjacent resolution images, +which can be expressed as: +⃗u = (∂x +∂l , ∂y +∂l ) +(8) +where l represents the varying resolution of feature maps and +⃗u is the elevation semantic flow vector, which represents the +rate of change of semantics along the x and y directions. +In space, the motion can be described by a motion field. +In the video, the motion of an object is often represented +by an optical flow field. In the feature map of the elevation +estimation network, the semantic motion can be defined by the +feature vectors represented by the pixels of the feature maps of +different resolutions. Thus, we propose to define an elevation +semantic field of F, which is formulated as: +−∂F +∂l = ∇F · ⃗u = ∂F +∂x +∂x +∂l + ∂F +∂y +∂y +∂l +(9) +Similar to the optical flow field, the elevation semantic field +is a two-dimensional vector field, which reflects the semantic +change trend of each point in the feature map. Classical optical +flow estimation is solved by a linear algebra method (such as +the LK algorithm [9]). We use an end-to-end training non- +linear optimization method and use Local-to-Global Elevation +Semantic Registration (L2G-ESR) as a constraint to learn the +elevation semantic flow field. +3) Local-to-Global Elevation Semantic Registration: Af- +ter the globalization of features, the perceptual ability of +features is extended from local to global. This enables the +network to not only perceive low-dimensional local features, +but also acquire the ability to perceive high-dimensional global +features. However, since low-dimensional local features and +global high-dimensional features are obtained by local convo- +lution and elevation semantic globalization (not convolution +operations) respectively, there is a huge span in the range of +feature perception between global features and local features. +In addition, these features do not have both local and global +perception capabilities at the same time. To address these +issues, local-to-global elevation semantic registration (L2G- +ESR) is introduced, as shown in Fig. 3. +Given the high-resolution local feature Fh and the low- +resolution globalized feature Fl, we first map Fh and Fl to +the same number of channels as: +� +�Fh, �Fl +� += +� +Conv1(Fh), Conv2(Fl) +� +(10) +where �Fh ∈ RHh×Wh×D and �Fl ∈ RHl×Wl×D are the new +features after mapping. Conv1 and Conv2 correspond to the + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +6 +Conv +Upsample +C +Flow Generation +Conv +C +Concat +Conv +Conv +Conv +Sum +Convolution +Conv +Registration Function +Elevation Semantic Flow +Output +Feature After Registration +Fig. 3. Overview of our local-to-global elevation semantic registration (L2G-ESR) module. The inputs to L2G-ESR are two features of different resolutions. +Flow generation and feature registration are performed sequentially. The pink and blue convolution blocks in the figure represent feature mapping operations +for low-resolution and high-resolution, respectively. Specifically, both convolution operations are implemented using 1x1 two-dimensional convolution, and +the input and output channel dimensions are the same. +blue and pink convolution blocks in the figure, respectively. +Specifically, both convolution operations are implemented +using 1x1 two-dimensional convolution, and the input and +output channel dimensions are the same. Then, we bilinearly +interpolate the new low-resolution features �Fl to the same +resolution as the high-resolution features �Fh. On this basis, +the two same-resolution features are fused and further encoded +into a 2D elevation semantic flow field. Mathematically, the +elevation semantic flow field S can be expressed as: +S = Conv +� +cat +� +upsample(�Fl), �Fh +�� +(11) +where upsample represents the bi-linear interpolation opera- +tion, cat is the concatenation operation, and Conv denotes +the convolution operation. The semantic flow field S +∈ +RHh×Wh×2 represents the change trend of elevation semantics +between different resolutions. The channel ‘2’ refers to the +change of semantics in both x and y directions. +Let L ∈ RHh×Hh×2 denote the coordinates of each pixel in +the feature map �Fh. Then the generated semantic flow field +S is employed to get the coordinates �L of each pixel of the +feature map after offset, as �L = L + S(x′ = x + ∆x, y′ = +y + ∆y). +Following the bi-linear sampling method in STN [59], the +pixel Freg;ab at (a, b) of the output feature Freg after feature +registration operation is defined as: +Freg;ab = R(�Fl) += +H +� +m=1 +W +� +n=1 +upsample(�Fl)mn · max(0, 1 − |�Lx;ab − m|) +· max(0, 1 − |�Ly;ab − n|) +(12) +where upsample(�Fl)mn is the pixel at (m, n) of the afore- +mentioned �Fl after upsampling. Furthermore, �Lx;ab and �Ly;ab +are the x and y coordinates of each pixel of �L. After that, the +feature Freg after registration is fused with aforementioned +�Fh, as: +Fout = I(Freg, �Fh) +(13) +where I is the aggregation function between the feature Freg +after registration and the feature �Fh. +4) Loss Function: In order to enable the network to better +regress the elevation value of the instance, we use berHu- +loss [56] as our loss function, which is expressed as +L(x) = +� |x| +|x| ≤ c +x2+c2 +2c +|x| > c +(14) +where c is the judgment threshold. Specifically, c = 0.2 × +max(|predict − gt|) in our experiments. +C. Building Extraction Network +Unlike regular segmentation network, we only focus on the +single category (buildings) of element. In the building mask +extraction process, we first perform binarization preprocessing +on the labels of the dataset. Specifically, the label value of +the pixel where the building is located is set to 1, and the +label value of the non-building pixel is set to 0. In order to +better extract building masks, we use the currently popular +Deeplabv3+ [55] as our building extraction network to extract +the building mask M, which is built on top of the backbone +ResNet-101. Given an input image, the building extraction +network outputs a mask M of the building. Specifically, the +building pixel value is 1, and the background is 0. During +training, the update of network parameters is driven by the +cross-entropy loss function. +What’s more, the canny edge detection algorithm is used +to extract the outlines of buildings. The extracted outlines +and building masks with fine pixel positioning give the next +procedures the precise building positioning. +D. Building Reconstruction +Building 3D reconstruction based on remote sensing im- +agery has always been a hot research topic. However, most +of the existing methods are limited to a single output of +the building CityGML model, and the real 3D model of +buildings has not been constructed. To address this issue, +we propose a building 3D reconstruction method based on + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +7 +building elevation information predicted by our SFFDE, Fig. 1. +After the aforementioned steps, we adopt the building masks +M to extract the elevation information of the buildings, filter +out the categories (such as vegetation) that are not of interest, +which is formulated as: +Ebuilding = E ◦ M +(15) +where E and Ebuilding are the elevation information before +and after filtering. ◦ is the Hadamard product operation. +After obtaining the elevation information of the buildings, +the two procedures of point cloud reconstruction and building +reconstruction (Surface Reconstruction or CityGML Recon- +struction) are performed sequentially. +Point Cloud Reconstruction. Generating the point cloud +data of the object is a key step to obtain the three-dimensional +structure model of the object. In this process, the obtained +DSM prediction results of each input image patch is first fused +through patch fusion to obtain a larger area of the scene. After +that, in order to smooth the gap between patches, Gaussian +filtering operation is employed to the DSM predicted results of +each large scene remote sensing image. Then, we perform 2D- +to-3D mapping of buildings based on the elevation information +of large-area building clusters to generate their 3D point cloud +data. The latitude and longitude coordinates corresponding to +the pixels are used as the x, y coordinates of the point cloud, +and the elevation information is used as the z coordinates of +the point cloud. +Mesh and CityGML Model. Mesh refers to a polygonal +grid, which is a data structure used in computer graphics for +modeling various irregular objects. In the face of the polygon +mesh, the triangular face is the smallest unit to be divided, +so it is often referred to as the triangular face. The basic +components of a mesh: vertices, edges, and faces. CityGML +is a data format used to construct virtual 3D city models, and +is a general data model used to express 3D city templates. +CityGML can not only express the graphic appearance of the +city model, but also take care of the semantic representation, +such as the classification and aggregation of digital terrain +models, vegetation and water systems, etc. All models can +be divided into five different coherent levels of detail (LOD), +with increasing level of detail to obtain more details about +the geometry and themes. The five consecutive levels of detail +are: LOD0, LOD1, LOD2, LOD3, and LOD4. The CityGML +model reconstructed in this paper is the LOD1 model in five +coherent levels of detail. +Surface Reconstruction. Based on the point cloud data of +the building generated in the previous steps, we first normalize +the point cloud to facilitate the subsequent reconstruction +process. Then, we perform Poisson [57] reconstruction on the +normalized point cloud data to obtain the mesh model of the +building. +CityGML Reconstruction. To verify the effectiveness of +our method, we also extend the SFFDE network to the +algorithm for building CityGML model reconstruction in our +Building3D. After our building3D performs the 3D point cloud +mapping operation, we also extract the polygonal structure of +the building from the image at the same time. Combining the +obtained 3D point cloud and building polygon structure, we +use 3dfier [61] to reconstruct the building CityGML model +from single-view remote sensing images. +IV. EXPERIMENTS +In this section, we first give an introduction to the datasets +used by our entire framework. Next, we introduce the spe- +cific experimental setup (including evaluation protocols and +completion details) in the experiments. Then, we show the +performance and visualization results of our proposed SFFDE +on elevation estimation. After that, a reconstruction analysis of +the entire reconstruction framework Building3D is presented. +Finally, to demonstrate the effectiveness of the proposed +elevation semantic globalization operation and local-to-global +elevation semantic registration operation, we conduct extensive +ablation experiments. +A. Datasets +1) ISPRS Vaihingen: There are a total of 33 slices in the IS- +PRS Vaihingen [64] dataset and each slice has approximately +2500×2500 pixels. Each remote sensing image is accompanied +by orthophoto images, semantic labels and digital surface +models (DSM and nDSM). The ground sampling distance of +each image is 9 cm, and it has three channels of near-infrared, +red and green. According to the official split, 16 slices that +provided ground truth are used for the training of models, +and the remaining 17 slices are used for evaluation by the +challenger organizer. +2) 2019 Data Fusion Contest: The 2019 Data Fusion Con- +test (DFC2019) [31] dataset currently includes approximately +100 square kilometers of coverage for Jacksonville, Florida, +and Omaha, Nebraska, USA. The ground sampling distance +(GSD) is about 30 cm, and each image with semantic labels +and normalized DSM is 1024×1024 pixel in size. The dataset +provides WorldView-3 panchromatic and 8-band visible and +near-infrared (VNIR) images. DFC2019 includes 26 images +collected in Jacksonville, Florida, and 43 images collected in +Omaha, Nebraska, USA. +B. Experimental Settings +1) Evaluation Protocols: We use six metrics to evaluate +the DSM estimation performance of our proposed method, +including mean relative error (Rel), RMSE, RMSE(log), and +the ratio of pixels with predicted elevation values close to +the ground truth (δ1, δ2, δ3). Among them, mean relative error +(Rel), RMSE, RMSE(log) are expressed as: +Rel = 1 +N +N +� +i=1 +|Di − D∗ +i | +D∗ +i +(16) +RMSE = +� +� +� +� 1 +N +N +� +i=1 +|Di − D∗ +i |2 +(17) +RMSE(log) = +� +� +� +� 1 +N +N +� +i=1 +|logDi − logD∗ +i |2 +(18) + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +8 +TABLE I +THE PERFORMANCE OF DSM ESTIMATION ON ISPRS VAIHINGEN DATASET. ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE +PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE. +Method +Rel↓ +RMSE↓/m +RMSE(log)↓ +δ1 ↑ +δ2 ↑ +δ3 ↑ +Amirkolaee et al. [11] +1.163 +2.871 +0.334 +0.330 +0.572 +0.741 +IMG2DSM [15] +- +2.58±0.09 +- +- +- +- +D3Net [16] +2.016 +2.123 +- +0.369 +0.533 +0.644 +Li et al. [14] +0.314 +1.698 +0.155 +0.451 +0.817 +0.939 +SFFDE + ResNet50 (ours) +0.225 +1.145 +0.087 +0.624 +0.841 +0.933 +SFFDE + ResNet101 (ours) +0.222 +1.133 +0.084 +0.595 +0.897 +0.970 +where N is the number of the pixels, Di is the predicted +elevation value of the i-th pixel, and D∗ +i is the ground truth +of the i-th pixel. What’s more, the δi is expressed as: +δi = max(hpred +hgt +, hgt +hpred +) +(19) +where hgt and hpred are the ground truth and predicted +elevation value. +2) Implementation Details: Our framework is implemented +based on PyTorch Library. The momentum SGD algorithm +with the momentum value set to 0.9 is employed to optimize +both the DSM estimation branch and the building extraction +branch. We train our model for 80000 iterations and the +initial and minimum learning rate is set to 0.005 and 0.00002, +respectively. The weight decay value is set to 0.0005 for regu- +larization. Our DSM estimation branch and building extraction +branch are both executed on a single NVIDIA TITAN RTX +GPU with batch size set to 4. Considering the huge size of +each image in both Vaihingen and DFC2019 datasets make +the images unable to directly be sent to the network due to +the GPU memory limit, we employ a sliding window strategy +to generate small image patches with 512×512 pixels. +When evaluating accuracy, for each dataset, we only select +the checkpoint saved in the last iteration (80000 iteration) for +testing. The number of training iterations is set in considera- +tion of ensuring the model is converged and stable. The choice +of checkpoint is based on the weight file saved in the last +iteration. +C. Performance Analysis of DSM Estimation +1) ISPRS Vaihingen: We compared the DSM estimation +performance by our SFFDE with other prediction networks, +such as Amirkolaee et al. [11], IMG2DSM [15], D3Net [16], +and Li et al. [14]. In Table I, the comparisons between our +SFFDE network and these methods on the ISPRS Vaihin- +gen dataset are given. It is clear that our SFFDE network +achieves the highest performance for the elevation estimation +task. Regardless of choosing ResNet50 or ResNet101 as the +backbone, our SFFDE outperforms state-of-the-art methods +on all metrics. Rel, RMSE and RMSE(log) are indicators +that describe the prediction error of the model. Among these +metrics, with the ResNet101 backbone, our SFFDE achieves +0.222 Rel, 1.133 RMSE and 0.084 RMSE(log), achieving +the best performance. This shows that the prediction results +of our SFFDE maintain a high consistency with the ground +truth. What’s more, δ1, δ2 and δ3 are indicators describing +the prediction accuracy of the model. Note that for the +indicators (δ1, δ2, δ3), SFFDE achieves the highest δi value, +which strongly demonstrates the elevation value predicted by +our SFFDE is close to the ground truth elevation value. This +again proves that the local and global semantic registration +implemented by SFFDE can improve the accuracy of elevation +prediction. +The reason is that our SFFDE can use elevation semantic +globalization (ESG) to achieve global feature extraction and +local-to-global elevation semantic registration (L2G-ESR) to +achieve global and local feature registration. Based on the +concept of elevation semantic flow, we can well explicitly +model the semantic change rate of semantic features describing +elevation across different resolutions. +2) DFC2019: In Table II, our SFFDE network is compared +with other state-of-the-art DSM estimation methods (including +D3Net [16], DORN [13], and FastDepth [12]) on DFC2019 +dataset. Clearly, our SFFDE outperforms all existing elevation +estimation methods on the DFC2019 dataset. Table II displays +the evaluation estimation results of our SFFDE network. +Whether we choose ResNet50 or ResNet101 as our backbone, +SFFDE again outperforms state-of-the-art methods on all +indicators. For the ResNet101 backbone, SFFDE improves +FastDepth by 0.108 (0.492 vs. 0.384) on δ1, 0.081 (0.782 vs. +0.701) on δ2, and 0.033 (0.908 vs. 0.875) on δ3, which are +large margins for the challenging DSM estimation problem. +Compared with the ISPRS Vaihingen dataset, the DFC2019 +dataset has more complex scenes and diverse instances, which +undoubtedly brings great difficulties to the depth estimation +problem. However, our SFFDE not only performs the best on +the ISPRS Vaihingen dataset, but also has the highest per- +formance on the DFC2019 dataset, which once again proves +that our proposed feature registration based on the elevation +semantic flow field can well improve complex scenes elevation +prediction performance. +D. Visualization Analysis +1) DSM Visualizations on ISPRS Vaihingen: As shown in +Fig. 4, local area visualizations of the DSM estimation results +of SFFDE is given on the ISPRS Vaihingen dataset. From +the visualized results, we can conclude that our SFFDE has +high accuracy for building elevation prediction, and the pre- +diction results are basically consistent with the ground truth. +Furthermore, the visualization clearly shows that our predicted + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +9 +TABLE II +THE PERFORMANCE OF DSM ESTIMATION ON DFC2019 DATASET. ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE +PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE. +Method +Rel↓ +RMSE(log)↓ +δ1 ↑ +δ2 ↑ +δ3 ↑ +D3Net [16] +0.526 +0.208 +0.256 +0.635 +0.846 +DORN [13] +0.488 +0.200 +0.317 +0.646 +0.859 +FastDepth [12] +0.383 +0.189 +0.384 +0.701 +0.875 +SFFDE + ResNet50 (ours) +0.272 +0.029 +0.601 +0.778 +0.882 +SFFDE + ResNet101 (ours) +0.330 +0.024 +0.492 +0.782 +0.908 +Input +Ground Truth +Result +Input +Ground Truth +Result +Fig. 4. Visualizations of the predicted elevation results (512 × 512 patches) of our SFFDE network on ISPRS Vaihingen dataset. +instance elevations are well-defined. At instance boundaries, +our method has small prediction errors and aliasing. +As shown in Fig. +5, we also present the visualization +results of the elevation prediction for a large area of the ISPRS +Vaihingen dataset. The images of three large scenes (Area 4 +contains a large number of buildings, Areas 27 and 29 have +both regular and irregular texture instances, and Area 33 has +more interior details of buildings) are selected as the inputs +of our SFFDE and the prediction results are visualized. From +the visualization results of Area 4, our method is able to make +good elevation predictions for areas with dense buildings. In +these densely built areas, the buildings are all structures with +high roofs in the center and low on both sides. Nonetheless, +our visualizations fit this phenomenon well, yielding high +predictive performance. This is highlighted in the middle of the +roof in the picture, and the sides are darker to demonstrate that. +Areas 27 and 29 contain a large number of regular and irregu- +lar instances such as buildings and trees. For the regions where +these regular and irregular instances coexist, this requires the +model to have high generalization performance. From the +visualization results, our SFFDE achieves superior elevation +prediction performance and can guarantee high accuracy for +both regular and irregular texture instances. This benefits from +the higher performance of our proposed elevation semantic +flow-based feature registration. Furthermore, our SFFDE can +predict the detailed structure of buildings well, as can be seen + +HHHHJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +10 +Area 4 +Our Result +Area 33 +Area 27 +Input Images +Our Result +Input Images +Area 29 +Fig. 5. Visualizations of the predicted elevation results (large areas) of our SFFDE network on ISPRS Vaihingen dataset. +from the results for Area 33. On top of complex buildings, +smooth roofs and complex structures coexist. In our prediction +results, the high accuracy of the smooth roof prediction is +reflected in the smoothness of the elevation prediction of the +roof, which is proved by the basically consistent colors of +the smooth areas in the figure. In addition, in the region of +complex structure, our SFFDE gives fine boundary structure +prediction results. This is superior to other advanced methods. +2) DSM Visualizations on DFC2019: To verify the perfor- +mance of our SFFDE, we also conduct experiments on the +DFC2019 dataset and give high performance. Furthermore, +we present the prediction visualization results of our SFFDE +on the DFC2019 dataset in Fig. 6. Since DFC2019 contains +complex instances such as bridges, buildings, trees, etc., our +visualization results all contain these complex instances. It +can be seen from the visualization results that the elevation +information of various instances we predicted is basically +consistent with the ground truth. Furthermore, for regularly +textured objects such as buildings and bridges, our prediction +results have clear boundary information and smooth internal +structures, which are extremely challenging problems in eleva- +tion prediction tasks. Nonetheless, our SFFDE exhibits high +prediction performance, which validates the effectiveness of +our method. In addition, we also achieved high prediction +accuracy for objects with irregular textures such as trees. +3) Feature Map Visualizations: Feature map visualizations +on the ISPRS Vaihingen dataset are given as shown in +Fig. +8. As noted in the figure, the visualization consists of +four columns, which are the input image, the feature map +before globalization and registration, the feature map after +globalization, and the feature map after global-local semantic +registration. From the feature map after globalization, we can +infer that the feature obtains a global receptive field, not only +limited to local perception. In addition, the registered feature +map can clearly observe the object and its detailed information, +and the internal features of the instance are smooth and the +pixel values tend to be continuous. This matches well with +better regression problems. Therefore, from the visualization +results of the two-part feature maps, it can be seen that our +network can simultaneously ensure the feature’s ability to +perceive the global and the local perception of details, and +achieve a better balance between global and local features. +E. Building3D Reconstruction Analysis +1) Building Extraction: As shown in Fig. 7, the visualiza- +tion results of the building extraction network in Building3D +framework are given. We not only visualize the local building +area in Vaihingen, but also visualize the extraction results of +building groups in a large area. Based on the superior building +extraction network, we can see that the extracted building area +is basically consistent with the actual building area, achieving +extremely high building extraction performance. This lays a +good foundation for subsequent building elevation extraction, +building point cloud reconstruction and surface reconstruction. +2) Surface Reconstruction: Given a single-view remote +sensing image of an area, after the building elevation pre- + +HJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +11 +Input +Ground Truth +Result +Input +Ground Truth +Result +Fig. 6. Visualizations of the predicted elevation results (512 × 512 patches) of our SFFDE network on DFC2019 dataset. +Result +Input +Result +Input +Result +Input +Fig. 7. Visualizations of the building extraction network in our Building3D framework. The left part is the building extraction results of the image patches, +and the right part is the extraction results of large area buildings. + +HHHHHJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +12 +Input +After +Globalization +After +Registration +Input +After +Globalization +After +Registration +Before +Globalization & +Registration +Before +Globalization & +Registration +Fig. 8. Visualizations of the feature maps after globalization and registration. The first column is the input of our SFFDE, the second column is the feature +before globalization and registration, the third column is the feature map after globalization, and the fourth column is the feature map after registration. +Single-view Image +Point Cloud +Mesh +Point Cloud with Color +Fig. 9. Visualizations of point cloud and surface mesh of the input single-view image. The first column is the input single-view images, the second column +is the reconstructed point clouds, the third column is the reconstructed point clouds with color, and the last column is the reconstructed mesh models of the +input images. + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +13 +TABLE III +ABLATION STUDIES ON ISPRS VAIHINGEN DATASET. ‘ESG’ DENOTES ELEVATION SEMANTIC GLOBALIZATION. ‘L2G-ESR’ REPRESENTS +LOCAL-TO-GLOBAL ELEVATION SEMANTIC REGISTRATION. ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND +↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE. +Method +Rel↓ +RMSE↓/m +RMSE(log)↓ +δ1 ↑ +δ2 ↑ +δ3 ↑ +ResNet-50 +Baseline +0.367 +1.330 +0.135 +0.357 +0.618 +0.819 ++ESG +0.277 +1.188 +0.109 +0.542 +0.800 +0.915 ++ESG + L2G-ESR (ours) +0.225 +1.145 +0.087 +0.624 +0.841 +0.933 +ResNet-101 +Baseline +0.358 +1.293 +0.130 +0.374 +0.701 +0.870 ++ESG +0.276 +1.282 +0.111 +0.534 +0.843 +0.952 ++ESG + L2G-ESR (ours) +0.222 +1.133 +0.084 +0.595 +0.897 +0.970 +Single-view Image +Output +Single-view Image +Output +Fig. 10. Visualizations of LOD1 model of buildings in the input single-view +image. +diction and building extraction steps mentioned above are +completed, the next process is to reconstruct the building in +3D. Based on the extracted building areas, we filter the pre- +dicted elevation information to obtain building elevations. The +visualization results of building surface reconstruction based +on single-view remote sensing images are given in the Fig. +9. Given a single-view remote sensing image, our Building3D +outputs a point cloud and mesh of the building. From Fig. 9 +we can see that the building has been converted into a 3D +structure, while other elements such as cars, vegetation, etc. +have not been converted. The first column in Fig. 9 shows the +input single-view image. On the basis of the obtained building +elevations, we perform 3D mapping on the recovered elevation +information to obtain 3D point clouds. The results of the 3D +point cloud visualization of the mapped buildings are given +in the second column of the figure. In order to better show +the point cloud results, we also attached the color to the point +cloud, which is given in the third column of the figure. Based +on the recovered 3D point cloud, the surface reconstruction +results of the building are shown in the fourth column of the +figure. Clearly, our framework generates high-quality 3D point +cloud data and builds a 3D model when there is only the +single-view image. This provides an insightful idea for rapid +3D reconstruction of large-scale buildings. +3) CityGML Reconstruction: For the reconstruction of the +CityGML model of the buildings, our Building3D adopts the +3dfier [61] approach. The input is the point cloud data obtained +in the previous steps and the polygon structure of the buildings, +and the output is the LOD1 model of the buildings. The +reconstruction results are given in Fig. +10. Obviously, the +building elevation information predicted by our SFFDE can +restore the building elevation well, laying a foundation for the +3D reconstruction of different forms of buildings. +F. Extension +1) Large area building reconstruction: We test the robust- +ness experiments on remote sensing images of the whole urban +area in Hefei, Anhui Province, China. As shown in Fig. 11, we +give the remote sensing images of the entire area, the building +extraction results, the DSM prediction results, and the building +LOD1 model reconstruction results, respectively. +G. Ablation Study +We conduct ablation studies on ISPRS Vaihingen dataset to +verify the effectiveness of our SFFDE. PSPNet [60] is selected +as the baseline. +1) ESG: As shown in Table III, with elevation semantic +globalization, our SFFDE with ResNet101 as the backbone +improves the DSM estimation performance by 0.082 (0.276 +vs. 0.358) on Rel, 0.011 (1.282 vs. 1.293) on RMSE, and +0.019 (0.111 vs. 0.130) on RMSE(log), which validates +that the features with global dependency improve estimation +performance more significantly. Before globalization, features +of the network are limited to local perception, so that the +perception of texture regular and irregular instances cannot +be provided at the same time. However, after adding ESG, +the perception ability of the network is extended from local +to global, laying the foundation for subsequent high-level +semantic extraction. At the same time, the introduction of +ESG also provides a priori global features for the subsequent +registration of global and local features. +Channel Number of ESG. In order to better utilize the +globalization ability of ESG operations, we conduct abla- +tion experiments on the number of input feature channels. +For better visualization, we show spider plots with different +channel numbers, as shown in Fig. +12. In order to better +display the spider chart, we have performed negative index +operations (e−x, x is the corresponding indicator) on the three +indicators of Rel, RMSE, and RMSE(log). Based on this, the +six indicators are all closer to the periphery on behalf of higher + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +14 +Building Extration +DSM Estimation +CityGML Reconstruction +(local area) +c +Large Area Image +CityGML Reconstruction +Fig. 11. Visualization Results of large area building reconstruction. The large image is obtained from the urban area of Hefei City, Anhui Province, China. +256 +512 +1024 +-RMSE +e +-Rel +e +-RMSE(log) +e +-RMSE +e +-Rel +e +-RMSE(log) +e +Fig. 12. +Ablation studies of the channel number of elevation semantic +globalization (ESG). +performance. As can be seen from the Fig. +12, when the +number of channels is 256, the values of all indicators are +located at the outermost periphery, which means that ESG has +the best performance at this time. +2) Backbone Selection: To verify the influence of dif- +ferent backbones on our method, we conduct experiments +on resnet50 and resnet101 respectively. As shown in the +table, we add the proposed elevation semantic globalization +operation and L2G-ESR operation on the basis of resnet50 +and resnet101, respectively. We make a horizontal comparison +of the backbone, then we come to the conclusion that the +prediction accuracy of selecting resnet101 as the backbone as +a whole is higher than resnet50. Similarly, after adding ESG +and L2G-ESR, the overall performance of the resnet101-based +network is also better than that of resnet50. This is consistent +with our prior knowledge perception. +3) L2G-ESR: In Table III, L2G-ESR further improves the +performance by 0.054 (0.222 vs. 0.276) on Rel, 0.149 +(1.133 vs. 1.282) on RMSE, and 0.027 (0.084 vs. 0.111) +on RMSE(log), which validates that L2G-ESR implements +the registration and trade-off of local and global features. +This clearly demonstrates the superiority of SFFDE over other +methods on local and global feature representation. After L2G- +ESR, the features of the network are locally and globally +registered through the concept of a defined elevation semantic +flow. This enables the network to perceive the surrounding +pixel features finely in both global and local structure. + +3 +J +B6] +04 +a.0 +8.0 +BW2EJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +15 +ISPRS Vaihingen +DFC2019 +-RMSE +-Rel +-RMSE(log) +-RMSE +-Rel +-RMSE(log) +e +e +e +-RMSE +-Rel +-RMSE(log) +e +e +e +-RMSE(log) +-Rel +-RMSE(log) +-Rel +e +e +-RMSE(log) +-Rel +e +e +Ours +Li et al. +Amirkolaee +et al. +Ours +FastDepth +DORN +D3Net +Fig. 13. Performance spider plots on ISPRS Vaihingen dataset and DFC2019 dataset. +TABLE IV +ABLATION STUDIES ON AGGREGATION OPERATION. ‘CONCAT JOINT CONV’ DENOTES CONCATENATION JOINT CONVOLUTION. ‘ELEMENT-WISE ADD’ +REPRESENTS THE ELEMENT-WISE ADDITION OPERATION. ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ +MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE. +Aggregation Operation +Rel↓ +RMSE↓/m +RMSE(log)↓ +δ1 ↑ +δ2 ↑ +δ3 ↑ +Concat joint Conv +0.263 +1.252 +0.101 +0.563 +0.718 +0.919 +Element-wise Add +0.225 +1.145 +0.087 +0.624 +0.841 +0.933 +TABLE V +ABLATION STUDIES ON LOSS FUNCTIONS. ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT +THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE. +Loss Function +Rel↓ +RMSE↓/m +RMSE(log)↓ +δ1 ↑ +δ2 ↑ +δ3 ↑ +L1Loss +0.298 +1.265 +0.100 +0.548 +0.820 +0.912 +MSELoss +0.293 +1.210 +0.099 +0.543 +0.836 +0.933 +berHuLoss +0.225 +1.145 +0.087 +0.624 +0.841 +0.933 +Aggregation Operation I. As shown in Eq. 13, there are +two options in our L2G-ESR feature aggregation: (1) con- +catenate operation combined with convolution; (2) element- +wise addition. We conduct ablation experiments for these two +operations, and the experimental results are shown in Table +IV. As can be seen from the table, element-wise addition +achieves higher performance. Compared with the operation of +concatenation joint convolution, element-by-element addition +not only does not add redundant parameters, but also enables +the network to run efficiently. +4) Loss Function: In order to choose the best loss function +as the learning direction of the network, we choose L1loss, +MSEloss, and berHuLoss for ablation experiments. As shown +in Table +V, choosing berHuloss as the loss function for +network training enables the network to achieve the best +prediction performance. Nonetheless, choosing L1loss and +MSEloss also achieves impressive performance, in contrast to +the baseline. This side reflects the effectiveness of our ESG +and L2G-ESR. +5) Performance Spider Plots: To illustrate the predicted +performance of our SFFDE, we visualize the spider plots of +the performance, Fig. +13. We compare with Li et al. [14] +and Amirkolaee et al. [11] on the ISPRS dataset. On the +DFC2019 dataset, comparisons with D3Net [16], DORN [13] +and FastDepth [12] are given. Since the three indicators of +Rel, RMSE, and RMSE(log) are lower, the better, so we +carry out negative index processing (e−x). Based on this, +these six indicators are all as high as possible. We present +the performance spider plots for the ISPRS Vaihingen dataset +and the DFC2019 dataset, respectively. Since the higher the +indicator value, the better the performance, the closer the +indicator value of the spider plot is to the periphery, the +higher the performance. It is obvious that our SFFDE is at +the outermost periphery of the spider plot, whether it is the +ISPRS Vaihingen dataset or the DFC2019 dataset. Therefore, +this shows that our SFFDE outperforms existing methods in +either metric. +V. CONCLUSION +We propose a framework (Building3D) for creating 3D +building models from single-view remote sensing imagery. +Our Building3D is rooted in the proposed SFFDE network to + +3 +5 +B6] +O'5 +04 +8.0 +J +ja(BW2E)m +J +B6] +04 +a.0 +8.0 +BW2EJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +16 +achieve globalization of semantics and registration of global +features with local features through the proposed ESG and +L2G-ESR. Extensive experiments on the commonly used +ISPRS Vaihingen and DFC2019 datasets demonstrate the +superiority of SFFDE for DSM estimation, providing accurate +elevation information for building reconstruction and δ1, δ2 +and δ3 metrics of our SFFDE are improved to 0.595, 0.897 +and 0.970. Building3D achieves 3D reconstruction of large- +area buildings in a single-view image by utilizing SFFDE +elevation estimation, building mask extraction, point cloud +reconstruction and building reconstruction, which is in sharp +contrast to other methods based on multi-view images. Build- +ing3D not only reduces data acquisition costs, but also enables +rapid and large-area building reconstruction. As a novel-and- +efficient method, Building3D provides a fresh perspective into +challenging 3D reconstruction of buildings. Although the 3D +reconstruction effect is still greatly improved, we will continue +to study to generate more refined 3D reconstruction results. +For the lattice-like stripes phenomenon, we will work in +future research. First, we will focus on large-scale images as +input to build a neural network for learning, which greatly +reduces the number of patch edges. In addition, we will +also work on the design of more accurate inter-patch fusion +methods. For the overall network architecture, although our +Building3D adopts the method of elevation estimation and +building extraction parallel reasoning in the overall architec- +ture to improve efficiency, the number of network parameters +has increased. In view of this, we plan to introduce a multi- +task learning method in the follow-up research, by inputting +a single image block and simultaneously performing multi- +task output (elevation regression head and building extraction +head). +REFERENCES +[1] X. Li, L. Wang, and Y. Fang, “Geometry-aware segmentation of re- +mote sensing images via implicit height estimation,” arXiv preprint +arXiv:2006.05848, 2020. +[2] E. Mahdi, Z. Ziming, and H. Xinming, “Aerial height prediction and +refinement neural networks with semantic and geometric guidance,” +arXiv preprint arXiv:2011.10697, 2020. +[3] L. Mou and X. X. Zhu, “Im2height: Height estimation from single +monocular imagery via fully residual convolutional-deconvolutional net- +work,” arXiv preprint arXiv:1802.10249, 2018. +[4] Y. Wang, W. Ding, R. Zhang, and H. Li, “Boundary-aware multitask +learning for remote sensing imagery,” IEEE Journal of selected topics +in applied earth observations and remote sensing, vol. 14, pp. 951–963, +2020. +[5] D. Batra and A. Saxena, “Learning the right model: Efficient max-margin +learning in laplacian crfs,” in 2012 IEEE Conference on Computer Vision +and Pattern Recognition. +IEEE, 2012, pp. 2136–2143. +[6] A. Saxena, S. Chung, and A. Ng, “Learning depth from single monocular +images,” Advances in neural information processing systems, vol. 18, +2005. +[7] W.-S. Hu, H.-C. Li, R. Wang, F. Gao, Q. Du, and A. Plaza, “Pseudo +complex-valued deformable convlstm neural network with mutual atten- +tion learning for hyperspectral image classification,” IEEE Transactions +on Geoscience and Remote Sensing, vol. 60, pp. 1–17, 2022. +[8] H.-C. Li, W.-S. Hu, W. Li, J. Li, Q. Du, and A. Plaza, “A3clnn: +Spatial, spectral and multiscale attention convlstm neural network +for multisource remote sensing data classification,” arXiv preprint +arXiv:2204.04462, 2022. +[9] B. D. Lucas, T. Kanade et al., An iterative image registration technique +with an application to stereo vision. +Vancouver, 1981, vol. 81. +[10] A. Saxena, S. H. Chung, and A. Y. Ng, “3-d depth reconstruction from +a single still image,” International journal of computer vision, vol. 76, +no. 1, pp. 53–69, 2008. +[11] H. A. Amirkolaee and H. Arefi, “Height estimation from single aerial +images using a deep convolutional encoder-decoder network,” ISPRS +journal of photogrammetry and remote sensing, vol. 149, pp. 50–66, +2019. +[12] D. Wofk, F. Ma, T.-J. Yang, S. Karaman, and V. Sze, “Fastdepth: Fast +monocular depth estimation on embedded systems,” in 2019 Interna- +tional Conference on Robotics and Automation (ICRA). +IEEE, 2019, +pp. 6101–6108. +[13] H. Fu, M. Gong, C. Wang, K. Batmanghelich, and D. Tao, “Deep ordinal +regression network for monocular depth estimation,” in Proceedings of +the IEEE conference on computer vision and pattern recognition, 2018, +pp. 2002–2011. +[14] X. Li, M. Wang, and Y. Fang, “Height estimation from single aerial +images using a deep ordinal regression network,” IEEE Geoscience and +Remote Sensing Letters, 2020. +[15] P. Ghamisi and N. Yokoya, “Img2dsm: Height simulation from single +imagery using conditional generative adversarial net,” IEEE Geoscience +and Remote Sensing Letters, vol. 15, no. 5, pp. 794–798, 2018. +[16] M. Carvalho, B. Le Saux, P. Trouv´e-Peloux, A. Almansa, and F. Cham- +pagnat, “On regression losses for deep depth estimation,” in 2018 25th +IEEE International Conference on Image Processing (ICIP). +IEEE, +2018, pp. 2915–2919. +[17] S. Srivastava, M. Volpi, and D. Tuia, “Joint height estimation and +semantic labeling of monocular aerial images with cnns,” in 2017 IEEE +International Geoscience and Remote Sensing Symposium (IGARSS). +IEEE, 2017, pp. 5173–5176. +[18] Y. Zhang and X. Chen, “Multi-path fusion network for high-resolution +height estimation from a single orthophoto,” in 2019 IEEE International +Conference on Multimedia & Expo Workshops (ICMEW). +IEEE, 2019, +pp. 186–191. +[19] P. Wang, X. Shen, Z. Lin, S. Cohen, B. Price, and A. L. Yuille, +“Towards unified depth and semantic prediction from a single image,” +in Proceedings of the IEEE conference on computer vision and pattern +recognition, 2015, pp. 2800–2809. +[20] C. Lin and R. Nevatia, “Building detection and description from a single +intensity image,” Computer vision and image understanding, vol. 72, +no. 2, pp. 101–121, 1998. +[21] M. Baatz, “Object-oriented and multi-scale image analysis in semantic +networks,” in Proc. the 2nd International Symposium on Operational- +ization of Remote Sensing, Enschede, ITC, Aug. 1999, 1999. +[22] Z. Wang and W. Liu, “Building extraction from high resolution imagery +based on multi-scale object oriented classification and probabilistic +hough transform,” in Proceedings of 2005 International Geoscience and +Remote Sensing Symposium (IGARSS’05), Seoul, South Korea, 2005, pp. +25–29. +[23] V. Mnih, Machine learning for aerial image labeling. +University of +Toronto (Canada), 2013. +[24] Z. Huang, G. Cheng, H. Wang, H. Li, L. Shi, and C. Pan, “Building +extraction from multi-source remote sensing images via deep deconvo- +lution neural networks,” in 2016 IEEE International Geoscience and +Remote Sensing Symposium (IGARSS). +Ieee, 2016, pp. 1835–1838. +[25] G. Wu, X. Shao, Z. Guo, Q. Chen, W. Yuan, X. Shi, Y. Xu, and +R. Shibasaki, “Automatic building segmentation of aerial imagery using +multi-constraint fully convolutional networks,” Remote Sensing, vol. 10, +no. 3, p. 407, 2018. +[26] D. Bulatov, G. H¨aufel, J. Meidow, M. Pohl, P. Solbrig, and P. Wernerus, +“Context-based automatic reconstruction and texturing of 3d urban +terrain for quick-response tasks,” ISPRS Journal of Photogrammetry and +Remote Sensing, vol. 93, pp. 157–170, 2014. +[27] Y. Yan, F. Gao, S. Deng, and N. Su, “A hierarchical building segmen- +tation in digital surface models for 3d reconstruction,” Sensors, vol. 17, +no. 2, p. 222, 2017. +[28] M. Li, L. Nan, N. Smith, and P. Wonka, “Reconstructing building mass +models from uav images,” Computers & Graphics, vol. 54, pp. 84–93, +2016. +[29] D. Yu, S. Ji, J. Liu, and S. Wei, “Automatic 3d building reconstruction +from multi-view aerial images with deep learning,” ISPRS Journal of +Photogrammetry and Remote Sensing, vol. 171, pp. 155–170, 2021. +[30] F. Alidoost, H. Arefi, and F. Tombari, “2d image-to-3d model: +Knowledge-based 3d building reconstruction (3dbr) using single aerial +images and convolutional neural networks (cnns),” Remote Sensing, +vol. 11, no. 19, p. 2219, 2019. +[31] M. Bosch, K. Foster, G. Christie, S. Wang, G. D. Hager, and M. Brown, +“Semantic stereo for incidental satellite images,” in 2019 IEEE Winter +Conference on Applications of Computer Vision (WACV). +IEEE, 2019, +pp. 1524–1532. + +JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 +17 +[32] J. Kim, “3d reconstruction from very high resolution satellite stereo and +its application to object identification,” The International Archives of +the Photogrammetry, remote sensing and spatial information Sciences, +vol. 4, pp. 420–426, 2002. +[33] G. Kuschk, “Model-free dense stereo reconstruction for creating realistic +3d city models,” in Joint Urban Remote Sensing Event 2013. +IEEE, +2013, pp. 202–205. +[34] O. C. Ozcanli, Y. Dong, J. L. Mundy, H. Webb, R. Hammoud, and +T. Victor, “Automatic geo-location correction of satellite imagery,” in +Proceedings of the IEEE Conference on Computer Vision and Pattern +Recognition Workshops, 2014, pp. 307–314. +[35] X. Sun, P. Wang, C. Wang, Y. Liu, and K. Fu, “Pbnet: Part-based +convolutional neural network for complex composite object detection in +remote sensing imagery,” ISPRS Journal of Photogrammetry and Remote +Sensing, vol. 173, pp. 50–65, 2021. +[36] C. R. Qi, H. Su, K. Mo, and L. J. Guibas, “Pointnet: Deep learning on +point sets for 3d classification and segmentation,” in Proceedings of the +IEEE conference on computer vision and pattern recognition, 2017, pp. +652–660. +[37] Y. Mao, X. Sun, W. Diao, K. Chen, Z. Guo, X. Lu, and K. Fu, “Semantic +segmentation for point cloud scenes via dilated graph feature aggregation +and pyramid decoders,” arXiv preprint arXiv:2204.04944, 2022. +[38] Y. Mao, K. Chen, W. Diao, X. Sun, X. Lu, K. Fu, and M. Weinmann, +“Beyond single receptive field: A receptive field fusion-and-stratification +network for airborne laser scanning point cloud classification,” ISPRS +Journal of Photogrammetry and Remote Sensing, vol. 188, pp. 45–61, +2022. +[39] G. Deng, Z. Wu, C. Wang, M. Xu, and Y. Zhong, “Ccanet: Class- +constraint coarse-to-fine attentional deep network for subdecimeter aerial +image semantic segmentation,” IEEE Transactions on Geoscience and +Remote Sensing, vol. 60, pp. 1–20, 2021. +[40] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, +Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in +neural information processing systems, vol. 30, 2017. +[41] L. Mou, Y. Hua, and X. X. Zhu, “Relation matters: Relational context- +aware fully convolutional network for semantic segmentation of high- +resolution aerial images,” IEEE Transactions on Geoscience and Remote +Sensing, vol. 58, no. 11, pp. 7557–7569, 2020. +[42] H. Wei, Y. Zhang, Z. Chang, H. Li, H. Wang, and X. Sun, “Oriented +objects as pairs of middle lines,” ISPRS Journal of Photogrammetry and +Remote Sensing, vol. 169, pp. 268–279, 2020. +[43] H. Wei, Y. Zhang, B. Wang, Y. Yang, H. Li, and H. Wang, “X-linenet: +Detecting aircraft in remote sensing images by a pair of intersecting +line segments,” IEEE Transactions on Geoscience and Remote Sensing, +vol. 59, no. 2, pp. 1645–1659, 2020. +[44] K. Wang, C. Stutts, E. Dunn, and J.-M. Frahm, “Efficient joint stereo +estimation and land usage classification for multiview satellite data,” +in 2016 IEEE Winter Conference on Applications of Computer Vision +(WACV). +IEEE, 2016, pp. 1–9. +[45] B. Wu, X. Sun, Q. Wu, M. Yan, H. Wang, and K. Fu, “Building +reconstruction from high-resolution multiview aerial imagery,” IEEE +Geoscience and Remote Sensing Letters, vol. 12, no. 4, pp. 855–859, +2014. +[46] B. Hepp, M. Nießner, and O. Hilliges, “Plan3d: Viewpoint and trajectory +optimization for aerial multi-view stereo reconstruction,” ACM Transac- +tions on Graphics (TOG), vol. 38, no. 1, pp. 1–17, 2018. +[47] M. Cramer, “The DGPF-test on digital airborne camera evaluation – +Overview and test design,” PFG Photogrammetrie – Fernerkundung – +Geoinformation, vol. 2 / 2010, pp. 73–82, 2010. +[48] S. Kim, I. Lee, and Y. J. Kwon, “Simulation of a geiger-mode imaging +ladar system for performance assessment,” sensors, vol. 13, no. 7, pp. +8461–8489, 2013. +[49] F. Rottensteiner, G. Sohn, J. Jung, M. Gerke, C. Baillard, S. Benitez, +and U. Breitkopf, “The ISPRS benchmark on urban object classification +and 3D building reconstruction,” ISPRS Annals of the Photogrammetry, +Remote Sensing and Spatial Information Sciences, vol. I-3, pp. 293–298, +2012. +[50] J. Niemeyer, F. Rottensteiner, and U. Soergel, “Contextual classification +of lidar data and building object detection in urban areas,” ISPRS Journal +of Photogrammetry and Remote Sensing, vol. 87, pp. 152–165, 2014. +[51] Z. Ye, Y. Xu, R. Huang, X. Tong, X. Li, X. Liu, K. Luan, L. Hoegner, and +U. Stilla, “Lasdu: A large-scale aerial lidar dataset for semantic labeling +in dense urban areas,” ISPRS International Journal of Geo-Information, +vol. 9, no. 7, p. 450, 2020. +[52] B. Le Saux, N. Yokoya, R. H¨ansch, and M. Brown, “2019 ieee grss data +fusion contest: large-scale semantic 3d reconstruction,” IEEE Geoscience +and Remote Sensing Magazine (GRSM), vol. 7, no. 4, pp. 33–36, 2019. +[53] X. Li, A. You, Z. Zhu, H. Zhao, M. Yang, K. Yang, S. Tan, and Y. Tong, +“Semantic flow for fast and accurate scene parsing,” in European +Conference on Computer Vision. +Springer, 2020, pp. 775–793. +[54] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image +recognition,” in Proceedings of the IEEE conference on computer vision +and pattern recognition, 2016, pp. 770–778. +[55] L.-C. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder- +decoder with atrous separable convolution for semantic image segmen- +tation,” in Proceedings of the European conference on computer vision +(ECCV), 2018, pp. 801–818. +[56] L. Zwald and S. Lambert-Lacroix, “The berhu penalty and the grouped +effect,” arXiv preprint arXiv:1207.6868, 2012. +[57] M. Kazhdan, M. Bolitho, and H. Hoppe, “Poisson surface recon- +struction,” in Proceedings of the fourth Eurographics symposium on +Geometry processing, vol. 7, 2006. +[58] J. L. Ba, J. R. Kiros, and G. E. Hinton, “Layer normalization,” arXiv +preprint arXiv:1607.06450, 2016. +[59] M. Jaderberg, K. Simonyan, A. Zisserman et al., “Spatial transformer +networks,” Advances in neural information processing systems, vol. 28, +2015. +[60] H. Zhao, J. Shi, X. Qi, X. Wang, and J. Jia, “Pyramid scene parsing +network,” in Proceedings of the IEEE conference on computer vision +and pattern recognition, 2017, pp. 2881–2890. +[61] H. Ledoux, F. Biljecki, B. Dukai, K. Kumar, R. Peters, J. Stoter, and +T. Commandeur, “3dfier: automatic reconstruction of 3d city models,” +Journal of Open Source Software, vol. 6, no. 57, p. 2866, 2021. +[62] P. Hajek, K. Jedliˇcka, and V. ˇCada, “Principles of cartographic design +for 3d maps–focused on urban areas,” in 6th International Conference +on Cartography and GIS Proceedings, vol. 1, 2016, pp. 297–307. +[63] M. Mittal, R. Mohan, W. Burgard, and A. Valada, “Vision-based +autonomous uav navigation and landing for urban search and rescue,” +arXiv preprint arXiv:1906.01304, 2019. +[64] “Isprs.2d semantic labeling contest-vaihingen,” [Online]. Available: +http://www2.isprs.org/commissions/comm3/wg4/2d-sem-label- +vaihingen.html. + diff --git a/m9E3T4oBgHgl3EQfigrM/content/tmp_files/load_file.txt b/m9E3T4oBgHgl3EQfigrM/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..3b6259bb33b259f818ddb6548f99b607fd8283a3 --- /dev/null +++ b/m9E3T4oBgHgl3EQfigrM/content/tmp_files/load_file.txt @@ -0,0 +1,1215 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf,len=1214 +page_content='JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 1 Elevation Estimation-Driven Building 3D Reconstruction from Single-View Remote Sensing Imagery Yongqiang Mao, Kaiqiang Chen, Liangjin Zhao, Wei Chen, Deke Tang, Wenjie Liu, Zhirui Wang, Wenhui Diao, Xian Sun, Kun Fu Abstract—Building 3D reconstruction from remote sensing images has a wide range of applications in smart cities, pho- togrammetry and other fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Methods for automatic 3D urban building modeling typically employ multi-view images as input to algorithms to recover point clouds and 3D models of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, such models rely heavily on multi-view images of buildings, which are time-intensive and limit the applicability and practicality of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To solve these issues, we focus on designing an efficient DSM estimation-driven reconstruction framework (Building3D), which aims to reconstruct 3D building models from the input single-view remote sensing image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Existing DSM estimation networks suffer from the imbalance between local features and global features, which leads to over-smooth DSM estimates at instance boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we propose a Semantic Flow Field-guided DSM Estimation (SFFDE) network, which utilizes the proposed concept of elevation seman- tic flow to achieve the registration of local and global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' First, in order to make the network semantics globally aware, we propose an Elevation Semantic Globalization (ESG) module to realize the semantic globalization of instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Further, in order to alleviate the semantic span of global features and original local features, we propose a Local-to-Global Elevation Semantic Registration (L2G-ESR) module based on elevation semantic flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Our Building3D is rooted in the SFFDE network for building elevation prediction, synchronized with a building extraction network for building masks, and then sequentially performs point cloud reconstruction, surface reconstruction (or CityGML model reconstruction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On this basis, our Building3D can optionally generate CityGML models or surface mesh models of the buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Extensive experiments on ISPRS Vaihingen and DFC2019 datasets on the DSM estimation task show that our SFFDE significantly improves upon state-of-the-arts and δ1, δ2 and δ3 metrics of our SFFDE are improved to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='595, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='897 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, our Building3D achieves impressive results This work was supported by National Key R&D Program of China under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2021YFB3900504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' (Corresponding author: Kaiqiang Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=') Yongqiang Mao,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wenjie Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Xian Sun,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' and Kun Fu are with the Aerospace Information Research Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Bei- jing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' the Key Laboratory of Network Information System Tech- nology (NIST),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Aerospace Information Research Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' the University of Chinese Academy of Sciences and the School of Electronic,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Electrical and Communication Engi- neering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' University of Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' China (e-mail: maoyongqiang19@mails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ucas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' liuwenjie18@mails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ucas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' sunxian@aircas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' kunfuiecas@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kaiqiang Chen, Liangjin Zhao, Zhirui Wang, and Wenhui Diao are with the Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China and the Key Laboratory of Network Information System Technology (NIST), Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China (e-mail: chenkaiqiang14@mails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ucas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wei Chen and Deke Tang are with the Geovis Technology Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' (e-mail: chenwei@geovis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' tangdk@geovis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='cn) in the 3D point cloud and 3D model reconstruction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Index Terms—DSM Estimation, 3D Building Reconstruction, Remote Sensing Images, Elevation Semantic Flow I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' INTRODUCTION T HANKS to the increasing development of various sen- sors, various remote sensing data have been applied in different fields [7], [8], including semantic segmentation [39], [41] and object detection [35], [42], [43] of 2D remote sensing image, and 3D point cloud classification [36]–[38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Among them, the interpretation of interactive information between two-dimensional data and three-dimensional data gradually enters researchers’ field of vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3D reconstruction of urban buildings is a significant constituent of remote sensing image interpretation, where the goal is to parse image or point cloud data to generate 3D model representations [32]–[34], [44]–[46] of urban buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In recent years, large-scale geospatial mesh models of urban buildings have been introduced widespreadly in many fields, such as navigation and urban planning [63], urban 3D maps [62], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Among the existing 3D model acquisition methods, there are mainly four approaches: airborne lidars, Geiger-mode lidars, reconstruction based on multi-view UAV images, and reconstruction based on single-view remote sensing images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Although airborne lidar can obtain accurate 3D point clouds [31], [47], [49]–[52] of buildings in the target area, it is limited by high acquisition cost and low acquisition efficiency and difficult to apply to large-scale tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Recent Geiger-mode lidars [48] can acquire data efficiently, they suffer from high noise and low penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building reconstruction based on multi-view UAV images [32], [34] can acquire 2D image data for 3D model reconstruction at low cost, but it has a very high time cost for large-scale regional reconstruction and requires a high degree of overlap between images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Unlike airborne lidar and drone images, single-view remote sensing imagery can cover a larger area with high stability and low cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Therefore, we focus on the 3D reconstruction of buildings based on single-view remote sensing imagery (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1), aiming to utilize low-cost large-scale remote sensing imagery for fast urban building reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For single-view-based building 3D reconstruction methods, some methods [29] derive 3D building models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=', CityGML) and only focus on the restoration of roof structure topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The researchers aim to reconstruct the roof topology using arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='04581v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='CV] 11 Jan 2023 JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 2 SFFDE Network Patch Fusion Building Extraction Network a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' DSM Estimation b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building Extraction Input: Single-view Remote Sensing Image c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Point Cloud Reconstruction Elevation Map Building Mask Surface Reconstruction e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Surface Reconstruction Output: 3D Mesh Model Point Cloud Reconstruction Building Edge Detection Point Cloud 3dfier Output: CityGML Model d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' CityGML Reconstruction Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Flowchart of the proposed Building3D framework for 3D reconstruction of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The input of Building3D is a single-view remote sensing image, the outputs are the corresponding elevation maps, building masks, point cloud, and 3D building model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The blue dotted line represents optional follow-up operations (CityGML models or Mesh models).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' traditional methods, and then obtain 3D data in the form of CityGML based on the building height information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Some researchers use pre-labeled roof structure types to train the network and then extract the roof topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, these methods are limited to the extraction of topology structure, which brings unnecessary extraction of artificial prior knowl- edge for building reconstruction, resulting in cumbersome and redundant reconstruction process, which is not conducive to building reconstruction in large-scale areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In order to solve this problem, based on the prediction of building elevation information, we perform 3D mapping of building elevation to obtain building point cloud data, and then selectively reconstruct the subsequent CityGML model or mesh model of the buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on this, our reconstruction framework (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1) can simultaneously reconstruct more realistic mesh models of buildings and virtual models like CityGML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For single-view remote sensing images, the elevation in- formation of buildings is a key factor in constructing the 3D building models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Although substantial progress has been made in existing elevation prediction methods [1]–[6] from remote sensing images, the problem of low prediction accuracy occurs when both regular and irregular textured objects are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Through our investigation, we realize that the low prediction accuracy of textured regular and irregular objects is caused by the inability of the receptive field to achieve a local-global trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The imbalance between global and local features will cause the network to suffer from insufficient receptive field in the learning process, and it cannot take into account the ex- traction of regular texture and irregular texture object features at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Since the features extracted by CNN have local perception, to solve this problem, we introduce elevation semantic globalization to obtain global feature perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, the network at this time does not have the ability to take into account and trade off local and global features at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we introduce the concept of elevation semantic flow embedded in a local-to-global feature registration module to explicitly model the changing trend between global and local features to trade off local and global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on this, we propose an Elevation Semantic Flow Field-guided DSM Estimation (SFFDE) network (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1) to obtain accurate elevation predictions for various textured objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In this paper, we propose a single-view remote sensing image-based building reconstruction framework (Building3D) based on the SFFDE network, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Unlike previous research schemes targeting roof topology, our Build- ing3D aims to recover both the CityGML model as well as the real mesh model of the buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Our Building3D framework consists of four parts: Semantic Flow Field-guided DSM Estimation (SFFDE) network, building extraction network, point cloud reconstruction process, and building reconstruc- tion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given a single-view remote sensing image, the elevation information of the image is first predicted through our SFFDE network, which is mainly composed of two parts: Elevation Semantic Globalization (ESG) and Local-to-Global Elevation Semantic Registration (L2G-ESR), which realize the purpose of feature globalization and local and global feature registration, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' At the same time, the building mask is extracted from the image through the building extraction network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Next, the building elevation is extracted using the building mask, and the elevations of other uninteresting objects are filtered out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on this, the building elevation is used to reconstruct the point cloud data to obtain the 3D point cloud of the building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, CityGML reconstruction or surface reconstruction is performed using the point cloud to obtain the final CityGML or 3D mesh model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The contributions of this study are summarized as follows: We introduce a Semantic Flow Field-guided DSM Esti- mation (SFFDE) network based on the proposed elevation semantic flow field for the local-to-global registration of elevation semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, Elevation Semantic Globalization (ESG) and Local-to-Global Elevation Se- mantic Registration (L2G-ESR) are designed to achieve the globalization and local-to-global registration of fea- tures, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We propose a single-view image based building 3D JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 3 reconstruction framework (Building3D) rooted in the proposed SFFDE network and extract building masks ac- cording to the building extraction network for subsequent 3D point cloud and building reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Experiments on ISPRS Vaihingen [64] and DFC2019 [31] datasets show that our SFFDE network significantly out- performs the baseline model, achieving new state-of-the- art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' What’s more, our Building3D achieves impressive results in the 3D point cloud and building reconstruction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The remainder of this article is organized as follows: In Section II, we give a brief review of the related works on DSM estimation, building extraction, and building reconstruc- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The details of our proposed framework Building3D and semantic flow field-guided DSM estimation (SFFDE) network are given in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In Section IV, extensive experiments are conducted on ISPRS Vaihingen dataset and DFC2019 dataset to demonstrate the effectiveness of our SFFDE net- work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Also, the 3D reconstruction experiments of buildings are given in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, Section V concludes this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' RELATED WORK A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' DSM Estimation The existing methods [1]–[4] for DSM elevation estimation in the remote sensing field are mainly divided into three types: random field-based methods, CNN-based methods, and some hybrid methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In random field-based methods, researchers [5], [6] utilize conditional random field (CRF) and Markov random field (MRF) to model the local and global structure of an image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Considering that local features cannot provide suffi- cient features for predicting depth values, Batra and Saxena [5] model the relationship between adjacent regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, in order to obtain global features beyond the local ones, Saxena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [6], [10] first compute the features of the four nearest neighbors of the specified patch, and then use the MRF and Laplacian models to estimate the depth of each patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In recent years, CNN has been widely used in the fields of object classification, semantic segmentation, and object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In- spired by this, some researchers [11] propose a ResNet-based convolutional network to predict DSM elevation information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In IMG2DSM [15], an adversarial loss function is introduced to improve the possibility of synthesizing DSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' It also em- ploys a conditional generative adversarial network to build image-to-DSM elevation translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang and Chen [18] improve the learning ability of abstract features of objects of different scales by means of multi-scale feature extraction through a multi-path fusion network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [14] divided the height values into intervals with increasing spacing, and transformed the regression problem into an ordinal regression problem, using an ordinal loss for network training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After that, a post-processing technique is designed to convert the predicted height map of each patch into a seamless height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Carvalho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [16] have studied various loss functions of depth regression in depth, and combined the encoder-decoder architecture with adversarial loss, and then proposed a new depth estimation network D3-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the hybrid methods, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [19] propose a joint framework incorporating hierarchical conditional random fields, aiming to predict depth and segmentation outcomes from a single-view remote sensing image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Srivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [17] use a method for supervised network training via a multi-task loss and introduce a unified framework for elevation estimation and semantic segmentation of single-view remote sensing image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, none of these methods take into account the need for accurate elevation prediction to simultaneously guarantee the extraction of representative features for both regular and irregular textured objects, which is caused by the imbalance between global and local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we propose a semantic flow field-guided DSM estimation network to trade off local and global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building Extraction Many researchers [20]–[22] have devoted themselves to designing efficient methods for automatically extracting build- ings, which mainly consists of methods based on hand- crafted features and methods based on deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the handcrafted feature-based methods, geometric, spectral, and contextual information of buildings are used to design rep- resentative features for accurate building extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lin and Nevatia [20] first apply edge detection to building extraction for the detection of roofs, walls and shadows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Later, the fractal network algorithm is proposed by Baatz [21] to segment the image at multiple scales and extract the target building by combining the texture and other features of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang and Liu [22] achieve the purpose of pixel-by-pixel classifica- tion of images by using machine learning methods to receive input from feature vectors constructed from image texture, shape, and structural features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, methods based on handcrafted features often only utilize the shallow features of objects, ignoring the semantics of deep features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Therefore, methods based on deep learning gradually enter the field of vision of researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Minh [23] applies an image patch- based building block extraction method to building extraction, an early work on convolutional neural networks applied to building extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On this basis, Minh also uses CRF or post-processing to refine the results of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Later, Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [24] introduce an improved DeconvNet that adds upsampling and cheat connection operations to deconvolution layers to achieve building extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [25] propose a multi-constraint FCN to perform feature learning on remote sensing images for the purpose of automatically extracting buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In this paper, we apply the popular segmentation network DeeplabV3+ [55] to generate binary masks for buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building Reconstruction The existing methods for 3D building reconstruction mainly focus on the roof topology restoration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Researchers [26]– [28], [30] extract roof vertices, eave lines, or segmented planes as primitives from an image or DSM through image segmentation, edge detection, plane patch detection, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After that, the combination, segmentation, topologically analysis of the individual geometric primitives are executed in sequence to generate the 3D shapes of the buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Bulatov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [26] JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 4 Elevation Semantic Globalization L2G-ESR PPM L2G-ESR L2G-ESR L2G-ESR Conv Sigmoid Linear Linear Linear Query Key Value Flatten HW×C T C×HW HW×HW HW×C HW×C berHu Loss Proj Proj L2G-ESR Project Operation Local-to-Global Elevation Semantic Registration PPM Pyramid Pooling Module Encoder Decoder Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Flowchart of the proposed Semantic Flow Field-guided DSM Estimation (SFFDE) network for DSM estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The proposed elevation semantic globalization (ESG) is responsible for the global semantic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, local-to-global elevation semantic registration (L2G-ESR) is introduced to achieve the trade-off of local and global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' extract building regions by performing vegetation and outlier filtering on a normalized DSM (nDSM), and then combine the extracted building pixels with operations such as graph- based orthophoto segmentation, dominant direction extraction, polygonization, and generalization to extract buildings contour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, they construct the building model by topologically analyzing the roof details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [28] classify MVS point clouds through graph-cut based Markov random fields (MRF), followed by RANSAC and regularized MRF for optimization and roof structure extraction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, these methods suffer from the limitations of multi- view image input or surfel geometric topology, thus bringing great difficulties to building reconstruction in large scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we propose a DSM estimation-driven framework for building 3D reconstruction with single-view remote sensing image as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' OUR APPROACH A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Overview The flowchart of our proposed building 3D reconstruction framework (Building3D) is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As a single- view image-based building 3D reconstruction approach, our framework consists of four stages: DSM estimation branch, building extraction branch, point cloud reconstruction branch and building reconstruction branch (surface reconstruction or CityGML reconstruction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given an input remote sensing image, the DSM estimation branch and the building extraction branch first come into play to estimate the elevation informa- tion and extract the buildings, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On this basis, the information obtained by the building extraction branch is used to filter the information from the elevation results predicted in the DSM estimation branch to obtain only the elevation information of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Next, the point cloud data corre- sponding to the building is recovered according to the input image and the predicted elevation information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, surface reconstruction or CityGML reconstruction is performed on the point cloud of buildings obtained by the point cloud reconstruction branch to obtain the final mesh or CityGML model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the following, we first introduce the semantic flow field-driven DSM estimation (SFFDE) network, and then intro- duce the framework’s building extraction process, point cloud reconstruction process, and building reconstruction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Semantic Flow Field-guided DSM Estimation Network Considering generating fine 3D point clouds, the accurate DSM information is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we design a Semantic Flow Field-guided DSM Estimation (SFFDE) net- work, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Our SFFDE selects PSPNet [60] as the baseline and consists of three stages: First, a single remote sensing image is sent into a feature extraction network (such as resnet101) and a PPM (Pyramid Pooling Module) [60] module to obtain high-level representations of features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Second, an Elevation Semantic Globalization (ESG) module is introduced for the globalization of semantic features to obtain high- level global semantic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, we propose a Local-to-Global Elevation Semantic Registration (L2G-ESR) module to achieve the registration of low-level local semantics and high-level global semantics of features between different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, our SFFDE network is driven by the berHuLoss [56] during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1) Elevation Semantic Globalization: The stacking of con- volutional layers and pooling layers can increase the receptive field, but the receptive field of the convolution kernel of a specific layer on the original image is limited, which is unavoidable in local operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, elevation estimation based on single view remote sensing image requires more information on the original image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' If the global information can be introduced in some layers, the problem that the local operation of the convolution cannot capture the global infor- mation can be well solved, and it can bring richer information to the subsequent layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Inspired by the transformer [40] ar- chitecture, we introduce the Elevation Semantic Globalization (ESG) module (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) for the global semantic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 5 Given feature maps F ∈ RH×W ×C(H, W, C stand for height, width, and number of channels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ), after the feature extraction of the backbone, these feature maps are high-level semantic features with local perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Before being sent to the ESG module, the feature map F is stretched from a 2D raster image into a 1D vector (regardless of the channel dimension), which can be formulated as: F = flatten (F) (1) where F ∈ RN×C(N = H × W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The stretched feature F goes through three fully connected layers in parallel for feature transformation, so that the 2D raster image features are mapped to the same space as the 1D vector features, which is formulated as: � Q, K, V � = � FC1(F), FC2(F), FC3(F) � = � WqF, WkF, WvF � (2) where Q, K, V ∈ RN×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' D is the number of channels of the output features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given query embeddings Query to be enhanced and feature maps Key, Value to be fused, the ESG operation is defined as Fesg = ESG � Q, K, V � = Softmax � WqF(WkF)⊤� WvF (3) where Fesg ∈ RN×D is the query feature after ESG operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After this, we set up a multi-head ESG operation module based on ESG operation and transformer architecture, the formula is as follows: Fout = MHE(WqF, WkF, WvF) (4) where Fout is the output features of MHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' MHE is the multi- head ESG operation which is similar to multi-head attention (MHA) operation [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, each ESG head can be expressed as: Headi = ESG(Q, K, V ) (5) where Q, K, V represents the Query, Key, and Value matrix, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then, based on this, multi-head ESG can be expressed mathematically as: MultiHead(Q, K, V ) = Cat(Head1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' , Head8)W (6) where Cat is the concatenate operation and W represent the weight of the final full connection operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Different ESG heads represent different subspaces, and the results of all ESG heads are spliced together to obtain the final result through full connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Next, a feature projection operation is adopted to perform feature mapping between spatial one-dimensional features and spatial two-dimensional features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Formally, the obtained projection feature Fproj can be defined as: Fproj = Relu � LN � FC(Fout) �� (7) where LN is the LayerNorm [58] operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, the projection feature Fproj ∈ RN×D is reshaped to the same resolution as F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) Elevation Semantic Flow: To register features at differ- ent resolutions, inspired by Optical Flow, we introduce the concept of Elevation Semantic Flow (ESF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The Optical Flow is the method that employs the changes of pixels in the image sequence in the time domain and the correlation between adjacent frames to find the corresponding relationship between the previous frame and the current frame, so as to calculate the motion of objects between adjacent frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Analogous to the instantaneous gray change rate of pixels at the same location between video frames in a short period of time,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' we define a semantic change rate of elevation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' that is,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' the semantic displacement of pixels between adjacent resolution images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' which can be expressed as: ⃗u = (∂x ∂l ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ∂y ∂l ) (8) where l represents the varying resolution of feature maps and ⃗u is the elevation semantic flow vector,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' which represents the rate of change of semantics along the x and y directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In space, the motion can be described by a motion field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the video, the motion of an object is often represented by an optical flow field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the feature map of the elevation estimation network, the semantic motion can be defined by the feature vectors represented by the pixels of the feature maps of different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Thus, we propose to define an elevation semantic field of F, which is formulated as: −∂F ∂l = ∇F · ⃗u = ∂F ∂x ∂x ∂l + ∂F ∂y ∂y ∂l (9) Similar to the optical flow field, the elevation semantic field is a two-dimensional vector field, which reflects the semantic change trend of each point in the feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Classical optical flow estimation is solved by a linear algebra method (such as the LK algorithm [9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We use an end-to-end training non- linear optimization method and use Local-to-Global Elevation Semantic Registration (L2G-ESR) as a constraint to learn the elevation semantic flow field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3) Local-to-Global Elevation Semantic Registration: Af- ter the globalization of features, the perceptual ability of features is extended from local to global.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This enables the network to not only perceive low-dimensional local features, but also acquire the ability to perceive high-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, since low-dimensional local features and global high-dimensional features are obtained by local convo- lution and elevation semantic globalization (not convolution operations) respectively, there is a huge span in the range of feature perception between global features and local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In addition, these features do not have both local and global perception capabilities at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address these issues, local-to-global elevation semantic registration (L2G- ESR) is introduced, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given the high-resolution local feature Fh and the low- resolution globalized feature Fl, we first map Fh and Fl to the same number of channels as: � �Fh, �Fl � = � Conv1(Fh), Conv2(Fl) � (10) where �Fh ∈ RHh×Wh×D and �Fl ∈ RHl×Wl×D are the new features after mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Conv1 and Conv2 correspond to the JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 6 Conv Upsample C Flow Generation Conv C Concat Conv Conv Conv Sum Convolution Conv Registration Function Elevation Semantic Flow Output Feature After Registration Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Overview of our local-to-global elevation semantic registration (L2G-ESR) module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The inputs to L2G-ESR are two features of different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Flow generation and feature registration are performed sequentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The pink and blue convolution blocks in the figure represent feature mapping operations for low-resolution and high-resolution, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, both convolution operations are implemented using 1x1 two-dimensional convolution, and the input and output channel dimensions are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' blue and pink convolution blocks in the figure, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, both convolution operations are implemented using 1x1 two-dimensional convolution, and the input and output channel dimensions are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then, we bilinearly interpolate the new low-resolution features �Fl to the same resolution as the high-resolution features �Fh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On this basis, the two same-resolution features are fused and further encoded into a 2D elevation semantic flow field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mathematically, the elevation semantic flow field S can be expressed as: S = Conv � cat � upsample(�Fl), �Fh �� (11) where upsample represents the bi-linear interpolation opera- tion, cat is the concatenation operation, and Conv denotes the convolution operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The semantic flow field S ∈ RHh×Wh×2 represents the change trend of elevation semantics between different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The channel ‘2’ refers to the change of semantics in both x and y directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Let L ∈ RHh×Hh×2 denote the coordinates of each pixel in the feature map �Fh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then the generated semantic flow field S is employed to get the coordinates �L of each pixel of the feature map after offset, as �L = L + S(x′ = x + ∆x, y′ = y + ∆y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Following the bi-linear sampling method in STN [59], the pixel Freg;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab at (a, b) of the output feature Freg after feature registration operation is defined as: Freg;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab = R(�Fl) = H � m=1 W � n=1 upsample(�Fl)mn · max(0, 1 − |�Lx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab − m|) max(0, 1 − |�Ly;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab − n|) (12) where upsample(�Fl)mn is the pixel at (m, n) of the afore- mentioned �Fl after upsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, �Lx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab and �Ly;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='ab are the x and y coordinates of each pixel of �L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After that, the feature Freg after registration is fused with aforementioned �Fh, as: Fout = I(Freg, �Fh) (13) where I is the aggregation function between the feature Freg after registration and the feature �Fh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4) Loss Function: In order to enable the network to better regress the elevation value of the instance, we use berHu- loss [56] as our loss function, which is expressed as L(x) = � |x| |x| ≤ c x2+c2 2c |x| > c (14) where c is the judgment threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='2 × max(|predict − gt|) in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building Extraction Network Unlike regular segmentation network, we only focus on the single category (buildings) of element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the building mask extraction process, we first perform binarization preprocessing on the labels of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, the label value of the pixel where the building is located is set to 1, and the label value of the non-building pixel is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In order to better extract building masks, we use the currently popular Deeplabv3+ [55] as our building extraction network to extract the building mask M, which is built on top of the backbone ResNet-101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given an input image, the building extraction network outputs a mask M of the building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Specifically, the building pixel value is 1, and the background is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' During training, the update of network parameters is driven by the cross-entropy loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' What’s more, the canny edge detection algorithm is used to extract the outlines of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The extracted outlines and building masks with fine pixel positioning give the next procedures the precise building positioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building Reconstruction Building 3D reconstruction based on remote sensing im- agery has always been a hot research topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, most of the existing methods are limited to a single output of the building CityGML model, and the real 3D model of buildings has not been constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To address this issue, we propose a building 3D reconstruction method based on JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 7 building elevation information predicted by our SFFDE, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After the aforementioned steps, we adopt the building masks M to extract the elevation information of the buildings, filter out the categories (such as vegetation) that are not of interest, which is formulated as: Ebuilding = E ◦ M (15) where E and Ebuilding are the elevation information before and after filtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ◦ is the Hadamard product operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After obtaining the elevation information of the buildings, the two procedures of point cloud reconstruction and building reconstruction (Surface Reconstruction or CityGML Recon- struction) are performed sequentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Point Cloud Reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Generating the point cloud data of the object is a key step to obtain the three-dimensional structure model of the object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In this process, the obtained DSM prediction results of each input image patch is first fused through patch fusion to obtain a larger area of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After that, in order to smooth the gap between patches, Gaussian filtering operation is employed to the DSM predicted results of each large scene remote sensing image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then, we perform 2D- to-3D mapping of buildings based on the elevation information of large-area building clusters to generate their 3D point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The latitude and longitude coordinates corresponding to the pixels are used as the x, y coordinates of the point cloud, and the elevation information is used as the z coordinates of the point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mesh and CityGML Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mesh refers to a polygonal grid, which is a data structure used in computer graphics for modeling various irregular objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In the face of the polygon mesh, the triangular face is the smallest unit to be divided, so it is often referred to as the triangular face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The basic components of a mesh: vertices, edges, and faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' CityGML is a data format used to construct virtual 3D city models, and is a general data model used to express 3D city templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' CityGML can not only express the graphic appearance of the city model, but also take care of the semantic representation, such as the classification and aggregation of digital terrain models, vegetation and water systems, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' All models can be divided into five different coherent levels of detail (LOD), with increasing level of detail to obtain more details about the geometry and themes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The five consecutive levels of detail are: LOD0, LOD1, LOD2, LOD3, and LOD4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The CityGML model reconstructed in this paper is the LOD1 model in five coherent levels of detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Surface Reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on the point cloud data of the building generated in the previous steps, we first normalize the point cloud to facilitate the subsequent reconstruction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then, we perform Poisson [57] reconstruction on the normalized point cloud data to obtain the mesh model of the building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' CityGML Reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' To verify the effectiveness of our method, we also extend the SFFDE network to the algorithm for building CityGML model reconstruction in our Building3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After our building3D performs the 3D point cloud mapping operation, we also extract the polygonal structure of the building from the image at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Combining the obtained 3D point cloud and building polygon structure, we use 3dfier [61] to reconstruct the building CityGML model from single-view remote sensing images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' EXPERIMENTS In this section, we first give an introduction to the datasets used by our entire framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Next, we introduce the spe- cific experimental setup (including evaluation protocols and completion details) in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Then, we show the performance and visualization results of our proposed SFFDE on elevation estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After that, a reconstruction analysis of the entire reconstruction framework Building3D is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Finally, to demonstrate the effectiveness of the proposed elevation semantic globalization operation and local-to-global elevation semantic registration operation, we conduct extensive ablation experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Datasets 1) ISPRS Vaihingen: There are a total of 33 slices in the IS- PRS Vaihingen [64] dataset and each slice has approximately 2500×2500 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Each remote sensing image is accompanied by orthophoto images, semantic labels and digital surface models (DSM and nDSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The ground sampling distance of each image is 9 cm, and it has three channels of near-infrared, red and green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' According to the official split, 16 slices that provided ground truth are used for the training of models, and the remaining 17 slices are used for evaluation by the challenger organizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) 2019 Data Fusion Contest: The 2019 Data Fusion Con- test (DFC2019) [31] dataset currently includes approximately 100 square kilometers of coverage for Jacksonville, Florida, and Omaha, Nebraska, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The ground sampling distance (GSD) is about 30 cm, and each image with semantic labels and normalized DSM is 1024×1024 pixel in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The dataset provides WorldView-3 panchromatic and 8-band visible and near-infrared (VNIR) images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' DFC2019 includes 26 images collected in Jacksonville, Florida, and 43 images collected in Omaha, Nebraska, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Experimental Settings 1) Evaluation Protocols: We use six metrics to evaluate the DSM estimation performance of our proposed method, including mean relative error (Rel), RMSE, RMSE(log), and the ratio of pixels with predicted elevation values close to the ground truth (δ1, δ2, δ3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Among them, mean relative error (Rel), RMSE, RMSE(log) are expressed as: Rel = 1 N N � i=1 |Di − D∗ i | D∗ i (16) RMSE = � � � � 1 N N � i=1 |Di − D∗ i |2 (17) RMSE(log) = � � � � 1 N N � i=1 |logDi − logD∗ i |2 (18) JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 8 TABLE I THE PERFORMANCE OF DSM ESTIMATION ON ISPRS VAIHINGEN DATASET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Method Rel↓ RMSE↓/m RMSE(log)↓ δ1 ↑ δ2 ↑ δ3 ↑ Amirkolaee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [11] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='163 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='334 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='330 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='572 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='741 IMG2DSM [15] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='09 D3Net [16] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='016 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='123 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='369 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='533 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='644 Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [14] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='314 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='698 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='155 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='451 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='817 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='939 SFFDE + ResNet50 (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='225 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='624 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='841 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='933 SFFDE + ResNet101 (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='222 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='133 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='084 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='595 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='897 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='970 where N is the number of the pixels, Di is the predicted elevation value of the i-th pixel, and D∗ i is the ground truth of the i-th pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' What’s more, the δi is expressed as: δi = max(hpred hgt , hgt hpred ) (19) where hgt and hpred are the ground truth and predicted elevation value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) Implementation Details: Our framework is implemented based on PyTorch Library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The momentum SGD algorithm with the momentum value set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='9 is employed to optimize both the DSM estimation branch and the building extraction branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We train our model for 80000 iterations and the initial and minimum learning rate is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='005 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='00002, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The weight decay value is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0005 for regu- larization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Our DSM estimation branch and building extraction branch are both executed on a single NVIDIA TITAN RTX GPU with batch size set to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Considering the huge size of each image in both Vaihingen and DFC2019 datasets make the images unable to directly be sent to the network due to the GPU memory limit, we employ a sliding window strategy to generate small image patches with 512×512 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' When evaluating accuracy, for each dataset, we only select the checkpoint saved in the last iteration (80000 iteration) for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The number of training iterations is set in considera- tion of ensuring the model is converged and stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The choice of checkpoint is based on the weight file saved in the last iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Performance Analysis of DSM Estimation 1) ISPRS Vaihingen: We compared the DSM estimation performance by our SFFDE with other prediction networks, such as Amirkolaee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [11], IMG2DSM [15], D3Net [16], and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In Table I, the comparisons between our SFFDE network and these methods on the ISPRS Vaihin- gen dataset are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' It is clear that our SFFDE network achieves the highest performance for the elevation estimation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Regardless of choosing ResNet50 or ResNet101 as the backbone, our SFFDE outperforms state-of-the-art methods on all metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Rel, RMSE and RMSE(log) are indicators that describe the prediction error of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Among these metrics, with the ResNet101 backbone, our SFFDE achieves 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='222 Rel, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='133 RMSE and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='084 RMSE(log), achieving the best performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This shows that the prediction results of our SFFDE maintain a high consistency with the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' What’s more, δ1, δ2 and δ3 are indicators describing the prediction accuracy of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Note that for the indicators (δ1, δ2, δ3), SFFDE achieves the highest δi value, which strongly demonstrates the elevation value predicted by our SFFDE is close to the ground truth elevation value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This again proves that the local and global semantic registration implemented by SFFDE can improve the accuracy of elevation prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The reason is that our SFFDE can use elevation semantic globalization (ESG) to achieve global feature extraction and local-to-global elevation semantic registration (L2G-ESR) to achieve global and local feature registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on the concept of elevation semantic flow, we can well explicitly model the semantic change rate of semantic features describing elevation across different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) DFC2019: In Table II, our SFFDE network is compared with other state-of-the-art DSM estimation methods (including D3Net [16], DORN [13], and FastDepth [12]) on DFC2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Clearly, our SFFDE outperforms all existing elevation estimation methods on the DFC2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Table II displays the evaluation estimation results of our SFFDE network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Whether we choose ResNet50 or ResNet101 as our backbone, SFFDE again outperforms state-of-the-art methods on all indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For the ResNet101 backbone, SFFDE improves FastDepth by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='108 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='492 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='384) on δ1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='081 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='782 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='701) on δ2, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='033 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='908 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='875) on δ3, which are large margins for the challenging DSM estimation problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Compared with the ISPRS Vaihingen dataset, the DFC2019 dataset has more complex scenes and diverse instances, which undoubtedly brings great difficulties to the depth estimation problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, our SFFDE not only performs the best on the ISPRS Vaihingen dataset, but also has the highest per- formance on the DFC2019 dataset, which once again proves that our proposed feature registration based on the elevation semantic flow field can well improve complex scenes elevation prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualization Analysis 1) DSM Visualizations on ISPRS Vaihingen: As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4, local area visualizations of the DSM estimation results of SFFDE is given on the ISPRS Vaihingen dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' From the visualized results, we can conclude that our SFFDE has high accuracy for building elevation prediction, and the pre- diction results are basically consistent with the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, the visualization clearly shows that our predicted JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 9 TABLE II THE PERFORMANCE OF DSM ESTIMATION ON DFC2019 DATASET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Method Rel↓ RMSE(log)↓ δ1 ↑ δ2 ↑ δ3 ↑ D3Net [16] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='526 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='208 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='256 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='635 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='846 DORN [13] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='488 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='646 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='859 FastDepth [12] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='383 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='189 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='384 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='701 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='875 SFFDE + ResNet50 (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='272 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='029 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='601 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='778 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='882 SFFDE + ResNet101 (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='330 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='024 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='492 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='782 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='908 Input Ground Truth Result Input Ground Truth Result Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of the predicted elevation results (512 × 512 patches) of our SFFDE network on ISPRS Vaihingen dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' instance elevations are well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' At instance boundaries, our method has small prediction errors and aliasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 5, we also present the visualization results of the elevation prediction for a large area of the ISPRS Vaihingen dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The images of three large scenes (Area 4 contains a large number of buildings, Areas 27 and 29 have both regular and irregular texture instances, and Area 33 has more interior details of buildings) are selected as the inputs of our SFFDE and the prediction results are visualized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' From the visualization results of Area 4, our method is able to make good elevation predictions for areas with dense buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In these densely built areas, the buildings are all structures with high roofs in the center and low on both sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nonetheless, our visualizations fit this phenomenon well, yielding high predictive performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This is highlighted in the middle of the roof in the picture, and the sides are darker to demonstrate that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Areas 27 and 29 contain a large number of regular and irregu- lar instances such as buildings and trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For the regions where these regular and irregular instances coexist, this requires the model to have high generalization performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' From the visualization results, our SFFDE achieves superior elevation prediction performance and can guarantee high accuracy for both regular and irregular texture instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This benefits from the higher performance of our proposed elevation semantic flow-based feature registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, our SFFDE can predict the detailed structure of buildings well, as can be seen HHHHJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 10 Area 4 Our Result Area 33 Area 27 Input Images Our Result Input Images Area 29 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of the predicted elevation results (large areas) of our SFFDE network on ISPRS Vaihingen dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' from the results for Area 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On top of complex buildings, smooth roofs and complex structures coexist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In our prediction results, the high accuracy of the smooth roof prediction is reflected in the smoothness of the elevation prediction of the roof, which is proved by the basically consistent colors of the smooth areas in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In addition, in the region of complex structure, our SFFDE gives fine boundary structure prediction results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This is superior to other advanced methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) DSM Visualizations on DFC2019: To verify the perfor- mance of our SFFDE, we also conduct experiments on the DFC2019 dataset and give high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, we present the prediction visualization results of our SFFDE on the DFC2019 dataset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Since DFC2019 contains complex instances such as bridges, buildings, trees, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=', our visualization results all contain these complex instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' It can be seen from the visualization results that the elevation information of various instances we predicted is basically consistent with the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Furthermore, for regularly textured objects such as buildings and bridges, our prediction results have clear boundary information and smooth internal structures, which are extremely challenging problems in eleva- tion prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nonetheless, our SFFDE exhibits high prediction performance, which validates the effectiveness of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In addition, we also achieved high prediction accuracy for objects with irregular textures such as trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3) Feature Map Visualizations: Feature map visualizations on the ISPRS Vaihingen dataset are given as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As noted in the figure, the visualization consists of four columns, which are the input image, the feature map before globalization and registration, the feature map after globalization, and the feature map after global-local semantic registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' From the feature map after globalization, we can infer that the feature obtains a global receptive field, not only limited to local perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In addition, the registered feature map can clearly observe the object and its detailed information, and the internal features of the instance are smooth and the pixel values tend to be continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This matches well with better regression problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Therefore, from the visualization results of the two-part feature maps, it can be seen that our network can simultaneously ensure the feature’s ability to perceive the global and the local perception of details, and achieve a better balance between global and local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building3D Reconstruction Analysis 1) Building Extraction: As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7, the visualiza- tion results of the building extraction network in Building3D framework are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We not only visualize the local building area in Vaihingen, but also visualize the extraction results of building groups in a large area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on the superior building extraction network, we can see that the extracted building area is basically consistent with the actual building area, achieving extremely high building extraction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This lays a good foundation for subsequent building elevation extraction, building point cloud reconstruction and surface reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) Surface Reconstruction: Given a single-view remote sensing image of an area, after the building elevation pre- HJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 11 Input Ground Truth Result Input Ground Truth Result Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of the predicted elevation results (512 × 512 patches) of our SFFDE network on DFC2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Result Input Result Input Result Input Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of the building extraction network in our Building3D framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The left part is the building extraction results of the image patches, and the right part is the extraction results of large area buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' HHHHHJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 12 Input After Globalization After Registration Input After Globalization After Registration Before Globalization & Registration Before Globalization & Registration Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of the feature maps after globalization and registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The first column is the input of our SFFDE, the second column is the feature before globalization and registration, the third column is the feature map after globalization, and the fourth column is the feature map after registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Single-view Image Point Cloud Mesh Point Cloud with Color Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of point cloud and surface mesh of the input single-view image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The first column is the input single-view images, the second column is the reconstructed point clouds, the third column is the reconstructed point clouds with color, and the last column is the reconstructed mesh models of the input images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 13 TABLE III ABLATION STUDIES ON ISPRS VAIHINGEN DATASET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ‘ESG’ DENOTES ELEVATION SEMANTIC GLOBALIZATION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ‘L2G-ESR’ REPRESENTS LOCAL-TO-GLOBAL ELEVATION SEMANTIC REGISTRATION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Method Rel↓ RMSE↓/m RMSE(log)↓ δ1 ↑ δ2 ↑ δ3 ↑ ResNet-50 Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='367 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='330 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='135 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='357 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='618 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='819 +ESG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='277 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='188 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='109 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='542 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='800 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='915 +ESG + L2G-ESR (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='225 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='624 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='841 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='933 ResNet-101 Baseline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='358 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='293 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='374 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='701 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='870 +ESG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='276 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='282 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='111 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='534 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='843 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='952 +ESG + L2G-ESR (ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='222 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='133 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='084 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='595 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='897 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='970 Single-view Image Output Single-view Image Output Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualizations of LOD1 model of buildings in the input single-view image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' diction and building extraction steps mentioned above are completed, the next process is to reconstruct the building in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on the extracted building areas, we filter the pre- dicted elevation information to obtain building elevations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The visualization results of building surface reconstruction based on single-view remote sensing images are given in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Given a single-view remote sensing image, our Building3D outputs a point cloud and mesh of the building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 9 we can see that the building has been converted into a 3D structure, while other elements such as cars, vegetation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' have not been converted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The first column in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 9 shows the input single-view image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On the basis of the obtained building elevations, we perform 3D mapping on the recovered elevation information to obtain 3D point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The results of the 3D point cloud visualization of the mapped buildings are given in the second column of the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In order to better show the point cloud results, we also attached the color to the point cloud, which is given in the third column of the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on the recovered 3D point cloud, the surface reconstruction results of the building are shown in the fourth column of the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Clearly, our framework generates high-quality 3D point cloud data and builds a 3D model when there is only the single-view image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This provides an insightful idea for rapid 3D reconstruction of large-scale buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3) CityGML Reconstruction: For the reconstruction of the CityGML model of the buildings, our Building3D adopts the 3dfier [61] approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The input is the point cloud data obtained in the previous steps and the polygon structure of the buildings, and the output is the LOD1 model of the buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The reconstruction results are given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Obviously, the building elevation information predicted by our SFFDE can restore the building elevation well, laying a foundation for the 3D reconstruction of different forms of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Extension 1) Large area building reconstruction: We test the robust- ness experiments on remote sensing images of the whole urban area in Hefei, Anhui Province, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 11, we give the remote sensing images of the entire area, the building extraction results, the DSM prediction results, and the building LOD1 model reconstruction results, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ablation Study We conduct ablation studies on ISPRS Vaihingen dataset to verify the effectiveness of our SFFDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' PSPNet [60] is selected as the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1) ESG: As shown in Table III, with elevation semantic globalization, our SFFDE with ResNet101 as the backbone improves the DSM estimation performance by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='082 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='276 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='358) on Rel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='011 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='282 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='293) on RMSE, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='019 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='111 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='130) on RMSE(log), which validates that the features with global dependency improve estimation performance more significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Before globalization, features of the network are limited to local perception, so that the perception of texture regular and irregular instances cannot be provided at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' However, after adding ESG, the perception ability of the network is extended from local to global, laying the foundation for subsequent high-level semantic extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' At the same time, the introduction of ESG also provides a priori global features for the subsequent registration of global and local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Channel Number of ESG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In order to better utilize the globalization ability of ESG operations, we conduct abla- tion experiments on the number of input feature channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For better visualization, we show spider plots with different channel numbers, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In order to better display the spider chart, we have performed negative index operations (e−x, x is the corresponding indicator) on the three indicators of Rel, RMSE, and RMSE(log).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on this, the six indicators are all closer to the periphery on behalf of higher JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 14 Building Extration DSM Estimation CityGML Reconstruction (local area) c Large Area Image CityGML Reconstruction Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Visualization Results of large area building reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' The large image is obtained from the urban area of Hefei City, Anhui Province, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 256 512 1024 RMSE e Rel e RMSE(log) e RMSE e Rel e RMSE(log) e Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ablation studies of the channel number of elevation semantic globalization (ESG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As can be seen from the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 12, when the number of channels is 256, the values of all indicators are located at the outermost periphery, which means that ESG has the best performance at this time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2) Backbone Selection: To verify the influence of dif- ferent backbones on our method, we conduct experiments on resnet50 and resnet101 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As shown in the table, we add the proposed elevation semantic globalization operation and L2G-ESR operation on the basis of resnet50 and resnet101, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We make a horizontal comparison of the backbone, then we come to the conclusion that the prediction accuracy of selecting resnet101 as the backbone as a whole is higher than resnet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Similarly, after adding ESG and L2G-ESR, the overall performance of the resnet101-based network is also better than that of resnet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This is consistent with our prior knowledge perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3) L2G-ESR: In Table III, L2G-ESR further improves the performance by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='054 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='222 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='276) on Rel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='149 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='133 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='282) on RMSE, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='027 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='084 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='111) on RMSE(log), which validates that L2G-ESR implements the registration and trade-off of local and global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This clearly demonstrates the superiority of SFFDE over other methods on local and global feature representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' After L2G- ESR, the features of the network are locally and globally registered through the concept of a defined elevation semantic flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This enables the network to perceive the surrounding pixel features finely in both global and local structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3 J B6] 04 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0 BW2EJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 15 ISPRS Vaihingen DFC2019 RMSE Rel RMSE(log) RMSE Rel RMSE(log) e e e RMSE Rel RMSE(log) e e e RMSE(log) Rel RMSE(log) Rel e e RMSE(log) Rel e e Ours Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Amirkolaee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ours FastDepth DORN D3Net Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Performance spider plots on ISPRS Vaihingen dataset and DFC2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' TABLE IV ABLATION STUDIES ON AGGREGATION OPERATION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ‘CONCAT JOINT CONV’ DENOTES CONCATENATION JOINT CONVOLUTION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ‘ELEMENT-WISE ADD’ REPRESENTS THE ELEMENT-WISE ADDITION OPERATION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Aggregation Operation Rel↓ RMSE↓/m RMSE(log)↓ δ1 ↑ δ2 ↑ δ3 ↑ Concat joint Conv 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='263 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='252 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='101 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='563 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='718 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='919 Element-wise Add 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='225 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='624 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='841 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='933 TABLE V ABLATION STUDIES ON LOSS FUNCTIONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ↑ MEANS THAT THE HIGHER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE, AND ↓ MEANS THAT THE LOWER THE INDICATOR VALUE, THE BETTER THE PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Loss Function Rel↓ RMSE↓/m RMSE(log)↓ δ1 ↑ δ2 ↑ δ3 ↑ L1Loss 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='298 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='265 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='548 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='820 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='912 MSELoss 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='293 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='210 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='099 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='543 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='836 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='933 berHuLoss 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='225 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='624 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='841 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='933 Aggregation Operation I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 13, there are two options in our L2G-ESR feature aggregation: (1) con- catenate operation combined with convolution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' (2) element- wise addition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We conduct ablation experiments for these two operations, and the experimental results are shown in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As can be seen from the table, element-wise addition achieves higher performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Compared with the operation of concatenation joint convolution, element-by-element addition not only does not add redundant parameters, but also enables the network to run efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4) Loss Function: In order to choose the best loss function as the learning direction of the network, we choose L1loss, MSEloss, and berHuLoss for ablation experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As shown in Table V, choosing berHuloss as the loss function for network training enables the network to achieve the best prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nonetheless, choosing L1loss and MSEloss also achieves impressive performance, in contrast to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' This side reflects the effectiveness of our ESG and L2G-ESR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 5) Performance Spider Plots: To illustrate the predicted performance of our SFFDE, we visualize the spider plots of the performance, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We compare with Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [14] and Amirkolaee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [11] on the ISPRS dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' On the DFC2019 dataset, comparisons with D3Net [16], DORN [13] and FastDepth [12] are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Since the three indicators of Rel, RMSE, and RMSE(log) are lower, the better, so we carry out negative index processing (e−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Based on this, these six indicators are all as high as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' We present the performance spider plots for the ISPRS Vaihingen dataset and the DFC2019 dataset, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Since the higher the indicator value, the better the performance, the closer the indicator value of the spider plot is to the periphery, the higher the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' It is obvious that our SFFDE is at the outermost periphery of the spider plot, whether it is the ISPRS Vaihingen dataset or the DFC2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Therefore, this shows that our SFFDE outperforms existing methods in either metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' CONCLUSION We propose a framework (Building3D) for creating 3D building models from single-view remote sensing imagery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=" Our Building3D is rooted in the proposed SFFDE network to 3 5 B6] O'5 04 8." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0 J ja(BW2E)m J B6] 04 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='0 BW2EJOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 16 achieve globalization of semantics and registration of global features with local features through the proposed ESG and L2G-ESR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Extensive experiments on the commonly used ISPRS Vaihingen and DFC2019 datasets demonstrate the superiority of SFFDE for DSM estimation, providing accurate elevation information for building reconstruction and δ1, δ2 and δ3 metrics of our SFFDE are improved to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='595, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='897 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Building3D achieves 3D reconstruction of large- area buildings in a single-view image by utilizing SFFDE elevation estimation, building mask extraction, point cloud reconstruction and building reconstruction, which is in sharp contrast to other methods based on multi-view images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Build- ing3D not only reduces data acquisition costs, but also enables rapid and large-area building reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' As a novel-and- efficient method, Building3D provides a fresh perspective into challenging 3D reconstruction of buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Although the 3D reconstruction effect is still greatly improved, we will continue to study to generate more refined 3D reconstruction results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For the lattice-like stripes phenomenon, we will work in future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' First, we will focus on large-scale images as input to build a neural network for learning, which greatly reduces the number of patch edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In addition, we will also work on the design of more accurate inter-patch fusion methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' For the overall network architecture, although our Building3D adopts the method of elevation estimation and building extraction parallel reasoning in the overall architec- ture to improve efficiency, the number of network parameters has increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' In view of this, we plan to introduce a multi- task learning method in the follow-up research, by inputting a single image block and simultaneously performing multi- task output (elevation regression head and building extraction head).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' REFERENCES [1] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fang, “Geometry-aware segmentation of re- mote sensing images via implicit height estimation,” arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='05848, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mahdi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ziming, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Xinming, “Aerial height prediction and refinement neural networks with semantic and geometric guidance,” arXiv preprint arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='10697, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mou and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhu, “Im2height: Height estimation from single monocular imagery via fully residual convolutional-deconvolutional net- work,” arXiv preprint arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='10249, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ding, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, “Boundary-aware multitask learning for remote sensing imagery,” IEEE Journal of selected topics in applied earth observations and remote sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 951–963, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Batra and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Saxena, “Learning the right model: Efficient max-margin learning in laplacian crfs,” in 2012 IEEE Conference on Computer Vision and Pattern Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2136–2143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Saxena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chung, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ng, “Learning depth from single monocular images,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 18, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [7] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Gao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Du, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Plaza, “Pseudo complex-valued deformable convlstm neural network with mutual atten- tion learning for hyperspectral image classification,” IEEE Transactions on Geoscience and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 60, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1–17, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Du, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Plaza, “A3clnn: Spatial, spectral and multiscale attention convlstm neural network for multisource remote sensing data classification,” arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='04462, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lucas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kanade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=', An iterative image registration technique with an application to stereo vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Vancouver, 1981, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Saxena, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chung, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ng, “3-d depth reconstruction from a single still image,” International journal of computer vision, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 76, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 53–69, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Amirkolaee and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Arefi, “Height estimation from single aerial images using a deep convolutional encoder-decoder network,” ISPRS journal of photogrammetry and remote sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 149, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 50–66, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wofk, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ma, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Karaman, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sze, “Fastdepth: Fast monocular depth estimation on embedded systems,” in 2019 Interna- tional Conference on Robotics and Automation (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 6101–6108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Gong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Batmanghelich, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tao, “Deep ordinal regression network for monocular depth estimation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2002–2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fang, “Height estimation from single aerial images using a deep ordinal regression network,” IEEE Geoscience and Remote Sensing Letters, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ghamisi and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yokoya, “Img2dsm: Height simulation from single imagery using conditional generative adversarial net,” IEEE Geoscience and Remote Sensing Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 794–798, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Carvalho, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Le Saux, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Trouv´e-Peloux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Almansa, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Cham- pagnat, “On regression losses for deep depth estimation,” in 2018 25th IEEE International Conference on Image Processing (ICIP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2915–2919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Srivastava, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Volpi, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tuia, “Joint height estimation and semantic labeling of monocular aerial images with cnns,” in 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 5173–5176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chen, “Multi-path fusion network for high-resolution height estimation from a single orthophoto,” in 2019 IEEE International Conference on Multimedia & Expo Workshops (ICMEW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 186–191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Cohen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Price, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yuille, “Towards unified depth and semantic prediction from a single image,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2800–2809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [20] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lin and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nevatia, “Building detection and description from a single intensity image,” Computer vision and image understanding, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 72, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 101–121, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Baatz, “Object-oriented and multi-scale image analysis in semantic networks,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' the 2nd International Symposium on Operational- ization of Remote Sensing, Enschede, ITC, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1999, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [22] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Liu, “Building extraction from high resolution imagery based on multi-scale object oriented classification and probabilistic hough transform,” in Proceedings of 2005 International Geoscience and Remote Sensing Symposium (IGARSS’05), Seoul, South Korea, 2005, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 25–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mnih, Machine learning for aerial image labeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' University of Toronto (Canada), 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [24] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Pan, “Building extraction from multi-source remote sensing images via deep deconvo- lution neural networks,” in 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ieee, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1835–1838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Guo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yuan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Xu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shibasaki, “Automatic building segmentation of aerial imagery using multi-constraint fully convolutional networks,” Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 407, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Bulatov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' H¨aufel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Meidow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Pohl, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Solbrig, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wernerus, “Context-based automatic reconstruction and texturing of 3d urban terrain for quick-response tasks,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 93, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 157–170, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [27] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Deng, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Su, “A hierarchical building segmen- tation in digital surface models for 3d reconstruction,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 222, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Smith, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wonka, “Reconstructing building mass models from uav images,” Computers & Graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 54, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 84–93, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ji, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Liu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wei, “Automatic 3d building reconstruction from multi-view aerial images with deep learning,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 171, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 155–170, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [30] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Alidoost, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Arefi, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tombari, “2d image-to-3d model: Knowledge-based 3d building reconstruction (3dbr) using single aerial images and convolutional neural networks (cnns),” Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 19, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2219, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Bosch, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Foster, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Christie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hager, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Brown, “Semantic stereo for incidental satellite images,” in 2019 IEEE Winter Conference on Applications of Computer Vision (WACV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1524–1532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8, AUGUST 2015 17 [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kim, “3d reconstruction from very high resolution satellite stereo and its application to object identification,” The International Archives of the Photogrammetry, remote sensing and spatial information Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 420–426, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [33] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kuschk, “Model-free dense stereo reconstruction for creating realistic 3d city models,” in Joint Urban Remote Sensing Event 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 202–205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [34] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ozcanli, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mundy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Webb, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hammoud, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Victor, “Automatic geo-location correction of satellite imagery,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 307–314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [35] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Liu, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fu, “Pbnet: Part-based convolutional neural network for complex composite object detection in remote sensing imagery,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 173, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 50–65, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [36] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Su, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Guibas, “Pointnet: Deep learning on point sets for 3d classification and segmentation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 652–660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Diao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lu, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fu, “Semantic segmentation for point cloud scenes via dilated graph feature aggregation and pyramid decoders,” arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='04944, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Diao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fu, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Weinmann, “Beyond single receptive field: A receptive field fusion-and-stratification network for airborne laser scanning point cloud classification,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 188, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 45–61, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [39] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Deng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Xu, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhong, “Ccanet: Class- constraint coarse-to-fine attentional deep network for subdecimeter aerial image semantic segmentation,” IEEE Transactions on Geoscience and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 60, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1–20, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Gomez, Ł.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kaiser, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Polosukhin, “Attention is all you need,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [41] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hua, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhu, “Relation matters: Relational context- aware fully convolutional network for semantic segmentation of high- resolution aerial images,” IEEE Transactions on Geoscience and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 58, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7557–7569, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [42] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, “Oriented objects as pairs of middle lines,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 169, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 268–279, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, “X-linenet: Detecting aircraft in remote sensing images by a pair of intersecting line segments,” IEEE Transactions on Geoscience and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1645–1659, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [44] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Stutts, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Dunn, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Frahm, “Efficient joint stereo estimation and land usage classification for multiview satellite data,” in 2016 IEEE Winter Conference on Applications of Computer Vision (WACV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' IEEE, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [45] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Fu, “Building reconstruction from high-resolution multiview aerial imagery,” IEEE Geoscience and Remote Sensing Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 855–859, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [46] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hepp, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Nießner, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hilliges, “Plan3d: Viewpoint and trajectory optimization for aerial multi-view stereo reconstruction,” ACM Transac- tions on Graphics (TOG), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1–17, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Cramer, “The DGPF-test on digital airborne camera evaluation – Overview and test design,” PFG Photogrammetrie – Fernerkundung – Geoinformation, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2 / 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 73–82, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kim, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lee, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kwon, “Simulation of a geiger-mode imaging ladar system for performance assessment,” sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 8461–8489, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [49] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Rottensteiner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sohn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Jung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Gerke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Baillard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Benitez, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Breitkopf, “The ISPRS benchmark on urban object classification and 3D building reconstruction,” ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' I-3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 293–298, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Niemeyer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Rottensteiner, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Soergel, “Contextual classification of lidar data and building object detection in urban areas,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 87, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 152–165, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [51] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ye, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Xu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Luan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hoegner, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Stilla, “Lasdu: A large-scale aerial lidar dataset for semantic labeling in dense urban areas,” ISPRS International Journal of Geo-Information, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 450, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [52] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Le Saux, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yokoya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' H¨ansch, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Brown, “2019 ieee grss data fusion contest: large-scale semantic 3d reconstruction,” IEEE Geoscience and Remote Sensing Magazine (GRSM), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 33–36, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [53] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' You, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Tong, “Semantic flow for fast and accurate scene parsing,” in European Conference on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Springer, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 775–793.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [54] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [55] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Papandreou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Schroff, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Adam, “Encoder- decoder with atrous separable convolution for semantic image segmen- tation,” in Proceedings of the European conference on computer vision (ECCV), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 801–818.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [56] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zwald and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Lambert-Lacroix, “The berhu penalty and the grouped effect,” arXiv preprint arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='6868, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kazhdan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Bolitho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hoppe, “Poisson surface recon- struction,” in Proceedings of the fourth Eurographics symposium on Geometry processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 7, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kiros, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hinton, “Layer normalization,” arXiv preprint arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='06450, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Jaderberg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Simonyan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zisserman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=', “Spatial transformer networks,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 28, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [60] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Qi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Jia, “Pyramid scene parsing network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2881–2890.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [61] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Ledoux, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Biljecki, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Dukai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Peters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Stoter, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Commandeur, “3dfier: automatic reconstruction of 3d city models,” Journal of Open Source Software, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 57, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 2866, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [62] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Hajek, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Jedliˇcka, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' ˇCada, “Principles of cartographic design for 3d maps–focused on urban areas,” in 6th International Conference on Cartography and GIS Proceedings, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 1, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' 297–307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [63] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mittal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Mohan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Burgard, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Valada, “Vision-based autonomous uav navigation and landing for urban search and rescue,” arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='01304, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' [64] “Isprs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='2d semantic labeling contest-vaihingen,” [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content=' Available: http://www2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='isprs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='org/commissions/comm3/wg4/2d-sem-label- vaihingen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQfigrM/content/2301.04581v1.pdf'} diff --git a/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/2301.05230v1.pdf.txt b/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/2301.05230v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b4d271d74012ded191ba14b9a3c30254f0eab3eb --- /dev/null +++ b/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/2301.05230v1.pdf.txt @@ -0,0 +1,3637 @@ +Ultraviolet photoabsorption in the B 3Σ− − X 3Σ− and +C 3Π − X 3Σ− band systems of SO sulphur isotopologues +A. N. Heays,a,b,c G. Stark,d J. R. Lyons,a,e N. de Oliveira,f B. R. Lewisg and +S. T. Gibsong +aSchool of Earth and Space Exploration, Arizona State University, Tempe, AZ 85281, USA; +bNASA Astrobiology Institute, NASA Ames Research Center, Moffett Field, California, +USA; cJ. Heyrovsk´y Institute of Physical Chemistry, Czech Academy of Sciences, Dolejˇskova +3, CZ18223 Prague 8, Czech Republic dDepartment of Physics, Wellesley College, Wellesley, +MA 02481, USA; ePlanetary Science Institute, Tucson AZ 85719, USA; fSynchrotron +SOLEIL, L’Orme des Merisiers, D´epartementale 128, 91190 Saint-Aubin, France; gResearch +School of Physics, The Australian National University, Canberra, ACT 2601, Australia +ARTICLE HISTORY +Compiled January 16, 2023 +ABSTRACT +High-resolution far-ultraviolet broadband Fourier-transform photoabsorption spec- +tra of 32S16O, 33S16O, 34S16O, and 36S16O are recorded in a microwave discharge +seeded with SO2. The B 3Σ−(v = 4 − 30) ← X 3Σ−(v = 0) and C 3Π(v = 0 − 7) ← +X 3Σ−(v = 0) bands are observed or inferred in the 43 000 to 51 000 cm−1 (196 to +233 nm) spectral range. This is the first experimental detection of a C 3Π(v > 2) +level and of any of these observed bands in an S-substituted isotopologue. Additional +measurements of A 3Π(v = 1 − 3) ← X 3Σ−(v = 0) provide a calibration of the SO +column density. Measured band profiles are fitted to an effective-Hamiltonian model +of coupled excited B 3Σ− and C 3Π states along with their predissociation linewidths +and absorption band strengths. Electronic-state potential-energy curves and transi- +tion moments are deduced. The end result is a list of line frequencies, f-values, and +dissociation widths describing the far-ultraviolet photodissociation spectrum of SO +that is accurate enough for computing atmospheric photolytic isotope-fractionation. +KEYWORDS +ultraviolet spectroscopy; photoabsorption; predissociation; sulphur monoxide; +isotopologues +1. Introduction +Sulphur monoxide (SO) occurs with observable abundance in the low-density inter- +stellar medium [1–4], where its spectroscopic signature has been used to investigate +the properties of shocked gas and to constrain the ages of star-forming molecular- +cloud cores. It is also a significant species within the Solar system, forming in Io’s +atmosphere [5–7] primarily through the photodissociation of SO2, and with detections +in cometary comae [8, 9] and the Venus atmosphere [10] where a vertical profile was +obtained by the Venus Express mission [11]. SO and its S-substituted isotopologues +may be key molecules in the sulphur cycle of a pre-oxygenated early-Earth atmosphere +(older than 2.4 Gyr) [12, 13]. Measurements of mineral S-isotopes from sedimentary +arXiv:2301.05230v1 [physics.atom-ph] 12 Jan 2023 + +1.5 +2.0 +2.5 +3.0 +3.5 +Internuclear distance (Å) +35000 +40000 +45000 +50000 +Potential energy (cm−1) +0 +1 +2 +0 1 2 3456789101112 +0 +1 +2 +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +1213141516 +0 +1 +2 +3 +4 +5 +6 +7 +X3 +− +shifted ++34000cm−1 +X3 +− +B3 +− +A3 +C3 +d1 +e1 +S(3P) + O(3P) +Figure 1. +Potential-energy curves of excited and ground states of SO referenced to the ground state equilib- +rium energy, along with 32S16O vibrational level energies. +rock reveal fractionating signatures that are likely due to gas-phase photochemistry +[14]. These signatures are the products of a low-O2 atmosphere in which sulphur al- +lotropes and elemental sulphur coexist with H2SO4 and provide a quantitative tracer +for the rise of O2 in Earth’s atmosphere. Additionally, SO and its sulphur isotopo- +logues derived from SO2 photolysis play a central role in the conversion of oxidised to +neutral sulphur [15, 16]. The successful modelling of astrochemical and planetary SO +observations, and S-isotopes in the early-Earth atmosphere, requires a full, detailed, +and accurate knowledge of the excited states of SO, their transition properties, and +temperature- and isotopologue-dependent ultraviolet photoabsorption and photodis- +sociation cross sections. +An overview of the experimentally-known photoabsorbing excited states of SO is +plotted in Fig. 1. The resulting ultraviolet absorption spectrum of SO is dominated by +the strong progression of B 3Σ− ← X 3Σ− vibrational bands between 240 and 190 nm +(42 000 and 53 000 cm−1), and is an analogue of the B 3Σ− +u − X 3Σ− +g systems in isova- +lent O2 and S2. The early SO spectroscopic study of Martin [17] observed a breaking +off in emission from high rotational levels of B 3Σ−(v = 0 − 3) that is attributable +to predissociation. Clerbaux and Colin [18] established the responsible dissociation +threshold in a study of emission from low-lying B(v) levels of 32S16O and 32S18O, +and identified multiple local perturbations affecting them. Colin [19] photographically +recorded absorption bands B 3Σ−(v′) ← X 3Σ−(v′′ = 0) as far as v′ = 30 using flash- +photolysis methods, and provided partial rotational analyses for some bands while +noting irregular vibrational spacings and significant line broadening throughout their +progression. A comprehensive study of B 3Σ−(v = 0 − 16) levels by Liu et al. [20] +combined degenerate four-wave mixing, laser-induced fluorescence, Fourier transform +emission, and photographic absorption measurements in a detailed rotational analy- +sis of multiple bands appearing between 41 000 and 50 000 cm−1 and found evidence +for numerous perturbations. They attributed the latter to spin-orbit and rotational +interactions between rovibronic levels of the B 3Σ−, A 3Π, C 3Π, and d 1Π states by +making use of earlier multi-photon ionisation measurements by Elks and Western [21] +2 + +and Archer et al. [22] characterising the A 3Π(v = 0 − 13) and C 3Π(v = 0 − 1) and +d 1Π(v = 0 − 3) levels, respectively. Liu et al. [20] estimated upper-limits varying +between 0.3 and 40 cm−1 for the linewidths of B 3Σ−(v = 4 − 16). +Yamasaki et al. [23, 24] measured radiative lifetimes for B 3Σ−(v = 0 − 3) and +Phillips [25] recorded a low-resolution absorption cross section covering the B 3Σ− ← +X 3Σ− progression in a flowing discharge. Several studies have experimentally mea- +sured the radiative lifetime of various A 3Π levels and their emission branching between +ground state vibrational levels [21, 26–29]. +Early theoretical studies [30, 31] determined potential-energy curves for the X 3Σ−, +B 3Σ−, and other low-lying excited states correlated to the two lowest SO dissocia- +tion channels, generating S(3P) + O(3P) and S(1D) + O(3P). Some of these excited +states can, in principle, interact with B 3Σ−. In particular, computed C 3Π and d 1Π +states [22, 32, 33] adiabatically correlate to S(3P) + O(3P), have minima supporting +bound vibrational levels, and possess inner and outer limb crossings with B 3Σ−. The +experimentally-observed variable line broadening of B 3Σ− suggests that, in addition +to any interactions with bound levels of A 3Π, C 3Π and d 1Π, it interacts with multiple +dissociating states. Multiple candidate predissociation pathways were noted by Yu and +Bian [34] following computation of spin-orbit couplings to numerous singlet, triplet, +and quintet states. More recently, potential-energy curves, transition dipole moments, +and couplings affecting B 3Σ−, and C 3Π have been computed by Danielache et al. [16] +and Sarka and Nanbu [35] for the purposes of studying the isotope-dependence of SO +photoabsorption and photodissociation. Sarka and Nanbu [35] also compute a higher- +lying unbound 3Σ− state that approaches B 3Σ− at large internuclear distance and +their associated nonadiabatic coupling. This interaction results in the peculiar shape of +the B 3Σ− potential-energy curve and a sharp alteration of its electronic-configuration +near 2.25 ˚A, as evidenced by an exchange of electronic transition moment between the +diabatic B 3Σ− −X 3Σ− and higher-energy 3Σ− −X 3Σ− transitions. Further ab initio +calculations of excited SO states have been recently performed by Feng and Zhu [36], +who also computed many spin-orbit interaction energies, and da Silva and Ballester +[37]. Previous experimental studies [18, 19] concerning the photodissociation spectrum +of SO isotopologues appear to be limited to 32S18O with theoretical results extended +to all S substitutions [35]. +In this report, we present spectroscopic analyses of high-resolution broadband ab- +sorption spectra of the B 3Σ−(v′ = 4 − 30) ← X 3Σ−(v′′ = 0) and C 3Π(v′ = 0 − 7) ← +X 3Σ−(v′′ = 0) systems for four SO isotopologues: +32S16O, +33S16O, +34S16O, and +36S16O. The observed absorption band profiles are reduced to deperturbed molecu- +lar constants and spin-orbit interaction energies mixing B 3Σ− and C 3Π electronic- +vibrational states, along with calibrated transition moments with the ground state and +a quantification of the observed predissociation line broadening. Empirical B 3Σ− and +C 3Π potential-energy curves and a global spin-orbit interaction are fitted to these +data and used to extrapolate the experimental data to include all bands up to the +B 3Σ− dissociation limit in all isotopologues. +2. Measurements +Photoabsorption measurements were performed on the high-resolution absorption +spectroscopy branch of the DESIRS beamline [38] at the SOLEIL synchrotron. This +facility was used in similar studies of the OH and S2 radicals [39, 40]. The beamline +undulator generates continuum bandpass radiation with a width of 7% of its central +3 + +frequency. Four overlapping measurements were required for complete coverage of the +43 000 to 52 000 cm−1 target region. The continuum radiation was passed through a +rare-gas-filled chamber to filter unwanted higher harmonics generated in the undula- +tor, then an absorption cell, and terminated at a vacuum-ultraviolet Fourier-transform +spectrometer [41, 42]. This is an all-reflection wave-front-division interferometer reliant +on spatial coherence of the synchrotron beam and a modified Fresnel bi-mirror config- +uration with the optical-path difference scanned by translating one reflector. The in- +strument was operated with spectral resolution between 0.15 and 0.86 cm−1 full-width +at half-maximum (FWHM) depending on the perceived sharpness of SO features in +each undulator bandpass and signal-to-noise considerations. +SO radicals were produced in a flowing discharge containing one of four sulphur +dioxide samples seeded in helium. Highly enriched 33SO2 (99% 33S), 34SO2 (99.8% +34S), and 36SO2 (approximately 70% 36S, 20% 34S, and 10% 32S) gases were used +to generate rare SO isotopologues, and natural abundance SO2 (95.02% 32S, 0.75% +33S, and 4.21% 34S) was used to study 32S16O. All three samples contained oxygen +in natural abundance but no absorption due to 18O-bearing species was detected. +A radio-frequency generator (13.5 MHz, 200 W power) was centred in a 1.5 m glass +absorption cell equipped with wedged MgF2 windows. Helium carrier gas with an +upstream pressure of 2 mbar flowed through the cell and was continuously evacuated +by a 600 m3 hr−1 Roots pump. Fluorescence in the discharge typically extended 40 cm +on either side of the central generator cavity. SO2 was seeded into the He flow prior +to the absorption cell with a partial pressure between 0.04 and 0.1 mbar. The cell flow +rate was significantly reduced when recording 33S16O, 34S16O, and 36S16O spectra to +minimise the consumption of rare SO2 isotopologues. +Strong absorption features of the parent SO2 ˜C 1B2 − ˜X 1A1 electronic system [43, +44] between 45 500 and 57 000 cm−1 overlap most SO B(v) ← X(0) absorption bands. +A sequence of three spectra were recorded for each bandpass. First, the synchrotron +radiation bandpass was established in a spectrum of pure helium. SO2 was then seeded +into the He flow and a reference absorption spectrum recorded with the discharge off. +Finally, a combined SO and SO2 spectrum was recorded after activating the discharge +source. The raw experimental spectra are available in an online archive [45]. +3. Analysis method +The X 3Σ− and B 3Σ− states of SO consist of three Hund’s case-(a) spin-, e/f-parity +sublevels, identifiable, in order of increasing energy, with the following quantum num- +bers: +(F1, e) : Λ = 0, Ω = 0, Σ = 0 ; +(F2, f) : Λ = 0, Ω = 1, Σ = 1 ; +and (F3, e) : Λ = 0, Ω = 1, Σ = 1, +while A 3Π consists of six sublevels: +(F1, e/f) : Λ = 1, Ω = 0, Σ = −1 ; +(F2, e/f) : Λ = 1, Ω = 1, Σ = 0 ; +and (F3, e/f) : Λ = 1, Ω = 2, Σ = +1, +4 + +and higher-Ω levels of C 3Π occur with lower energy: +(F1, e/f) : Λ = 1, Ω = 2, Σ = +1 ; +(F2, e/f) : Λ = 1, Ω = 1, Σ = 0 ; +and (F3, e/f) : Λ = 1, Ω = 0, Σ = −1. +Here, Λ and Σ are the usual electronic-orbital and spin angular momentum pro- +jection quantum numbers, and Ω = |Λ + Σ|. States of common parity within each +Fi manifold become mixed with increasing molecular rotation, although relatively +slowly in the cases of A 3Π and C 3Π because of their large spin-orbit splittings. +In principle, B 3Σ−(v′) ← X 3Σ−(v′′) bands consist of 14 overlapping rotational +branches but with reduced contributions from spin-forbidden ∆Σ ̸= 0 transitions. +The rotational structure of A 3Π(v′) ← X 3Σ−(v′′) and C 3Π(v′) ← X 3Σ−(v′′) bands +consists of 27 branches, but transitions terminating on different C 3Π Ω-substates +are well separated in energy. In what follows, fully-specified electronic-vibrational +states and transitions are sometimes abbreviated, e.g., X 3Σ−(v = 0) to X(0), and +C 3ΠΩ=0(v′ = 1) ← X 3Σ−(v′′ = 0) to C(v = 1, Ω = 0) ← X(0). +3.1. Vibrational state model +The significant predissociation broadening of nearly all B(v′) ← X(0) bands and poor +signal-to-noise of the observed C(v′) ← X(0) absorption precludes their line-by-line +analysis in most cases. Instead, the ground and excited vibrational levels are modelled +with a minimal set of molecular parameters in a Hund’s case-(a) parity-symmetrised +basis, and consideration is made for spin-rotational mixing of Ω-sublevels within each +electronic-vibrational state and for spin-orbit mixing of neighbouring B(vB) and C(vC) +levels. +An effective-Hamiltonian matrix is built with diagonal deperturbed rotational level +energies and off-diagonal interaction energies. Diagonalising this matrix produces a +model of observable energies and mixing coefficients for the interacting case-(a) levels. +The form, symbols, and phase conventions adopted in our matrix diagonalisation and +line strength calculation are the same as those used for linear molecules by the PGO- +PHER program [46], that is, the effective Hamiltonian of Brown et al. [47] with explicit +matrix elements for 3Σ− and 3Π spin-rotation-mixed manifolds listed in Cheung et al. +[48] and Brown and Merer [49], respectively. The o and p Λ-doubling terms of Brown +and Merer [49] were used in the analysis of some C 3Π and A 3Π levels. +The interaction of B 3Σ−(vB) and C 3Π(vC) levels is modelled as a spin-orbit mixing +of levels differing by ∆Σ = ±1, ∆Λ = ∓1, and ∆Ω = 0, and with common e/f +symmetry. A reduced matrix element [50] is fitted to each pair of interacting B(vB) +and C(vC) levels following the definition and phase convention of PGOPHER. This +reduced matrix element is − +√ +6 times larger than the conventionally-referenced matrix +element between Ω = 1 levels: +⟨B 3Σ− +Ω=1,e/f|HSO|C 3ΠΩ=1,e/f⟩ = ξvBvC, +(1) +that we quote below. The corresponding matrix element mixing Ω = 0 levels is +⟨B 3Σ− +Ω=0,e/f|HSO|C 3ΠΩ=0,e/f⟩ = +√ +2ξvBvC. +(2) +5 + +43600 +43700 +43800 +43900 +44000 +44100 +44200 +44300 +44400 +Transition wavenumber (cm−1) +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +Transmission (arb. units) +Experimental +32S16O + 32S16O2 +spectrum +(scaled) +Residual error of best-fit model (shifted from zero) +Residual error neglecting absorption from X(1) (shifted from zero) +Residual error neglecting SO (shifted from zero) +B(4) +X(0) +B(5) +X(0) +Figure 2. +An experimental spectrum showing 32S16O B(4) ← X(0) and B(5) ← X(0) absorption and the +residual error of a best-fit model of these bands. Residual errors are also shown for models neglecting all 32S16O +absorption and absorption from vibrationally-excited X(v = 1) levels. +Fitted scalar electric-dipole vibronic transition moments, µB(v)−X(0) and µC(v)−X(0), +are used to simulate the observed 3Σ− ← 3Σ− and 3Π ← 3Σ− absorption bands. +The transition moments for parity-allowed ∆J = −1, 0 and +1 rovibronic transitions +between unmixed case-(a) levels are computed according to [50–52]: +µi(v′J ′Ω′)−X(v′′J ′′Ω′′) = µi(v′)−X(v′′) +� +(2J′′ + 1)(2J′ + 1) +× (−1)J ′−Ω′+δΛ′0 +� +J′ +1 +J′′ +−Ω′ +Ω′ − Ω′′ +Ω′′ +� +, +(3) +where the final term is a Wigner-3j coefficient. The mixing coefficients calculated +while diagonalising the excited and ground state level energies are used to compute +mixed line strengths which should match the observed transition strengths. The mixed +absorption f-values are +f = 3.038 × 10−6 × ν0 +� +µmixed +i(v′J ′Ω′)−X(v′′J ′′Ω′′) +�2 +, +(4) +where the given numerical constant assumes µ in atomic units and a transition +wavenumber, ν0, with units of cm−1. +Lorentzian predissociation line broadening is modelled by adopting complex-valued +diagonal level energies in the effective Hamiltonian, where the imaginary component is +equivalent to the FWHM linewidth, Γ. Aside from conveniently accounting for mixed +linewidths, the adoption of complex level energies also slightly modifies the computed +lineshifts due to level interactions between nearby case-(a) levels with overlapping line +wings. The observed line broadening is caused by repulsive states not included in our +deperturbation matrix, and the broadening of each deperturbed electronic-vibrational +levels is experimentally determined. In some cases, Ω- and J-dependent widths of +case-(a) states are required to reproduce the experimental spectra. +6 + +45800 +45900 +46000 +46100 +46200 +46300 +46400 +Transition wavenumber (cm−1) +0.00 +0.25 +0.50 +0.75 +1.00 +Transmission (arb. units) + P11ee + P22ff + P33ee + Q23fe + Q32ef + R11ee + R22ff + R33ee +C(v = 3, += 2) +X(0) +C(v = 3, += 1) +X(0) +C(v = 3, += 0) +X(0) +Rotational branches +of B(8) +X(0) +Experimental +32S16O + 32S16O2 spectrum +Model 32S16O +cross section +(shifted and +scaled) +Reference SO2 cross section +(shifted and scaled) +Residual error of best-fit model +Residual error neglecting CX (shifted) +Figure 3. +A rotationally-assigned experimental spectrum showing 32S16O B(8) ← X(0) and C(3) ← X(0) +absorption. The plotted reference SO2 and modelled SO cross sections were used to synthesise a spectrum with +residual error as shown. Also shown is the residual error of a model neglecting the µC(v=3)−X(v=0) transition +moment. +46600 +46800 +47000 +47200 +47400 +47600 +Transition wavenumber (cm−1) +0.00 +0.25 +0.50 +0.75 +1.00 + Transmission (arb. units) +B(9) +X(0) +B(10) +X(0) +B(11) +X(0) +C(v = 4, += 2) +X(0) +C(v = 4, += 1) +X(0) +C(v = 4, += 0) +X(0) +C(v = 5, += 2) +X(0) +C(v = 5, += 1) +X(0) +C(v = 5, += 0) +X(0) +Experimental +32S16O + 32S16O2 spectrum +Residual error of the best-fit 32S16O model +36S16O +34S16O +33S16O +32S16O +Residual error neglecting SO absorption (shifted) +Figure 4. +An experimental spectrum showing +32S16O B(9) ← X(0), B(10) ← X(0), B(11) ← X(0), +C(4) ← X(0), and C(5) ← X(0) absorption and the residual error of a best-fit model labelled with band- +head assignments. Also shown are residual errors of similar models for other S-substituted isotopologues. +7 + +A list of perturbed line frequencies, νi, f-values, fi, and linewidths, Γi, was com- +puted for rotational lines with J′′ ≤ 50 for all observed bands. A cross section com- +posed of all transitions was computed assuming a thermal population distribution of +ground-state rotational levels, αF ′′ +i J ′′ and a Voigt line profile, V (ν, Γ, ΓD), constructed +assuming a Gaussian Doppler width, ΓD, +σ(ν) = +� +i +8.853 × 10−13fiαF ′′ +i J ′′ +i V (ν − ν0i, Γi, ΓD), +(5) +where the numerical constant assumes a cross section in units of cm2. +The synchrotron radiation generated by the beamline undulator possesses a peaked +band pass of approximately 5 nm FWHM and its curvature, I0(ν), was modelled with +a spline function with knots separated by 500 cm−1. The Beer-Lambert law was used +to compute an ideal absorption spectrum: +I(ν) = I0(ν) exp +� +−NSOσ(ν) − τother(ν) +� +, +(6) +assuming a column density of SO radicals, NSO, and including extra opacity due to +contaminant absorbers in the spectrum, τother. The ideal spectrum was convolved with +a function defining the instrumental resolution, primarily a sinc function with a small +amount of additional broadening previously found to be generated by this instrument +[53] and modelled as a Gaussian of 0.1 cm−1 FWHM. This final spectrum is compared +pointwise with the measured spectra and the various parameters governing the model +were adjusted iteratively until a best agreement was found in the least-squares sense. +Examples of this comparison for several B(v) ← X(0) bands are plotted in Figs. 2, +3, and 4 and include spectra exhibiting varied SO2 contamination and line confusion +due to predissociation broadening. Figure 3 is annotated to show the full rotational +structure of B(8) ← X(0), including all rotational transitions stronger than 2% of the +most absorbed. The same structure underlies the unresolved B − X bands. +The overlapping absorption of parent-gas SO2 isotopologues was comparable to that +of SO itself and high-spectral-resolution SO2 cross sections measured for the purpose +were included in our modelling. An increase of SO2 rotational temperature apparently +occurs when the discharge is struck so the reference spectra do not quite account for +all SO2 absorption near its bandheads. The recorded spectra of 36S16O were contami- +nated by 32S16O and 34S16O beyond the expected amount given the known impurity +of the 36SO2 parent gas. These spectra were recorded subsequent to and on the same +apparatus as other studies of 32S- and 34S-containing molecules, and outgassing of +earlier-deposited sulphur might explain the extra contamination. Ultimately the mix- +ture of SO isotopologues was assessed directly from the spectra and has a ratio near +36S : 34S : 32S = 1 : 0.28 : 0.16, with some variation between measurements. Additional +SO absorption from super-thermally excited X 3Σ−(v = 1) and electronically-excited +a 1∆(v = 0) was also recorded and accounted for with additional vibrational state +models. Significant absorption due to B(v′ + 2) ← X(1) hot bands was found to +overlap B(v′) ← X(0) for v′ = 5 − 8 in all isotopologues. +Multiple overlapping spectra were recorded to span the desired spectral range and +some additional spectra were recorded under varied discharge conditions. Up to five +independent spectra were recorded for some bands and the parameters governing their +upper-state levels and transition moments were fitted simultaneously. This effectively +increased the signal-to-noise-ratio for these bands. +8 + +Many trials were necessary before arriving at a set of well-fitting and physically- +reasonable deperturbed level energies and B 3Σ− ∼ C 3Π interaction parameters, due +to the non-resolution of most B(v) ← X(0) rotational structure and the weakness +or non-observation of C(v) ← X(0) bands. The inclusion of higher-order centrifugal- +distortion parameters (for example H, λD, γD, and AD) was found mostly unnecessary +during this process and some small but significant parameters (for example D and γ) +were set to fixed values for some bands once their overall pattern-forming values had +been determined. Statistical fitting uncertainties of the model parameters are esti- +mated by the least-squares fitting routine but do not account for correlation between +model parameters or reflect model error introduced by the assumption of a particular +effective Hamiltonian, constraints imposed on its parameters, or the incomplete deper- +turbation of any level. The scatter of our fitted parameters significantly exceeds these +model parameter uncertainties. Therefore, in this work we prefer to list estimated un- +certainties more reflective of the experimental scatter. However, the listed uncertainty +estimates are best considered as relative. +An SO rotational temperature of 360 ± 15 K was determined from the strengths of +rotational lines in the well-resolved B(8) ← X(0) band, and was used to define the +model Doppler width, ΓD. A thermalised population of ground-state levels peaks near +J = 13 at 360 K, falls below 5% of its peak value by J = 40, and consists of 98% v = 0. +Sufficient overlap exists between spectra to calculate relative column densities sep- +arately for each isotopologue. A calibration of the 32S16O column-density, and B − X +and C − X transition moments, was determined from a measurement of well-known +A(v) − X(0) transitions. A calibration of transition moments of other isotopologues +was made relative to 32S16O assuming an isotopologue-independent summation of +B(v = 7 − 14) ← X(0) transition intensity. +3.2. Electronic state model +The band-by-band analysis of spectroscopic constants described above is necessary for +analysing the blended spectra. Each single-band model, or model of a few interacting +bands, results in a computed rotational line list that provides, within experimental +uncertainty, the frequencies, strengths, and widths of all unresolved lines that signif- +icantly contribute to the experimental band profiles. A more fundamental model of +X 3Σ−, B 3Σ−, and C 3Π potential-energy curves; B 3Σ− and C 3Π spin-orbit inter- +action mixing; and electronic transition moments controlling B 3Σ− ← X 3Σ− and +C 3Π ← X 3Σ− absorption; was fitted to the band-by-band rotational line lists. +Parameterised forms for the diabatic B 3Σ−, and C 3Π potential-energy curves, T(R) +where R is the internuclear-distance, are discussed in Sec. 5.2. Separate curves for Ω +and e/f-parity substates were generated assuming R-independent spin-orbit and spin- +spin interaction parameters, A and λ, respectively. To simulate a rotating molecule, +R− and reduced-mass-dependent diagonal and off-diagonal matrix elements were com- +puted to represent centrifugal effects and the spin-rotation mixing of Ω levels within +each electronic state. The specific matrix elements used are given in Table 1 and follow +the formulation of Brown et al. [47]. +A ladder of uncoupled vibrational energy eigenvalues and wavefunctions, χi(vJ), +was computed from the potential-energy curve of each electronic state for a range +of J, using the Numerov method [54]. Band transition moments between unmixed +9 + +Table 1. +Matrix elements of spin-rotation mixed spin-electronic states, |Ω, e/f⟩.a +3Σ−: +⟨0, e|H|0, e⟩ += T(R) + B(R) [J(J + 1) + 2] − 2γ − 4 +3λ +⟨1, e/f|H|1, e/f⟩= T(R) + B(R)J(J + 1) − γ + 2 +3λ +⟨0, e|H|1, e⟩ += 2 +� +J(J + 1) +� +−B(R) + 1 +2γ +� +3Π: +⟨0, e/f|H|0, e/f⟩= T(R) + B(R) [J(J + 1) + 2] − 2γ − 4 +3λ +⟨1, e/f|H|1, e/f⟩= T(R) + A + B(R) [J(J + 1) − 2] + 2 +3λ +⟨2, e/f|H|2, e/f⟩= T(R) − A + B(R) [J(J + 1) + 2] − 2γ + 2 +3λ +⟨0, e/f|H|1, e/f⟩= +� +J(J + 1) +� +− +√ +2B(R) + +1 +√ +2γ +� +⟨0, e/f|H|2, e/f⟩= 0 +⟨1, e/f|H|2, e/f⟩= +� +− +√ +2B(R) + +1 +√ +2γ +� � +J(J + 1) − 2 +aB(R) = +ℏ2 +2µR2 +electronic-vibrational states were computed according to: +µi(v′J ′)−X(v′′J ′′) = µi−X +� ∞ +0 +χi(v′J ′)(R)χX(v′′J ′′)(R) dR, +(7) +where transitions are only allowed between states of common Σ, i represents either the +B or C state, and µi−X is an isotopologue- and R-independent electronic transition +moment. +Spin-orbit reduced matrix elements mixing all neighbouring and remote B(vB) and +C(vC) levels were computed from a fitted scalar parameter, ξBC, according to: +ξvBvCJ = ξBC +� ∞ +0 +χB(vB,J)(R) χC(vC,J)(R) dR, +(8) +and specific Ω′ ∼ Ω′′ matrix elements were computed as in Eqs. (1) and (2). +For each value of J, full sets of ground- and excited-state uncoupled vibrational +energy levels and the spin-orbit interaction energies mixing them were diagonalised. +From the mixed levels a spectrum for all optically-allowed rotational transitions was +computed. The parameters of this global model are mass-independent and simultane- +ously constrained by all isotopologue measurements. +In the following analysis we also employ band-integrated f-values that neglect B ∼ +C spin-orbit coupling computed according to [55]: +fi(v′)−X(v′′) = 3.038 × 10−6 × νµ2 +i(v′0)−X(v′′0) +2 − δ0,Λ′+Λ′′ +2 − δ0,Λ′′ +, +(9) +and band-averaged emission rates (s−1) computed according to +Ai(v′)−X(v′′) = 2.026 × 10−6 × ν3µ2 +i(v′0)−X(v′′0) +2 − δ0,Λ′+Λ′′ +2 − δ0,Λ′ +. +(10) +10 + +Table 2.: Deperturbed molecular constants and predissociation broadening parame- +ters.b +Level +T c +B +D +A +λ +γ +Γ(all-Ω)d Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ωe +32S16O +X 3Σ−(v = 0)f +573.791 05 +0.718 +1.13 × 10−6 +− +5.28 +−0.005 61 +− +− +− +− +0, 1 +X 3Σ−(v = 1)g +1 711.7999 +0.712 +1.13 × 10−6 +− +5.31 +−0.005 66 +− +− +− +− +0, 1 +A 3Π(v = 1)h +39 083.313(15) 0.585 +4.35 × 10−6 157 +2.31 +0.0531 +− +− +− +− +0, 1, 2 +A 3Π(v = 2)i +39 491.262(27) 0.568 24(10) +6.43(12) × 10−6 155.416(16) +2.266(17) +0.091(12) +− +− +− +− +0, 1, 2 +A 3Π(v = 3)j +39 895.360(39) 0.553 80(14) +3.71(18) × 10−6 153.481(23) +2.261(19) +0.097(18) +− +− +− +− +0, 1, 2 +B 3Σ−(v = 4) +44 368.8(13) +0.4799(44) +1.00 × 10−6 +− +3.2(13) +−0.024(13) +1.55(78) +− +− +− +0, 1 +B 3Σ−(v = 5) +44 954.26(16) +0.473 79(50) +1.00 × 10−6 +− +3.45(19) +−0.0194(72) +0.77(23) +− +− +− +0, 1 +B 3Σ−(v = 6) +45 528.39(26) +0.470 57(86) +1.00 × 10−6 +− +2.89(34) +− +3.01(29) +− +− +− +0, 1 +B 3Σ−(v = 7) +46 094.16(21) +0.464 42(61) +1.44(51) × 10−6 +− +2.834(88) +−0.0105(31) +1.77(12) +− +− +− +0, 1 +B 3Σ−(v = 8)k +46 651.185(69) 0.459 011(73) +1.43(15) × 10−6 +− +3.051(12) +−0.012 87(26) +− +0.0168 +0.109 +− +0, 1 +B 3Σ−(v = 9)l +47 197.571(78) 0.452 98(26) +1.04(19) × 10−6 +− +2.932(95) +−0.0130(53) +− +0.51(13) +3.00(18) +− +0, 1 +Table continued on next page. +aΓ has units of cm−1 FWHM and all other parameters units of cm−1. Fitting uncertainties are given parenthetically in units of the least significant digit and are relative +only, not accounting for parameter correlation or any inadequacy in the spectral model specification. Fixed parameters are given without uncertainties. Blanked parameters +were fixed to zero. +bTerm value T is referenced to the X 3Σ− potential-energy minimum and is related to a virtual TΣ=0,J=0 energy level according to TΣ=0,J=0 = T + 2B − 2γ − 4 +3 λ. +cWidths entered in this column are fitted to all Ω levels simultaneously, otherwise widths are given in the following columns for individual Ω. A few bands have J dependent +widths as described in footnotes. +dΩ-states of this level that directly contribute to the observed absorption. +f Computed from the isotopically-invariant ground-state parameters of Lattanzi et al. [56]. Additional parameters: H = −2.16×10−13, λD = 1.02×10−5, γD = −1.76×10−8 +gAdditional parameters: H = −2.16 × 10−13, λD = 1.04 × 10−5, γD = −1.72 × 10−8 +hFixed parameters taken from Elks and Western [21]. Additional parameters: o = 0.576, p = 0.0137 +iAdditional parameters: H = 2.63(19) × 10−9, o = 0.578(20) +j Additional parameters: o = 0.581(24) +kJ-dependent widths are described in Sec. 4.5. The value in this table is extrapolated to J = 0. Additional parameters: H = 5.3(26) × 10−11, λD = 2.26(28) × 10−4 +lAdditional parameters: λD = −5.5(28) × 10−4 +11 + +Table continued from previous page. +Level +T +B +D +A +λ +γ +Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ω +B 3Σ−(v = 10) 47 733.17(24) +0.447 18(84) +6.6(33) × 10−7 +− +3.99(29) +− +− +3.47(70) +4.95(57) +− +0, 1 +B 3Σ−(v = 11) +48 258.64(13) +0.442 33(62) +1.75(54) × 10−6 +− +2.64(14) +−0.0178(65) +− +3.86(48) +3.10(20) +− +0, 1 +B 3Σ−(v = 12)a 48 768.81(29) +0.4361(11) +2.3(11) × 10−6 +− +1.89(77) +−0.045(23) +− +2.5(10) +5.68(73) +− +0, 1 +B 3Σ−(v = 13) +49 265.31(53) +0.429 04(99) +1.00 × 10−6 +− +0.99(49) +− +− +4.7(15) +9.4(11) +− +0, 1 +B 3Σ−(v = 14) +49 750.83(61) +0.4208(23) +1.00 × 10−6 +− +3.00 +− +17.2(13) +− +− +− +0, 1 +B 3Σ−(v = 15)b 50 214.6(10) +0.4102(10) +1.00 × 10−6 +− +3.00 +− +19.5(13) +− +− +− +0, 1 +B 3Σ−(v = 16) +50 624.68(14) +0.384 24(76) +5.38(90) × 10−6 +− +4.42(30) +0.119(11) +− +5.99(78) +5.24(36) +− +0, 1 +B 3Σ−(v = 17) +50 951.18(40) +0.3281(16) +1.00 × 10−6 +− +5.8(29) +− +14.6(10) +− +− +− +0, 1 +B 3Σ−(v = 18) +51 160.50(27) +0.309 66(54) +1.00 × 10−6 +− +3.00 +− +5.65(31) +− +− +− +0, 1 +B 3Σ−(v = 19) +51 365.43(32) +0.303 45(92) +1.00 × 10−6 +− +1.80(65) +− +8.02(83) +− +− +− +0, 1 +B 3Σ−(v = 20) +51 565.48(12) +0.292 89(34) +1.00 × 10−6 +− +4.26(20) +0.0954(80) +4.16(17) +− +− +− +0, 1 +B 3Σ−(v = 21) +51 759.97(10) +0.284 25(30) +1.00 × 10−6 +− +3.13(21) +0.0727(79) +3.95(17) +− +− +− +0, 1 +B 3Σ−(v = 22) +51 943.00(18) +0.274 63(44) +1.00 × 10−6 +− +3.19(54) +− +5.80(33) +− +− +− +0, 1 +B 3Σ−(v = 23) +52 115.45(10) +0.263 06(30) +1.00 × 10−6 +− +3.06(24) +0.055(11) +3.80(23) +− +− +− +0, 1 +B 3Σ−(v = 24) +52 275.08(11) +0.250 44(35) +1.00 × 10−6 +− +3.49(24) +0.100(11) +4.20(20) +− +− +− +0, 1 +B 3Σ−(v = 25) +52 419.46(18) +0.237 79(44) +1.00 × 10−6 +− +2.42(24) +0.0600 +5.20(32) +− +− +− +0, 1 +B 3Σ−(v = 26) +52 549.46(33) +0.222 95(84) +1.00 × 10−6 +− +1.39(37) +0.0600 +5.34(51) +− +− +− +0, 1 +B 3Σ−(v = 27) +52 665.41(14) +0.204 96(43) +1.00 × 10−6 +− +3.58(16) +0.178(11) +2.77(19) +− +− +− +0, 1 +B 3Σ−(v = 28) +52 763.438(43) 0.183 92(11) +1.00 × 10−6 +− +3.623(41) +0.1199(29) +1.00 +− +− +− +0, 1 +B 3Σ−(v = 29) +52 842.1(24) +0.1621(73) +1.00 × 10−6 +− +3.00 +0.0600 +15.0 +− +− +− +0, 1 +B 3Σ−(v = 30) +52 916.4(33) +0.1332(92) +1.00 × 10−6 +− +3.00 +0.0600 +15.0 +− +− +− +0, 1 +C 3Π(v = 0) +44 729.30(37) +0.5686(11) +− +−181 +1.00 +− +− +− +− +− +None +C 3Π(v = 1)c +45 420.583(79) 0.563 02(24) +2.00 × 10−6 −181.858(92) 0.888(83) +− +0.039(19) +− +− +− +0, 1, 2 +C 3Π(v = 2) +46 098.41(29) +0.554 42(77) +− +−181 +1.00 +− +1.13(27) +− +− +− +1 +C 3Π(v = 3)d +46 760.454(75) 0.547 31(16) +1.37(16) × 10−6 −180.436(26) 1.118(92) +− +− +0.197(54) 1.39(37) +0.392(96) +0, 1, 2 +Table continued on next page. +aDeperturbed linewidths of Ω = 0 were fitted to a J-dependent formula: 2.5(10) + 0.011(4)J(J + 1). +bT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec. 4.12. +cThe fitted width may be below the experimental sensitivity and a clear upper limit is determined to be 0.1 cm−1 FWHM. +dAdditional parameters: o = 0.907(60), p = 0.129(18) +12 + +Table continued from previous page. +Level +T +B +D +A +λ +γ +Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ω +C 3Π(v = 4)a +47 405.243(35) 0.540 820(79) +3.486(87) × 10−6 −180.596(34) 0.915(27) +− +− +0.136(33) 0.55(10) +0.163(35) +0, 1, 2 +C 3Π(v = 5) +48 030.778(65) 0.531 974(99) 2.774(100) × 10−6 −179.881(89) 0.936(44) +− +− +0.83(33) +0.142(55) 0.055(28) +0, 1, 2 +C 3Π(v = 6)b +48 634.8(10) +0.520 25(63) +− +−179.8(16) +0.67(34) +− +− +6.5(33) +0.86(32) +0.92(45) +0, 1, 2 +C 3Π(v = 7) +49 214.4(26) +0.507 +− +−180 +1.00 +− +11.0(41) +− +− +− +0, 1, 2 +33S16O +X 3Σ−(v = 0)c +570.890 75 +0.711 +1.11 × 10−6 +− +5.28 +−0.005 56 +− +− +− +− +0, 1 +X 3Σ−(v = 1)d +1 703.1956 +0.705 +1.11 × 10−6 +− +5.31 +−0.005 60 +− +− +− +− +0, 1 +B 3Σ−(v = 4) +44 355.65(14) +0.474 52(44) +1.00 × 10−6 +− +3.47(15) +−0.0273(76) +1.09(21) +− +− +− +0, 1 +B 3Σ−(v = 5) +44 938.01(11) +0.469 72(48) +1.44(43) × 10−6 +− +3.433(96) +−0.0185(42) +1.00(13) +− +− +− +0, 1 +B 3Σ−(v = 6) +45 510.30(23) +0.463 65(69) +1.00 × 10−6 +− +2.90(39) +−0.0130 +3.92(27) +− +− +− +0, 1 +B 3Σ−(v = 7) +46 072.50(30) +0.460 42(48) +1.57(32) × 10−6 +− +2.82(11) +−0.0097(29) +1.25(11) +− +− +− +0, 1 +B 3Σ−(v = 8)e +46 627.846(70) 0.454 316(74) +1.186(78) × 10−6 +− +3.1507(94) −0.013 05(44) +− +0.0813 +0.107 +− +0, 1 +B 3Σ−(v = 9) +47 171.50(12) +0.448 88(36) +9.1(31) × 10−7 +− +2.53(13) +−0.0129(65) +− +0.46(23) +3.12(31) +− +0, 1 +B 3Σ−(v = 10) +47 706.28(56) +0.4446(18) +5.9(29) × 10−8 +− +3.00 +−0.0120 +− +5.2(22) +5.6(17) +− +0, 1 +B 3Σ−(v = 11) +48 228.48(32) +0.4384(14) +2.04(100) × 10−6 +− +2.54(33) +−0.0120 +− +4.6(12) +3.41(48) +− +0, 1 +B 3Σ−(v = 12) +48 736.72(46) +0.4305(16) +8.8(44) × 10−7 +− +2.22(87) +−0.021(11) +− +2.8(14) +7.1(13) +− +0, 1 +B 3Σ−(v = 13) +49 232.29(71) +0.4251(14) +1.00 × 10−6 +− +2.2(11) +− +− +5.00 +10.0(19) +− +0, 1 +B 3Σ−(v = 14) +49 714.34(72) +0.4180(33) +1.00 × 10−6 +− +3.00 +− +16.9(16) +− +− +− +0, 1 +B 3Σ−(v = 15)f 50 178.1(10) +0.4061(10) +1.00 × 10−6 +− +3.00 +− +19.5(13) +− +− +− +0, 1 +B 3Σ−(v = 16) +50 593.32(51) +0.3782(12) +1.00 × 10−6 +− +4.9(25) +− +5.95(63) +− +− +− +0, 1 +B 3Σ−(v = 17) +50 926.1(33) +0.324 +1.00 × 10−6 +− +3.00 +− +17.8(79) +− +− +− +0, 1 +C 3Π(v = 0) +44 727.52(21) +0.563 02(58) +− +−181 +1.00 +− +− +− +− +− +None +Table continued on next page. +aAdditional parameters: AD = 1.28(63) × 10−4, o = 0.308(62), p = 0.0156(78) +bThe Ω = 0 linewidth is quite uncertain but a lower limit of 2 cm−1 FWHM is inferred from the measured spectrum. +cComputed from the isotopically-invariant ground-state parameters of Lattanzi et al. [56]. Additional parameters: H = −2.10×10−13, λD = 1.01×10−5, γD = −1.73×10−8 +dAdditional parameters: H = −2.10 × 10−13, λD = 1.03 × 10−5, γD = −1.69 × 10−8 +eJ-dependent widths are described in Sec. 4.5. The value in this table is extrapolated to J = 0. +f T and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec. 4.12. +13 + +Table continued from previous page. +Level +T +B +D +A +λ +γ +Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ω +C 3Π(v = 1) +45 415.38(17) +0.556 45(49) +− +−181 +1.00 +− +− +− +− +− +None +C 3Π(v = 2) +46 090.21(43) +0.5480(12) +− +−181 +1.00 +− +2.60(54) +− +− +− +1, 2 +C 3Π(v = 3) +46 748.12(23) +0.544 56(73) +3.85(70) × 10−6 −180.324(77) 1.27(28) +− +− +0.220 +1.60 +0.390 +0, 1, 2 +C 3Π(v = 5)a +48 013.57(14) +0.525 63(37) +− +−179.73(17) +0.91(10) +− +− +0.61(31) +0.47(24) +0.29(15) +0, 1, 2 +C 3Π(v = 6) +48 615.87(38) +0.5162(10) +− +−180.60(40) +1.00 +− +− +2.00 +0.89(45) +0.85(42) +0, 1, 2 +C 3Π(v = 7) +49 186.8(60) +0.502(12) +− +−180 +1.00 +− +7.4(37) +− +− +− +0, 1, 2 +34S16O +X 3Σ−(v = 0)b +568.156 44 +0.704 +1.09 × 10−6 +− +5.28 +−0.005 50 +− +− +− +− +0, 1 +X 3Σ−(v = 1)c +1 695.0833 +0.698 +1.09 × 10−6 +− +5.31 +−0.005 55 +− +− +− +− +0, 1 +B 3Σ−(v = 4) +44 342.98(24) +0.4705(14) +1.17(58) × 10−6 +− +3.56(19) +−0.0239(98) +1.01(25) +− +− +− +0, 1 +B 3Σ−(v = 5) +44 922.97(14) +0.464 73(59) +9.2(46) × 10−7 +− +3.48(13) +−0.0166(53) +0.89(16) +− +− +− +0, 1 +B 3Σ−(v = 6) +45 492.50(35) +0.460 16(98) +1.00 × 10−6 +− +2.99(68) +−0.0130 +3.74(44) +− +− +− +0, 1 +B 3Σ−(v = 7) +46 052.75(47) +0.455 80(73) +1.40(44) × 10−6 +− +2.91(15) +−0.0093(38) +1.24(14) +− +− +− +0, 1 +B 3Σ−(v = 8)d +46 605.46(11) +0.450 26(12) +1.27(14) × 10−6 +− +3.167(17) +−0.012 91(97) +− +0.0217 +0.0465 +− +0, 1 +B 3Σ−(v = 9) +47 146.96(21) +0.445 15(67) +9.2(46) × 10−7 +− +2.59(24) +−0.0129(65) +− +0.66(33) +2.99(56) +− +0, 1 +B 3Σ−(v = 10) +47 677.96(63) +0.4398(26) +1.59(80) × 10−6 +− +4.14(64) +−0.0196(98) +4.38(75) +− +− +− +0, 1 +B 3Σ−(v = 11) +48 199.78(37) +0.4337(18) +1.16(58) × 10−6 +− +2.88(39) +−0.0043(22) +4.22(43) +− +− +− +0, 1 +B 3Σ−(v = 12) +48 706.51(38) +0.4264(14) +4.3(22) × 10−7 +− +2.74(73) +−0.0075(38) +− +2.7(12) +6.3(10) +− +0, 1 +B 3Σ−(v = 13) +49 201.06(82) +0.4206(13) +1.00 × 10−6 +− +3.00 +− +− +4.2(21) +10.6(26) +− +0, 1 +B 3Σ−(v = 14) +49 682.10(60) +0.4140(27) +1.00 × 10−6 +− +3.00 +− +16.5(13) +− +− +− +0, 1 +B 3Σ−(v = 15)e 50 145.5(10) +0.4022(10) +1.00 × 10−6 +− +3.00 +− +19.5(13) +− +− +− +0, 1 +B 3Σ−(v = 16) +50 562.98(34) +0.377 30(80) +1.00 × 10−6 +− +4.5(20) +− +4.60(63) +− +− +− +0, 1 +B 3Σ−(v = 17) +50 905.2(29) +0.322 +1.00 × 10−6 +− +3.00 +− +16.0(70) +− +− +− +0, 1 +Table continued on next page. +aLinewidths are tentatively measured only. +bComputed from the isotopically-invariant ground-state parameters of Lattanzi et al. [56]. Additional parameters: H = −2.04×10−13, λD = 1.00×10−5, γD = −1.69×10−8 +cAdditional parameters: H = −2.04 × 10−13, λD = 1.02 × 10−5, γD = −1.65 × 10−8 +dJ-dependent widths are described in Sec. 4.5. The value in this table is extrapolated to J = 0. +eT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec. 4.12. +14 + +Table continued from previous page. +Level +T +B +D +A +λ +γ +Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ω +C 3Π(v = 0) +44 725.72(31) +0.557 85(78) +− +−181 +1.00 +− +− +− +− +− +None +C 3Π(v = 1) +45 409.28(15) +0.552 +− +−181 +1.00 +− +− +− +− +− +None +C 3Π(v = 2) +46 081.76(61) +0.5438(14) +− +−181 +1.00 +− +1.48(66) +− +− +− +1 +C 3Π(v = 3) +46 737.22(34) +0.537 61(84) +1.99(84) × 10−6 −179.711(99) 0.85(42) +− +− +0.220 +1.60 +0.390 +0, 1, 2 +C 3Π(v = 4) +47 377.244(85) 0.529 85(27) +1.79(27) × 10−6 −180.740(58) 0.968(86) +− +− +0.090(45) 0.460 +0.083(42) +0, 1, 2 +C 3Π(v = 5) +47 996.84(11) +0.526 87(53) +− +−179.858(95) 1.00 +− +− +0.830 +0.140 +0.0600 +0, 1, 2 +C 3Π(v = 6) +48 597.37(35) +0.510 95(97) +− +−180.54(43) +1.00 +− +− +2.00 +0.82(41) +1.05(53) +0, 1, 2 +C 3Π(v = 7) +49 167.9(53) +0.496(11) +− +−180 +1.00 +− +9.2(46) +− +− +− +0, 1, 2 +36S16O +X 3Σ−(v = 0)a +563.092 65 +0.691 +1.05 × 10−6 +− +5.28 +−0.005 41 +− +− +− +− +0, 1 +X 3Σ−(v = 1)b +1 680.0586 +0.686 +1.05 × 10−6 +− +5.31 +−0.005 45 +− +− +− +− +0, 1 +B 3Σ−(v = 4) +44 319.67(39) +0.4618(25) +3.9(19) × 10−7 +− +3.52(29) +−0.024(13) +1.00(39) +− +− +− +0, 1 +B 3Σ−(v = 5) +44 894.92(45) +0.4573(13) +1.63(81) × 10−6 +− +3.19(60) +−0.031(16) +1.36(33) +− +− +− +0, 1 +B 3Σ−(v = 6) +45 459.67(32) +0.4514(10) +1.00 × 10−6 +− +3.25(48) +−0.0130 +3.87(52) +− +− +− +0, 1 +B 3Σ−(v = 7) +46 016.30(35) +0.447 35(40) +1.07(23) × 10−6 +− +3.200(87) +−0.0075(18) +0.996(57) +− +− +− +0, 1 +B 3Σ−(v = 8)c +46 564.078(72) 0.442 577(75) +1.174(80) × 10−6 +− +3.198(12) +−0.013 32(91) +− +0.113 +0.240 +− +0, 1 +B 3Σ−(v = 9) +47 101.60(12) +0.437 80(40) +7.6(33) × 10−7 +− +2.46(15) +−0.0142(71) +− +0.58(28) +2.92(34) +− +0, 1 +B 3Σ−(v = 10) +47 628.28(51) +0.4329(19) +1.38(69) × 10−6 +− +4.17(55) +−0.021(11) +− +3.5(12) +5.05(99) +− +0, 1 +B 3Σ−(v = 11) +48 146.49(33) +0.4281(13) +1.99(100) × 10−6 +− +2.97(34) +−0.024(12) +− +5.4(11) +3.78(55) +− +0, 1 +B 3Σ−(v = 12) +48 650.18(20) +0.419 92(76) +9.3(46) × 10−7 +− +2.50(23) +−0.0234(82) +− +1.49(40) +5.77(39) +− +0, 1 +B 3Σ−(v = 13) +49 140.57(44) +0.415 11(50) +1.00 × 10−6 +− +1.10(45) +−0.0059(30) +− +3.09(94) +8.8(14) +− +0, 1 +B 3Σ−(v = 14) +49 621.13(41) +0.4069(12) +1.00 × 10−6 +− +3.00 +− +13.68(80) +− +− +− +0, 1 +B 3Σ−(v = 15)d 50 082.7(10) +0.3950(10) +1.00 × 10−6 +− +3.00 +− +19.5(13) +− +− +− +0, 1 +B 3Σ−(v = 16) +50 506.06(11) +0.374 69(29) +1.00 × 10−6 +− +5.41(34) +0.0540(80) +3.12(15) +− +− +− +0, 1 +Table continued on next page. +aComputed from the isotopically-invariant ground-state parameters of Lattanzi et al. [56]. Additional parameters: H = −1.93×10−13, λD = 9.83×10−6, γD = −1.63×10−8 +bAdditional parameters: H = −1.93 × 10−13, λD = 9.98 × 10−6, γD = −1.60 × 10−8 +cJ-dependent widths are described in Sec. 4.5. The value in this table is extrapolated to J = 0. +dT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec. 4.12. +15 + +Table continued from previous page. +Level +T +B +D +A +λ +γ +Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs. Ω +B 3Σ−(v = 17) 50 858.4(14) +0.3096(34) +1.00 × 10−6 +− +3.00 +− +11.9(26) +− +− +− +0, 1 +B 3Σ−(v = 18) +51 093.7(15) +0.2952(23) +1.00 × 10−6 +− +3.00 +− +6.00 +− +− +− +0, 1 +B 3Σ−(v = 19) +51 291.8(24) +0.2907(36) +1.00 × 10−6 +− +3.00 +− +8.00 +− +− +− +0, 1 +B 3Σ−(v = 20) +51 491.8(17) +0.2818(28) +1.00 × 10−6 +− +3.00 +− +4.00 +− +− +− +0, 1 +C 3Π(v = 0) +44 722.1(14) +0.5477(21) +2.00 × 10−6 −181 +1.00 +− +− +− +− +− +None +C 3Π(v = 1) +45 400.91(30) +0.541 70(86) +2.00 × 10−6 −181 +1.00 +− +− +− +− +− +None +C 3Π(v = 2) +46 066.42(31) +0.535 67(63) +2.00 × 10−6 −180.44(25) +1.07(21) +− +0.81(31) +− +− +− +1 +C 3Π(v = 3)a +46 717.12(18) +0.527 12(77) +5.1(26) × 10−7 −179.68(11) +0.88(13) +− +− +0.80(40) +1.26(48) +0.55(16) +0, 1, 2 +C 3Π(v = 4) +47 351.869(63) 0.520 64(30) +1.68(28) × 10−6 −180.728(36) 1.036(44) +− +− +0.025(13) 0.36(17) +0.120(60) +0, 1, 2 +C 3Π(v = 5) +47 967.15(11) +0.512 62(48) +1.75(46) × 10−6 −179.47(11) +0.770(70) +− +− +0.43(22) +0.26(13) +0.199(99) +0, 1, 2 +C 3Π(v = 6)b +48 562.79(30) +0.501 87(34) +− +−179.66(42) +0.71(22) +− +− +1.99(99) +0.51(21) +0.53(26) +1, 2 +C 3Π(v = 7) +49 134.4(17) +0.487 +− +−181 +1.00 +− +10.9(13) +− +− +− +1, 2 +aLinewidths are tentatively measured only. +bThe Ω = 0 linewidth is quite uncertain but a lower limit of 1.5 cm−1 FWHM is inferred from the measured spectrum. +16 + +Table 3. +Spin-orbit interaction energies, ξvBvC .a +Levels +32S16O +33S16O +34S16O +36S16O +B(5)/C(0) +−8.86(13) +−8.969(64) +−9.030(69) +−9.43(59) +B(6)/C(1) +−14.99(23) +−14.74(20) +−14 +−14.53(24) +B(7)/C(2) +−16.95(12) +−16.59(32) +−16.85(60) +−17.80(62) +B(8)/C(3) +−14.88(28) +−15.84(29) +−15.39(51) +−14.81(38) +B(10)/C(4) +−13.65(34) +– +−14.86(19) +−14.66(13) +B(11)/C(5) +−12.08(12) +−11.92(22) +−12.09(23) +−12.41(19) +B(12)/C(6) +−10.7(12) +−11.46(83) +−10.60(78) +−9.70(25) +B(13)/C(7) +−12.8(11) +−10.9(12) +−9.6(14) +−8.08(72) +aAs defined in Eqs. (1) and (2) and in units of cm−1. Fitting uncertainties are given parenthetically in units +of the least significant digit and are relative only, not accounting for parameter correlation or any inadequacy +in the spectral model specification. +4. Results +A detailed discussion of the observed SO bands is provided in this section. Listings +of the deduced deperturbed molecular constants of A 3Π(v), B 3Σ−(v), and C 3Π(v) +electronic-vibrational levels and their predissociation widths, along with B 3Σ−(vB) ∼ +C 3Π(vC) interaction parameters, and A(v = 1 − 3) ← X(0), B(v = 4 − 30) ← +X(0) and C(v = 0 − 7) ← X(0) transition moments are given in Tables 2, 3, and +4, respectively. In order to provide data directly comparable with the experimental +spectra, a full list of perturbed (coupled) level energies and predissociation widths, +as well as line frequencies, widths, and intensities is provided in an online appendix +[45]. All level energies are given relative to the ground-state equilibrium energy with +X(v = 0) vibrational energies (T in Table 2) computed from the isotopically-invariant +parameters of Lattanzi et al. [56]: 573.79, 570.89, 568.16, and 563.09 cm−1 for 32S16O, +33S16O, 34S16O, and 36S16O, respectively. Spin and rotational constants for X 3Σ−(v = +0) are also taken from Lattanzi et al. [56]. +4.1. B(4) ← X(0) +The predissociation-broadened B(4) ← X(0) spectrum is plotted in Fig. 2 and is +overlapped with significant absorption from B(6) ← X(1). This is highlighted in Fig. 2 +by the residual error of a model neglecting this extra absorption. +4.2. B(5)/C(0) ← X(0) +Previous analyses of 32S16O B(5) ← X(0) and C(0) ← X(0) photoabsorption [20] and +multiphoton-ionisation [22] spectra reveal spin-orbit and rotational interactions locally +mixing the B(5) and C(0) states. Further interaction of C(0) with d(1) and additional +Λ-doubling of C(0) are also revealed by these studies. We observed the B(5) ← X(0) +transition in four isotopologues and find similar interactions occurring between B(5) +and C(0) in all of them. +An experimental 32S16O B(5) ← X(0) absorption spectrum is shown in Fig. 2 and +17 + +Table 4. +Deperturbed electric-dipole vibronic transition moments.a +Transition +32S16O +33S16O +34S16O +36S16O +A(1) ← X(0) +0.0179 +– +– +– +A(2) ← X(0) +0.0235(20) +– +– +– +A(3) ← X(0) +0.0253(26) +– +– +– +B(4) ← X(0) +0.061(22) +0.0469(42) +0.0453(38) +0.0543(43) +B(5) ← X(0) +0.0677(95) +0.0656(47) +0.0630(47) +0.0751(47) +B(6) ← X(0) +0.0992(22) +0.1044(20) +0.0933(24) +0.1046(13) +B(7) ← X(0) +0.1187(18) +0.1034(29) +0.1092(32) +0.1250(13) +B(8) ← X(0) +0.1407(14) +0.1370(23) +0.1323(39) +0.1476(10) +B(9) ← X(0) +0.16426(88) +0.1560(17) +0.1550(22) +0.1650(12) +B(10) ← X(0) +0.1834(12) +0.1773(25) +0.1751(27) +0.1803(13) +B(11) ← X(0) +0.1933(11) +0.1946(28) +0.1964(21) +0.1998(12) +B(12) ← X(0) +0.2132(14) +0.2108(35) +0.2106(22) +0.21154(89) +B(13) ← X(0) +0.2188(26) +0.2182(40) +0.2161(35) +0.2166(16) +B(14) ← X(0) +0.2168(22) +0.2185(34) +0.2211(23) +0.21005(80) +B(15) ← X(0) +0.21897(86) +0.2224(33) +0.2257(21) +0.21618(78) +B(16) ← X(0) +0.20123(72) +0.2079(48) +0.2117(31) +0.2026(10) +B(17) ← X(0) +0.1621(10) +0.1773(96) +0.1768(62) +0.1749(20) +B(18) ← X(0) +0.1424(11) +– +– +0.1441(32) +B(19) ← X(0) +0.14232(94) +– +– +0.1533(39) +B(20) ← X(0) +0.15346(96) +– +– +0.1243(64) +B(21) ← X(0) +0.13924(79) +– +– +– +B(22) ← X(0) +0.1344(10) +– +– +– +B(23) ← X(0) +0.1199(10) +– +– +– +B(24) ← X(0) +0.1174(12) +– +– +– +B(25) ← X(0) +0.1178(12) +– +– +– +B(26) ← X(0) +0.100 +– +– +– +B(27) ← X(0) +0.0931 +– +– +– +B(28) ← X(0) +0.0857 +– +– +– +B(29) ← X(0) +0.0783 +– +– +– +B(30) ← X(0) +0.0705 +– +– +– +C(1) ← X(0) +0.0160(42) +– +– +– +C(2) ← X(0) +0.0315(31) +0.0542(26) +0.0402(39) +0.0316(21) +C(3) ← X(0) +0.0403(18) +0.0292(38) +0.0323(47) +0.0476(18) +C(4) ← X(0) +0.0523(16) +– +0.0431(40) +0.0509(20) +C(5) ← X(0) +0.0386(23) +0.0483(46) +0.0289(54) +0.0503(26) +C(6) ← X(0) +0.0417(38) +0.0446(74) +0.0478(49) +0.0441(24) +C(7) ← X(0) +0.0327(60) +0.033(11) +0.0482(48) +0.0315(39) +aIn atomic units. Fitting uncertainties are given parenthetically in units of the least significant digit and are +relative only, not accounting for parameter correlation or any inadequacy in the spectral model specification. +18 + +45200 +45250 +45300 +45350 +45400 +45450 +45500 +45550 +45600 +Transition wavenumber (cm−1) +0.00 +0.25 +0.50 +0.75 +1.00 +Transmission (arb. units) +Experimental +32S16O + 32S16O2 spectrum +Residual error of best-fit model +Model SO +cross section +(shifted and +scaled) +B(7) +X(0) +C(2) +X(0) +Figure 5. +An experimental photoabsorption spectrum showing 32S16O B(7) ← X(0) and C(2) ← X(0) and +the residual error of a best-fit model. The model SO cross section is also indicated with separate contributions +from nominal B(7) ← X(0) and C(2) ← X(0) transitions. +is overlapped with SO2 absorption. The signal attributable to SO after accounting for +SO2 and hot-band contamination is plotted as a residual error of a model neglecting +SO absorption from X(0). Our measurements are significantly less sensitive than the +laser-based absorption of Liu et al. [20] but our analysis benefits from a well defined +rotational temperature and predictable line intensities. +No C(0) ← X(0) or d(1) ← X(0) absorption is evident in our spectra and no +sensitivity to the C(0) ∼ d(1) interaction was found. We then neglect d(1) in our +analysis of 33S16O, 34S16O and 36S16O, and, for self-consistency, also for 32S16O. The +perturbative influence of C(v = 0, Ω = 0) on B(5) is significant in all isotopologues and +the C(0) level was included along with a spin-orbit interaction parameter. The C(0) +spin-orbit and spin-spin constants were fixed to values in line with our measurements +of other C(v) ← X(0) bands. Our 32S16O B(5) ∼ C(0) model differs from that of Liu +et al. [20] and will not therefore reproduce their spectrum of C(0) Ω = 2 and 1 levels +that are perturbed by d(1). +4.3. B(6)/C(1) ← X(0) +The B(6) level is perturbed by C(1) and there is a level crossing of their nominal Σ = 0 +levels near J = 30. Direct C(1) ← X(0) absorption is only observed for 32S16O but +its interaction with B(6) is strong enough to constrain some molecular parameters +in all isotopologues and a spin-orbit interaction energy in the cases of 33S16O and +36S16O. The broadening of C(1) levels deduced from its appearance in 32S16O is near +to or below the sensitivity of the experiment and we estimate a rigorous upper limit +of 0.1 cm−1 FWHM. +19 + +0 +10 +20 +30 +0.00 +0.25 +0.50 +0.75 +1.00 +32S16O +0 +10 +20 +30 +0.00 +0.25 +0.50 +0.75 +1.00 +33S16O +0 +10 +20 +30 +0.00 +0.25 +0.50 +0.75 +1.00 +34S16O += 0, e += 1, f += 1, e += 0, e += 1, f += 1, e +0 +10 +20 +30 +0.00 +0.25 +0.50 +0.75 +1.00 +36S16O +Rotational quantum number, J +Linewidth, (cm−1 FWHM) +Figure 6. Perturbed linewidths fitted to B(8). +4.4. B(7)/C(2) ← X(0) +This band is visibly perturbed and has an unusual multi-headed band structure that is +most obvious for 32S16O. This is shown in Fig. 5 and is due to an interaction between +B(7) and the Ω = 1 level of C(2), as discussed previously [20, 32]. A best-fit model of +our measured spectra places the C(v = 2, Ω = 1) level at slightly higher energy than +B(7), with no crossing of their rotational series, and includes significant absorption +from C(2) ← X(0) transitions. A similar picture applies to 33S16O, 34S16O, and 36S16O +absorption but these are less dramatically perturbed because of a greater separation +of mass-shifted B(7) and C(2) levels. +4.5. B(8)/C(3) ← X(0) +This is the least predissociation-broadened B(v) ← X(0) band appearing in our spec- +tra, and its rotational structure is analysed in greater detail. We fitted multiple absorp- +tion spectra showing B(8) ← X(0) for each isotopologue and observe C(3) ← X(0) +absorption, perturbations mixing B(8) and C(3), and J- and Ω-dependent predis- +sociation widths. A measured and modelled spectrum of 32S16O B(8) ← X(0) and +C(3) ← X(0) is shown in Fig. 3 as well as a reference 32S16O2 spectrum used to +account for contamination. +Trial models assuming deperturbed B(8) J- and Ω-independent linewidths imper- +fectly fitted measured spectra of all isotopologues. More freely fitted widths are shown +in Fig. 6 and satisfactorily fitted all data. +The deperturbed B(8) widths of 33S16O and 34S16O were modelled as Ω-independent +and piecewise-linear in J. The perturbed widths are shown in Fig. 6 and show local +perturbations where the B(8) sublevels are crossed by C(v = 3, Ω = 1). The spectra +showing 32S16O are of sufficient quality that the perturbed widths of all B(8) levels +for 6 < J < 33 are fitted individually, as shown in Fig. 6, and show increasingly broad +spin-sublevels in the ordering ΓΩ=1,e < ΓΩ=1,f < ΓΩ=0,e. A different width ordering +was found in the case of 36S16O for levels with J > 10 with ΓΩ=1,e < ΓΩ=0,e < ΓΩ=1,f. +20 + +The 36S16O widths shown in Fig. 6 are less constrained by the experimental data +but their overall Ω and J dependencies are necessary to reproduce our spectra. The +possibility of similar-magnitude Ω-dependences for the 33S16O and 34S16O widths is +not ruled out. +Modelled J-independent and Ω-dependent deperturbed widths were assumed for +C(3), with values for the Ω = 0, 1, and 2 32S16O levels found to be 0.20 ± 0.05, +1.4±0.4, and 0.4±0.1 cm−1 FWHM, respectively. This strong Ω-dependence is evident +in Fig. 3 where the C(3) ← X(0) transition moment has been set to zero to reveal its +absorption as a model residual error. Spectra containing 33S16O and 34S16O absorption +are relatively noisy and the C(3) widths similar to 32S16O were assumed for these +isotopologues. A different Ω-ordering of C(3) linewidths was tentatively deduced from +the 36S16O spectrum with 0.8 ± 0.4, 1.3 ± 0.5, and 0.6 ± 0.2 cm−1 FWHM for Ω = 0, +1, and 2, respectively. +4.6. B(9) ← X(0) +No interaction between B(9) and any C(v) level was required to adequately repro- +duce the observed B(9) ← X(0) absorption (shown in Fig. 4 for 32S16O) and any +actual interaction with the neighbouring but non-crossing C(3) and C(4) levels has +been adequately incorporated into the molecular parameters of B(9). It was necessary +to assume quite different predissociation broadening for the Ω = 0 and 1 sublevels, +with consistent values of about 0.6 and 3 cm−1 FWHM, respectively, found for all four +isotopologues. +4.7. B(10)/C(4) ← X(0) +A 32S16O absorption spectrum of the region containing B(10) ← X(0), and C(4) ← +X(0) is shown in Fig. 4 along with the absorption due to SO of all isotopologues +highlighted by models accounting for all spectral contributions apart from SO. In this +figure, rotational structure arising from all three Ω-components of C(4) in 32S16O is +clearly resolved and is well-modelled along with its spin-orbit interaction with B(10). +This model also necessitated the inclusion of C(4) Λ-doubling parameters to best fit +the 32S16O spectra. An attempt to replace the fitted Λ-doubling parameters with an +additional rotational interaction between B(10) and C(4) was ineffective, as were trial +additions of B(9)/C(4) and B(11)/C(4) interactions. +Too few C(4) ← X(0) lines appear in our spectra of 33S16O for a positive assignment +to be made. A list of unassigned lines comprising C(v = 4, Ω = 0) ← X(0) is given +in the online appendix. Fewer C(4) ← X(0) lines are evident in our 34S16O spectrum +than for 32S16O so the deperturbed width of C(4) Ω = 1 levels was fixed to the 32S16O +value. +4.8. B(11)/C(5) ← X(0) +The B(11) level is perturbed by C(5), which itself contributes significantly to the +observed 32S16O spectrum, as shown in Fig. 4. Only a weak signal of C(v = 5, Ω = +0 and 1) ← X(0) absorption is evident in our 34S16O spectra so these levels have +widths fixed to their 32S16O values, while the Ω-dependent widths of 33S16O are +marginally measurable. +21 + +49400 +49500 +49600 +49700 +49800 +Transition wavenumber (cm−1) +0.00 +0.25 +0.50 +0.75 +1.00 + Transmission (arb. units) +Experimental +SO + SO2 +optical depth +Residual error +neglecting SO +B(15) +X(0) +1 (0) +a(0) +Residual error of best-fit model +32S16O +Model SO optical depth +(shifted and +scaled) +49400 +49500 +49600 +49700 +49800 +Transition wavenumber (cm−1) +0.00 +0.25 +0.50 +0.75 +1.00 + Transmission (arb. units) +B(15) +X(0) +1 (0) +a(0) +36S16O +Figure 7. +Experimental and modelled spectra of B(15) ← X(0) and overlapping SO and SO2 absorption in +two isotopologues. The residual error neglecting SO includes some contribution from high-excitation rotational +transitions of B(16) ← X(0). +4.9. B(12)/C(6) ← X(0) +There is a clear spin-orbit interaction mixing B(12) and C(6), with weak C(6) ← X(0) +absorption evident for all isotopologues. +The measured predissociation widths of 32S16O and 36S16O C(v = 6, Ω = 0) levels +are significantly broader than for either Ω = 1 or 2, with fitted Ω = 0 widths of 6.5±0.3 +and 2 ± 1 cm−1 FWHM, respectively. It is difficult to estimate the true uncertainty of +these widths from the weakly-absorbing C(6) ← X(0) transitions, but they have clear +lower bounds of 2 and 1.5 cm−1 FWHM, respectively. C(v = 6, Ω = 0) widths could +not be measured for 33S16O and 34S16O. +4.10. B(13)/C(7) ← X(0) +A spin-orbit interaction between B(13) and C(7) was determined for all isotopologues +and constrained by weak C(7) ← X(0) absorption that is too broadened to reveal any +distinct line structure. The deperturbed Ω = 1 linewidths of B(13) are consistently +smaller than for Ω = 0 in the 32S16O, 34S16O, and 36S16O isotopologues, and a similar +Ω = 0 width was assumed for 33S16O. +4.11. B(14) ← X(0) +The B(14) level is more broadened than most other B(v) vibrational levels, and only +term origins, rotational constants and J- and Ω-independent widths are fitted to the +observed B(14) ← X(0) spectrum. +22 + +4.12. B(15) ← X(0) +The analysis of B(15) ← X(0) was complicated by its overlap with a broadened +and previously unobserved SO absorption band that occurs near 49 620 cm−1 in all +isotopologues. We assign this to absorption from the metastable a 1∆(v = 0) level non- +thermally excited in the discharge to a previously-unobserved 1Π(v = 0) upper level. +A further difficulty arises because B(15) occurs at an energy near the configurational +change of the B 3Σ− state. Its rotational constant cannot then be reliably extrapolated +from lower vibrational levels and is a key constraint on the irregular shape of the B 3Σ− +potential-energy curve near 2.4 ˚A, as shown in Fig. 1. +To disentangle B − X and 1Π − a absorption we simultaneously analysed all iso- +topologues and simulated the new 1Π level with Dunham constants for 32S16O and +mass-scaled these [57] to the other isotopologues. The relevant spectra and band- +simulations for 32S16O and 36S16O are shown in Fig. 7, with the two bands completely +overlapped in the former case and well separated but less prominent in the latter +spectrum. Intermediate overlap occurs for 33S16O and 34S16O. Mass-independent line +broadening was assumed for both the 1Π level and B(15). +We defer a detailed discussion of absorption observed in our spectra originating from +a 1∆ to a future study, but the proposed upper state assignment of the 49 620 cm−1 +band to a 1Π(v = 0) fundamental level is based on the electronic state constants +determined under this assumption. These are Te = 55 397±5 and ωe = 1321±5, Be = +0.766 ± 0.010, and αe = 0.025 ± 0.020 cm−1 for 32S16O. The separate determinations +of Te and ωe, and Be and αe is possible because of the identification of additional new +absorption attributed to the corresponding 1Π(v = 1) level overlapping B(20) ← X(0), +and discussed in Sec. 4.14, and supported by the range of measured isotopologues. +4.13. B(16) ← X(0) +The B(16) level is less predissociated than the neighbouring vibrational levels and the +fitted widths decrease with increasing reduced mass. The width fitted to deperturbed +Ω = 0 levels is slightly greater than for Ω = 1 in 32S16O but no such distinction was +observed in the other isotopologues despite their being observed with similar precision. +An anomalously large B(16) centrifugal distortion was fitted to the 32S16O spectrum +but not for the other isotopologues. +4.14. B(17 − 30) ← X(0) +The B(v) ← X(0) progression was followed in all isotopologues as far as v = 17 with +additional measurements approaching the B 3Σ− dissociation limit made for 32S16O, +with an example spectrum shown in Fig. 8, and as far as v = 20 in 36S16O. The +decreasing vibrational spacing of B(v) levels leads to severely overlapped rotational +structure near the dissociation limit. +Widths were fitted to the B(v = 17 − 25) ← X(0) levels independently of Ω. The +fitted parameters governing B(v = 26 − 30) ← X(0) absorption are less satisfactory +due to the weakness of these bands, decreasing linewidths approaching the dissociation +limit, and a complete overlap of their rotational structure. Reasonable agreement with +the resolved rotational structure in the region of B(28) ← X(0) was found assuming +a fixed broadening of 1 cm−1 FWHM for B(28), but no consistent fit to the many +overlapping lines at higher frequencies could be found. These are then represented +approximately by absorption into effective B(29) and B(30) levels artificially broad- +23 + +50250 +50500 +50750 +51000 +51250 +51500 +51750 +52000 +52250 +Transition wavenumber (cm−1) +0.0 +0.4 +0.8 +1.2 + Transmission (arb. units) +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +B(v) +X(0) +Experimental 32S16O + 32S16O2 +spectrum +Residual error of best-fit model +Residual error +neglecting SO +Figure 8. +Measured spectrum of 32S16O showing B(25−30) ← X(0), as well as the residual error of a best-fit +model and neglecting 32S16O absorption. +ened by 15 cm−1 FWHM to smooth over their confused band profiles. Additionally, +it was necessary to constrain the transition moments of B(26 − 30) ← X(0) absorp- +tion bands to values extrapolated from lower vibrational levels. This extrapolation +was made assuming an R-independent electronic transition moment, as presented in +Sec. 5.3. +4.15. A(1 − 3) ← X(0) +The A(v = 1 − 3) ← X(0) absorption bands are weakly observed between 38 000 +and 39 500 cm−1 in the 32S16O2 discharge, and their rotational structure is illustrated +in Fig. 9 along with an effective-Hamiltonian band model. These were measured and +analysed in order to calibrate the column density of SO radicals. +The A(1) level was modelled with the molecular parameters deduced by Elks and +Western [21] with consideration of a local perturbation shifting its Ω = 1 J = 15 +level [58]. Entirely new parameterisations were made for the A(2) and A(3) levels +and fitted the experimental spectrum marginally better than the A(2) constants of +Elks and Western [21] and significantly better in the case of A(3), for which previous +measurements are relatively limited. +The ratio of squared transition moments fitted to the A(v) ← X(0) bands with +v = 1:2:3 is 1:1.71:1.63 and is comparable with the ratio of Einstein-A coefficients +computed for these transitions by Borin and Ornellas [59], 1:1.47:1.61. The difference +in A(2)/A(1) ratios may result from a greater error in our fitted transition moments +than implied by their statistical uncertainties listed in Table 2, although a manual ad- +justment to match the Borin and Ornellas [59] ratio visibly degrades the experimental +fits. Alternatively, there may be some error associated with the highly R-dependent +electronic transition moment controlling the calculated ratios [21, 59]. +The total decay rate of A(1) by all processes is experimentally known [21] and +is J- and Ω-independent with a measured value of Atotal +A(1) = 74 100 ± 1100 s−1. The +relative and rotationally-unresolved branching ratios, ηA(1)→X(v′′), for partial decay +24 + +38000 +38200 +38400 +38600 +38800 +39000 +39200 +39400 +39600 +Transition wavenumber (cm−1) +0.0 +0.2 +0.4 +0.6 +0.8 +Transmission (arb. units) +A(v = 1, += 0) +X(0) +A(v = 1, += 1) +X(0) +A(v = 1, += 2) +X(0) +A(v = 2, += 0) +X(0) +A(v = 2, += 1) +X(0) +A(v = 2, += 2) +X(0) +A(v = 3, += 0) +X(0) +A(v = 3, += 1) +X(0) +A(v = 3, += 2) +X(0) +Experimental +32S16O + 32S16O2 +spectrum +Model spectrum +(shifted) +Residual error of best-fit model +Continuum radiation +Model 32S16O cross section +(shifted, scaled) +Reference 32S16O2 cross section +(shifted, scaled) +Figure 9. +An experimental spectrum showing 32S16O A(1) ← X(0), A(2) ← X(0), and A(3) ← X(0) +absorption compared with a model simulation accounting for variable background continuum radiation and +absorption by 32S16O and 32S16O2, and the residual error of this model. +via emission to v′′ = 0 to 11 are also measured [28]. We deduce a band-averaged +emission rate, AA(1)→X(0), from these data according to: +AA(1)→X(0) = Atotal +A(1) +ηA(1)→X(0) +�11 +v=0 ηA(1)→X(v) += (3.73 ± 0.37) × 105 s−1, +(11) +and also a band-integrated absorption f-value and electronic-vibrational transition +moment: +fA(1)←X(0) = (7.55 ± 0.76) × 10−5, +(12) +and µA(1)←X(0) = 0.0179 ± 0.0009 au, +(13) +respectively, using Eqs. (9) and (10). We assign a 10% uncertainty to AA(1)→X(0) +and fA(1)←X(0), corresponding to a 5% uncertainty in µA(1)←X(0) that is higher than +estimated for the A(1) lifetime by Elks and Western [21]. This is to account for possible +systematic error in the experimental lifetime, which is 30% larger than an earlier +determination [26], and a possible error contribution from the experimental emission +branching ratios. +A trial calculation was made of A(1) → X(v′′) emission rates using X 3Σ− and +A 3Π potential-energy curves taken from Lattanzi et al. [56] and Sarka and Nanbu +[35], respectively, and the experimentally-deduced µA−X electronic transition moment +of Elks and Western [21]. This confirmed that emission to levels with v′′ > 11 is +negligible and the experimental branching ratios in Eq. (11) are adequately normalised +when compared with their statistical uncertainties. +By fixing our model A(1) ← X(0) transition moment using the f-value from Eq. (12) +we constrain the 32S16O column-density in Fig. 9 to (2.0 ± 0.4) × 1016 cm−2, where +the fractional uncertainty is greater than for the reference f-value due to the fitting +25 + +B(5)~C(0) +B(6)~C(1) +B(7)~C(2) +B(8)~C(3) +B(10)~C(4) +B(11)~C(5) +B(12)~C(6) +B(13)~C(7) +20 +15 +10 +5 +0 +Spin-orbit interaction, vBvC (cm−1) +32S16O +33S16O +34S16O +36S16O +Figure 10. +Spin-orbit interaction energies of neighbouring B(vB) and C(vC) states. Symbols: Band-by-band +fitted parameters. Curve vertices: 32S16O interaction energies computed from the global model. +uncertainty of our rather weak A(1) ← X(0) spectrum. The separation in frequency +between the A(v) ← X(0) bands, and B(v) ← X(0) and C(v) ← X(0) band is too +great to permit their simultaneous measurement at DESIRS. Instead, the A(1) ← +X(0) and B(8) ← X(0) bands were measured consecutively under identical discharge +conditions and a calibration of all 32S16O-spectra column densities thus attained. This +procedure was repeated several times during the experiment and the ratio of A(v) ← +X(0) to B(v) ← X(0) f-values and found to be consistent within 5%. +A rotational temperature of 290 K was found to best match A − X spectra and is +somewhat lower than the 360 K temperature consistently deduced from the B − X +spectrum. The reason for this difference is not clear but comparing fitted spectra of +A−X at 290 and 360 K only results in a marginal change in their quality-of-fit and f- +values that differ by about 5%. Further confirmation of the SO column density deduced +here is provided in Secs. 5.3 and 5.6. +5. Discussion +5.1. Spectroscopic constants +The fitted Hamiltonian parameters describing deperturbed energy levels are listed in +Table 2. The fitted B(vB) ∼ C(vC) spin-orbit interaction parameters are plotted in +Fig. 10 and a level-energy map of fitted 32S16O levels up to J = 30 and B(v = 14) is +plotted in Fig. 11 showing various near-degeneracies and crossings of the B 3Σ− and +C 3Π rotational series. +Parameters for some particularly broadened or perturbed bands could not be de- +termined independently and were fixed to values in line with the spectrum as a whole +and tabulated without uncertainties. No spin-rotation interaction energies, γ, could +be determined for any C 3Π levels. Outlying values of D, λ, and γ are mostly associ- +ated with absorption bands suffering from a combination of broadening, weakness, or +contaminant overlap. +The rotational constants of B 3Σ− and C 3Π levels scaled by their reduced-mass are +plotted in Fig. 12 and are in good agreement for the studied isotopologues. A discon- +tinuity between B(16) and B(17) is associated with the B 3Σ− outer limb irregularity +depicted in Fig. 1. This is also coincident with a change in the measured spin-rotation +26 + +0 +5 +10 +15 +20 +25 +30 +Rotational quantum number, J +44000 +45000 +46000 +47000 +48000 +49000 +50000 +Term value (cm−1) +B(4) +B(5) +B(6) +B(7) +B(8) +B(9) +B(10) +B(11) +B(12) +B(13) +B(14) +C(0) +C(1) +C(2) +C(3) +C(4) +C(5) +C(6) +C(7) += 0 += 1 += 2 +Figure 11. Observed or inferred 32S16O B 3Σ− and C 3Π levels. +27 + +0 +4 +8 +12 +16 +20 +24 +28 +Vibrational quantum number, v +0.2 +0.3 +0.4 +0.5 +Rotational constant (B, cm−1) +32S16O +33S16O +34S16O +36S16O +B 3Σ − +C 3Π +Figure 12. +Fitted rotational constants of the observed B 3Σ−(v) and C 3Π(v) levels. The values for heavier +isotopologues are reduced-mass-scaled upwards for comparison with 32S16O. +0 +4 +8 +12 +16 +20 +24 +28 +Vibrational quantum number, v +0.1 +0.0 +0.1 +0.2 +Spin-rotation constant ( , cm−1) +32S16O +33S16O +34S16O +36S16O +Figure 13. Fitted B 3Σ−(v) spin-rotation constants. +28 + +parameter, γ, from approximately −0.02 cm−1 for B(v ≤ 15) to about 0.1 cm−1 above, +as shown in Fig. 13. The larger value may be identifiable with the higher-lying 3Σ− +state “3” computed by Sarka and Nanbu [35] and shown to exchange electronic char- +acter with B 3Σ− at large v, although the γ-constant was not calculated in that study. +The large scatter of fitted γ values for v ≥ 16 is indicative of significant model error in +the band-by-band parameterisation of the congested spectrum approaching the B 3Σ− +dissociation threshold, although the overall increase noted above is robustly measured. +A discontinuity of measured spin-spin interaction energies, λ, near B(v = 15) is not +observed. +The fitted C(v) spin-orbit constants, A, fall in the range −182 to −179.5 cm−1, and +compare well with the A = −181.4 ± 0.1 cm−1 values deduced by Liu et al. [20] from +a well-resolved spectrum of 32S16O C(0) ← X(0). The approximate 1 cm−1 scatter of +values is due to the broadening and weakness of some C(v, Ω) levels, in which case +they are correlated with both T and λ when fixing bandhead positions of the three +Ω-sublevels, with further correlation with spin-orbit interactions connecting nearby +B 3Σ− levels. Fixing all the T and λ parameters of C 3Π levels, along with their spin- +orbit interaction with nearby B 3Σ− levels, to completely uncorrelated values requires +a clear observation of transitions to all three Ω-levels and their rotational structure. +Significant spin-orbit interactions are found to couple B(v = 5−8, 10−13) levels in +all isotopologues with the nearest C(v) level, with rotational term series crossings and +near-crossings for 32S16O shown in Fig. 11. No assumptions were made when fitting +spin-orbit interaction energies, and their similarity across isotopologues and smooth +dependence with increasing vibrational quantum numbers is evident in Fig. 10. The +interaction energies mixing B(13) with C(7) for the various isotopologues are more +scattered than for the mixing of lower-energy levels, and larger than might be antic- +ipated from a simple extrapolation of vibrational excitation. This apparent inconsis- +tency is likely attributable to the particular difficulty in fitting the broadened B(13) +and C(7) states and the weakness of absorption due to C(7) ← X(0) absorption. In +a simple test, a trial re-fitting of the 32S16O experimental spectrum was made as- +suming a ξ = −8 cm−1 interaction energy, consistent with an extrapolation of lower-v +interactions, and resulted in only a marginal reduction of its quality of fit. +Liu et al. [20] list T and B parameters fitted to their 32S16O spectra of B(v = +0 − 16) that are in reasonable agreement with our results. However, there are large +differences with respect to D, λ, and γ constants, with those of Liu et al. including +large magnitude and sign inconsistencies. This is no doubt due to the difficulty of +fitting rotational structure to the low-sensitivity and uncertain-excitation B(v) ← +X(0) absorption spectra of Liu et al. [20], which also prevented a deperturbation with +respect to interacting C(v > 0) levels, as was possible here. In general, the present +B(v > 3) constants should be preferred. A superior sensitivity to C(0) ← X(0) in the +combined spectra of Liu et al. [20] means that their fitted C(0) parameters including a +mutual deperturbation with both d(1) and B(5) are the more complete. Their analysis +includes several rotationally-mediated interaction terms mixing C(0) and B(5) which +were not found necessary in our analysis of various B(vB) ∼ C(vC) couplings. We +find all B ∼ C perturbations to be well described by a single spin-orbit interaction +energy, and the inclusion of rotational mixing of the order found by Liu et al. would +be quite noticeable in our spectral modelling of the well-resolved B(8) and C(3) levels. +The cause of this difference is not clear but may arise from a greater sensitivity to +C(0) and higher-J B(5) levels in the combined spectra available to Liu et al., leading +to a good definition of level crossings near the J = 21 and 28, with fitted rotational +interactions being more sensitive to higher-J crossings. +29 + +1.5 +2.0 +2.5 +3.0 +3.5 +Internuclear distance (Å) +42000 +44000 +46000 +48000 +50000 +52000 +54000 +Potential energy (cm−1) +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +18 +21 +24 +0 +1 +2 +3 +4 +5 +6 +7 +B 3Σ − this work +C 3Π this work +3Σ − Sarka et al +3Π Sarka et al. +Figure 14. +Empirical diabatic potential-energy curves for (Ω = 0, J = 0) B 3Σ− and C 3Π states relative +to the ground-state equilibrium energy, and 32S16O vibrational level energies. Also shown are comparable +adiabatic ab initio curves computed by Sarka and Nanbu [35]. +5.2. Potential-energy curves +The rotational level energies fitted to experimental spectra were used to deduce exper- +imental diabatic B 3Σ− and C 3Π potential-energy curves and a spin-orbit interaction +energy mixing the two electronic states. The B 3Σ− experimental data were reinforced +with 32S16O v = 0 to 3 levels computed from the molecular constants given by Liu +et al. [20] to better constrain the B 3Σ− potential-energy minimum, but neglecting +their perturbation by levels of A 3Π. The solution of uncoupled vibrational energy +levels and wavefunctions and the subsequent matrix diagonalisation to compute a +perturbed spectrum are described in Sec. 3.2. +Fitted parameters governing this model are listed in Table 5 and the standard +deviation of residual differences between globally-computed rotational energy levels +and those fitted band-by-band to the experimental spectra is 1.3 cm−1. The resulting +potential-energy curves corresponding to T(R) in Table 1 are plotted in Fig. 14. For +each curve, the well and inner limb is fitted to one Morse function [60] and the outer +limb described by another. These regions are joined by a cubic-spline-interpolated +region consisting of 9 spline knots between 2.1 and 2.7˚A spanning the B 3Σ− poten- +tial inflection, and 2 knots at 1.88 and 1.95˚A for C 3Π. The C 3Π dissociation energy +is unconstrained by our measurements and kept fixed at a value corresponding to +the S(1D2)+O(3P1) excited atomic limit and relative to the ground-state dissociation +energy deduced by Clerbaux and Colin [18]. The B 3Σ− dissociation limit was ad- +30 + +Table 5. +Morse potential-energy wells and interaction parameters.a +B 3Σ− +(Valid for v ≤ 14) +Te = 41633.0(5) cm−1, c2 = 20204.3(6) cm−1, +Re = 1.77526(5) ˚A, β = +1.7634(3) ˚A−1, +λ = 3.05(8) cm−1. +C 3Π +(Valid for v ≤ 4) +Te = 44372.8(4) cm−1, c2 = 14215.4(2) cm−1, +Re = 1.65708(6) ˚A, β = 2.372(2) ˚A−1, +A = −180.50(8) cm−1, +λ = 1.35(7) cm−1 +ξBC = −56(4) cm−1 +aThe potential well formula: +T(R) = Te + c2 [1 − exp(−β(R − Re))]2 , +applies to the given v-range. Higher-energy potential-energy curves are given numerically in the supplemen- +tary material. Uncertainties estimated by the least-squares optimisation of potential-energy curves and state +interactions are given in parentheses in terms of the least-significant digit. +justed to best fit the experiment and its fitted value, 53 020 cm−1, lies between the +S(1D2)+O(3P1) and S(1D2)+O(3P2) limits, but is poorly constrained given the un- +certain appearance of B(v > 28) levels in our spectra. All potential-energy curves are +provided in numerical form in the supplementary material [45]. +Spin-spin interaction energies for B 3Σ− and C 3Π, λ in Table 5, were optimised in +order to model all Ω-levels and are in agreement with their values deduced band-by- +band, as is the C 3Π spin-orbit splitting. The spin-orbit interaction energy, ξBC, was +fitted to an R-independent value of −56±4 cm−1, where the uncertainty is estimated by +testing alternative values. Specific B(vB) ∼ C(vC) interaction energies are computed +from ξBC and shown in Fig. 10 to be in good agreement with the band-by-band +interaction energies fitted to the experimental spectra. Absolute magnitudes of the +R-dependent B ∼ C spin-orbit interaction energies are calculated ab initio by Archer +et al. [22] and Yu and Bian [34] and are 60 and 35 cm−1, respectively, near 1.6 ˚A +where the B 3Σ− and C 3Π potential-energy curves cross. The former value is in good +agreement with the present results. +5.3. Transition moments +Vibronic transition moments, µi(v)−X(0), deduced from the experimentally-observed +B(v) ← X(0) and C(v) ← X(0) bands are listed in Table 1 and plotted in Fig. 15 +for B(v) ← X(0). The absolute scaling of these dipole moments was determined by +reference to the observed A(v) ← X(0) spectrum with an estimated 10% uncertainty, +as discussed in Sec. 4.15. The product of signs of the µB(vB)−X(0), µC(vC)−X(0), and +31 + +0 +10 +20 +30 +v′ +0.00 +0.05 +0.10 +0.15 +0.20 +Vib. trans. moment ( i(v′) − X(v′′), au) +B(v′) ← X(0) +(a) +32S16O +33S16O +34S16O +36S16O +1.475 +1.500 +1.525 +1.550 +1.575 +Internuclear distance / R-centroid (Å) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +Elec. trans. moment ( i − X, au) +v = 0 +v = 30 +v = 1 +v = 7 +B(v′) ← X(0) +C(v′) ← X(0) +(b) +Figure 15. +(a) Vibrational B(v) − X(0) transition moments fitted band-by-band (error bars) and computed +for 32S16O from the electronic-state model (curve). (b) Electronic transition moment deduced from vibronic +values (error bars) and computed ab initio by Sarka and Nanbu [35] (curves). +ξB(vB)C(vC) parameters significantly affects the simulated spectrum of B(vB) − X(0) +and C(vC) − X(0), and we find this product to be negative for all interacting bands +observed here. The uniquely-signed member of each triple is not determinable from +our experimental data but may be identified in an ab initio calculation computing ma- +trix elements with self-consistent phase. Feng and Zhu [36] and Sarka and Nanbu [35] +simultaneously compute µBX and µCX but find opposite and common signs, respec- +tively. Here, we assume both transition moments to be positive, defining the spin-orbit +interactions as negative. +Vibrational wavefunctions of X(v = 0), B(v), and C(v) levels were computed from a +ground-state potential-energy curve generated by the Rydberg-Klein-Rees method [61] +from data in Lattanzi et al. [56] along with the excited-state potential-energy curves +described in Sec. 5.2. Franck-Condon factors and R-centroids [50] for the B(v′)−X(v′′) +and C(v′) − X(v′′) transitions, computed using these wavefunctions are used to factor +out the vibrational-dependence of experimental µi(v)−X(0) values, and the resulting +R-centroid dependent µB−X and µC−X electronic transition moments are plotted in +Fig. 15. We judge these to be R-independent within experimental uncertainty, with +mean values µB−X = 0.9 ± 0.1 and µC−X = 0.12 ± 0.02 au, where the estimated +uncertainties are a combination of the 10% calibration uncertainty and approximately +0.02 au scatter of the experimental data in Fig. 15. There is a systematic overestimate +of high-v 36S16O B(v) ← X(0) transition moments that could not be eliminated +satisfactorily, even with a biased refit of the 36S16O spectrum and its overlapping +contaminants. This distortion is thus unexplained, but may arise from the “jitter” +effect occasionally affecting SOLEIL FTS spectra and leading to an incorrect zero- +intensity level [42]. +The present B − X electronic transition moment for SO lies between the values +determined experimentally for the analogous transitions in the isovalent molecules +O2 [62] and S2 [40, 63], ∼ 0.87 and 0.97 ± 0.05, respectively. On the other hand, +B−X electronic transition moments for SO calculated ab initio [35–37] are significantly +smaller than our experimental value in the region of internuclear distance probed by +absorption from X(v = 0). The cause of this difference is not clear. Representative R- +dependent ab initio B−X and C−X electronic transition moments calculated by Sarka +and Nanbu [35] are plotted in Fig. 15, together with our experimental determinations. +32 + +Table 6. +Radiative lifetime (ns) of B 3Σ−(v = 0 − 3). +v +This work +Elks and Western [21] +Yamasaki et al. [24] +0 +37(4) +33.6(6) +29(2) +1 +37(4) +32.3(6) +30(4) +2 +38(4) +36.4(5) +27(4) +3 +37(4) +52(2) +29(4) +4 +6 +8 +10 +12 +14 +16 +18 +20 +22 +24 +26 +28 +10-1 +100 +101 +B(v, += 0) +32S16O +33S16O +34S16O +36S16O +2 +3 +4 +5 +6 +7 +10-1 +100 +101 +C(v, += 1) +32S16O +33S16O +34S16O +36S16O +4 +6 +8 +10 +12 +14 +16 +18 +20 +22 +24 +26 +28 +10-1 +100 +101 +32S16O B(v) +Ω = 0 +Ω = 1 +2 +3 +4 +5 +6 +7 +10-1 +100 +101 +32S16O C(v) +Ω = 0 +Ω = 1 +Ω = 2 + Vibrational level + Deperturbed linewidth ( , cm−1 FWHM) +Figure 16. +Deperturbed predissociation linewidths of the observed B(v) and C(v) states. The rotation- +dependent widths of B(8) are shown extrapolated to J = 0. Open symbols: Fitted parameters. Closed symbols: +Fixed to assumed values. Upper figures: Widths of Ω = 0 sublevels for all isotopologues. Lower figures: Widths +of all Ω levels for 32S16O only. +While the large discrepancy in the B − X case is evident, very good agreement occurs +for the C − X transition. +Our scaled electronic transition moments were further assessed by comparison with +emission lifetimes measured previously for the unpredissociated B(v = 0 − 3) levels. +For this we computed vibrationally-averaged emission rates corresponding to B(v′ = +0−3) → X(v′′ = 0−30) according to Eq. (10) and computed the total B(v′) emission +lifetime by summing over v′′. The results are listed in Table 6 with uncertainties +following from the estimated 11% uncertainty of our deduced B−X transition moment. +Our predicted lifetimes are 10% and 30% longer than the time-domain measurements of +Elks and Western [21] and Yamasaki et al. [23, 24], respectively (ignoring the outlying +B(3) lifetime of Elks and Western [21]). +33 + +5.4. Predissociation broadening +The deperturbed line broadening fitted to observed B(v) ← X(0) and C(v) ← X(0) +bands is plotted in Fig. 16 and shows significant vibrational, isotopologue and Ω de- +pendence. The deperturbed widths for Ω = 0 and 1 e-parity B 3Σ− levels become +rapidly mixed with increasing rotation so that the observed widths of high-J levels +converge. +The upper limits of 32S16O B(v) widths estimated by Liu et al. [20] are in agreement +with the values determined here, apart from their limits ΓB(6) < 1.2 and ΓB(11) < +1 cm−1 that fall below our measured widths of (3.0 ± 0.3) cm−1 FWHM and 3.1 − +3.9 cm−1 FWHM, respectively. +The modelled B 3Σ− predissociation width pattern is likely caused by spin-orbit +interaction between B 3Σ− and various crossing unbound states known from quantum- +chemical calculations. Yu and Bian [34] compute all singlet, triplet, and quintet states +dissociating to ground state S(3P) and O(3P) atoms which may provide such pre- +dissociation channels. They find significant interaction energies mixing B 3Σ− with +their (1) 5Π and (2) 5Π states, and the outer limb of an adiabatic C 3Π state. The +bound (1) 5Π state crosses B 3Σ− below the S(3P) + O(3P) dissociation limit and pro- +vides a threshold dissociation channel beginning with B(v = 4). This crossing likely +also explains the predissociation of rotationally-excited B(v = 0 − 3) with their J- +thresholds known experimentally [17, 18]. The (2) 5Π state is predicted to cross B 3Σ− +near v = 13 and could provide an explanation for the rapidly increasing predissoci- +ation widths of higher levels. An outer-limb crossing with the adiabatic C 3Π state +may further enhance B 3Σ− predissociation near v = 10. The rapid variation of width +with v between threshold and these crossings likely results from the varying overlap +of bound- and unbound-state radial wavefunctions, as is typical of predissociation by +outer-limb crossing repulsive states [50]. Yu and Bian [34] predict additional crossings +and spin-orbit interactions between B 3Σ− near v = 7 and 11, and the repulsive outer +limbs of two 1Π states. This purely Ω = 1 interaction could explain the enhanced +Ω = 1 dissociation widths we find for B(9) and B(10). Finally, we note that the J- +and Ω-dependencies of the B(v = 8) linewidths for 32S16O, displayed in Fig. 6, are +typically characteristic of predissociation by a 3Π state [64], also observed in some +levels of the B state of O2 [65]. Thus, the C 3Π state is likely to be partially involved +in the, possibly complex, B(v = 8) predissociation mechanism. +Our analysis of C(v) levels reveals a broad width minimum around v = 4 and up +to factor-of-five differences between Ω-substates of the same vibrational level, with +either Ω = 0 or 1 being the most broadened. The large widths of C(v = 6, Ω = 0) +and C(v = 7) are consistent with being nearest to the 3Π avoided crossing shown in +Fig. 14. +5.5. Rotational line lists and cross sections +The band-by-band modelling detailed in Sec. 4 results in a rotational line list for all +observed bands, while the global model described in Secs. 5.2 and 5.3 also permits +the calculation of line frequencies and strengths for bands that are not experimentally +observed in some isotopologues. We combine band-by-band and global-model derived +line lists in order to generate a complete line list that is as accurate as possible. +A global-model line list of rotational transitions terminating on B(v = 0 − 30) and +C(v = 0 − 7) levels up to J = 50 was computed using the potential-energy curves, +electronic state interactions, and transition moments presented in Secs. 5.2 and 5.3 +34 + +45150 +45200 +45250 +45300 +45350 +45400 +45450 +45500 +45550 +Transition wavenumber (cm−1) +0 +1 +2 +3 +4 +5 +6 +7 +Cross section (cm2) +×10 +17 +32S16O +33S16O (shifted) +34S16O (shifted) +36S16O (shifted) +Band model +Electronic-state model +Figure 17. +Simulations of absorption into the mixed B(7) ∼ C(2) levels computed from constants fitted +band-by-band and a global electronic-state potential-energy-curve model. +44000 +46000 +48000 +50000 +52000 +Transition wavenumber (cm−1) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +Cross section (cm2) +×10 +16 +36S16O +34S16O (shifted) +33S16O (shifted) +32S16O (shifted) +v = 4 +5 +6 +7 +9 +10 +11 +12 +13 +14 +15 +16 17 18 +20 +22 24 26 +30 +v = 0 +1 +2 +3 +4 +5 +6 +7 += 0 + += 1 + += 2 +B 3 +− +C 3 +Figure 18. Synthetic photodissociation spectra computed at 360 K. +35 + +for all measured isotopologues and, for good measure, 18O-substituted species. Band- +by-band-fitted deperturbed linewidths are added to the global-model line list. The +unmeasured linewidths of S-substituted isotopologues for B(v > 16) levels, and all +levels of O-substituted isotopologues are set to their 32S16O values. +A cross section for absorption into the strongly-coupled B(7) ∼ C(2) levels is com- +puted from the band-by-band constants fitted to the experimental spectra, as well +as from the global-model line list. These are compared at 360 K in Fig. 17, and the +detailed rotational structure and mass-dependent spin-orbit mixing of levels is well +reproduced by the global model. The cross sections of other SO bands show similar +agreement when making this comparison, with the principal differences being due to +band-strength differences and small frequency shifts. The globally-modelled strengths +smooth over the background intensity and contaminant absorption uncertainties affect- +ing band-by-band analysis, and are therefore more accurate. For example, the band- +by-band 36S16O cross section in Fig. 17 is clearly an overestimate when compared with +the isotopically self-consistent global model. Conversely, the band-by-band modelled +line frequencies of observed bands are more accurate than the global model. We con- +struct a final hybrid line list by substituting band-by-band measured line frequencies +into the electronic-state model. Photoabsorption cross sections computed from this +hybrid list for all S-isotopes are shown in Fig. 18. +Absorption into B(v > 3) and all C(v) levels is completely dissociative given the +short lifetimes implied by the large measured transition widths. Additionally, levels +of 32S16O B(v = 3) with quantum-number N ≥ 10 are known to dissociate, with +only lower-N levels contributing to the emission spectra of 32S16O [17, 18]. Emission +spectra of S-substituted isotopologues have not been measured and will likely have +higher-N predissociation thresholds, as found for 12S18O by Clerbaux and Colin [18]. +We neglect this difference given the rather small contribution of B(3) to the overall +photodissociation cross section and adopt the N = 10 threshold for all species. Then +we compute a photodissociation cross section from the hybrid line list by including +only dissociative upper levels. +Band-by-band and global model rotational line lists, and the recommended hybrid +of the two, are permanently available in an online data archive [45]. +5.6. Comparison with other published cross sections +Phillips [25] measured the B(v) ← X(0) cross section for 32S16O at low spectral res- +olution and a digitised version is plotted in Fig. 19. We compare this with a 32S16O +cross section computed from our final hybrid line list assuming a rotational tem- +perature of 400 K and broadened by convolution with a Gaussian function of width +50 cm−1 FWHM, in order to approximately match the Phillips [25] instrumentally- +broadened band profiles. The relative band strengths are similar and integrated cross +sections over the region plotted agree within 15%, with the new cross section being +larger. +There are absorption features appearing in the cross section of Phillips [25] which are +not found in our analysis of SO spectra, for example at 48 400 and 52 400 cm−1. These +are broadly aligned with SO2 absorption bandheads and likely result from an imperfect +subtraction of contaminant SO2. Danielache et al. [16] make a similar comparison of +their cross section computed ab initio with Phillips [25], finding reasonable relative +agreement but with some differences in relative B(v) ← X(0) band strengths and +frequencies, but, more importantly, the ab initio cross section was found to have a +36 + +46000 +48000 +50000 +Transition wavenumber (cm−1) +0 +1 +2 +3 +Cross section (cm2) +×10 +17 +Present work +Phillips (1981) +Figure 19. +The present 32S16O cross section computed assuming a rotational temperature of 400 K and +degraded by convolution with a unit Gaussian of width 50 cm−1 FWHM, compared with the low-resolution +photoabsorption cross section of Phillips [25]. +three-times smaller magnitude overall. +6. Summary +Detailed spectroscopic data on the B 3Σ−(v = 4 − 30) and C 3Π(v = 0 − 7) states of +SO and its S-substituted isotopologues are determined from high-resolution absorption +spectra covering the 43 000 to 51 000 cm−1 (190 to 233 nm) spectral region. This is +the first observation of C 3Π levels above v = 2 or a B 3Σ− or C 3Π level in any +S-substituted isotopologue. +Most of the observed bands are severely blended due to a high line density and +predissociation broadening, and their profiles were fitted to minimally-specified effec- +tive Hamiltonians including spin-orbit interactions between neighbouring B(vB) and +C(vC) levels. The fitted linewidths are quite variable with respect to vibrational level +and quantum number Ω and likely arise from further interactions with unbound elec- +tronic states. An empirical model of B 3Σ− and C 3Π electronic states was constructed +to ensure globally-reliable band strengths and to enable extrapolation to unmeasured +vibrational levels and isotopologues. +The fitted cross section has a band-by-band relative uncertainty within 5% and an +additional 10% absolute uncertainty based on published lifetime and radiative data, +and their uncertainties, for the A 3Π(v = 1) level [21, 28]. The estimated total uncer- +tainty encompasses agreement with a previously measured 32S16O cross section [25] +and B 3Σ−(v = 0 − 2) lifetimes [21], but somewhat disagrees with a further set of +B 3Σ−(v = 0 − 3) lifetimes [24]. However, the new B 3Σ− − X 3Σ− transition moment +is in significant disagreement with previous ab initio calculations [35, 37] that suggest +a 50% smaller cross section, while C 3Π − X 3Σ− transition moments are found to +agree well. +The final result is a comprehensive and spectroscopically-accurate line list of pho- +todissociating far-ultraviolet rovibronic transitions for all xS16O isotopologues. These +data, available in an online archive [45], are ideally suited for computing SO lifetimes +against photodissociation in atmospheres and the interstellar medium, and the result- +ing likelihood of photolytic S-isotope fractionation. +37 + +Acknowledgements +The authors are very pleased to contribute to this special issue in honour of Prof. Wim +Ubachs. We have benefited enormously from his pioneering work in high-resolution and +time-resolved spectroscopy and his insightful and energised collaboration on numerous +projects. We thank B´erenger Gans of the Institut des Sciences Mol´eculaires d’Orsay +for permitting the use of the radio-frequency discharge source. AH was funded by the +NASA Postdoctoral Program through the NASA Astrobiology Institute, by grant num- +ber 19-03314S of the Czech Science Foundation, and the ERDF/ESF “Centre of Ad- +vanced Applied Sciences” (grant number CZ.02.1. 01/0.0/0.0/16 019/0000778). JRL +acknowledges support from the NASA Exobiology program (grant #80NSSC19K0475 +to Arizona State University). +References +[1] C. A. Gottlieb and J. A. Ball, Astrophys. J. Lett. 184, L59 (1973). +[2] M. Mateen, P. Hofner, and E. Araya, Astrophys. J. Suppl. Ser. 167, 239 (2006). +[3] Guilloteau, S., Di Folco, E., Dutrey, A., Simon, M., Grosso, N., and Pi´etu, V., +Astron. Astrophys. 549, A92 (2013). +[4] Rivi`ere-Marichalar, P., Fuente, A., Goicoechea, J. R., Pety, J., Le Gal, R., Gratier, +P., Guzm´an, V., Roueff, E., Loison, J. C., Wakelam, V., et al., Astron. Astrophys. +628, A16 (2019). +[5] E. Lellouch, D. F. Strobel, M. J. S. Belton, M. E. Summers, G. Paubert, and +R. Moreno, Astrophys. J. Lett. 459, L107 (1996). +[6] A. Moullet, E. Lellouch, R. Moreno, M. Gurwell, J. H. Black, and B. Butler, +Astrophys. J. 776, 32 (2013). +[7] K. de Kleer, I. de Pater, and M. ´Ad´amkovics, Icarus 317, 104 (2019). +[8] D. Bockel´ee-Morvan, D. C. Lis, J. E. Wink, D. Despois, J. Crovisier, R. Bachiller, +D. J. Benford, N. Biver, P. Colom, J. K. Davies, et al., Astron. Astrophys. 353, +1101 (2000). +[9] Boissier, J., Bockel´ee-Morvan, D., Biver, N., Crovisier, J., Despois, D., Marsden, +B. G., and Moreno, R., Astron. Astrophys. 475, 1131 (2007). +[10] C. Y. Na, L. W. Esposito, and T. E. Skinner, J. Geophys. Res. – Atmos. 95, 7485 +(1990). +[11] D. A. Belyaev, F. Montmessin, J.-L. Bertaux, A. Mahieux, A. A. Fedorova, O. I. +Korablev, E. Marcq, Y. L. Yung, and X. Zhang, Icarus 217, 740 (2012), advances +in Venus Science. +[12] A. Pavlov and J. Kasting, Astrobiology 2, 27 (2002). +[13] S. Ono, Annu. Rev. Earth Pl. Sc. 45, 301 (2017). +[14] J. Farquhar, H. Bao, and M. Thiemens, Science 289, 756 (2000). +[15] J. R. Lyons, Chem. Geo. 267, 164 (2009), advances in experimental and theo- +retical isotope geochemistry. +[16] S. O. Danielache, S. Tomoya, A. Kondorsky, I. Tokue, and S. Nanbu, J. Chem. +Phys. 140, 044319 (2014). +[17] E. V. Martin, Phys. Rev. 41, 167 (1932). +[18] C. Clerbaux and R. Colin, J. Mol. Spectrosc. 165, 334 (1994). +[19] R. Colin, Can. J. Phys. 47, 979 (1969). +[20] C.-P. Liu, N. L. Elliott, C. M. Western, Y.-P. Lee, and R. Colin, J. Mol. Spectrosc. +238, 213 (2006). +38 + +[21] J. M. F. Elks and C. M. Western, J. Chem. Phys. 110, 7699 (1999). +[22] C. P. Archer, J. M. F. Elks, and C. M. Western, J. Chem. Phys. 112, 6293 (2000). +[23] K. Yamasaki, F. Taketani, S. Tomita, K. Sugiura, and I. Tokue, J. Phys. Chem. +A 107, 2442 (2003). +[24] K. Yamasaki, S. Tomita, T. Hatano, F. Taketani, and I. Tokue, Chem. Phys. Lett. +413, 231 (2005). +[25] L. F. Phillips, J. Phys. Chem. 85, 3994 (1981). +[26] M. A. A. Clyne and J. P. Liddy, J. Chem. Soc. Farad. Trans. 2 78, 1127 (1982). +[27] M. A. A. Clyne and P. H. Tennyson, J. Chem. Soc. Farad. Trans. 2 82, 1315 +(1986). +[28] G. Lo, R. Beaman, and D. Setser, Chem. Phys. Lett. 149, 384 (1988). +[29] B. C. Stuart, S. M. Cameron, and H. T. Powell, J. Phys. Chem. 98, 11499 (1994). +[30] R. Dixon, P. Tasker, and G. Balint-Kurti, Mol. Phys. 34, 1455 (1977). +[31] W. C. Swope, Y.-P. Lee, and H. F. Schaefer, J. Chem. Phys. 71, 3761 (1979). +[32] F. R. Ornellas and A. C. Borin, Mol. Phys. 94, 139 (1998). +[33] A. C. Borin and F. R. Ornellas, Chem. Phys. 247, 351 (1999). +[34] L. Yu and W. Bian, J. Comput. Chem. 32, 1577 (2011). +[35] K. Sarka and S. Nanbu, J. Phys. Chem. A 123, 3697 (2019). +[36] Y. Feng and Z. Zhu, J. Quant. Spectrosc. Radiat. Transfer 234, 98 (2019). +[37] R. S. da Silva and M. Y. Ballester, Theor. Chem. Acc. 139 (2020). +[38] L. Nahon, N. de Oliveira, G. A. Garcia, J.-F. Gil, B. Pilette, O. Marcouille, +B. Lagarde, and F. Polack, J. Synchrotron Rad. 19, 508 (2012). +[39] A. N. Heays, N. de Oliveira, B. Gans, K. Ito, S. Boy´e-P´eronne, S. Douin, K. Hick- +son, L. Nahon, and J. Loison, J. Quant. Spectrosc. Radiat. Transfer 204, 12 +(2018). +[40] G. Stark, H. Herde, J. R. Lyons, A. N. Heays, N. de Oliveira, G. Nave, B. R. +Lewis, and S. T. Gibson, J. Chem. Phys. 148, 244302 (2018). +[41] N. de Oliveira, M. Roudjane, D. Joyeux, D. Phalippou, J.-C. Rodier, and L. Na- +hon, Nat. Photonics 5, 149 (2011). +[42] N. de Oliveira, D. Joyeux, M. Roudjane, J.-F. Gil, B. Pilette, L. Archer, K. Ito, +and L. Nahon, J. Synchrotron Rad. 23, 887 (2016). +[43] D. Freeman, K. Yoshino, J. Esmond, and W. Parkinson, Planet. Space Sci. 32, +1125 (1984). +[44] G. Stark, P. L. Smith, J. Rufus, A. P. Thorne, J. C. Pickering, and G. Cox, J. +Geophys. Res. – Planet. 104, 16585 (1999). +[45] A. N. Heays, G. Stark, J. R. Lyons, N. de Oliveira, B. R. Lewis, and S. T. Gibson, +https://zenodo.org/record/7423903 (2022). +[46] C. M. Western, J. Quant. Spectrosc. Radiat. Transfer 186, 221 (2017), satellite +Remote Sensing and Spectroscopy: Joint ACE-Odin Meeting, October 2015. +[47] J. Brown, E. Colbourn, J. Watson, and F. Wayne, J. Mol. Spectrosc. 74, 294 +(1979). +[48] A.-C. Cheung, K. Yoshino, W. Parkinson, and D. Freeman, J. Mol. Spectrosc. +119, 1 (1986). +[49] J. M. Brown and A. J. Merer, J. Mol. Spectrosc. 74, 488 (1979). +[50] H. Lefebvre-Brion and R. W. Field, The spectra and dynamics of diatomic +molecules (Elsevier, Amsterdam, 2004). +[51] J. T. Hougen, The calculation of rotational energy levels and rotational line in- +tensities in diatomic molecules (Physics Laboratory Publications, NIST, 1970). +[52] A. Hansson and J. K. G. Watson, J. Mol. Spectrosc. 233, 169 (2005). +[53] A. N. Heays, G. D. Dickenson, E. J. Salumbides, N. de Oliveira, D. Joyeux, +39 + +L. Nahon, B. R. Lewis, and W. Ubachs, J. Chem. Phys. 135, 244301 (2011). +[54] B. Johnson, J. Chem. Phys. 67, 4086 (1977). +[55] M. Larsson, Astron. Astrophys. 128, 291 (1983). +[56] V. Lattanzi, G. Cazzoli, and C. Puzzarini, Astrophys. J. 813, 4 (2015). +[57] R. J. Le Roy, J. Mol. Spectrosc. 194, 189 (1999). +[58] R. Colin, J. Chem. Soc. Farad. Trans. 2 78, 1139 (1982). +[59] A. C. Borin and F. R. Ornellas, Chem. Phys. Lett. 322, 149 (2000). +[60] P. M. Morse, Phys. Rev. 34, 57 (1929). +[61] A. L. G. Rees, Proc. Phys. Soc. London 59, 998 (1947). +[62] B. R. Lewis, S. T. Gibson, F. T. Hawes, and L. Torop, Phys. Chem. Earth 26, +519 (2001). +[63] B. R. Lewis, S. T. Gibson, G. Stark, and A. N. Heays, J. Chem. Phys. 148, 244303 +(2018). +[64] P. S. Julienne and M. Krauss, J. Mol. Spectrosc. 56, 270 (1975). +[65] B. R. Lewis, S. T. Gibson, and P. M. Dooley, J. Chem. Phys. 100, 7012 (1994). +40 + diff --git a/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/load_file.txt b/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..cb4b174931b015f26ae8c622d42baeab89b750bc --- /dev/null +++ b/m9E4T4oBgHgl3EQfuQ0Y/content/tmp_files/load_file.txt @@ -0,0 +1,2311 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf,len=2310 +page_content='Ultraviolet photoabsorption in the B 3Σ− − X 3Σ− and C 3Π − X 3Σ− band systems of SO sulphur isotopologues A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays,a,b,c G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stark,d J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lyons,a,e N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira,f B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewisg and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibsong aSchool of Earth and Space Exploration, Arizona State University, Tempe, AZ 85281, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' bNASA Astrobiology Institute, NASA Ames Research Center, Moffett Field, California, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' cJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heyrovsk´y Institute of Physical Chemistry, Czech Academy of Sciences, Dolejˇskova 3, CZ18223 Prague 8, Czech Republic dDepartment of Physics, Wellesley College, Wellesley, MA 02481, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' ePlanetary Science Institute, Tucson AZ 85719, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' fSynchrotron SOLEIL, L’Orme des Merisiers, D´epartementale 128, 91190 Saint-Aubin, France;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' gResearch School of Physics, The Australian National University, Canberra, ACT 2601, Australia ARTICLE HISTORY Compiled January 16, 2023 ABSTRACT High-resolution far-ultraviolet broadband Fourier-transform photoabsorption spec- tra of 32S16O, 33S16O, 34S16O, and 36S16O are recorded in a microwave discharge seeded with SO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The B 3Σ−(v = 4 − 30) ← X 3Σ−(v = 0) and C 3Π(v = 0 − 7) ← X 3Σ−(v = 0) bands are observed or inferred in the 43 000 to 51 000 cm−1 (196 to 233 nm) spectral range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is the first experimental detection of a C 3Π(v > 2) level and of any of these observed bands in an S-substituted isotopologue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional measurements of A 3Π(v = 1 − 3) ← X 3Σ−(v = 0) provide a calibration of the SO column density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Measured band profiles are fitted to an effective-Hamiltonian model of coupled excited B 3Σ− and C 3Π states along with their predissociation linewidths and absorption band strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Electronic-state potential-energy curves and transi- tion moments are deduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The end result is a list of line frequencies, f-values, and dissociation widths describing the far-ultraviolet photodissociation spectrum of SO that is accurate enough for computing atmospheric photolytic isotope-fractionation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' KEYWORDS ultraviolet spectroscopy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' photoabsorption;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' predissociation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' sulphur monoxide;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' isotopologues 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Introduction Sulphur monoxide (SO) occurs with observable abundance in the low-density inter- stellar medium [1–4], where its spectroscopic signature has been used to investigate the properties of shocked gas and to constrain the ages of star-forming molecular- cloud cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' It is also a significant species within the Solar system, forming in Io’s atmosphere [5–7] primarily through the photodissociation of SO2, and with detections in cometary comae [8, 9] and the Venus atmosphere [10] where a vertical profile was obtained by the Venus Express mission [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' SO and its S-substituted isotopologues may be key molecules in the sulphur cycle of a pre-oxygenated early-Earth atmosphere (older than 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 Gyr) [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Measurements of mineral S-isotopes from sedimentary arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05230v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='atom-ph] 12 Jan 2023 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 Internuclear distance (Å) 35000 40000 45000 50000 Potential energy (cm−1) 0 1 2 0 1 2 3456789101112 0 1 2 0 0 1 2 3 4 5 6 7 8 9 10 11 1213141516 0 1 2 3 4 5 6 7 X3 − shifted +34000cm−1 X3 − B3 − A3 C3 d1 e1 S(3P) + O(3P) Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Potential-energy curves of excited and ground states of SO referenced to the ground state equilib- rium energy, along with 32S16O vibrational level energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' rock reveal fractionating signatures that are likely due to gas-phase photochemistry [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These signatures are the products of a low-O2 atmosphere in which sulphur al- lotropes and elemental sulphur coexist with H2SO4 and provide a quantitative tracer for the rise of O2 in Earth’s atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additionally, SO and its sulphur isotopo- logues derived from SO2 photolysis play a central role in the conversion of oxidised to neutral sulphur [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The successful modelling of astrochemical and planetary SO observations, and S-isotopes in the early-Earth atmosphere, requires a full, detailed, and accurate knowledge of the excited states of SO, their transition properties, and temperature- and isotopologue-dependent ultraviolet photoabsorption and photodis- sociation cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An overview of the experimentally-known photoabsorbing excited states of SO is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The resulting ultraviolet absorption spectrum of SO is dominated by the strong progression of B 3Σ− ← X 3Σ− vibrational bands between 240 and 190 nm (42 000 and 53 000 cm−1), and is an analogue of the B 3Σ− u − X 3Σ− g systems in isova- lent O2 and S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The early SO spectroscopic study of Martin [17] observed a breaking off in emission from high rotational levels of B 3Σ−(v = 0 − 3) that is attributable to predissociation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Clerbaux and Colin [18] established the responsible dissociation threshold in a study of emission from low-lying B(v) levels of 32S16O and 32S18O, and identified multiple local perturbations affecting them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colin [19] photographically recorded absorption bands B 3Σ−(v′) ← X 3Σ−(v′′ = 0) as far as v′ = 30 using flash- photolysis methods, and provided partial rotational analyses for some bands while noting irregular vibrational spacings and significant line broadening throughout their progression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A comprehensive study of B 3Σ−(v = 0 − 16) levels by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] combined degenerate four-wave mixing, laser-induced fluorescence, Fourier transform emission, and photographic absorption measurements in a detailed rotational analy- sis of multiple bands appearing between 41 000 and 50 000 cm−1 and found evidence for numerous perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' They attributed the latter to spin-orbit and rotational interactions between rovibronic levels of the B 3Σ−, A 3Π, C 3Π, and d 1Π states by making use of earlier multi-photon ionisation measurements by Elks and Western [21] 2 and Archer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [22] characterising the A 3Π(v = 0 − 13) and C 3Π(v = 0 − 1) and d 1Π(v = 0 − 3) levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] estimated upper-limits varying between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 and 40 cm−1 for the linewidths of B 3Σ−(v = 4 − 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [23, 24] measured radiative lifetimes for B 3Σ−(v = 0 − 3) and Phillips [25] recorded a low-resolution absorption cross section covering the B 3Σ− ← X 3Σ− progression in a flowing discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Several studies have experimentally mea- sured the radiative lifetime of various A 3Π levels and their emission branching between ground state vibrational levels [21, 26–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Early theoretical studies [30, 31] determined potential-energy curves for the X 3Σ−, B 3Σ−, and other low-lying excited states correlated to the two lowest SO dissocia- tion channels, generating S(3P) + O(3P) and S(1D) + O(3P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Some of these excited states can, in principle, interact with B 3Σ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In particular, computed C 3Π and d 1Π states [22, 32, 33] adiabatically correlate to S(3P) + O(3P), have minima supporting bound vibrational levels, and possess inner and outer limb crossings with B 3Σ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The experimentally-observed variable line broadening of B 3Σ− suggests that, in addition to any interactions with bound levels of A 3Π, C 3Π and d 1Π, it interacts with multiple dissociating states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Multiple candidate predissociation pathways were noted by Yu and Bian [34] following computation of spin-orbit couplings to numerous singlet, triplet, and quintet states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' More recently, potential-energy curves, transition dipole moments, and couplings affecting B 3Σ−, and C 3Π have been computed by Danielache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [16] and Sarka and Nanbu [35] for the purposes of studying the isotope-dependence of SO photoabsorption and photodissociation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Sarka and Nanbu [35] also compute a higher- lying unbound 3Σ− state that approaches B 3Σ− at large internuclear distance and their associated nonadiabatic coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This interaction results in the peculiar shape of the B 3Σ− potential-energy curve and a sharp alteration of its electronic-configuration near 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 ˚A, as evidenced by an exchange of electronic transition moment between the diabatic B 3Σ− −X 3Σ− and higher-energy 3Σ− −X 3Σ− transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Further ab initio calculations of excited SO states have been recently performed by Feng and Zhu [36], who also computed many spin-orbit interaction energies, and da Silva and Ballester [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Previous experimental studies [18, 19] concerning the photodissociation spectrum of SO isotopologues appear to be limited to 32S18O with theoretical results extended to all S substitutions [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In this report, we present spectroscopic analyses of high-resolution broadband ab- sorption spectra of the B 3Σ−(v′ = 4 − 30) ← X 3Σ−(v′′ = 0) and C 3Π(v′ = 0 − 7) ← X 3Σ−(v′′ = 0) systems for four SO isotopologues: 32S16O, 33S16O, 34S16O, and 36S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The observed absorption band profiles are reduced to deperturbed molecu- lar constants and spin-orbit interaction energies mixing B 3Σ− and C 3Π electronic- vibrational states, along with calibrated transition moments with the ground state and a quantification of the observed predissociation line broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Empirical B 3Σ− and C 3Π potential-energy curves and a global spin-orbit interaction are fitted to these data and used to extrapolate the experimental data to include all bands up to the B 3Σ− dissociation limit in all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Measurements Photoabsorption measurements were performed on the high-resolution absorption spectroscopy branch of the DESIRS beamline [38] at the SOLEIL synchrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This facility was used in similar studies of the OH and S2 radicals [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The beamline undulator generates continuum bandpass radiation with a width of 7% of its central 3 frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Four overlapping measurements were required for complete coverage of the 43 000 to 52 000 cm−1 target region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The continuum radiation was passed through a rare-gas-filled chamber to filter unwanted higher harmonics generated in the undula- tor, then an absorption cell, and terminated at a vacuum-ultraviolet Fourier-transform spectrometer [41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is an all-reflection wave-front-division interferometer reliant on spatial coherence of the synchrotron beam and a modified Fresnel bi-mirror config- uration with the optical-path difference scanned by translating one reflector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The in- strument was operated with spectral resolution between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='86 cm−1 full-width at half-maximum (FWHM) depending on the perceived sharpness of SO features in each undulator bandpass and signal-to-noise considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' SO radicals were produced in a flowing discharge containing one of four sulphur dioxide samples seeded in helium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Highly enriched 33SO2 (99% 33S), 34SO2 (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8% 34S), and 36SO2 (approximately 70% 36S, 20% 34S, and 10% 32S) gases were used to generate rare SO isotopologues, and natural abundance SO2 (95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02% 32S, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75% 33S, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21% 34S) was used to study 32S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' All three samples contained oxygen in natural abundance but no absorption due to 18O-bearing species was detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A radio-frequency generator (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 MHz, 200 W power) was centred in a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 m glass absorption cell equipped with wedged MgF2 windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Helium carrier gas with an upstream pressure of 2 mbar flowed through the cell and was continuously evacuated by a 600 m3 hr−1 Roots pump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fluorescence in the discharge typically extended 40 cm on either side of the central generator cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' SO2 was seeded into the He flow prior to the absorption cell with a partial pressure between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The cell flow rate was significantly reduced when recording 33S16O, 34S16O, and 36S16O spectra to minimise the consumption of rare SO2 isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Strong absorption features of the parent SO2 ˜C 1B2 − ˜X 1A1 electronic system [43, 44] between 45 500 and 57 000 cm−1 overlap most SO B(v) ← X(0) absorption bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A sequence of three spectra were recorded for each bandpass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' First, the synchrotron radiation bandpass was established in a spectrum of pure helium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' SO2 was then seeded into the He flow and a reference absorption spectrum recorded with the discharge off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Finally, a combined SO and SO2 spectrum was recorded after activating the discharge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The raw experimental spectra are available in an online archive [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Analysis method The X 3Σ− and B 3Σ− states of SO consist of three Hund’s case-(a) spin-, e/f-parity sublevels, identifiable, in order of increasing energy, with the following quantum num- bers: (F1, e) : Λ = 0, Ω = 0, Σ = 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (F2, f) : Λ = 0, Ω = 1, Σ = 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' and (F3, e) : Λ = 0, Ω = 1, Σ = 1, while A 3Π consists of six sublevels: (F1, e/f) : Λ = 1, Ω = 0, Σ = −1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (F2, e/f) : Λ = 1, Ω = 1, Σ = 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' and (F3, e/f) : Λ = 1, Ω = 2, Σ = +1, 4 and higher-Ω levels of C 3Π occur with lower energy: (F1, e/f) : Λ = 1, Ω = 2, Σ = +1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (F2, e/f) : Λ = 1, Ω = 1, Σ = 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' and (F3, e/f) : Λ = 1, Ω = 0, Σ = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Here, Λ and Σ are the usual electronic-orbital and spin angular momentum pro- jection quantum numbers, and Ω = |Λ + Σ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' States of common parity within each Fi manifold become mixed with increasing molecular rotation, although relatively slowly in the cases of A 3Π and C 3Π because of their large spin-orbit splittings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In principle, B 3Σ−(v′) ← X 3Σ−(v′′) bands consist of 14 overlapping rotational branches but with reduced contributions from spin-forbidden ∆Σ ̸= 0 transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The rotational structure of A 3Π(v′) ← X 3Σ−(v′′) and C 3Π(v′) ← X 3Σ−(v′′) bands consists of 27 branches, but transitions terminating on different C 3Π Ω-substates are well separated in energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In what follows, fully-specified electronic-vibrational states and transitions are sometimes abbreviated, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', X 3Σ−(v = 0) to X(0), and C 3ΠΩ=0(v′ = 1) ← X 3Σ−(v′′ = 0) to C(v = 1, Ω = 0) ← X(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Vibrational state model The significant predissociation broadening of nearly all B(v′) ← X(0) bands and poor signal-to-noise of the observed C(v′) ← X(0) absorption precludes their line-by-line analysis in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Instead, the ground and excited vibrational levels are modelled with a minimal set of molecular parameters in a Hund’s case-(a) parity-symmetrised basis, and consideration is made for spin-rotational mixing of Ω-sublevels within each electronic-vibrational state and for spin-orbit mixing of neighbouring B(vB) and C(vC) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An effective-Hamiltonian matrix is built with diagonal deperturbed rotational level energies and off-diagonal interaction energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Diagonalising this matrix produces a model of observable energies and mixing coefficients for the interacting case-(a) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The form, symbols, and phase conventions adopted in our matrix diagonalisation and line strength calculation are the same as those used for linear molecules by the PGO- PHER program [46], that is, the effective Hamiltonian of Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [47] with explicit matrix elements for 3Σ− and 3Π spin-rotation-mixed manifolds listed in Cheung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [48] and Brown and Merer [49], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The o and p Λ-doubling terms of Brown and Merer [49] were used in the analysis of some C 3Π and A 3Π levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The interaction of B 3Σ−(vB) and C 3Π(vC) levels is modelled as a spin-orbit mixing of levels differing by ∆Σ = ±1, ∆Λ = ∓1, and ∆Ω = 0, and with common e/f symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A reduced matrix element [50] is fitted to each pair of interacting B(vB) and C(vC) levels following the definition and phase convention of PGOPHER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This reduced matrix element is − √ 6 times larger than the conventionally-referenced matrix element between Ω = 1 levels: ⟨B 3Σ− Ω=1,e/f|HSO|C 3ΠΩ=1,e/f⟩ = ξvBvC, (1) that we quote below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The corresponding matrix element mixing Ω = 0 levels is ⟨B 3Σ− Ω=0,e/f|HSO|C 3ΠΩ=0,e/f⟩ = √ 2ξvBvC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (2) 5 43600 43700 43800 43900 44000 44100 44200 44300 44400 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) Experimental 32S16O + 32S16O2 spectrum (scaled) Residual error of best-fit model (shifted from zero) Residual error neglecting absorption from X(1) (shifted from zero) Residual error neglecting SO (shifted from zero) B(4) X(0) B(5) X(0) Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An experimental spectrum showing 32S16O B(4) ← X(0) and B(5) ← X(0) absorption and the residual error of a best-fit model of these bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Residual errors are also shown for models neglecting all 32S16O absorption and absorption from vibrationally-excited X(v = 1) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitted scalar electric-dipole vibronic transition moments, µB(v)−X(0) and µC(v)−X(0), are used to simulate the observed 3Σ− ← 3Σ− and 3Π ← 3Σ− absorption bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The transition moments for parity-allowed ∆J = −1, 0 and +1 rovibronic transitions between unmixed case-(a) levels are computed according to [50–52]: µi(v′J ′Ω′)−X(v′′J ′′Ω′′) = µi(v′)−X(v′′) � (2J′′ + 1)(2J′ + 1) × (−1)J ′−Ω′+δΛ′0 � J′ 1 J′′ −Ω′ Ω′ − Ω′′ Ω′′ � , (3) where the final term is a Wigner-3j coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The mixing coefficients calculated while diagonalising the excited and ground state level energies are used to compute mixed line strengths which should match the observed transition strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The mixed absorption f-values are f = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='038 × 10−6 × ν0 � µmixed i(v′J ′Ω′)−X(v′′J ′′Ω′′) �2 , (4) where the given numerical constant assumes µ in atomic units and a transition wavenumber, ν0, with units of cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lorentzian predissociation line broadening is modelled by adopting complex-valued diagonal level energies in the effective Hamiltonian, where the imaginary component is equivalent to the FWHM linewidth, Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Aside from conveniently accounting for mixed linewidths, the adoption of complex level energies also slightly modifies the computed lineshifts due to level interactions between nearby case-(a) levels with overlapping line wings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The observed line broadening is caused by repulsive states not included in our deperturbation matrix, and the broadening of each deperturbed electronic-vibrational levels is experimentally determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In some cases, Ω- and J-dependent widths of case-(a) states are required to reproduce the experimental spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6 45800 45900 46000 46100 46200 46300 46400 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) P11ee P22ff P33ee Q23fe Q32ef R11ee R22ff R33ee C(v = 3, = 2) X(0) C(v = 3, = 1) X(0) C(v = 3, = 0) X(0) Rotational branches of B(8) X(0) Experimental 32S16O + 32S16O2 spectrum Model 32S16O cross section (shifted and scaled) Reference SO2 cross section (shifted and scaled) Residual error of best-fit model Residual error neglecting CX (shifted) Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A rotationally-assigned experimental spectrum showing 32S16O B(8) ← X(0) and C(3) ← X(0) absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The plotted reference SO2 and modelled SO cross sections were used to synthesise a spectrum with residual error as shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Also shown is the residual error of a model neglecting the µC(v=3)−X(v=0) transition moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 46600 46800 47000 47200 47400 47600 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) B(9) X(0) B(10) X(0) B(11) X(0) C(v = 4, = 2) X(0) C(v = 4, = 1) X(0) C(v = 4, = 0) X(0) C(v = 5, = 2) X(0) C(v = 5, = 1) X(0) C(v = 5, = 0) X(0) Experimental 32S16O + 32S16O2 spectrum Residual error of the best-fit 32S16O model 36S16O 34S16O 33S16O 32S16O Residual error neglecting SO absorption (shifted) Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An experimental spectrum showing 32S16O B(9) ← X(0), B(10) ← X(0), B(11) ← X(0), C(4) ← X(0), and C(5) ← X(0) absorption and the residual error of a best-fit model labelled with band- head assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Also shown are residual errors of similar models for other S-substituted isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 7 A list of perturbed line frequencies, νi, f-values, fi, and linewidths, Γi, was com- puted for rotational lines with J′′ ≤ 50 for all observed bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A cross section com- posed of all transitions was computed assuming a thermal population distribution of ground-state rotational levels, αF ′′ i J ′′ and a Voigt line profile, V (ν, Γ, ΓD), constructed assuming a Gaussian Doppler width, ΓD, σ(ν) = � i 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='853 × 10−13fiαF ′′ i J ′′ i V (ν − ν0i, Γi, ΓD), (5) where the numerical constant assumes a cross section in units of cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The synchrotron radiation generated by the beamline undulator possesses a peaked band pass of approximately 5 nm FWHM and its curvature, I0(ν), was modelled with a spline function with knots separated by 500 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The Beer-Lambert law was used to compute an ideal absorption spectrum: I(ν) = I0(ν) exp � −NSOσ(ν) − τother(ν) � , (6) assuming a column density of SO radicals, NSO, and including extra opacity due to contaminant absorbers in the spectrum, τother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The ideal spectrum was convolved with a function defining the instrumental resolution, primarily a sinc function with a small amount of additional broadening previously found to be generated by this instrument [53] and modelled as a Gaussian of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 FWHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This final spectrum is compared pointwise with the measured spectra and the various parameters governing the model were adjusted iteratively until a best agreement was found in the least-squares sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Examples of this comparison for several B(v) ← X(0) bands are plotted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2, 3, and 4 and include spectra exhibiting varied SO2 contamination and line confusion due to predissociation broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Figure 3 is annotated to show the full rotational structure of B(8) ← X(0), including all rotational transitions stronger than 2% of the most absorbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The same structure underlies the unresolved B − X bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The overlapping absorption of parent-gas SO2 isotopologues was comparable to that of SO itself and high-spectral-resolution SO2 cross sections measured for the purpose were included in our modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An increase of SO2 rotational temperature apparently occurs when the discharge is struck so the reference spectra do not quite account for all SO2 absorption near its bandheads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The recorded spectra of 36S16O were contami- nated by 32S16O and 34S16O beyond the expected amount given the known impurity of the 36SO2 parent gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These spectra were recorded subsequent to and on the same apparatus as other studies of 32S- and 34S-containing molecules, and outgassing of earlier-deposited sulphur might explain the extra contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ultimately the mix- ture of SO isotopologues was assessed directly from the spectra and has a ratio near 36S : 34S : 32S = 1 : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28 : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16, with some variation between measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional SO absorption from super-thermally excited X 3Σ−(v = 1) and electronically-excited a 1∆(v = 0) was also recorded and accounted for with additional vibrational state models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Significant absorption due to B(v′ + 2) ← X(1) hot bands was found to overlap B(v′) ← X(0) for v′ = 5 − 8 in all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Multiple overlapping spectra were recorded to span the desired spectral range and some additional spectra were recorded under varied discharge conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Up to five independent spectra were recorded for some bands and the parameters governing their upper-state levels and transition moments were fitted simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This effectively increased the signal-to-noise-ratio for these bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 8 Many trials were necessary before arriving at a set of well-fitting and physically- reasonable deperturbed level energies and B 3Σ− ∼ C 3Π interaction parameters, due to the non-resolution of most B(v) ← X(0) rotational structure and the weakness or non-observation of C(v) ← X(0) bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The inclusion of higher-order centrifugal- distortion parameters (for example H, λD, γD, and AD) was found mostly unnecessary during this process and some small but significant parameters (for example D and γ) were set to fixed values for some bands once their overall pattern-forming values had been determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Statistical fitting uncertainties of the model parameters are esti- mated by the least-squares fitting routine but do not account for correlation between model parameters or reflect model error introduced by the assumption of a particular effective Hamiltonian, constraints imposed on its parameters, or the incomplete deper- turbation of any level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The scatter of our fitted parameters significantly exceeds these model parameter uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Therefore, in this work we prefer to list estimated un- certainties more reflective of the experimental scatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' However, the listed uncertainty estimates are best considered as relative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An SO rotational temperature of 360 ± 15 K was determined from the strengths of rotational lines in the well-resolved B(8) ← X(0) band, and was used to define the model Doppler width, ΓD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A thermalised population of ground-state levels peaks near J = 13 at 360 K, falls below 5% of its peak value by J = 40, and consists of 98% v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Sufficient overlap exists between spectra to calculate relative column densities sep- arately for each isotopologue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A calibration of the 32S16O column-density, and B − X and C − X transition moments, was determined from a measurement of well-known A(v) − X(0) transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A calibration of transition moments of other isotopologues was made relative to 32S16O assuming an isotopologue-independent summation of B(v = 7 − 14) ← X(0) transition intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Electronic state model The band-by-band analysis of spectroscopic constants described above is necessary for analysing the blended spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Each single-band model, or model of a few interacting bands, results in a computed rotational line list that provides, within experimental uncertainty, the frequencies, strengths, and widths of all unresolved lines that signif- icantly contribute to the experimental band profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A more fundamental model of X 3Σ−, B 3Σ−, and C 3Π potential-energy curves;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B 3Σ− and C 3Π spin-orbit inter- action mixing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' and electronic transition moments controlling B 3Σ− ← X 3Σ− and C 3Π ← X 3Σ− absorption;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' was fitted to the band-by-band rotational line lists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Parameterised forms for the diabatic B 3Σ−, and C 3Π potential-energy curves, T(R) where R is the internuclear-distance, are discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Separate curves for Ω and e/f-parity substates were generated assuming R-independent spin-orbit and spin- spin interaction parameters, A and λ, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' To simulate a rotating molecule, R− and reduced-mass-dependent diagonal and off-diagonal matrix elements were com- puted to represent centrifugal effects and the spin-rotation mixing of Ω levels within each electronic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The specific matrix elements used are given in Table 1 and follow the formulation of Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A ladder of uncoupled vibrational energy eigenvalues and wavefunctions, χi(vJ), was computed from the potential-energy curve of each electronic state for a range of J, using the Numerov method [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Band transition moments between unmixed 9 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Matrix elements of spin-rotation mixed spin-electronic states, |Ω, e/f⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='a 3Σ−: ⟨0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e|H|0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e⟩ = T(R) + B(R) [J(J + 1) + 2] − 2γ − 4 3λ ⟨1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= T(R) + B(R)J(J + 1) − γ + 2 3λ ⟨0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e|H|1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e⟩ = 2 � J(J + 1) � −B(R) + 1 2γ � 3Π: ⟨0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= T(R) + B(R) [J(J + 1) + 2] − 2γ − 4 3λ ⟨1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= T(R) + A + B(R) [J(J + 1) − 2] + 2 3λ ⟨2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= T(R) − A + B(R) [J(J + 1) + 2] − 2γ + 2 3λ ⟨0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= � J(J + 1) � − √ 2B(R) + 1 √ 2γ � ⟨0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= 0 ⟨1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f|H|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' e/f⟩= � − √ 2B(R) + 1 √ 2γ � � J(J + 1) − 2 aB(R) = ℏ2 2µR2 electronic-vibrational states were computed according to: µi(v′J ′)−X(v′′J ′′) = µi−X � ∞ 0 χi(v′J ′)(R)χX(v′′J ′′)(R) dR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (7) where transitions are only allowed between states of common Σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' i represents either the B or C state,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' and µi−X is an isotopologue- and R-independent electronic transition moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spin-orbit reduced matrix elements mixing all neighbouring and remote B(vB) and C(vC) levels were computed from a fitted scalar parameter, ξBC, according to: ξvBvCJ = ξBC � ∞ 0 χB(vB,J)(R) χC(vC,J)(R) dR, (8) and specific Ω′ ∼ Ω′′ matrix elements were computed as in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (1) and (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' For each value of J, full sets of ground- and excited-state uncoupled vibrational energy levels and the spin-orbit interaction energies mixing them were diagonalised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' From the mixed levels a spectrum for all optically-allowed rotational transitions was computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The parameters of this global model are mass-independent and simultane- ously constrained by all isotopologue measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In the following analysis we also employ band-integrated f-values that neglect B ∼ C spin-orbit coupling computed according to [55]: fi(v′)−X(v′′) = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='038 × 10−6 × νµ2 i(v′0)−X(v′′0) 2 − δ0,Λ′+Λ′′ 2 − δ0,Λ′′ , (9) and band-averaged emission rates (s−1) computed according to Ai(v′)−X(v′′) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='026 × 10−6 × ν3µ2 i(v′0)−X(v′′0) 2 − δ0,Λ′+Λ′′ 2 − δ0,Λ′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (10) 10 Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=': Deperturbed molecular constants and predissociation broadening parame- ters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='b Level T c B D A λ γ Γ(all-Ω)d Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ωe 32S16O X 3Σ−(v = 0)f 573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='791 05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='718 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 61 − − − − 0, 1 X 3Σ−(v = 1)g 1 711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7999 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='712 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 66 − − − − 0, 1 A 3Π(v = 1)h 39 083.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='313(15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='585 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='35 × 10−6 157 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0531 − − − − 0, 1, 2 A 3Π(v = 2)i 39 491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='262(27) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='568 24(10) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='43(12) × 10−6 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='416(16) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='266(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='091(12) − − − − 0, 1, 2 A 3Π(v = 3)j 39 895.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='360(39) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='553 80(14) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='71(18) × 10−6 153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='481(23) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='261(19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='097(18) − − − − 0, 1, 2 B 3Σ−(v = 4) 44 368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4799(44) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(13) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='024(13) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='55(78) − − − 0, 1 B 3Σ−(v = 5) 44 954.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='26(16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='473 79(50) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='45(19) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0194(72) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='77(23) − − − 0, 1 B 3Σ−(v = 6) 45 528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='39(26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='470 57(86) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='89(34) − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='01(29) − − − 0, 1 B 3Σ−(v = 7) 46 094.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='464 42(61) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='44(51) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='834(88) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0105(31) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='77(12) − − − 0, 1 B 3Σ−(v = 8)k 46 651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='185(69) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='459 011(73) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='43(15) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='051(12) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='012 87(26) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0168 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='109 − 0, 1 B 3Σ−(v = 9)l 47 197.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='571(78) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='452 98(26) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04(19) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='932(95) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0130(53) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='51(13) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00(18) − 0, 1 Table continued on next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' aΓ has units of cm−1 FWHM and all other parameters units of cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitting uncertainties are given parenthetically in units of the least significant digit and are relative only, not accounting for parameter correlation or any inadequacy in the spectral model specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fixed parameters are given without uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Blanked parameters were fixed to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' bTerm value T is referenced to the X 3Σ− potential-energy minimum and is related to a virtual TΣ=0,J=0 energy level according to TΣ=0,J=0 = T + 2B − 2γ − 4 3 λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' cWidths entered in this column are fitted to all Ω levels simultaneously, otherwise widths are given in the following columns for individual Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A few bands have J dependent widths as described in footnotes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' dΩ-states of this level that directly contribute to the observed absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' f Computed from the isotopically-invariant ground-state parameters of Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16×10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02×10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='76×10−8 gAdditional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16 × 10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04 × 10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='72 × 10−8 hFixed parameters taken from Elks and Western [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: o = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='576, p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0137 iAdditional parameters: H = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='63(19) × 10−9, o = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='578(20) j Additional parameters: o = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='581(24) kJ-dependent widths are described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The value in this table is extrapolated to J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: H = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(26) × 10−11, λD = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='26(28) × 10−4 lAdditional parameters: λD = −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(28) × 10−4 11 Table continued from previous page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Level T B D A λ γ Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ω B 3Σ−(v = 10) 47 733.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='17(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='447 18(84) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(33) × 10−7 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(29) − − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='47(70) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='95(57) − 0, 1 B 3Σ−(v = 11) 48 258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='64(13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='442 33(62) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75(54) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='64(14) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0178(65) − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='86(48) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10(20) − 0, 1 B 3Σ−(v = 12)a 48 768.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='81(29) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4361(11) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(11) × 10−6 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='89(77) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='045(23) − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(10) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='68(73) − 0, 1 B 3Σ−(v = 13) 49 265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31(53) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='429 04(99) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(49) − − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7(15) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(11) − 0, 1 B 3Σ−(v = 14) 49 750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='83(61) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4208(23) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(13) − − − 0, 1 B 3Σ−(v = 15)b 50 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4102(10) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(13) − − − 0, 1 B 3Σ−(v = 16) 50 624.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='68(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='384 24(76) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='38(90) × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='42(30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='119(11) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(78) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='24(36) − 0, 1 B 3Σ−(v = 17) 50 951.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='18(40) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3281(16) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(29) − 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(10) − − − 0, 1 B 3Σ−(v = 18) 51 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(27) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='309 66(54) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='65(31) − − − 0, 1 B 3Σ−(v = 19) 51 365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='43(32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='303 45(92) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='80(65) − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02(83) − − − 0, 1 B 3Σ−(v = 20) 51 565.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='48(12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='292 89(34) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='26(20) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0954(80) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16(17) − − − 0, 1 B 3Σ−(v = 21) 51 759.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='97(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='284 25(30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0727(79) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='95(17) − − − 0, 1 B 3Σ−(v = 22) 51 943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='274 63(44) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='19(54) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='80(33) − − − 0, 1 B 3Σ−(v = 23) 52 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='45(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='263 06(30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='06(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='055(11) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='80(23) − − − 0, 1 B 3Σ−(v = 24) 52 275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='08(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='250 44(35) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='49(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='100(11) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='20(20) − − − 0, 1 B 3Σ−(v = 25) 52 419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='237 79(44) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='42(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0600 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='20(32) − − − 0, 1 B 3Σ−(v = 26) 52 549.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='222 95(84) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='39(37) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0600 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='34(51) − − − 0, 1 B 3Σ−(v = 27) 52 665.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='41(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='204 96(43) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='58(16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='178(11) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='77(19) − − − 0, 1 B 3Σ−(v = 28) 52 763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='438(43) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='183 92(11) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='623(41) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1199(29) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − 0, 1 B 3Σ−(v = 29) 52 842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1621(73) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0600 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 − − − 0, 1 B 3Σ−(v = 30) 52 916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1332(92) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0600 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 − − − 0, 1 C 3Π(v = 0) 44 729.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='30(37) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5686(11) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 1)c 45 420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='583(79) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='563 02(24) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 −181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='858(92) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='888(83) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='039(19) − − − 0, 1, 2 C 3Π(v = 2) 46 098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='41(29) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='554 42(77) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13(27) − − − 1 C 3Π(v = 3)d 46 760.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='454(75) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='547 31(16) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='37(16) × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='436(26) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='118(92) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='197(54) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='39(37) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='392(96) 0, 1, 2 Table continued on next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' aDeperturbed linewidths of Ω = 0 were fitted to a J-dependent formula: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(10) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='011(4)J(J + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' bT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' cThe fitted width may be below the experimental sensitivity and a clear upper limit is determined to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 FWHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' dAdditional parameters: o = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='907(60), p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='129(18) 12 Table continued from previous page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Level T B D A λ γ Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ω C 3Π(v = 4)a 47 405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='243(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='540 820(79) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='486(87) × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='596(34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='915(27) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='136(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='55(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='163(35) 0, 1, 2 C 3Π(v = 5) 48 030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='778(65) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='531 974(99) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='774(100) × 10−6 −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='881(89) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='936(44) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='83(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='142(55) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='055(28) 0, 1, 2 C 3Π(v = 6)b 48 634.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='520 25(63) − −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='67(34) − − 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='86(32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='92(45) 0, 1, 2 C 3Π(v = 7) 49 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='507 − −180 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0(41) − − − 0, 1, 2 33S16O X 3Σ−(v = 0)c 570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='890 75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='711 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='11 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 56 − − − − 0, 1 X 3Σ−(v = 1)d 1 703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1956 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='705 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='11 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 60 − − − − 0, 1 B 3Σ−(v = 4) 44 355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='65(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='474 52(44) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='47(15) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0273(76) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09(21) − − − 0, 1 B 3Σ−(v = 5) 44 938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='01(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='469 72(48) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='44(43) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='433(96) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0185(42) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00(13) − − − 0, 1 B 3Σ−(v = 6) 45 510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='30(23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='463 65(69) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='90(39) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0130 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='92(27) − − − 0, 1 B 3Σ−(v = 7) 46 072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='460 42(48) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='57(32) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='82(11) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0097(29) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25(11) − − − 0, 1 B 3Σ−(v = 8)e 46 627.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='846(70) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='454 316(74) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='186(78) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1507(94) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='013 05(44) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0813 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='107 − 0, 1 B 3Σ−(v = 9) 47 171.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='448 88(36) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(31) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='53(13) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0129(65) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(23) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12(31) − 0, 1 B 3Σ−(v = 10) 47 706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28(56) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4446(18) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(29) × 10−8 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0120 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(22) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(17) − 0, 1 B 3Σ−(v = 11) 48 228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='48(32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4384(14) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04(100) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='54(33) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0120 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(12) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='41(48) − 0, 1 B 3Σ−(v = 12) 48 736.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='72(46) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4305(16) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(44) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='22(87) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='021(11) − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(14) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(13) − 0, 1 B 3Σ−(v = 13) 49 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='29(71) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4251(14) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(11) − − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0(19) − 0, 1 B 3Σ−(v = 14) 49 714.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='34(72) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4180(33) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(16) − − − 0, 1 B 3Σ−(v = 15)f 50 178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4061(10) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(13) − − − 0, 1 B 3Σ−(v = 16) 50 593.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='32(51) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3782(12) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(25) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='95(63) − − − 0, 1 B 3Σ−(v = 17) 50 926.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='324 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(79) − − − 0, 1 C 3Π(v = 0) 44 727.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='52(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='563 02(58) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None Table continued on next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' aAdditional parameters: AD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28(63) × 10−4, o = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='308(62), p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0156(78) bThe Ω = 0 linewidth is quite uncertain but a lower limit of 2 cm−1 FWHM is inferred from the measured spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' cComputed from the isotopically-invariant ground-state parameters of Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10×10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='01×10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='73×10−8 dAdditional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10 × 10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='03 × 10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='69 × 10−8 eJ-dependent widths are described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The value in this table is extrapolated to J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' f T and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 13 Table continued from previous page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Level T B D A λ γ Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ω C 3Π(v = 1) 45 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='38(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='556 45(49) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 2) 46 090.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21(43) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5480(12) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60(54) − − − 1, 2 C 3Π(v = 3) 46 748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12(23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='544 56(73) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='85(70) × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='324(77) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='27(28) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='220 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='390 0, 1, 2 C 3Π(v = 5)a 48 013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='57(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='525 63(37) − −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='73(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='91(10) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='61(31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='47(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='29(15) 0, 1, 2 C 3Π(v = 6) 48 615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='87(38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5162(10) − −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60(40) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='89(45) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='85(42) 0, 1, 2 C 3Π(v = 7) 49 186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='502(12) − −180 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(37) − − − 0, 1, 2 34S16O X 3Σ−(v = 0)b 568.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='156 44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='704 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 50 − − − − 0, 1 X 3Σ−(v = 1)c 1 695.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0833 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='698 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 55 − − − − 0, 1 B 3Σ−(v = 4) 44 342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='98(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4705(14) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='17(58) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='56(19) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0239(98) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='01(25) − − − 0, 1 B 3Σ−(v = 5) 44 922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='97(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='464 73(59) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(46) × 10−7 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='48(13) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0166(53) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='89(16) − − − 0, 1 B 3Σ−(v = 6) 45 492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='460 16(98) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(68) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0130 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='74(44) − − − 0, 1 B 3Σ−(v = 7) 46 052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75(47) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='455 80(73) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='40(44) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='91(15) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0093(38) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='24(14) − − − 0, 1 B 3Σ−(v = 8)d 46 605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='450 26(12) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='27(14) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='167(17) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='012 91(97) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0217 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0465 − 0, 1 B 3Σ−(v = 9) 47 146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='96(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='445 15(67) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(46) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='59(24) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0129(65) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='66(33) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(56) − 0, 1 B 3Σ−(v = 10) 47 677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='96(63) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4398(26) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='59(80) × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='14(64) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0196(98) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='38(75) − − − 0, 1 B 3Σ−(v = 11) 48 199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='78(37) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4337(18) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16(58) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='88(39) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0043(22) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='22(43) − − − 0, 1 B 3Σ−(v = 12) 48 706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='51(38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4264(14) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(22) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='74(73) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0075(38) − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7(12) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(10) − 0, 1 B 3Σ−(v = 13) 49 201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='06(82) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4206(13) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(21) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(26) − 0, 1 B 3Σ−(v = 14) 49 682.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10(60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4140(27) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(13) − − − 0, 1 B 3Σ−(v = 15)e 50 145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4022(10) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(13) − − − 0, 1 B 3Σ−(v = 16) 50 562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='98(34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='377 30(80) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(20) − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60(63) − − − 0, 1 B 3Σ−(v = 17) 50 905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(29) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='322 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0(70) − − − 0, 1 Table continued on next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' aLinewidths are tentatively measured only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' bComputed from the isotopically-invariant ground-state parameters of Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04×10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00×10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='69×10−8 cAdditional parameters: H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='04 × 10−13, λD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02 × 10−5, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='65 × 10−8 dJ-dependent widths are described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The value in this table is extrapolated to J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' eT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 14 Table continued from previous page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Level T B D A λ γ Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ω C 3Π(v = 0) 44 725.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='72(31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='557 85(78) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 1) 45 409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28(15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='552 − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 2) 46 081.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='76(61) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5438(14) − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='48(66) − − − 1 C 3Π(v = 3) 46 737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='22(34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='537 61(84) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(84) × 10−6 −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='711(99) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='85(42) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='220 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='390 0, 1, 2 C 3Π(v = 4) 47 377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='244(85) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='529 85(27) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='79(27) × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='740(58) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='968(86) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='090(45) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='460 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='083(42) 0, 1, 2 C 3Π(v = 5) 47 996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='84(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='526 87(53) − −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='858(95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='830 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='140 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0600 0, 1, 2 C 3Π(v = 6) 48 597.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='37(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='510 95(97) − −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='54(43) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='82(41) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05(53) 0, 1, 2 C 3Π(v = 7) 49 167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(53) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='496(11) − −180 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2(46) − − − 0, 1, 2 36S16O X 3Σ−(v = 0)a 563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='092 65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='691 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 41 − − − − 0, 1 X 3Σ−(v = 1)b 1 680.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0586 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='686 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='005 45 − − − − 0, 1 B 3Σ−(v = 4) 44 319.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='67(39) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4618(25) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(19) × 10−7 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='52(29) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='024(13) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00(39) − − − 0, 1 B 3Σ−(v = 5) 44 894.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='92(45) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4573(13) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='63(81) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='19(60) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='031(16) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='36(33) − − − 0, 1 B 3Σ−(v = 6) 45 459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='67(32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4514(10) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25(48) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0130 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='87(52) − − − 0, 1 B 3Σ−(v = 7) 46 016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='30(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='447 35(40) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='07(23) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='200(87) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0075(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='996(57) − − − 0, 1 B 3Σ−(v = 8)c 46 564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='078(72) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='442 577(75) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='174(80) × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='198(12) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='013 32(91) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='113 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='240 − 0, 1 B 3Σ−(v = 9) 47 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60(12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='437 80(40) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(33) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(15) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0142(71) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='58(28) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='92(34) − 0, 1 B 3Σ−(v = 10) 47 628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='28(51) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4329(19) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='38(69) × 10−6 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='17(55) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='021(11) − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(12) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05(99) − 0, 1 B 3Σ−(v = 11) 48 146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='49(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4281(13) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(100) × 10−6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='97(34) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='024(12) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(11) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='78(55) − 0, 1 B 3Σ−(v = 12) 48 650.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='18(20) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='419 92(76) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(46) × 10−7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(23) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0234(82) − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='49(40) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='77(39) − 0, 1 B 3Σ−(v = 13) 49 140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='57(44) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='415 11(50) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10(45) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0059(30) − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09(94) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(14) − 0, 1 B 3Σ−(v = 14) 49 621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13(41) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4069(12) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='68(80) − − − 0, 1 B 3Σ−(v = 15)d 50 082.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3950(10) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5(13) − − − 0, 1 B 3Σ−(v = 16) 50 506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='06(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='374 69(29) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='41(34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0540(80) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12(15) − − − 0, 1 Table continued on next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' aComputed from the isotopically-invariant ground-state parameters of Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additional parameters: H = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='93×10−13, λD = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='83×10−6, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='63×10−8 bAdditional parameters: H = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='93 × 10−13, λD = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='98 × 10−6, γD = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60 × 10−8 cJ-dependent widths are described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The value in this table is extrapolated to J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' dT and B computed by mass-scaling in a common fit to all isotopologues, as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 15 Table continued from previous page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Level T B D A λ γ Γ(all-Ω) Γ(Ω = 0) Γ(Ω = 1) Γ(Ω = 2) Obs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ω B 3Σ−(v = 17) 50 858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3096(34) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(26) − − − 0, 1 B 3Σ−(v = 18) 51 093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7(15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2952(23) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − 0, 1 B 3Σ−(v = 19) 51 291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2907(36) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − 0, 1 B 3Σ−(v = 20) 51 491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2818(28) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − 0, 1 C 3Π(v = 0) 44 722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5477(21) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 1) 45 400.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='91(30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='541 70(86) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − − − − − None C 3Π(v = 2) 46 066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='42(31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='535 67(63) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='44(25) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='07(21) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='81(31) − − − 1 C 3Π(v = 3)a 46 717.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='527 12(77) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1(26) × 10−7 −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='68(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='88(13) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='80(40) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='26(48) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='55(16) 0, 1, 2 C 3Π(v = 4) 47 351.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='869(63) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='520 64(30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='68(28) × 10−6 −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='728(36) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='036(44) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='025(13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='36(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='120(60) 0, 1, 2 C 3Π(v = 5) 47 967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='512 62(48) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75(46) × 10−6 −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='47(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='770(70) − − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='43(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='26(13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='199(99) 0, 1, 2 C 3Π(v = 6)b 48 562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='79(30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='501 87(34) − −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='66(42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='71(22) − − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(99) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='51(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='53(26) 1, 2 C 3Π(v = 7) 49 134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='487 − −181 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 − 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(13) − − − 1, 2 aLinewidths are tentatively measured only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' bThe Ω = 0 linewidth is quite uncertain but a lower limit of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 cm−1 FWHM is inferred from the measured spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 16 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spin-orbit interaction energies, ξvBvC .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='a Levels 32S16O 33S16O 34S16O 36S16O B(5)/C(0) −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='86(13) −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='969(64) −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='030(69) −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='43(59) B(6)/C(1) −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='99(23) −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='74(20) −14 −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='53(24) B(7)/C(2) −16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='95(12) −16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='59(32) −16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='85(60) −17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='80(62) B(8)/C(3) −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='88(28) −15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='84(29) −15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='39(51) −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='81(38) B(10)/C(4) −13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='65(34) – −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='86(19) −14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='66(13) B(11)/C(5) −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='08(12) −11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='92(22) −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09(23) −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='41(19) B(12)/C(6) −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7(12) −11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='46(83) −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='60(78) −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='70(25) B(13)/C(7) −12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(11) −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9(12) −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(14) −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='08(72) aAs defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (1) and (2) and in units of cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitting uncertainties are given parenthetically in units of the least significant digit and are relative only, not accounting for parameter correlation or any inadequacy in the spectral model specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Results A detailed discussion of the observed SO bands is provided in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Listings of the deduced deperturbed molecular constants of A 3Π(v), B 3Σ−(v), and C 3Π(v) electronic-vibrational levels and their predissociation widths, along with B 3Σ−(vB) ∼ C 3Π(vC) interaction parameters, and A(v = 1 − 3) ← X(0), B(v = 4 − 30) ← X(0) and C(v = 0 − 7) ← X(0) transition moments are given in Tables 2, 3, and 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In order to provide data directly comparable with the experimental spectra, a full list of perturbed (coupled) level energies and predissociation widths, as well as line frequencies, widths, and intensities is provided in an online appendix [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' All level energies are given relative to the ground-state equilibrium energy with X(v = 0) vibrational energies (T in Table 2) computed from the isotopically-invariant parameters of Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56]: 573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='79, 570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='89, 568.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16, and 563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='09 cm−1 for 32S16O, 33S16O, 34S16O, and 36S16O, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spin and rotational constants for X 3Σ−(v = 0) are also taken from Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(4) ← X(0) The predissociation-broadened B(4) ← X(0) spectrum is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 and is overlapped with significant absorption from B(6) ← X(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is highlighted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 by the residual error of a model neglecting this extra absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(5)/C(0) ← X(0) Previous analyses of 32S16O B(5) ← X(0) and C(0) ← X(0) photoabsorption [20] and multiphoton-ionisation [22] spectra reveal spin-orbit and rotational interactions locally mixing the B(5) and C(0) states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Further interaction of C(0) with d(1) and additional Λ-doubling of C(0) are also revealed by these studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We observed the B(5) ← X(0) transition in four isotopologues and find similar interactions occurring between B(5) and C(0) in all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An experimental 32S16O B(5) ← X(0) absorption spectrum is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 and 17 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Deperturbed electric-dipole vibronic transition moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='a Transition 32S16O 33S16O 34S16O 36S16O A(1) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0179 – – – A(2) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0235(20) – – – A(3) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0253(26) – – – B(4) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='061(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0469(42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0453(38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0543(43) B(5) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0677(95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0656(47) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0630(47) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0751(47) B(6) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0992(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1044(20) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0933(24) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1046(13) B(7) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1187(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1034(29) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1092(32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1250(13) B(8) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1407(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1370(23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1323(39) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1476(10) B(9) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='16426(88) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1560(17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1550(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1650(12) B(10) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1834(12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1773(25) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1751(27) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1803(13) B(11) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1933(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1946(28) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1964(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1998(12) B(12) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2132(14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2108(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2106(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21154(89) B(13) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2188(26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2182(40) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2161(35) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2166(16) B(14) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2168(22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2185(34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2211(23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21005(80) B(15) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21897(86) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2224(33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2257(21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='21618(78) B(16) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='20123(72) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2079(48) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2117(31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2026(10) B(17) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1621(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1773(96) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1768(62) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1749(20) B(18) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1424(11) – – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1441(32) B(19) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='14232(94) – – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1533(39) B(20) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15346(96) – – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1243(64) B(21) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13924(79) – – – B(22) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1344(10) – – – B(23) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1199(10) – – – B(24) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1174(12) – – – B(25) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1178(12) – – – B(26) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='100 – – – B(27) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0931 – – – B(28) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0857 – – – B(29) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0783 – – – B(30) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0705 – – – C(1) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0160(42) – – – C(2) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0315(31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0542(26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0402(39) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0316(21) C(3) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0403(18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0292(38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0323(47) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0476(18) C(4) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0523(16) – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0431(40) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0509(20) C(5) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0386(23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0483(46) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0289(54) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0503(26) C(6) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0417(38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0446(74) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0478(49) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0441(24) C(7) ← X(0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0327(60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='033(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0482(48) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0315(39) aIn atomic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitting uncertainties are given parenthetically in units of the least significant digit and are relative only, not accounting for parameter correlation or any inadequacy in the spectral model specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 18 45200 45250 45300 45350 45400 45450 45500 45550 45600 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) Experimental 32S16O + 32S16O2 spectrum Residual error of best-fit model Model SO cross section (shifted and scaled) B(7) X(0) C(2) X(0) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An experimental photoabsorption spectrum showing 32S16O B(7) ← X(0) and C(2) ← X(0) and the residual error of a best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The model SO cross section is also indicated with separate contributions from nominal B(7) ← X(0) and C(2) ← X(0) transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' is overlapped with SO2 absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The signal attributable to SO after accounting for SO2 and hot-band contamination is plotted as a residual error of a model neglecting SO absorption from X(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Our measurements are significantly less sensitive than the laser-based absorption of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] but our analysis benefits from a well defined rotational temperature and predictable line intensities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' No C(0) ← X(0) or d(1) ← X(0) absorption is evident in our spectra and no sensitivity to the C(0) ∼ d(1) interaction was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We then neglect d(1) in our analysis of 33S16O, 34S16O and 36S16O, and, for self-consistency, also for 32S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The perturbative influence of C(v = 0, Ω = 0) on B(5) is significant in all isotopologues and the C(0) level was included along with a spin-orbit interaction parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The C(0) spin-orbit and spin-spin constants were fixed to values in line with our measurements of other C(v) ← X(0) bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Our 32S16O B(5) ∼ C(0) model differs from that of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] and will not therefore reproduce their spectrum of C(0) Ω = 2 and 1 levels that are perturbed by d(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(6)/C(1) ← X(0) The B(6) level is perturbed by C(1) and there is a level crossing of their nominal Σ = 0 levels near J = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Direct C(1) ← X(0) absorption is only observed for 32S16O but its interaction with B(6) is strong enough to constrain some molecular parameters in all isotopologues and a spin-orbit interaction energy in the cases of 33S16O and 36S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The broadening of C(1) levels deduced from its appearance in 32S16O is near to or below the sensitivity of the experiment and we estimate a rigorous upper limit of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 FWHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 19 0 10 20 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 32S16O 0 10 20 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 33S16O 0 10 20 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 34S16O = 0, e = 1, f = 1, e = 0, e = 1, f = 1, e 0 10 20 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 36S16O Rotational quantum number, J Linewidth, (cm−1 FWHM) Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Perturbed linewidths fitted to B(8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(7)/C(2) ← X(0) This band is visibly perturbed and has an unusual multi-headed band structure that is most obvious for 32S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5 and is due to an interaction between B(7) and the Ω = 1 level of C(2), as discussed previously [20, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A best-fit model of our measured spectra places the C(v = 2, Ω = 1) level at slightly higher energy than B(7), with no crossing of their rotational series, and includes significant absorption from C(2) ← X(0) transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A similar picture applies to 33S16O, 34S16O, and 36S16O absorption but these are less dramatically perturbed because of a greater separation of mass-shifted B(7) and C(2) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(8)/C(3) ← X(0) This is the least predissociation-broadened B(v) ← X(0) band appearing in our spec- tra, and its rotational structure is analysed in greater detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We fitted multiple absorp- tion spectra showing B(8) ← X(0) for each isotopologue and observe C(3) ← X(0) absorption, perturbations mixing B(8) and C(3), and J- and Ω-dependent predis- sociation widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A measured and modelled spectrum of 32S16O B(8) ← X(0) and C(3) ← X(0) is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3 as well as a reference 32S16O2 spectrum used to account for contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Trial models assuming deperturbed B(8) J- and Ω-independent linewidths imper- fectly fitted measured spectra of all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' More freely fitted widths are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6 and satisfactorily fitted all data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The deperturbed B(8) widths of 33S16O and 34S16O were modelled as Ω-independent and piecewise-linear in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The perturbed widths are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6 and show local perturbations where the B(8) sublevels are crossed by C(v = 3, Ω = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The spectra showing 32S16O are of sufficient quality that the perturbed widths of all B(8) levels for 6 < J < 33 are fitted individually, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6, and show increasingly broad spin-sublevels in the ordering ΓΩ=1,e < ΓΩ=1,f < ΓΩ=0,e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A different width ordering was found in the case of 36S16O for levels with J > 10 with ΓΩ=1,e < ΓΩ=0,e < ΓΩ=1,f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 20 The 36S16O widths shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6 are less constrained by the experimental data but their overall Ω and J dependencies are necessary to reproduce our spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The possibility of similar-magnitude Ω-dependences for the 33S16O and 34S16O widths is not ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Modelled J-independent and Ω-dependent deperturbed widths were assumed for C(3), with values for the Ω = 0, 1, and 2 32S16O levels found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 FWHM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This strong Ω-dependence is evident in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3 where the C(3) ← X(0) transition moment has been set to zero to reveal its absorption as a model residual error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectra containing 33S16O and 34S16O absorption are relatively noisy and the C(3) widths similar to 32S16O were assumed for these isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A different Ω-ordering of C(3) linewidths was tentatively deduced from the 36S16O spectrum with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 cm−1 FWHM for Ω = 0, 1, and 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(9) ← X(0) No interaction between B(9) and any C(v) level was required to adequately repro- duce the observed B(9) ← X(0) absorption (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4 for 32S16O) and any actual interaction with the neighbouring but non-crossing C(3) and C(4) levels has been adequately incorporated into the molecular parameters of B(9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' It was necessary to assume quite different predissociation broadening for the Ω = 0 and 1 sublevels, with consistent values of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 and 3 cm−1 FWHM, respectively, found for all four isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(10)/C(4) ← X(0) A 32S16O absorption spectrum of the region containing B(10) ← X(0), and C(4) ← X(0) is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4 along with the absorption due to SO of all isotopologues highlighted by models accounting for all spectral contributions apart from SO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In this figure, rotational structure arising from all three Ω-components of C(4) in 32S16O is clearly resolved and is well-modelled along with its spin-orbit interaction with B(10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This model also necessitated the inclusion of C(4) Λ-doubling parameters to best fit the 32S16O spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An attempt to replace the fitted Λ-doubling parameters with an additional rotational interaction between B(10) and C(4) was ineffective, as were trial additions of B(9)/C(4) and B(11)/C(4) interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Too few C(4) ← X(0) lines appear in our spectra of 33S16O for a positive assignment to be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A list of unassigned lines comprising C(v = 4, Ω = 0) ← X(0) is given in the online appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fewer C(4) ← X(0) lines are evident in our 34S16O spectrum than for 32S16O so the deperturbed width of C(4) Ω = 1 levels was fixed to the 32S16O value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(11)/C(5) ← X(0) The B(11) level is perturbed by C(5), which itself contributes significantly to the observed 32S16O spectrum, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Only a weak signal of C(v = 5, Ω = 0 and 1) ← X(0) absorption is evident in our 34S16O spectra so these levels have widths fixed to their 32S16O values, while the Ω-dependent widths of 33S16O are marginally measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 21 49400 49500 49600 49700 49800 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) Experimental SO + SO2 optical depth Residual error neglecting SO B(15) X(0) 1 (0) a(0) Residual error of best-fit model 32S16O Model SO optical depth (shifted and scaled) 49400 49500 49600 49700 49800 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) B(15) X(0) 1 (0) a(0) 36S16O Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Experimental and modelled spectra of B(15) ← X(0) and overlapping SO and SO2 absorption in two isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The residual error neglecting SO includes some contribution from high-excitation rotational transitions of B(16) ← X(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(12)/C(6) ← X(0) There is a clear spin-orbit interaction mixing B(12) and C(6), with weak C(6) ← X(0) absorption evident for all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The measured predissociation widths of 32S16O and 36S16O C(v = 6, Ω = 0) levels are significantly broader than for either Ω = 1 or 2, with fitted Ω = 0 widths of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 and 2 ± 1 cm−1 FWHM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' It is difficult to estimate the true uncertainty of these widths from the weakly-absorbing C(6) ← X(0) transitions, but they have clear lower bounds of 2 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 cm−1 FWHM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C(v = 6, Ω = 0) widths could not be measured for 33S16O and 34S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(13)/C(7) ← X(0) A spin-orbit interaction between B(13) and C(7) was determined for all isotopologues and constrained by weak C(7) ← X(0) absorption that is too broadened to reveal any distinct line structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The deperturbed Ω = 1 linewidths of B(13) are consistently smaller than for Ω = 0 in the 32S16O, 34S16O, and 36S16O isotopologues, and a similar Ω = 0 width was assumed for 33S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(14) ← X(0) The B(14) level is more broadened than most other B(v) vibrational levels, and only term origins, rotational constants and J- and Ω-independent widths are fitted to the observed B(14) ← X(0) spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 22 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(15) ← X(0) The analysis of B(15) ← X(0) was complicated by its overlap with a broadened and previously unobserved SO absorption band that occurs near 49 620 cm−1 in all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We assign this to absorption from the metastable a 1∆(v = 0) level non- thermally excited in the discharge to a previously-unobserved 1Π(v = 0) upper level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A further difficulty arises because B(15) occurs at an energy near the configurational change of the B 3Σ− state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Its rotational constant cannot then be reliably extrapolated from lower vibrational levels and is a key constraint on the irregular shape of the B 3Σ− potential-energy curve near 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 ˚A, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' To disentangle B − X and 1Π − a absorption we simultaneously analysed all iso- topologues and simulated the new 1Π level with Dunham constants for 32S16O and mass-scaled these [57] to the other isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The relevant spectra and band- simulations for 32S16O and 36S16O are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 7, with the two bands completely overlapped in the former case and well separated but less prominent in the latter spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Intermediate overlap occurs for 33S16O and 34S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mass-independent line broadening was assumed for both the 1Π level and B(15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We defer a detailed discussion of absorption observed in our spectra originating from a 1∆ to a future study, but the proposed upper state assignment of the 49 620 cm−1 band to a 1Π(v = 0) fundamental level is based on the electronic state constants determined under this assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These are Te = 55 397±5 and ωe = 1321±5, Be = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='766 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='010, and αe = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='025 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='020 cm−1 for 32S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The separate determinations of Te and ωe, and Be and αe is possible because of the identification of additional new absorption attributed to the corresponding 1Π(v = 1) level overlapping B(20) ← X(0), and discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='14, and supported by the range of measured isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(16) ← X(0) The B(16) level is less predissociated than the neighbouring vibrational levels and the fitted widths decrease with increasing reduced mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The width fitted to deperturbed Ω = 0 levels is slightly greater than for Ω = 1 in 32S16O but no such distinction was observed in the other isotopologues despite their being observed with similar precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An anomalously large B(16) centrifugal distortion was fitted to the 32S16O spectrum but not for the other isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' B(17 − 30) ← X(0) The B(v) ← X(0) progression was followed in all isotopologues as far as v = 17 with additional measurements approaching the B 3Σ− dissociation limit made for 32S16O, with an example spectrum shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 8, and as far as v = 20 in 36S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The decreasing vibrational spacing of B(v) levels leads to severely overlapped rotational structure near the dissociation limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Widths were fitted to the B(v = 17 − 25) ← X(0) levels independently of Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The fitted parameters governing B(v = 26 − 30) ← X(0) absorption are less satisfactory due to the weakness of these bands, decreasing linewidths approaching the dissociation limit, and a complete overlap of their rotational structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Reasonable agreement with the resolved rotational structure in the region of B(28) ← X(0) was found assuming a fixed broadening of 1 cm−1 FWHM for B(28), but no consistent fit to the many overlapping lines at higher frequencies could be found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These are then represented approximately by absorption into effective B(29) and B(30) levels artificially broad- 23 50250 50500 50750 51000 51250 51500 51750 52000 52250 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 B(v) X(0) Experimental 32S16O + 32S16O2 spectrum Residual error of best-fit model Residual error neglecting SO Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Measured spectrum of 32S16O showing B(25−30) ← X(0), as well as the residual error of a best-fit model and neglecting 32S16O absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' ened by 15 cm−1 FWHM to smooth over their confused band profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additionally, it was necessary to constrain the transition moments of B(26 − 30) ← X(0) absorp- tion bands to values extrapolated from lower vibrational levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This extrapolation was made assuming an R-independent electronic transition moment, as presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A(1 − 3) ← X(0) The A(v = 1 − 3) ← X(0) absorption bands are weakly observed between 38 000 and 39 500 cm−1 in the 32S16O2 discharge, and their rotational structure is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 9 along with an effective-Hamiltonian band model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These were measured and analysed in order to calibrate the column density of SO radicals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The A(1) level was modelled with the molecular parameters deduced by Elks and Western [21] with consideration of a local perturbation shifting its Ω = 1 J = 15 level [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Entirely new parameterisations were made for the A(2) and A(3) levels and fitted the experimental spectrum marginally better than the A(2) constants of Elks and Western [21] and significantly better in the case of A(3), for which previous measurements are relatively limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The ratio of squared transition moments fitted to the A(v) ← X(0) bands with v = 1:2:3 is 1:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='71:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='63 and is comparable with the ratio of Einstein-A coefficients computed for these transitions by Borin and Ornellas [59], 1:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='47:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The difference in A(2)/A(1) ratios may result from a greater error in our fitted transition moments than implied by their statistical uncertainties listed in Table 2, although a manual ad- justment to match the Borin and Ornellas [59] ratio visibly degrades the experimental fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Alternatively, there may be some error associated with the highly R-dependent electronic transition moment controlling the calculated ratios [21, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The total decay rate of A(1) by all processes is experimentally known [21] and is J- and Ω-independent with a measured value of Atotal A(1) = 74 100 ± 1100 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The relative and rotationally-unresolved branching ratios, ηA(1)→X(v′′), for partial decay 24 38000 38200 38400 38600 38800 39000 39200 39400 39600 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 Transmission (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' units) A(v = 1, = 0) X(0) A(v = 1, = 1) X(0) A(v = 1, = 2) X(0) A(v = 2, = 0) X(0) A(v = 2, = 1) X(0) A(v = 2, = 2) X(0) A(v = 3, = 0) X(0) A(v = 3, = 1) X(0) A(v = 3, = 2) X(0) Experimental 32S16O + 32S16O2 spectrum Model spectrum (shifted) Residual error of best-fit model Continuum radiation Model 32S16O cross section (shifted, scaled) Reference 32S16O2 cross section (shifted, scaled) Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An experimental spectrum showing 32S16O A(1) ← X(0), A(2) ← X(0), and A(3) ← X(0) absorption compared with a model simulation accounting for variable background continuum radiation and absorption by 32S16O and 32S16O2, and the residual error of this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' via emission to v′′ = 0 to 11 are also measured [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We deduce a band-averaged emission rate, AA(1)→X(0), from these data according to: AA(1)→X(0) = Atotal A(1) ηA(1)→X(0) �11 v=0 ηA(1)→X(v) = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='37) × 105 s−1, (11) and also a band-integrated absorption f-value and electronic-vibrational transition moment: fA(1)←X(0) = (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='76) × 10−5, (12) and µA(1)←X(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0179 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0009 au, (13) respectively, using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (9) and (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We assign a 10% uncertainty to AA(1)→X(0) and fA(1)←X(0), corresponding to a 5% uncertainty in µA(1)←X(0) that is higher than estimated for the A(1) lifetime by Elks and Western [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is to account for possible systematic error in the experimental lifetime, which is 30% larger than an earlier determination [26], and a possible error contribution from the experimental emission branching ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A trial calculation was made of A(1) → X(v′′) emission rates using X 3Σ− and A 3Π potential-energy curves taken from Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56] and Sarka and Nanbu [35], respectively, and the experimentally-deduced µA−X electronic transition moment of Elks and Western [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This confirmed that emission to levels with v′′ > 11 is negligible and the experimental branching ratios in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (11) are adequately normalised when compared with their statistical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' By fixing our model A(1) ← X(0) transition moment using the f-value from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (12) we constrain the 32S16O column-density in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 9 to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4) × 1016 cm−2, where the fractional uncertainty is greater than for the reference f-value due to the fitting 25 B(5)~C(0) B(6)~C(1) B(7)~C(2) B(8)~C(3) B(10)~C(4) B(11)~C(5) B(12)~C(6) B(13)~C(7) 20 15 10 5 0 Spin-orbit interaction, vBvC (cm−1) 32S16O 33S16O 34S16O 36S16O Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spin-orbit interaction energies of neighbouring B(vB) and C(vC) states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Symbols: Band-by-band fitted parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Curve vertices: 32S16O interaction energies computed from the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' uncertainty of our rather weak A(1) ← X(0) spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The separation in frequency between the A(v) ← X(0) bands, and B(v) ← X(0) and C(v) ← X(0) band is too great to permit their simultaneous measurement at DESIRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Instead, the A(1) ← X(0) and B(8) ← X(0) bands were measured consecutively under identical discharge conditions and a calibration of all 32S16O-spectra column densities thus attained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This procedure was repeated several times during the experiment and the ratio of A(v) ← X(0) to B(v) ← X(0) f-values and found to be consistent within 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A rotational temperature of 290 K was found to best match A − X spectra and is somewhat lower than the 360 K temperature consistently deduced from the B − X spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The reason for this difference is not clear but comparing fitted spectra of A−X at 290 and 360 K only results in a marginal change in their quality-of-fit and f- values that differ by about 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Further confirmation of the SO column density deduced here is provided in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Discussion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectroscopic constants The fitted Hamiltonian parameters describing deperturbed energy levels are listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The fitted B(vB) ∼ C(vC) spin-orbit interaction parameters are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 10 and a level-energy map of fitted 32S16O levels up to J = 30 and B(v = 14) is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 11 showing various near-degeneracies and crossings of the B 3Σ− and C 3Π rotational series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Parameters for some particularly broadened or perturbed bands could not be de- termined independently and were fixed to values in line with the spectrum as a whole and tabulated without uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' No spin-rotation interaction energies, γ, could be determined for any C 3Π levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Outlying values of D, λ, and γ are mostly associ- ated with absorption bands suffering from a combination of broadening, weakness, or contaminant overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The rotational constants of B 3Σ− and C 3Π levels scaled by their reduced-mass are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 12 and are in good agreement for the studied isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A discon- tinuity between B(16) and B(17) is associated with the B 3Σ− outer limb irregularity depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is also coincident with a change in the measured spin-rotation 26 0 5 10 15 20 25 30 Rotational quantum number, J 44000 45000 46000 47000 48000 49000 50000 Term value (cm−1) B(4) B(5) B(6) B(7) B(8) B(9) B(10) B(11) B(12) B(13) B(14) C(0) C(1) C(2) C(3) C(4) C(5) C(6) C(7) = 0 = 1 = 2 Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Observed or inferred 32S16O B 3Σ− and C 3Π levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 27 0 4 8 12 16 20 24 28 Vibrational quantum number, v 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 Rotational constant (B, cm−1) 32S16O 33S16O 34S16O 36S16O B 3Σ − C 3Π Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitted rotational constants of the observed B 3Σ−(v) and C 3Π(v) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The values for heavier isotopologues are reduced-mass-scaled upwards for comparison with 32S16O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 0 4 8 12 16 20 24 28 Vibrational quantum number, v 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 Spin-rotation constant ( , cm−1) 32S16O 33S16O 34S16O 36S16O Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitted B 3Σ−(v) spin-rotation constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 28 parameter, γ, from approximately −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02 cm−1 for B(v ≤ 15) to about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 above, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The larger value may be identifiable with the higher-lying 3Σ− state “3” computed by Sarka and Nanbu [35] and shown to exchange electronic char- acter with B 3Σ− at large v, although the γ-constant was not calculated in that study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The large scatter of fitted γ values for v ≥ 16 is indicative of significant model error in the band-by-band parameterisation of the congested spectrum approaching the B 3Σ− dissociation threshold, although the overall increase noted above is robustly measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A discontinuity of measured spin-spin interaction energies, λ, near B(v = 15) is not observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The fitted C(v) spin-orbit constants, A, fall in the range −182 to −179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 cm−1, and compare well with the A = −181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 cm−1 values deduced by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] from a well-resolved spectrum of 32S16O C(0) ← X(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The approximate 1 cm−1 scatter of values is due to the broadening and weakness of some C(v, Ω) levels, in which case they are correlated with both T and λ when fixing bandhead positions of the three Ω-sublevels, with further correlation with spin-orbit interactions connecting nearby B 3Σ− levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fixing all the T and λ parameters of C 3Π levels, along with their spin- orbit interaction with nearby B 3Σ− levels, to completely uncorrelated values requires a clear observation of transitions to all three Ω-levels and their rotational structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Significant spin-orbit interactions are found to couple B(v = 5−8, 10−13) levels in all isotopologues with the nearest C(v) level, with rotational term series crossings and near-crossings for 32S16O shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' No assumptions were made when fitting spin-orbit interaction energies, and their similarity across isotopologues and smooth dependence with increasing vibrational quantum numbers is evident in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The interaction energies mixing B(13) with C(7) for the various isotopologues are more scattered than for the mixing of lower-energy levels, and larger than might be antic- ipated from a simple extrapolation of vibrational excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This apparent inconsis- tency is likely attributable to the particular difficulty in fitting the broadened B(13) and C(7) states and the weakness of absorption due to C(7) ← X(0) absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In a simple test, a trial re-fitting of the 32S16O experimental spectrum was made as- suming a ξ = −8 cm−1 interaction energy, consistent with an extrapolation of lower-v interactions, and resulted in only a marginal reduction of its quality of fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] list T and B parameters fitted to their 32S16O spectra of B(v = 0 − 16) that are in reasonable agreement with our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' However, there are large differences with respect to D, λ, and γ constants, with those of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' including large magnitude and sign inconsistencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is no doubt due to the difficulty of fitting rotational structure to the low-sensitivity and uncertain-excitation B(v) ← X(0) absorption spectra of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20], which also prevented a deperturbation with respect to interacting C(v > 0) levels, as was possible here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' In general, the present B(v > 3) constants should be preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A superior sensitivity to C(0) ← X(0) in the combined spectra of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] means that their fitted C(0) parameters including a mutual deperturbation with both d(1) and B(5) are the more complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Their analysis includes several rotationally-mediated interaction terms mixing C(0) and B(5) which were not found necessary in our analysis of various B(vB) ∼ C(vC) couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We find all B ∼ C perturbations to be well described by a single spin-orbit interaction energy, and the inclusion of rotational mixing of the order found by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' would be quite noticeable in our spectral modelling of the well-resolved B(8) and C(3) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The cause of this difference is not clear but may arise from a greater sensitivity to C(0) and higher-J B(5) levels in the combined spectra available to Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', leading to a good definition of level crossings near the J = 21 and 28, with fitted rotational interactions being more sensitive to higher-J crossings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 29 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5 Internuclear distance (Å) 42000 44000 46000 48000 50000 52000 54000 Potential energy (cm−1) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 21 24 0 1 2 3 4 5 6 7 B 3Σ − this work C 3Π this work 3Σ − Sarka et al 3Π Sarka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Empirical diabatic potential-energy curves for (Ω = 0, J = 0) B 3Σ− and C 3Π states relative to the ground-state equilibrium energy, and 32S16O vibrational level energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Also shown are comparable adiabatic ab initio curves computed by Sarka and Nanbu [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Potential-energy curves The rotational level energies fitted to experimental spectra were used to deduce exper- imental diabatic B 3Σ− and C 3Π potential-energy curves and a spin-orbit interaction energy mixing the two electronic states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The B 3Σ− experimental data were reinforced with 32S16O v = 0 to 3 levels computed from the molecular constants given by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] to better constrain the B 3Σ− potential-energy minimum, but neglecting their perturbation by levels of A 3Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The solution of uncoupled vibrational energy levels and wavefunctions and the subsequent matrix diagonalisation to compute a perturbed spectrum are described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fitted parameters governing this model are listed in Table 5 and the standard deviation of residual differences between globally-computed rotational energy levels and those fitted band-by-band to the experimental spectra is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The resulting potential-energy curves corresponding to T(R) in Table 1 are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' For each curve, the well and inner limb is fitted to one Morse function [60] and the outer limb described by another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These regions are joined by a cubic-spline-interpolated region consisting of 9 spline knots between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7˚A spanning the B 3Σ− poten- tial inflection, and 2 knots at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='88 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='95˚A for C 3Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The C 3Π dissociation energy is unconstrained by our measurements and kept fixed at a value corresponding to the S(1D2)+O(3P1) excited atomic limit and relative to the ground-state dissociation energy deduced by Clerbaux and Colin [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The B 3Σ− dissociation limit was ad- 30 Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Morse potential-energy wells and interaction parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='a B 3Σ− (Valid for v ≤ 14) Te = 41633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0(5) cm−1, c2 = 20204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(6) cm−1, Re = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='77526(5) ˚A, β = +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='7634(3) ˚A−1, λ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05(8) cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C 3Π (Valid for v ≤ 4) Te = 44372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8(4) cm−1, c2 = 14215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(2) cm−1, Re = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='65708(6) ˚A, β = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='372(2) ˚A−1, A = −180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='50(8) cm−1, λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='35(7) cm−1 ξBC = −56(4) cm−1 aThe potential well formula: T(R) = Te + c2 [1 − exp(−β(R − Re))]2 , applies to the given v-range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Higher-energy potential-energy curves are given numerically in the supplemen- tary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Uncertainties estimated by the least-squares optimisation of potential-energy curves and state interactions are given in parentheses in terms of the least-significant digit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' justed to best fit the experiment and its fitted value, 53 020 cm−1, lies between the S(1D2)+O(3P1) and S(1D2)+O(3P2) limits, but is poorly constrained given the un- certain appearance of B(v > 28) levels in our spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' All potential-energy curves are provided in numerical form in the supplementary material [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spin-spin interaction energies for B 3Σ− and C 3Π, λ in Table 5, were optimised in order to model all Ω-levels and are in agreement with their values deduced band-by- band, as is the C 3Π spin-orbit splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The spin-orbit interaction energy, ξBC, was fitted to an R-independent value of −56±4 cm−1, where the uncertainty is estimated by testing alternative values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Specific B(vB) ∼ C(vC) interaction energies are computed from ξBC and shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 10 to be in good agreement with the band-by-band interaction energies fitted to the experimental spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Absolute magnitudes of the R-dependent B ∼ C spin-orbit interaction energies are calculated ab initio by Archer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [22] and Yu and Bian [34] and are 60 and 35 cm−1, respectively, near 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 ˚A where the B 3Σ− and C 3Π potential-energy curves cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The former value is in good agreement with the present results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Transition moments Vibronic transition moments, µi(v)−X(0), deduced from the experimentally-observed B(v) ← X(0) and C(v) ← X(0) bands are listed in Table 1 and plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 15 for B(v) ← X(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The absolute scaling of these dipole moments was determined by reference to the observed A(v) ← X(0) spectrum with an estimated 10% uncertainty, as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The product of signs of the µB(vB)−X(0), µC(vC)−X(0), and 31 0 10 20 30 v′ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='20 Vib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' moment ( i(v′) − X(v′′), au) B(v′) ← X(0) (a) 32S16O 33S16O 34S16O 36S16O 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='475 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='500 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='525 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='550 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='575 Internuclear distance / R-centroid (Å) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 Elec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' moment ( i − X, au) v = 0 v = 30 v = 1 v = 7 B(v′) ← X(0) C(v′) ← X(0) (b) Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (a) Vibrational B(v) − X(0) transition moments fitted band-by-band (error bars) and computed for 32S16O from the electronic-state model (curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (b) Electronic transition moment deduced from vibronic values (error bars) and computed ab initio by Sarka and Nanbu [35] (curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' ξB(vB)C(vC) parameters significantly affects the simulated spectrum of B(vB) − X(0) and C(vC) − X(0), and we find this product to be negative for all interacting bands observed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The uniquely-signed member of each triple is not determinable from our experimental data but may be identified in an ab initio calculation computing ma- trix elements with self-consistent phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Feng and Zhu [36] and Sarka and Nanbu [35] simultaneously compute µBX and µCX but find opposite and common signs, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Here, we assume both transition moments to be positive, defining the spin-orbit interactions as negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Vibrational wavefunctions of X(v = 0), B(v), and C(v) levels were computed from a ground-state potential-energy curve generated by the Rydberg-Klein-Rees method [61] from data in Lattanzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56] along with the excited-state potential-energy curves described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Franck-Condon factors and R-centroids [50] for the B(v′)−X(v′′) and C(v′) − X(v′′) transitions, computed using these wavefunctions are used to factor out the vibrational-dependence of experimental µi(v)−X(0) values, and the resulting R-centroid dependent µB−X and µC−X electronic transition moments are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We judge these to be R-independent within experimental uncertainty, with mean values µB−X = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 and µC−X = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02 au, where the estimated uncertainties are a combination of the 10% calibration uncertainty and approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02 au scatter of the experimental data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' There is a systematic overestimate of high-v 36S16O B(v) ← X(0) transition moments that could not be eliminated satisfactorily, even with a biased refit of the 36S16O spectrum and its overlapping contaminants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This distortion is thus unexplained, but may arise from the “jitter” effect occasionally affecting SOLEIL FTS spectra and leading to an incorrect zero- intensity level [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The present B − X electronic transition moment for SO lies between the values determined experimentally for the analogous transitions in the isovalent molecules O2 [62] and S2 [40, 63], ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='87 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='05, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' On the other hand, B−X electronic transition moments for SO calculated ab initio [35–37] are significantly smaller than our experimental value in the region of internuclear distance probed by absorption from X(v = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The cause of this difference is not clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Representative R- dependent ab initio B−X and C−X electronic transition moments calculated by Sarka and Nanbu [35] are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 15, together with our experimental determinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 32 Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Radiative lifetime (ns) of B 3Σ−(v = 0 − 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' v This work Elks and Western [21] Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [24] 0 37(4) 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6(6) 29(2) 1 37(4) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3(6) 30(4) 2 38(4) 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4(5) 27(4) 3 37(4) 52(2) 29(4) 4 6 8 10 12 14 16 18 20 22 24 26 28 10-1 100 101 B(v, = 0) 32S16O 33S16O 34S16O 36S16O 2 3 4 5 6 7 10-1 100 101 C(v, = 1) 32S16O 33S16O 34S16O 36S16O 4 6 8 10 12 14 16 18 20 22 24 26 28 10-1 100 101 32S16O B(v) Ω = 0 Ω = 1 2 3 4 5 6 7 10-1 100 101 32S16O C(v) Ω = 0 Ω = 1 Ω = 2 Vibrational level Deperturbed linewidth ( , cm−1 FWHM) Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Deperturbed predissociation linewidths of the observed B(v) and C(v) states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The rotation- dependent widths of B(8) are shown extrapolated to J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Open symbols: Fitted parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Closed symbols: Fixed to assumed values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Upper figures: Widths of Ω = 0 sublevels for all isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lower figures: Widths of all Ω levels for 32S16O only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' While the large discrepancy in the B − X case is evident, very good agreement occurs for the C − X transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Our scaled electronic transition moments were further assessed by comparison with emission lifetimes measured previously for the unpredissociated B(v = 0 − 3) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' For this we computed vibrationally-averaged emission rates corresponding to B(v′ = 0−3) → X(v′′ = 0−30) according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' (10) and computed the total B(v′) emission lifetime by summing over v′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The results are listed in Table 6 with uncertainties following from the estimated 11% uncertainty of our deduced B−X transition moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Our predicted lifetimes are 10% and 30% longer than the time-domain measurements of Elks and Western [21] and Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [23, 24], respectively (ignoring the outlying B(3) lifetime of Elks and Western [21]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 33 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Predissociation broadening The deperturbed line broadening fitted to observed B(v) ← X(0) and C(v) ← X(0) bands is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 16 and shows significant vibrational, isotopologue and Ω de- pendence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The deperturbed widths for Ω = 0 and 1 e-parity B 3Σ− levels become rapidly mixed with increasing rotation so that the observed widths of high-J levels converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The upper limits of 32S16O B(v) widths estimated by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] are in agreement with the values determined here, apart from their limits ΓB(6) < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 and ΓB(11) < 1 cm−1 that fall below our measured widths of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3) cm−1 FWHM and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1 − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='9 cm−1 FWHM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The modelled B 3Σ− predissociation width pattern is likely caused by spin-orbit interaction between B 3Σ− and various crossing unbound states known from quantum- chemical calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yu and Bian [34] compute all singlet, triplet, and quintet states dissociating to ground state S(3P) and O(3P) atoms which may provide such pre- dissociation channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' They find significant interaction energies mixing B 3Σ− with their (1) 5Π and (2) 5Π states, and the outer limb of an adiabatic C 3Π state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The bound (1) 5Π state crosses B 3Σ− below the S(3P) + O(3P) dissociation limit and pro- vides a threshold dissociation channel beginning with B(v = 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This crossing likely also explains the predissociation of rotationally-excited B(v = 0 − 3) with their J- thresholds known experimentally [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The (2) 5Π state is predicted to cross B 3Σ− near v = 13 and could provide an explanation for the rapidly increasing predissoci- ation widths of higher levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An outer-limb crossing with the adiabatic C 3Π state may further enhance B 3Σ− predissociation near v = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The rapid variation of width with v between threshold and these crossings likely results from the varying overlap of bound- and unbound-state radial wavefunctions, as is typical of predissociation by outer-limb crossing repulsive states [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yu and Bian [34] predict additional crossings and spin-orbit interactions between B 3Σ− near v = 7 and 11, and the repulsive outer limbs of two 1Π states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This purely Ω = 1 interaction could explain the enhanced Ω = 1 dissociation widths we find for B(9) and B(10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Finally, we note that the J- and Ω-dependencies of the B(v = 8) linewidths for 32S16O, displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6, are typically characteristic of predissociation by a 3Π state [64], also observed in some levels of the B state of O2 [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Thus, the C 3Π state is likely to be partially involved in the, possibly complex, B(v = 8) predissociation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Our analysis of C(v) levels reveals a broad width minimum around v = 4 and up to factor-of-five differences between Ω-substates of the same vibrational level, with either Ω = 0 or 1 being the most broadened.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The large widths of C(v = 6, Ω = 0) and C(v = 7) are consistent with being nearest to the 3Π avoided crossing shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rotational line lists and cross sections The band-by-band modelling detailed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 4 results in a rotational line list for all observed bands, while the global model described in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 also permits the calculation of line frequencies and strengths for bands that are not experimentally observed in some isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We combine band-by-band and global-model derived line lists in order to generate a complete line list that is as accurate as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A global-model line list of rotational transitions terminating on B(v = 0 − 30) and C(v = 0 − 7) levels up to J = 50 was computed using the potential-energy curves, electronic state interactions, and transition moments presented in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='3 34 45150 45200 45250 45300 45350 45400 45450 45500 45550 Transition wavenumber (cm−1) 0 1 2 3 4 5 6 7 Cross section (cm2) ×10 17 32S16O 33S16O (shifted) 34S16O (shifted) 36S16O (shifted) Band model Electronic-state model Figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Simulations of absorption into the mixed B(7) ∼ C(2) levels computed from constants fitted band-by-band and a global electronic-state potential-energy-curve model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 44000 46000 48000 50000 52000 Transition wavenumber (cm−1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='2 Cross section (cm2) ×10 16 36S16O 34S16O (shifted) 33S16O (shifted) 32S16O (shifted) v = 4 5 6 7 9 10 11 12 13 14 15 16 17 18 20 22 24 26 30 v = 0 1 2 3 4 5 6 7 = 0 = 1 = 2 B 3 − C 3 Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Synthetic photodissociation spectra computed at 360 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 35 for all measured isotopologues and, for good measure, 18O-substituted species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Band- by-band-fitted deperturbed linewidths are added to the global-model line list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The unmeasured linewidths of S-substituted isotopologues for B(v > 16) levels, and all levels of O-substituted isotopologues are set to their 32S16O values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A cross section for absorption into the strongly-coupled B(7) ∼ C(2) levels is com- puted from the band-by-band constants fitted to the experimental spectra, as well as from the global-model line list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These are compared at 360 K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 17, and the detailed rotational structure and mass-dependent spin-orbit mixing of levels is well reproduced by the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The cross sections of other SO bands show similar agreement when making this comparison, with the principal differences being due to band-strength differences and small frequency shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The globally-modelled strengths smooth over the background intensity and contaminant absorption uncertainties affect- ing band-by-band analysis, and are therefore more accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' For example, the band- by-band 36S16O cross section in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 17 is clearly an overestimate when compared with the isotopically self-consistent global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Conversely, the band-by-band modelled line frequencies of observed bands are more accurate than the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We con- struct a final hybrid line list by substituting band-by-band measured line frequencies into the electronic-state model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Photoabsorption cross sections computed from this hybrid list for all S-isotopes are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Absorption into B(v > 3) and all C(v) levels is completely dissociative given the short lifetimes implied by the large measured transition widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Additionally, levels of 32S16O B(v = 3) with quantum-number N ≥ 10 are known to dissociate, with only lower-N levels contributing to the emission spectra of 32S16O [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Emission spectra of S-substituted isotopologues have not been measured and will likely have higher-N predissociation thresholds, as found for 12S18O by Clerbaux and Colin [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We neglect this difference given the rather small contribution of B(3) to the overall photodissociation cross section and adopt the N = 10 threshold for all species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Then we compute a photodissociation cross section from the hybrid line list by including only dissociative upper levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Band-by-band and global model rotational line lists, and the recommended hybrid of the two, are permanently available in an online data archive [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Comparison with other published cross sections Phillips [25] measured the B(v) ← X(0) cross section for 32S16O at low spectral res- olution and a digitised version is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We compare this with a 32S16O cross section computed from our final hybrid line list assuming a rotational tem- perature of 400 K and broadened by convolution with a Gaussian function of width 50 cm−1 FWHM, in order to approximately match the Phillips [25] instrumentally- broadened band profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The relative band strengths are similar and integrated cross sections over the region plotted agree within 15%, with the new cross section being larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' There are absorption features appearing in the cross section of Phillips [25] which are not found in our analysis of SO spectra, for example at 48 400 and 52 400 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These are broadly aligned with SO2 absorption bandheads and likely result from an imperfect subtraction of contaminant SO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Danielache et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [16] make a similar comparison of their cross section computed ab initio with Phillips [25], finding reasonable relative agreement but with some differences in relative B(v) ← X(0) band strengths and frequencies, but, more importantly, the ab initio cross section was found to have a 36 46000 48000 50000 Transition wavenumber (cm−1) 0 1 2 3 Cross section (cm2) ×10 17 Present work Phillips (1981) Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The present 32S16O cross section computed assuming a rotational temperature of 400 K and degraded by convolution with a unit Gaussian of width 50 cm−1 FWHM, compared with the low-resolution photoabsorption cross section of Phillips [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' three-times smaller magnitude overall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Summary Detailed spectroscopic data on the B 3Σ−(v = 4 − 30) and C 3Π(v = 0 − 7) states of SO and its S-substituted isotopologues are determined from high-resolution absorption spectra covering the 43 000 to 51 000 cm−1 (190 to 233 nm) spectral region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' This is the first observation of C 3Π levels above v = 2 or a B 3Σ− or C 3Π level in any S-substituted isotopologue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Most of the observed bands are severely blended due to a high line density and predissociation broadening, and their profiles were fitted to minimally-specified effec- tive Hamiltonians including spin-orbit interactions between neighbouring B(vB) and C(vC) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The fitted linewidths are quite variable with respect to vibrational level and quantum number Ω and likely arise from further interactions with unbound elec- tronic states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' An empirical model of B 3Σ− and C 3Π electronic states was constructed to ensure globally-reliable band strengths and to enable extrapolation to unmeasured vibrational levels and isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The fitted cross section has a band-by-band relative uncertainty within 5% and an additional 10% absolute uncertainty based on published lifetime and radiative data, and their uncertainties, for the A 3Π(v = 1) level [21, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The estimated total uncer- tainty encompasses agreement with a previously measured 32S16O cross section [25] and B 3Σ−(v = 0 − 2) lifetimes [21], but somewhat disagrees with a further set of B 3Σ−(v = 0 − 3) lifetimes [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' However, the new B 3Σ− − X 3Σ− transition moment is in significant disagreement with previous ab initio calculations [35, 37] that suggest a 50% smaller cross section, while C 3Π − X 3Σ− transition moments are found to agree well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' The final result is a comprehensive and spectroscopically-accurate line list of pho- todissociating far-ultraviolet rovibronic transitions for all xS16O isotopologues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' These data, available in an online archive [45], are ideally suited for computing SO lifetimes against photodissociation in atmospheres and the interstellar medium, and the result- ing likelihood of photolytic S-isotope fractionation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 37 Acknowledgements The authors are very pleased to contribute to this special issue in honour of Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Wim Ubachs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We have benefited enormously from his pioneering work in high-resolution and time-resolved spectroscopy and his insightful and energised collaboration on numerous projects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' We thank B´erenger Gans of the Institut des Sciences Mol´eculaires d’Orsay for permitting the use of the radio-frequency discharge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' AH was funded by the NASA Postdoctoral Program through the NASA Astrobiology Institute, by grant num- ber 19-03314S of the Czech Science Foundation, and the ERDF/ESF “Centre of Ad- vanced Applied Sciences” (grant number CZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 01/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='0/16 019/0000778).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' JRL acknowledges support from the NASA Exobiology program (grant #80NSSC19K0475 to Arizona State University).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' References [1] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gottlieb and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ball, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 184, L59 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mateen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hofner, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Araya, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 167, 239 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [3] Guilloteau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Di Folco, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Dutrey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Simon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Grosso, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', and Pi´etu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 549, A92 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [4] Rivi`ere-Marichalar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Fuente, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Goicoechea, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Pety, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Le Gal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Gratier, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Guzm´an, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Roueff, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Loison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Wakelam, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 628, A16 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lellouch, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Strobel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Belton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Summers, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Paubert, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Moreno, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 459, L107 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Moullet, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lellouch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Moreno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gurwell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Black, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Butler, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 776, 32 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [7] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Kleer, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Pater, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' ´Ad´amkovics, Icarus 317, 104 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Bockel´ee-Morvan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Wink, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Despois, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Crovisier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Bachiller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Benford, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Biver, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Davies, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 353, 1101 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [9] Boissier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Bockel´ee-Morvan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Biver, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Crovisier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Despois, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Marsden, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', and Moreno, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=', Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 475, 1131 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Na, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Esposito, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Skinner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' – Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 95, 7485 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Belyaev, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Montmessin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Bertaux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mahieux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Fedorova, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Korablev, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Marcq, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yung, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Zhang, Icarus 217, 740 (2012), advances in Venus Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Pavlov and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Kasting, Astrobiology 2, 27 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ono, Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Earth Pl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 45, 301 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Farquhar, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Bao, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Thiemens, Science 289, 756 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lyons, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Geo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 267, 164 (2009), advances in experimental and theo- retical isotope geochemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Danielache, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tomoya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Kondorsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tokue, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nanbu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 140, 044319 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [17] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Martin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 41, 167 (1932).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Clerbaux and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 165, 334 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colin, Can.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 47, 979 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [20] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Liu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Elliott, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Western, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lee, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 238, 213 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 38 [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Elks and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Western, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 110, 7699 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [22] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Archer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Elks, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Western, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 112, 6293 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yamasaki, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Taketani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tomita, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Sugiura, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tokue, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A 107, 2442 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yamasaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tomita, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hatano, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Taketani, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tokue, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 413, 231 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [25] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phillips, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 85, 3994 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Clyne and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Liddy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Farad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 78, 1127 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Clyne and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Farad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 82, 1315 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [28] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Beaman, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Setser, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 149, 384 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stuart, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Cameron, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Powell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 98, 11499 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Dixon, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Tasker, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Balint-Kurti, Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 34, 1455 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [31] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Swope, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lee, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Schaefer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 71, 3761 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ornellas and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Borin, Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 94, 139 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Borin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ornellas, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 247, 351 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [34] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yu and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Bian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 32, 1577 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [35] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Sarka and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nanbu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A 123, 3697 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [36] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Feng and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Radiat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Transfer 234, 98 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [37] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' da Silva and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ballester, Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 139 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [38] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nahon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Garcia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gil, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Pilette, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Marcouille, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lagarde, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Polack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Synchrotron Rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 19, 508 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gans, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ito, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Boy´e-P´eronne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Douin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hick- son, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nahon, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Loison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Radiat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Transfer 204, 12 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [40] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stark, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Herde, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lyons, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nave, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 148, 244302 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [41] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Roudjane, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Joyeux, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phalippou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rodier, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Na- hon, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Photonics 5, 149 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [42] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Joyeux, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Roudjane, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gil, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Pilette, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Archer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ito, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nahon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Synchrotron Rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 23, 887 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [43] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Freeman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yoshino, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Esmond, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Parkinson, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 32, 1125 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [44] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stark, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Smith, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rufus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Thorne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Pickering, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Cox, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' – Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 104, 16585 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lyons, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibson, https://zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='org/record/7423903 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [46] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Western, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Radiat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Transfer 186, 221 (2017), satellite Remote Sensing and Spectroscopy: Joint ACE-Odin Meeting, October 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [47] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Brown, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colbourn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Watson, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Wayne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 74, 294 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Cheung, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Yoshino, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Parkinson, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Freeman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 119, 1 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [49] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Brown and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Merer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 74, 488 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [50] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lefebvre-Brion and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Field, The spectra and dynamics of diatomic molecules (Elsevier, Amsterdam, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [51] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hougen, The calculation of rotational energy levels and rotational line in- tensities in diatomic molecules (Physics Laboratory Publications, NIST, 1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [52] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hansson and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Watson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 233, 169 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [53] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Dickenson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Salumbides, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' de Oliveira, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Joyeux, 39 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Nahon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ubachs, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 135, 244301 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [54] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Johnson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 67, 4086 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Larsson, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 128, 291 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [56] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lattanzi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Cazzoli, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Puzzarini, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 813, 4 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [57] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Le Roy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 194, 189 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [58] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Colin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Farad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 2 78, 1139 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Borin and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Ornellas, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 322, 149 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [60] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Morse, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 34, 57 (1929).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Rees, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' London 59, 998 (1947).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [62] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Hawes, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Torop, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Earth 26, 519 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [63] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Stark, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Heays, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 148, 244303 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [64] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Julienne and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Krauss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Spectrosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 56, 270 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' [65] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Lewis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Gibson, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Dooley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 100, 7012 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} +page_content=' 40' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E4T4oBgHgl3EQfuQ0Y/content/2301.05230v1.pdf'} diff --git a/mdE2T4oBgHgl3EQfJQZR/content/2301.03689v1.pdf b/mdE2T4oBgHgl3EQfJQZR/content/2301.03689v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c4df77cd2c3767ee482c542a7649c9d188a77f77 --- /dev/null +++ b/mdE2T4oBgHgl3EQfJQZR/content/2301.03689v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:50b75aec94b577158d9e18e3546f2eac7a36a961046e9cad49eb41ea12b9394b +size 9625094 diff --git a/ntAyT4oBgHgl3EQfy_ls/content/2301.00694v1.pdf b/ntAyT4oBgHgl3EQfy_ls/content/2301.00694v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8ba4c519d28ed4ba3beee84749a7fdb76e21cf7e --- /dev/null +++ b/ntAyT4oBgHgl3EQfy_ls/content/2301.00694v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:21da8ba8398375b236c28b07c45b90e1b92a9225ca7eeb2acebce880adcc944b +size 169251 diff --git a/ntAyT4oBgHgl3EQfy_ls/vector_store/index.faiss b/ntAyT4oBgHgl3EQfy_ls/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..0f2c26bca95e7d46dc039f4fe7b3fb902d090591 --- /dev/null +++ b/ntAyT4oBgHgl3EQfy_ls/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:21cdd8266aa81fc11b92dfa7d4654b9c6de6a13797a6600478a796e77bab3bc3 +size 1114157 diff --git a/ntAyT4oBgHgl3EQfy_ls/vector_store/index.pkl b/ntAyT4oBgHgl3EQfy_ls/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..4d8e5f73613c7f75e07542dcc1d2a374c05332fc --- /dev/null +++ b/ntAyT4oBgHgl3EQfy_ls/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:983a250386aba1140a3c25e3ff392a3adab3820b049ad0e8c374853fd66b1c7c +size 60133 diff --git a/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/2301.03016v1.pdf.txt b/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/2301.03016v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9e674cca01b6a9a95c247ef329e700f60bb0482 --- /dev/null +++ b/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/2301.03016v1.pdf.txt @@ -0,0 +1,1224 @@ +A contextually objective approach +to the extended Wigner’s friend thought experiment +Maxime Federico +Laboratoire Interdisciplinaire Carnot de Bourgogne, +CNRS - Universit´e Bourgogne Franche-Comt´e, UMR 6303, BP 47870, 21078 Dijon, France +Philippe Grangier +Laboratoire Charles Fabry, IOGS, CNRS, Universit´e Paris Saclay, F91127 Palaiseau, France. +(Dated: January 10, 2023) +We present a discussion of the extended Wigner’s friend thought experiment proposed by +Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum +mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradic- +tion arises if one admits that agents must agree on what is considered as a system and what is not. +In such a contextually objective approach of quantum mechanics, the apparent contradiction is au- +tomatically removed. We also discuss why this mutual agreement between agents is already implicit +in the standard formulations of quantum mechanics, and why removing it leads to inconsistencies. +I. +INTRODUCTION +Wigner’s friend thought experiment has been proposed +by Wigner in 1967 [2]. +Recently, an extended version +was proposed [1] in order to test how quantum mechan- +ics describes agents who themselves use that theory to +predict results of experiments, that may include other +agents. This article triggered a large number of reactions +[3] and it is not our purpose here to analyse all of them. +We will rather summarize the argument, and show that +the claimed contradiction between three arguments is re- +moved not by giving up one of these three arguments, but +rather by adding a fourth one. We will justify this ad- +ditional argument by different approaches, including e.g. +textbook quantum mechanics (QM), and the ontologi- +cal approach of Contexts, Systems, Modalities (CSM). +It may be concluded that the theory presented as QM +by Frauchiger and Renner is not the actual QM, but a +different theory that is not consistent indeed. +In Sections II and III we present the argument and +the contradiction as introduced in [1], and in Sec. +IV +how to remove it by adding a simple fourth requirement. +Then we discuss how to relate this argument to Hardy’s +paradox [4, 5] (Sec. V), to textbook QM as discussed by +Lalo¨e [6] (Sec. VI), and finally to the CSM point of view +(Sec. VII). We conclude in Sec. VIII, and present some +additional issues in Appendices 1 and 2. +II. +THE FRAUCHIGER-RENNER THOUGHT +EXPERIMENT +The experimental protocol is the following (see Fig. 1): +an agent F uses a quantum random generator (quantum +coin) with output r ∈ {heads, tails}. The coin quantum +state is +|r⟩ = +1 +√ +3 |h⟩ + +� +2 +3 |t⟩ , +(1) +FIG. 1. Sketch of the thought experiment. Image adapted +from [1]. +where |h⟩ and |t⟩ are the states of heads and tails re- +spectively. Probabilities are therefore 1/3 for heads and +2/3 for tails. During her measurement F gets entangled +with the coin, so the state of the total system including +F (and her lab) becomes +|Ψ⟩ = +1 +√ +3 |h⟩ +��F : h +� ++ +� +2 +3 |t⟩ +��F : t +� +, +(2) +using the notations [6] where +��F : h +� +is the state of F +(and her lab) if she observes heads and +��F : t +� +if she +observes tails. +Depending on the result, she prepares +the spin of an electron in state |↓⟩ if r = heads or in +state |→⟩ = +1 +√ +2(|↓⟩ + |↑⟩) if r = tails. +Therefore the +total state becomes +|Ψ⟩ = +1 +√ +3 |h⟩ +��F : h +� +|↓⟩ + +� +2 +3 |t⟩ +��F : t +� 1 +√ +2 +� +|↓⟩ + |↑⟩ +� +. +(3) +Then, she sends this electron to a second agent F, lo- +cated in an other lab isolated from F one (except during +arXiv:2301.03016v1 [quant-ph] 8 Jan 2023 + +2 +the exchange of the electron assumed very short) who +can measure the spin projection of that electron in the +basis {|↓⟩ , |↑⟩}. At this point, the total system including +agents themselves is in the overall entangled state +|Ψ⟩ = +1 +√ +3 +� +|h⟩ +��F : h +� +|↓⟩ |F : ↓⟩ ++ |t⟩ +��F : t +� +|↓⟩ |F : ↓⟩ + |t⟩ +��F : t +� +|↑⟩ |F : ↑⟩ +� +, +(4) +where |F : ↑⟩ and |F : ↓⟩ are the states of F (and her lab) +observing spin up or down. +Two other separate agents W and W can moreover +perform measurements on the systems F and F respec- +tively with respect to the basis states +��OK +� += +1 +√ +2 +� +|h⟩ +��F : h +� +− |t⟩ +��F : t +� � +, +(5) +��fail +� += +1 +√ +2 +� +|h⟩ +��F : h +� ++ |t⟩ +��F : t +� � +, +(6) +|OK⟩ = +1 +√ +2 +� +|↓⟩ |F : ↓⟩ − |↑⟩ |F : ↑⟩ +� +, +(7) +|fail⟩ = +1 +√ +2 +� +|↓⟩ |F : ↓⟩ + |↑⟩ |F : ↑⟩ +� +. +(8) +Here we name the “sub-experiments” that composed the +thought experiment by the name of agents corresponding +to the different measurements F, F, W and W. However, +it should be clear that F and F, who were agents in the +initial step, are then considered as systems from the point +of view of W and W. Therefore the states (5)-(8) writ- +ten above contain agents, labs and measured systems on +which W and W are supposed to make quantum measure- +ments, so that the whole ensemble of F and F agents, +labs and measured systems are projected into superposi- +tion states. This is clearly not feasible in practice, but +the whole idea is to consider this operation feasible as a +thought experiment, and to examine which consequences +can be drawn from it. +Formally, considering the four situations where the ac- +tive agents are either (F, F), (W, F), (F, W), or (W, +W), by using and combining appropriate bases, |Ψ⟩ can +be written equivalently as +|Ψ⟩ = +1 +√ +3 +� +|h⟩ +��F : h +� +|↓⟩ |F : ↓⟩ ++ |t⟩ +��F : t +� +|↓⟩ |F : ↓⟩ + |t⟩ +��F : t +� +|↑⟩ |F : ↑⟩ +� +(9a) += +� +2 +3 +��fail +� +|↓⟩ |F : ↓⟩ + 1 +√ +6 +� ��fail +� +− +��OK +� � +|↑⟩ |F : ↑⟩ +(9b) += +1 +√ +6 |h⟩ +��F : h +� � +|OK⟩ + |fail⟩ +� ++ +� +2 +3 |t⟩ +��F : t +� +|fail⟩ +(9c) += +1 +√ +12 +��OK +� +|OK⟩ − +1 +√ +12 +��OK +� +|fail⟩ ++ +1 +√ +12 +��fail +� +|OK⟩ + +√ +3 +2 +��fail +� +|fail⟩ . +(9d) +Using these four expressions for the state vector |Ψ⟩, one +can deduce the following statements, which are close to +the ones listed in [1]: +• F and F cannot get results heads and spin up [1.A] +• If W gets OK, then F gets spin up +[1.B] +• If W gets OK, then F gets heads +[1.C] +• W and W can get OK and OK with probability +1/12 +[1.D] +If considered all true together, it is clear that these four +statements lead to a contradiction, indeed from [1.D] W +and W can get OK and OK, and in that case F and +F should get spin up and heads from [1.B] and [1.C], +contradicting [1.A]. +However this contradiction may likely be attributed to +the undefined status of F and F, who switch between +being agents (able to make quantum measurements) and +systems (being acted upon by quantum measurements). +It is therefore required to clarify the definition and the +role of agents. From here, several points of view exist +and we are going to explore some of them. +III. +FRAUCHIGER & RENNER: GETTING A +CONTRADICTION. +This point of view is based on three assumptions which +allow authors of Ref [1] to show a “no-go theorem”. +First assumption (Q) : This defines what an agent +must do to interpret and predict measurements. Suppose +that a system S (external to the agent) is in state |ψ⟩ of a +Hilbert space at time t0; an outcome x can be measured +on S at time t with respect to a family of projectors {πx} +in Heisenberg representation. If ⟨ψ| πξ |ψ⟩ = 1, then the +agent can conclude that x = ξ at time t. From the point +of view on this individual agent, this theory looks like +quantum mechanics, and it will be used successively from +the “subjective” point of view of different agents, in order +to get a serie of statements. +First, if r = heads, the spin is in state |↓⟩, and a +measurement made by agent F with respect to the basis +{π↓ = |↓⟩ ⟨↓| , π↑ = |↑⟩ ⟨↑|} gives ⟨↓| π↓ |↓⟩ = 1. +Therefore agents F and F can conclude that if F gets +heads, F will get spin down; which is logically equivalent +to: if F gets spin up, F got tails, in agreement with eq. +(9a). By considering successively the different pairs of +agents, other statements can be obtained and lead to +• If F gets spin up, then F gets tails +[2.A] +• If W gets OK, then F gets spin up +[2.B] +• If F gets tails, then W gets fail +[2.C] +• W and W can have OK and OK +[2.D] +which are either the same or logically equivalent state- +ments compared to Section I (in the same order). + +3 +Additional assumptions (C) and (S): These two +hypotheses stipulate that agents can trust predictions +made by other agents, irrespective of their status, and +that all predictions apply in the same universe, avoiding +Everett’s multi world interpretation. It is under those +three assumptions that a contradiction arises. +Indeed, if statement [2.D] is valid, [2.B] implies that +F gets spin up, [2.A] that F gets tails, and [2.C] that +W gets fail. The last statement clearly contradicts the +starting point that W gets OK. Using their assumptions +as just shown, the authors of [1] can thus formulate the +following no-go theorem: +(Q) + (C) + (S) ⇒ Contradiction +(10) +which has been formulated as the statement “quantum +theory cannot consistently describe the use of itself” [1]. +IV. +REMOVING THE CONTRADICTION BY +AN AGREEMENT BETWEEN AGENTS. +A major remark is that, though it is presented as +equivalent to quantum mechanics (QM), the assumption +(Q) of Frauchiger and Renner implies a very unusual +use of the quantum formalism, where “self-proclaimed” +agents may become systems for other agents. It means +that the usual measurement postulate can hardly be +applied in a consistent way [6]. A simple way to remove +this problem, and also the contradiction, is to consider +the additional assumption +(A) All agents must agree on the definition of the +quantum system to which they apply assumption (Q); +as a consequence, no agent should be included in what +another agent considers as the measured system. +The second part of (A), i.e. +that no agent should be +included in what another agent considers as the measured +system, is a joint consequence of (Q), stating that the +agents apply QM to a system external to themselves, +and of the first part of (A), i.e. the agents agreement on +the definition of the system. Then the quantum system +is the same for all agents, and contains no agent. +Given (A), it is clear that the previous contradiction +vanishes since the four statements cannot be true to- +gether: +(i) if F and F are agents, the first statement is true, +but then the other three make no sense since F and F +cannot behave as (superposable) systems from the point +of view of W and W; +(ii) if F and F are systems, then the four lines corre- +spond to the agents W and W making four incompatible +measurements on the global system composed of F, F, +the coin and the spin. Incompatible measurements can- +not be true together as it is usual in QM, such that there +is no contradiction. +Therefore, with all of the four assumptions, we obtain +(Q) + (C) + (S) + (A) ⇒ No contradiction +(11) +which means that assumption (A) restricts (Q) to some +safe range where no contradiction arises. This could be +summarized as : “Objective quantum mechanics can de- +scribe the use of itself”, where “objective” is meant as +requiring a mutual agreement between all the agents. +In the following we will develop these arguments, and +in particular give more justifications and illustrations of +the points (i) and (ii) above, as well as some intermediary +situations. +We will also see that assumption (A) can +take different forms depending on which point of view +we adopt, but always removes the contradiction. +V. +LOOKING AT W AND W AS AGENTS: LINK +TO HARDY’S PARADOX +The Frauchiger and Renner (F&R) paradox is, as it +was pointed out by Bub [4], not only a new formulation +of Wigner’s friend experiment but also a twisted version +of Hardy’s paradox originally presented to show a similar +result as Bell’s theorem [7]. To do that, Hardy [5] used a +Mach-Zehnder interferometer for electrons and positrons +in order to get four entangled states which are similar +to those of the F&R Gedankenexperiment. The differ- +ence arises only with the way one imposes that these +four statements must be true together. In the following, +we will assume that a hidden variable exists to describe +the various states of eq. (9), in agreement with the for- +mulation proposed in [5]. +Let λ be the hidden variable which describes the states +before measurements and assume that QM is a local re- +alist theory. It means that results of measurements do +not depend on the choice of measurement done by other +agents. We introduce notations F(h, λ) = 1 if F mea- +sures the state |h⟩, and F(h, λ) = 0 otherwise. The same +notations will be applied to other agents and their re- +spective measurable states. The statements obtained in +the preceding sections can be recovered using the expres- +sions of |Ψ⟩ in the different bases. Indeed, from (9a) and +for every experiment described by a given value of λ, +F(h, λ)F(↑, λ) = 0. +(12) +From (9b) we additionally have +if W(OK, λ) = 1 then F(↑, λ) = 1, +(13) +from (9c) +if W(OK, λ) = 1 then F(h, λ) = 1, +(14) +and from (9d) +W(OK, λ)W(OK, λ) = 1 for 1/12th of experiments, +(15) +which can be summed up in the four following statements +completely equivalent to [1.A]-[1.D]: + +4 +• F(h, λ) and F(↑, λ) cannot occur at the same time +• W(OK, λ) is true ⇒ F(↑, λ) is true +• W(OK, λ) is true ⇒ F(h, λ) is true +• W(OK, λ) and W(OK, λ) occur one time out of 12 +One can see that even if the assumptions and conse- +quently the formalism are not exactly the same, the con- +tradiction arises in the same way as when the four states +of eq. (9) are considered simultaneously true. In that +case inspired by Hardy’s paradox, this is due to the hid- +den variable hypothesis. +Therefore, it appears that in +both situation, the contradiction is not due to QM itself +but to the assumption that all conclusions drawn from eq. +(9) are simultaneously true. This explains why the use +of assumption (A) removes the contradiction, by making +clear that they are incompatible in a quantum sense. +VI. +TEXTBOOK QM: PROJECTIVE +MEASUREMENTS DEFINE AGENTS +Another approach to the F&R contradiction can be +found in [6]. This point of view stipulates that defining +agents is equivalent to define where the projective mea- +surements are done, i.e. where the state is projected. For +instance, without any projection, the state of the total +system after “measurements” by F, F, W and W should +be written as +|Ψ⟩ = +1 +√ +12 +��OK +� ��W : OK +� +|OK⟩ |W : OK⟩ +− 1 +√ +12 +��OK +� ��W : OK +� +|fail⟩ |W : fail⟩ ++ 1 +√ +12 +��fail +� ��W : fail +� +|OK⟩ |W : OK⟩ ++ +√ +3 +2 +��fail +� ��W : fail +� +|fail⟩ |W : fail⟩ . +(16) +In this state, all observers are entangled as if we had +considered Everett’s multi-world interpretation. Then all +possibilities can be investigated by choosing where the +projections are made. The calculations are detailed in +[6] and Appendix 2, here we simply describe qualitatively +the results. +First, we consider F and F as agent (point (i) of Sec- +tion IV), and project states in agreement with their mea- +surements. The result (see Appendix 2) is that whatever +W and W measure, they cannot obtain informations on +spin state or coin state. Therefore, the statements [2.B] +and [2.C] of Section III cannot be formulated and the +contradiction does not arise. +In the second option which considers F and F as sys- +tems, and only W and W as agents, W cannot say any- +thing about the spin state, therefore using this way of +defining agents and writing states after measurements, +also prevent from any contradiction. +It is also instructive to consider the slightly modified +situation where F can “protect” her result by using an +other qubit stored in her lab, in such a way that it escapes +to W’s measurement (refered as “hidden qubit” [6]). If +F observes “heads”, the hidden qubit is in state +��G : h +� +and in state +��G : t +� +if she observes “tails”. The overall +state can thus be written as +|Ψ⟩ = +1 +√ +3 +� +|h⟩ +��F : h +� ��G : h +� +|↓⟩ |F : ↓⟩ ++ |t⟩ +��F : t +� ��G : t +� +|↓⟩ |F : ↓⟩ ++ |t⟩ +��F : t +� ��G : t +� +|↑⟩ |F : ↑⟩ +� +. +(17) +In the following, to simplify notations, we will replace +|h⟩ +��F : h +� +by |h⟩, |t⟩ +��F : t +� +by |t⟩, |↓⟩ |F : ↓⟩ by |↓⟩ and +|↑⟩ |F : ↑⟩ by |↑⟩ since agents (and their labs) are always +in the state corresponding to the outcome they have mea- +sured. We also condense the hidden qubit notation in +|hG⟩ and |tG⟩. The state becomes +|Ψ⟩ = +1 +√ +3 +� +|h⟩ |hG⟩ + |t⟩ |tG⟩ +� +|↓⟩ + 1 +√ +3 |t⟩ |tG⟩ |↑⟩ , +(18) +and the bases used by W and W to perform their respec- +tive measurements are +��OK +� += +1 +√ +2(|h⟩ − |t⟩), +��fail +� += +1 +√ +2(|h⟩ + |t⟩), +(19) +|OK⟩ = +1 +√ +2(|↓⟩ − |↑⟩), |fail⟩ = +1 +√ +2(|↓⟩ + |↑⟩). +(20) +The global state can then be put in the form +|Ψ⟩ = +��OK +� +|OK⟩ +1 +√ +12 |hG⟩ ++ +��OK +� +|fail⟩ +� 1 +√ +12 |hG⟩ − 1 +√ +3 |tG⟩ +� ++ +��fail +� +|OK⟩ +1 +√ +12 |hG⟩ ++ +��fail +� +|fail⟩ +� 1 +√ +12 |hG⟩ + 1 +√ +3 |tG⟩ +� +. +(21) +As it was pointed out in [6], the state |tG⟩ is only corre- +lated with the result |fail⟩ which is not surprising since +when F sends a spin in the state |→⟩, it is orthogonal to +|OK⟩. It means that the hidden qubit keeps a memory +of F’s measurement and therefore all statements derived +before do not hold anymore. We emphasize that there +is no need to read out the value of the hidden qubit: +as in an interference experiment, it is enough that the +“which path information” is stored somewhere to forbid +the quantum superposition. +It is also interesting to investigate different scenarii +for the two accessible states of the hidden qubit e.g. if +⟨hG|tG⟩ = 1 i.e. |hG⟩ and |tG⟩ are the same state, de- +noted for instance |G⟩, then the overall system is in the + +5 +following state +|Ψ⟩ = +1 +√ +12 +��OK +� +|OK⟩ |G⟩ − +1 +√ +12 +��OK +� +|fail⟩ |G⟩ ++ +1 +√ +12 +��fail +� +|OK⟩ |G⟩ + +√ +3 +2 +��fail +� +|fail⟩ |G⟩ , +(22) +which is the same as state (9d) without the hidden qubit. +|G⟩ can be factored out and the hidden qubit plays no role +since it is no more entangled with F’s results. Otherwise, +if ⟨hG|tG⟩ = 0 i.e. the qubit states are orthogonal and +the overall state is identical to (21). If we project this +global state onto each state of the hidden qubit +⟨hG|Ψ⟩ = +1 +√ +12 +� ��OK +� +|OK⟩ + +��OK +� +|fail⟩ ++ +��fail +� +|OK⟩ + +��fail +� +|fail⟩ +� += +1 +√ +3 |h⟩|F : h⟩|OK⟩ + |fail⟩ +√ +2 +, +(23) +⟨tG|Ψ⟩ = +1 +√ +3 +� ��fail +� +|fail⟩ − +��OK +� +|fail⟩ +� += +� +2 +3 |t⟩ +��F : t +� +|fail⟩ , +(24) +we recover the situation where F is an agent, and W +cannot project her in a superposition. +This calculation has two consequences: first, it gives a +way to make a transition between the different options, +by allowing ⟨hG|tG⟩ to take any value between 0 and +1. +We emphasize that this calculation makes sense in +a framework where the only agents are W and W. +If +⟨hG|tG⟩ = 0 then F and F should be considered as +decohered systems, as they appear in the usual theory +of decoherence after tracing out the “ancilla” qubits. +Second, it provides a “toy model” for a situation where +a system actually does not behave as such: if W tries +to make a projective measurement on F, including her +lab and all the surrounding environment, it is enough +that a single qubit escapes from the action of W to +make the projective measurement failed. When F is a +macroscopic system, it can be considered impossible for +W to get full control on every single qubit entangled +with F; then considering F as a system makes no sense. +Following the idea of Section IV, this can be seen as a +reformulation of assumption (A): +(A) All agents must agree on the definition of the quan- +tum system to which they apply assumption (Q), that is to +say where the state projection is done; as a consequence, +no agent should be included in what another agent con- +siders as the measured system. +VII. +CONTEXTS, SYSTEMS AND +MODALITIES: THE CSM APPROACH. +Here, we want to show that in the framework of the +CSM (Contexts, Systems and Modalities) approach, de- +velopped by A. Auff`eves and P. Grangier [8–11], the as- +sumption (A) introduced and discussed above is no more +an assumption but a theorem. We recall some basics of +CSM which starts with a new physical ontology (i.e. a +definition of all objects that are described by the theory), +by considering three entities: +• System = subpart of the world, isolated well +enough to have physical properties that can be +studied. +• Context = all other physical systems external and +possibly in contact with the studied one (ex: mea- +surement apparatus, labs, etc); in CSM, the con- +text corresponds to a classically defined measure- +ment setup, and it acts like an interface between +the system and the observer, see Fig. 2. +• Modalities = the set of answers (or values) that +can be predicted with certainty and obtained re- +peatedly for a given system in a given context. +These definitions are bound together by the following rule +(or axiom): in quantum mechanics, modalities are at- +tributed jointly to the system and the context. It means +that the quantum properties of a system do not “belong” +to the system alone, but to the system within a context. +In order to give an operational content to CSM, we +need a second axiom called Quantization Principle: +(i) For each well-defined system and context, there is a +discrete number N of mutually exclusive modalities. This +number N depends on the system, but does not depend +on any particular context. +(ii) Modalities, when defined in different contexts, are +generally not mutually exclusive, and they are said to be +“incompatible”. +CSM is based on a physically realistic point of view, i.e. +physics is applied to objects which exist independently +from any observer. +However, the “object” for CSM is +a system within a context, which makes it highly non- +classical. As it can be shown on Figure 2(c), in CSM +the observer is outside of the context, illustrating again +that the (objective) state of the context must be taken +into account in defining the modality. Such a “contextual +objectivity” [8] is quite different from the classical “abso- +lute objectivity” of Figure 2(a), but it fully agrees with +quantum reality as deduced from empirical evidence. +Now, coming back to the original problem, CSM was +hidden so far but in fact already there. +In order to +define systems and contexts according to CSM, we have +to avoid mixing notations between agents, labs and +experimental set ups. First, as it was pointed out before, + +6 +FIG. 2. +Graphic representations of different ontologies: +(a) Classical ontology: the observer can know the “real” phys- +ical properties of the system, and the context is only used as +an auxiliary tool for measurements. (b) Usual quantum on- +tology: through successive “entangling” interactions and uni- +tary evolution, the system will include the context, and also +(ultimately) the observer or “agent”, whose status may be +problematic. (c) CSM ontology: the context appears always +between the system and the observer, and definite values of +the relevant physical properties (modalities) are attributed +jointly to the system and the context. +FIG. 3. (o) Naive way to see Wigner’s friends thought ex- +periment. Such a picture is impossible for CSM, because a +(quantum) system cannot include a (classical) context. +(i) +Case where F and F are agents making quantum measure- +ments on systems with their “own” classical contexts. +(ii) +Second option where F and F are considered as systems. +there is only one ultimate reality which imposes that a +context cannot be included in a system and vice versa +(see Figure 3 (o)). For consistency, different agents must +agree on the definition of systems and contexts which +is exactly the purpose of assumption (A), formulated +according to CSM as: +(A) All agents must agree on the definition of the system +and context to which they apply assumption (Q); as +a consequence, no agent should be included in what +another agent considers as the measured system. +Again, several cases are possible, corresponding e.g. to +point (i) and (ii) of Section IV, and are drawn in Figure +3. In case (i), F and F perform quantum measurements +on their systems within their respective contexts. Then +W and W cannot make quantum measurements on them +(composite systems in yellow and orange dash lines of +Figure 3), and the F&R reasoning does not hold. In case +(ii), F and F are considered as systems so W and W can +perform quantum measurements on those systems in two +different contexts on each side (i.e. projecting F or F +in superposed or non-superposed states). The modalities +defined in these different contexts are incompatible and +thus not simultaneously true, no contradiction can arise. +To conclude, we have shown that within the CSM in- +terpretation, the F&R contradiction is removed without +additional assumption because CSM is already an “con- +textually objective” theory [8], where agents cannot be- +come systems for other agents. +VIII. +CONCLUSION +To conclude, we have presented several ways to escape +the “no-go theorem” introduced by F&R. Our arguments +can be summed up by “Contextually objective quan- +tum mechanics can describe the use of itself”. +This statement does not allow every single world inter- +pretation of quantum mechanics to be self-consistent, but +only those which rely on some form of objectivity. A con- +sequence is that the (single world) quantum rules must +introduce a clear distinction between agents and systems, +embedded in the additional assumption (A). Then we +have shown that in the framework of CSM approach, no +F&R contradiction can arise since CSM already contains +(A) as a theorem, deduced from the central concept of +contextual objectivity [8] which governs quantum mea- +surements in the CSM framework. +APPENDIX 1: ABOUT THE TIME EVOLUTION +OF THE EXPERIMENT +In their article [1], F&R insist on the temporal order +of measurements made by successive agents, associated +to changing the status of F and F between system and +context. In the CSM interpretation, changing the agents +status in a same experiment cannot occur, therefore the +chronology is not relevant. It could be if we had adopted +Everett’s point of view also called “multi-world”; but +this interpretation is in conflict with assumption (S), so +the F&R no-go theorem also does not apply. + +7 +More precisely, through the usual quantum or CSM +point of view, an ideal measurement takes place as fol- +lows: (a) entanglement of the system with the pointer +(also quantum) and then (b) reading of the pointer, +which brings the result at the single classical context +level. From the Everett’s point of view, there is no single +classical context level but many possible results which +are associated to differents universe branches. Then it +is, in principle, possible to reverse the evolution of these +branches, rewriting the history as if no measurement were +done, and to make another different measurement, cre- +ating again new branches. So in Everett’s point of view, +temporal order makes sense to describe first a measure- +ment by F, and then its “erasure” by W, followed by a +new measurement in the (OK; fail) basis. +In CSM, the measurement can be reversed only if it +has not reached the context level, i.e. between steps (a) +and (b). When the measurement is over (step b), the +result is macroscopic and unique and the modalities cor- +responding to other results in other contexts cannot co- +exist. Explicitly, if F and F are superposable systems, +we can measure them in superposed bases +S = {OK; fail}, +S = {OK; fail} +or in non superposed ones +N = {heads; tails}, +N = {up; down}. +The four situations we have discussed correspond to four +combined measurements (N, N), (N, S), (S, N), (S, S). +In that case, temporal order is not relevant since only one +of these four measurements can be made, as in Hardy’s +paradox, such that there is a unique objective macro- +scopic world in which QM is consistent. +We note also that the CSM point of view makes a clear +distinction between the usual “pre-measurement” stage, +that is entangling the system with a probe in a reversible +way, and the actual irreversible measurement that brings +the result to the context level. It can be told that the +F&R paradox fails because it mixes these two stages in +an inappropriate way, as explained in details in [12]. +APPENDIX 2: ADDING A HIDDEN QUBIT +Another approach to the F&R contradiction can be +found in [6]. This point of view stipulates that defining +agents is equivalent to define where projective measure- +ments are done, that is to say, where mathematically the +state is projected. For instance, without any projection, +the state of the total system after “measurements” by F, +F, W and W is +|Ψ⟩ = +1 +√ +12 +��OK +� ��W : OK +� +|OK⟩ |W : OK⟩ +− +1 +√ +12 +��OK +� ��W : OK +� +|fail⟩ |W : fail⟩ ++ +1 +√ +12 +��fail +� ��W : fail +� +|OK⟩ |W : OK⟩ ++ +√ +3 +2 +��fail +� ��W : fail +� +|fail⟩ |W : fail⟩ . +(25) +In this state, all observers are entangled as if we had +considered Everett’s multi-world interpretation. +Then all possibilities can be investigated for the pro- +jections. First, we consider F and F as agent (point (i) +of Section IV). Therefore, they have to project states in +agreement with their measurements. +According to F, +two states are available +|Ψ⟩tails = |t⟩ +��F : t +� 1 +√ +2 +� +|↓⟩ + |↑⟩ +� +, +(26) +|Ψ⟩heads = |h⟩ +��F : h +� +|↓⟩ . +(27) +If then we consider F’s projections which lead to many +cases depending of the result she gets but also of F’s +results, we have the states +|Ψ↓⟩tails = |t⟩ +��F : t +� +|↓⟩ |F : ↓⟩ , +(28) +|Ψ↑⟩tails = |t⟩ +��F : t +� +|↑⟩ |F : ↑⟩ , +(29) +|Ψ↓⟩heads = |h⟩ +��F : h +� +|↓⟩ |F : ↓⟩ , +(30) +or equivalently written in the other bases +|Ψ↓⟩tails = 1 +2 +� ��fail +� +− +��OK +� �� +|fail⟩ + |OK⟩ +� +, (31) +|Ψ↑⟩tails = 1 +2 +� ��fail +� +− +��OK +� �� +|fail⟩ − |OK⟩ +� +, (32) +|Ψ↓⟩heads = 1 +2 +� ��fail +� ++ +��OK +� �� +|fail⟩ − |OK⟩ +� +. (33) +Here we see that all these states are products; whatever +W and W measure, they cannot obtain informations on +spin state or coin state. Therefore, statements [2.B] and +[2.C] of Section III are wrong and no contradiction can +appear. +The second option is to consider F and F as systems, +and W and W as agents (point (ii) of Section IV). Be- +fore they perform measurements, the system is in state +(4). Then, two outcomes are possible for W and give the +states +|Ψ⟩OK = − |↑⟩ |F : ↑⟩ +��OK +� ��W : OK +� += +1 +√ +2 +� +|OK⟩ − |fail⟩ +� ��OK +� ��W : OK +� +, +(34) +|Ψ⟩fail = +� +2 |↓⟩ |F : ↓⟩ + |↑⟩ |F : ↑⟩ +� ��fail +� ��W : fail +� += +� 3 +√ +2 |fail⟩ |W : fail⟩ + 1 +√ +2 |OK⟩ |W : OK⟩ +� +⊗ +��fail +� ��W : fail +� +. +(35) + +8 +We see again, that the result OK is only correlated to +spin up, and that W cannot predict anything on W’s +measurement since both results OK and fail are still +available. In the second option where W gets fail, no +predictions can be obtained about the spin state. If we +furthemore add the projection made by W we obtain +|ΨOK⟩OK = |OK⟩ |W : OK⟩ +��OK +� ��W : OK +� +, +(36) +|Ψfail⟩OK = − |fail⟩ |W : fail⟩ +��OK +� ��W : OK +� +, (37) +|ΨOK⟩fail = |OK⟩ |W : OK⟩ +��fail +� ��W : fail +� +, +(38) +|Ψfail⟩fail = |fail⟩ |W : fail⟩ +��fail +� ��W : fail +� +, +(39) +or equivalently expressed in F and F basis +|ΨOK⟩OK = 1 +2 +� +|h⟩ − |t⟩ +�� +|↓⟩ − |↑⟩ +� +, +(40) +|Ψfail⟩OK = 1 +2 +� +|h⟩ + |t⟩ +�� +|↑⟩ − |↓⟩ +� +, +(41) +|ΨOK⟩fail = 1 +2 +� +|h⟩ − |t⟩ +�� +|↓⟩ + |↑⟩ +� +, +(42) +|Ψfail⟩fail = 1 +2 +� +|h⟩ + |t⟩ +�� +|↓⟩ + |↑⟩ +� +. +(43) +Again, since every state is a product state, statements +[2.B] and [2.C] cannot be true and the contradiction dis- +appears. Therefore this way to define agents and to write +states after measurements, also erases the contradiction. +[1] D. Frauchiger and R. Renner, “Quantum theory cannot +consistently describe the use of itself” Nature Comm. 9, +3711 (2018); a previous version is “Single-world inter- +pretations of quantum theory cannot be self-consistent”, +arXiv:1604.07422v1 (2016). +[2] E.P. Wigner, “Symmetries and Reflections”, chapter Re- +marks on the Mind-Body Question, pages 171-184. Indi- +ana University Press, 1967. +[3] A search on arxiv in December 2022 gives more than 50 +articles commenting or criticizing [1]. +[4] J. Bub, “In a defense of a “Single World” interpretation +of quantum mechanics”, arXiv:1804.03267v1 (2018) +[5] L. Hardy, “Quantum Mechanics, Local Realistic Theo- +ries, and Lorentz-Invariant Realistic Theories.”, Physical +Review Letters 68, 2981 2984 (1992). +[6] F. Lalo¨e, “Can quantum mechanics be considered con- +sistent? a discussion of Frauchiger and Renner’s argu- +ment.”, arXiv:1802.06396v2 (2018). +[7] J.S. Bell, +On the Einstein-Podolski-Rosen paradox, +Physics 1, 195 (1964). +[8] P. Grangier, “Contextual objectivity: a realistic inter- +pretation of quantum mechanics”, European Journal of +Physics 23:3, 331 (2002) [arXiv: quant-ph/0012122]. +[9] A. Auff`eves and P. Grangier, “Contexts, Systems and +Modalities: +a new ontology for quantum mechanics”. +Found. Phys. 46, 121 (2016), eprint arXiv:1409.2120 +[quant-ph] (2014). +[10] A. Auff`eves and P. Grangier “Deriving Born’s rule from +an Inference to the Best Explanation”, Found Phys 50, +1781 (2020) [arXiv:1910.13738 quant-ph] +[11] P. +Grangier, +“Revisiting +Quantum +Mysteries”, +https://arxiv.org/abs/2105.14448 +[12] M. Zukowski and M. Markiewicz, “Physics and Meta- +physics of Wigner’s Friends: Even Performed Premea- +surements Have No Results”, Phys. Rev. Lett. 126, +130402 (2021) + diff --git a/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/load_file.txt b/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..4eb5007c87e90b1455497aef9db1c5420e9be53b --- /dev/null +++ b/ntE1T4oBgHgl3EQfOgOc/content/tmp_files/load_file.txt @@ -0,0 +1,331 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf,len=330 +page_content='A contextually objective approach to the extended Wigner’s friend thought experiment Maxime Federico Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS - Universit´e Bourgogne Franche-Comt´e, UMR 6303, BP 47870, 21078 Dijon, France Philippe Grangier Laboratoire Charles Fabry, IOGS, CNRS, Universit´e Paris Saclay, F91127 Palaiseau, France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (Dated: January 10, 2023) We present a discussion of the extended Wigner’s friend thought experiment proposed by Frauchiger and Renner in [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradic- tion arises if one admits that agents must agree on what is considered as a system and what is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In such a contextually objective approach of quantum mechanics, the apparent contradiction is au- tomatically removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We also discuss why this mutual agreement between agents is already implicit in the standard formulations of quantum mechanics, and why removing it leads to inconsistencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' INTRODUCTION Wigner’s friend thought experiment has been proposed by Wigner in 1967 [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Recently, an extended version was proposed [1] in order to test how quantum mechan- ics describes agents who themselves use that theory to predict results of experiments, that may include other agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This article triggered a large number of reactions [3] and it is not our purpose here to analyse all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We will rather summarize the argument, and show that the claimed contradiction between three arguments is re- moved not by giving up one of these three arguments, but rather by adding a fourth one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We will justify this ad- ditional argument by different approaches, including e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' textbook quantum mechanics (QM), and the ontologi- cal approach of Contexts, Systems, Modalities (CSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It may be concluded that the theory presented as QM by Frauchiger and Renner is not the actual QM, but a different theory that is not consistent indeed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In Sections II and III we present the argument and the contradiction as introduced in [1], and in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' IV how to remove it by adding a simple fourth requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then we discuss how to relate this argument to Hardy’s paradox [4, 5] (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' V), to textbook QM as discussed by Lalo¨e [6] (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VI), and finally to the CSM point of view (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We conclude in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VIII, and present some additional issues in Appendices 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' THE FRAUCHIGER-RENNER THOUGHT EXPERIMENT The experimental protocol is the following (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 1): an agent F uses a quantum random generator (quantum coin) with output r ∈ {heads, tails}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The coin quantum state is |r⟩ = 1 √ 3 |h⟩ + � 2 3 |t⟩ , (1) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Sketch of the thought experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Image adapted from [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' where |h⟩ and |t⟩ are the states of heads and tails re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Probabilities are therefore 1/3 for heads and 2/3 for tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' During her measurement F gets entangled with the coin, so the state of the total system including F (and her lab) becomes |Ψ⟩ = 1 √ 3 |h⟩ ��F : h � + � 2 3 |t⟩ ��F : t � , (2) using the notations [6] where ��F : h � is the state of F (and her lab) if she observes heads and ��F : t � if she observes tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Depending on the result, she prepares the spin of an electron in state |↓⟩ if r = heads or in state |→⟩ = 1 √ 2(|↓⟩ + |↑⟩) if r = tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore the total state becomes |Ψ⟩ = 1 √ 3 |h⟩ ��F : h � |↓⟩ + � 2 3 |t⟩ ��F : t � 1 √ 2 � |↓⟩ + |↑⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (3) Then, she sends this electron to a second agent F, lo- cated in an other lab isolated from F one (except during arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='03016v1 [quant-ph] 8 Jan 2023 2 the exchange of the electron assumed very short) who can measure the spin projection of that electron in the basis {|↓⟩ , |↑⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' At this point, the total system including agents themselves is in the overall entangled state |Ψ⟩ = 1 √ 3 � |h⟩ ��F : h � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � |↑⟩ |F : ↑⟩ � , (4) where |F : ↑⟩ and |F : ↓⟩ are the states of F (and her lab) observing spin up or down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Two other separate agents W and W can moreover perform measurements on the systems F and F respec- tively with respect to the basis states ��OK � = 1 √ 2 � |h⟩ ��F : h � − |t⟩ ��F : t � � , (5) ��fail � = 1 √ 2 � |h⟩ ��F : h � + |t⟩ ��F : t � � , (6) |OK⟩ = 1 √ 2 � |↓⟩ |F : ↓⟩ − |↑⟩ |F : ↑⟩ � , (7) |fail⟩ = 1 √ 2 � |↓⟩ |F : ↓⟩ + |↑⟩ |F : ↑⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (8) Here we name the “sub-experiments” that composed the thought experiment by the name of agents corresponding to the different measurements F, F, W and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' However, it should be clear that F and F, who were agents in the initial step, are then considered as systems from the point of view of W and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore the states (5)-(8) writ- ten above contain agents, labs and measured systems on which W and W are supposed to make quantum measure- ments, so that the whole ensemble of F and F agents, labs and measured systems are projected into superposi- tion states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This is clearly not feasible in practice, but the whole idea is to consider this operation feasible as a thought experiment, and to examine which consequences can be drawn from it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Formally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' considering the four situations where the ac- tive agents are either (F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' W),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' or (W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' W),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' by using and combining appropriate bases,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' |Ψ⟩ can be written equivalently as |Ψ⟩ = 1 √ 3 � |h⟩ ��F : h � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � |↑⟩ |F : ↑⟩ � (9a) = � 2 3 ��fail � |↓⟩ |F : ↓⟩ + 1 √ 6 � ��fail � − ��OK � � |↑⟩ |F : ↑⟩ (9b) = 1 √ 6 |h⟩ ��F : h � � |OK⟩ + |fail⟩ � + � 2 3 |t⟩ ��F : t � |fail⟩ (9c) = 1 √ 12 ��OK � |OK⟩ − 1 √ 12 ��OK � |fail⟩ + 1 √ 12 ��fail � |OK⟩ + √ 3 2 ��fail � |fail⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (9d) Using these four expressions for the state vector |Ψ⟩, one can deduce the following statements, which are close to the ones listed in [1]: F and F cannot get results heads and spin up [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='A] If W gets OK, then F gets spin up [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] If W gets OK, then F gets heads [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] W and W can get OK and OK with probability 1/12 [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='D] If considered all true together, it is clear that these four statements lead to a contradiction, indeed from [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='D] W and W can get OK and OK, and in that case F and F should get spin up and heads from [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] and [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C], contradicting [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' However this contradiction may likely be attributed to the undefined status of F and F, who switch between being agents (able to make quantum measurements) and systems (being acted upon by quantum measurements).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It is therefore required to clarify the definition and the role of agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' From here, several points of view exist and we are going to explore some of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' FRAUCHIGER & RENNER: GETTING A CONTRADICTION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This point of view is based on three assumptions which allow authors of Ref [1] to show a “no-go theorem”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' First assumption (Q) : This defines what an agent must do to interpret and predict measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Suppose that a system S (external to the agent) is in state |ψ⟩ of a Hilbert space at time t0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' an outcome x can be measured on S at time t with respect to a family of projectors {πx} in Heisenberg representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' If ⟨ψ| πξ |ψ⟩ = 1, then the agent can conclude that x = ξ at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' From the point of view on this individual agent, this theory looks like quantum mechanics, and it will be used successively from the “subjective” point of view of different agents, in order to get a serie of statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' First, if r = heads, the spin is in state |↓⟩, and a measurement made by agent F with respect to the basis {π↓ = |↓⟩ ⟨↓| , π↑ = |↑⟩ ⟨↑|} gives ⟨↓| π↓ |↓⟩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore agents F and F can conclude that if F gets heads, F will get spin down;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' which is logically equivalent to: if F gets spin up, F got tails, in agreement with eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (9a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' By considering successively the different pairs of agents, other statements can be obtained and lead to If F gets spin up, then F gets tails [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='A] If W gets OK, then F gets spin up [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] If F gets tails, then W gets fail [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] W and W can have OK and OK [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='D] which are either the same or logically equivalent state- ments compared to Section I (in the same order).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 3 Additional assumptions (C) and (S): These two hypotheses stipulate that agents can trust predictions made by other agents, irrespective of their status, and that all predictions apply in the same universe, avoiding Everett’s multi world interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It is under those three assumptions that a contradiction arises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Indeed, if statement [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='D] is valid, [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] implies that F gets spin up, [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='A] that F gets tails, and [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] that W gets fail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The last statement clearly contradicts the starting point that W gets OK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Using their assumptions as just shown, the authors of [1] can thus formulate the following no-go theorem: (Q) + (C) + (S) ⇒ Contradiction (10) which has been formulated as the statement “quantum theory cannot consistently describe the use of itself” [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' REMOVING THE CONTRADICTION BY AN AGREEMENT BETWEEN AGENTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' A major remark is that, though it is presented as equivalent to quantum mechanics (QM), the assumption (Q) of Frauchiger and Renner implies a very unusual use of the quantum formalism, where “self-proclaimed” agents may become systems for other agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It means that the usual measurement postulate can hardly be applied in a consistent way [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' A simple way to remove this problem, and also the contradiction, is to consider the additional assumption (A) All agents must agree on the definition of the quantum system to which they apply assumption (Q);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' as a consequence, no agent should be included in what another agent considers as the measured system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The second part of (A), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' that no agent should be included in what another agent considers as the measured system, is a joint consequence of (Q), stating that the agents apply QM to a system external to themselves, and of the first part of (A), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' the agents agreement on the definition of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then the quantum system is the same for all agents, and contains no agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Given (A), it is clear that the previous contradiction vanishes since the four statements cannot be true to- gether: (i) if F and F are agents, the first statement is true, but then the other three make no sense since F and F cannot behave as (superposable) systems from the point of view of W and W;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (ii) if F and F are systems, then the four lines corre- spond to the agents W and W making four incompatible measurements on the global system composed of F, F, the coin and the spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Incompatible measurements can- not be true together as it is usual in QM, such that there is no contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore, with all of the four assumptions, we obtain (Q) + (C) + (S) + (A) ⇒ No contradiction (11) which means that assumption (A) restricts (Q) to some safe range where no contradiction arises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This could be summarized as : “Objective quantum mechanics can de- scribe the use of itself”, where “objective” is meant as requiring a mutual agreement between all the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In the following we will develop these arguments, and in particular give more justifications and illustrations of the points (i) and (ii) above, as well as some intermediary situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We will also see that assumption (A) can take different forms depending on which point of view we adopt, but always removes the contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' LOOKING AT W AND W AS AGENTS: LINK TO HARDY’S PARADOX The Frauchiger and Renner (F&R) paradox is, as it was pointed out by Bub [4], not only a new formulation of Wigner’s friend experiment but also a twisted version of Hardy’s paradox originally presented to show a similar result as Bell’s theorem [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' To do that, Hardy [5] used a Mach-Zehnder interferometer for electrons and positrons in order to get four entangled states which are similar to those of the F&R Gedankenexperiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The differ- ence arises only with the way one imposes that these four statements must be true together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In the following, we will assume that a hidden variable exists to describe the various states of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (9), in agreement with the for- mulation proposed in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Let λ be the hidden variable which describes the states before measurements and assume that QM is a local re- alist theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It means that results of measurements do not depend on the choice of measurement done by other agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We introduce notations F(h, λ) = 1 if F mea- sures the state |h⟩, and F(h, λ) = 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The same notations will be applied to other agents and their re- spective measurable states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The statements obtained in the preceding sections can be recovered using the expres- sions of |Ψ⟩ in the different bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Indeed, from (9a) and for every experiment described by a given value of λ, F(h, λ)F(↑, λ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (12) From (9b) we additionally have if W(OK, λ) = 1 then F(↑, λ) = 1, (13) from (9c) if W(OK, λ) = 1 then F(h, λ) = 1, (14) and from (9d) W(OK, λ)W(OK, λ) = 1 for 1/12th of experiments, (15) which can be summed up in the four following statements completely equivalent to [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='A]-[1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='D]: 4 F(h, λ) and F(↑, λ) cannot occur at the same time W(OK, λ) is true ⇒ F(↑, λ) is true W(OK, λ) is true ⇒ F(h, λ) is true W(OK, λ) and W(OK, λ) occur one time out of 12 One can see that even if the assumptions and conse- quently the formalism are not exactly the same, the con- tradiction arises in the same way as when the four states of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (9) are considered simultaneously true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In that case inspired by Hardy’s paradox, this is due to the hid- den variable hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore, it appears that in both situation, the contradiction is not due to QM itself but to the assumption that all conclusions drawn from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (9) are simultaneously true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This explains why the use of assumption (A) removes the contradiction, by making clear that they are incompatible in a quantum sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' TEXTBOOK QM: PROJECTIVE MEASUREMENTS DEFINE AGENTS Another approach to the F&R contradiction can be found in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This point of view stipulates that defining agents is equivalent to define where the projective mea- surements are done, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' where the state is projected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' For instance, without any projection, the state of the total system after “measurements” by F, F, W and W should be written as |Ψ⟩ = 1 √ 12 ��OK � ��W : OK � |OK⟩ |W : OK⟩ − 1 √ 12 ��OK � ��W : OK � |fail⟩ |W : fail⟩ + 1 √ 12 ��fail � ��W : fail � |OK⟩ |W : OK⟩ + √ 3 2 ��fail � ��W : fail � |fail⟩ |W : fail⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (16) In this state, all observers are entangled as if we had considered Everett’s multi-world interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then all possibilities can be investigated by choosing where the projections are made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The calculations are detailed in [6] and Appendix 2, here we simply describe qualitatively the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' First, we consider F and F as agent (point (i) of Sec- tion IV), and project states in agreement with their mea- surements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The result (see Appendix 2) is that whatever W and W measure, they cannot obtain informations on spin state or coin state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore, the statements [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] and [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] of Section III cannot be formulated and the contradiction does not arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In the second option which considers F and F as sys- tems, and only W and W as agents, W cannot say any- thing about the spin state, therefore using this way of defining agents and writing states after measurements, also prevent from any contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It is also instructive to consider the slightly modified situation where F can “protect” her result by using an other qubit stored in her lab, in such a way that it escapes to W’s measurement (refered as “hidden qubit” [6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' If F observes “heads”, the hidden qubit is in state ��G : h � and in state ��G : t � if she observes “tails”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The overall state can thus be written as |Ψ⟩ = 1 √ 3 � |h⟩ ��F : h � ��G : h � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � ��G : t � |↓⟩ |F : ↓⟩ + |t⟩ ��F : t � ��G : t � |↑⟩ |F : ↑⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (17) In the following, to simplify notations, we will replace |h⟩ ��F : h � by |h⟩, |t⟩ ��F : t � by |t⟩, |↓⟩ |F : ↓⟩ by |↓⟩ and |↑⟩ |F : ↑⟩ by |↑⟩ since agents (and their labs) are always in the state corresponding to the outcome they have mea- sured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We also condense the hidden qubit notation in |hG⟩ and |tG⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The state becomes |Ψ⟩ = 1 √ 3 � |h⟩ |hG⟩ + |t⟩ |tG⟩ � |↓⟩ + 1 √ 3 |t⟩ |tG⟩ |↑⟩ , (18) and the bases used by W and W to perform their respec- tive measurements are ��OK � = 1 √ 2(|h⟩ − |t⟩), ��fail � = 1 √ 2(|h⟩ + |t⟩), (19) |OK⟩ = 1 √ 2(|↓⟩ − |↑⟩), |fail⟩ = 1 √ 2(|↓⟩ + |↑⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (20) The global state can then be put in the form |Ψ⟩ = ��OK � |OK⟩ 1 √ 12 |hG⟩ + ��OK � |fail⟩ � 1 √ 12 |hG⟩ − 1 √ 3 |tG⟩ � + ��fail � |OK⟩ 1 √ 12 |hG⟩ + ��fail � |fail⟩ � 1 √ 12 |hG⟩ + 1 √ 3 |tG⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (21) As it was pointed out in [6], the state |tG⟩ is only corre- lated with the result |fail⟩ which is not surprising since when F sends a spin in the state |→⟩, it is orthogonal to |OK⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It means that the hidden qubit keeps a memory of F’s measurement and therefore all statements derived before do not hold anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We emphasize that there is no need to read out the value of the hidden qubit: as in an interference experiment, it is enough that the “which path information” is stored somewhere to forbid the quantum superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It is also interesting to investigate different scenarii for the two accessible states of the hidden qubit e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' if ⟨hG|tG⟩ = 1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' |hG⟩ and |tG⟩ are the same state, de- noted for instance |G⟩, then the overall system is in the 5 following state |Ψ⟩ = 1 √ 12 ��OK � |OK⟩ |G⟩ − 1 √ 12 ��OK � |fail⟩ |G⟩ + 1 √ 12 ��fail � |OK⟩ |G⟩ + √ 3 2 ��fail � |fail⟩ |G⟩ , (22) which is the same as state (9d) without the hidden qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' |G⟩ can be factored out and the hidden qubit plays no role since it is no more entangled with F’s results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Otherwise, if ⟨hG|tG⟩ = 0 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' the qubit states are orthogonal and the overall state is identical to (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' If we project this global state onto each state of the hidden qubit ⟨hG|Ψ⟩ = 1 √ 12 � ��OK � |OK⟩ + ��OK � |fail⟩ + ��fail � |OK⟩ + ��fail � |fail⟩ � = 1 √ 3 |h⟩|F : h⟩|OK⟩ + |fail⟩ √ 2 , (23) ⟨tG|Ψ⟩ = 1 √ 3 � ��fail � |fail⟩ − ��OK � |fail⟩ � = � 2 3 |t⟩ ��F : t � |fail⟩ , (24) we recover the situation where F is an agent, and W cannot project her in a superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This calculation has two consequences: first, it gives a way to make a transition between the different options, by allowing ⟨hG|tG⟩ to take any value between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We emphasize that this calculation makes sense in a framework where the only agents are W and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' If ⟨hG|tG⟩ = 0 then F and F should be considered as decohered systems, as they appear in the usual theory of decoherence after tracing out the “ancilla” qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Second, it provides a “toy model” for a situation where a system actually does not behave as such: if W tries to make a projective measurement on F, including her lab and all the surrounding environment, it is enough that a single qubit escapes from the action of W to make the projective measurement failed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' When F is a macroscopic system, it can be considered impossible for W to get full control on every single qubit entangled with F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' then considering F as a system makes no sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Following the idea of Section IV, this can be seen as a reformulation of assumption (A): (A) All agents must agree on the definition of the quan- tum system to which they apply assumption (Q), that is to say where the state projection is done;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' as a consequence, no agent should be included in what another agent con- siders as the measured system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' CONTEXTS, SYSTEMS AND MODALITIES: THE CSM APPROACH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Here, we want to show that in the framework of the CSM (Contexts, Systems and Modalities) approach, de- velopped by A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Auff`eves and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Grangier [8–11], the as- sumption (A) introduced and discussed above is no more an assumption but a theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We recall some basics of CSM which starts with a new physical ontology (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' a definition of all objects that are described by the theory), by considering three entities: System = subpart of the world, isolated well enough to have physical properties that can be studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Context = all other physical systems external and possibly in contact with the studied one (ex: mea- surement apparatus, labs, etc);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' in CSM, the con- text corresponds to a classically defined measure- ment setup, and it acts like an interface between the system and the observer, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Modalities = the set of answers (or values) that can be predicted with certainty and obtained re- peatedly for a given system in a given context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' These definitions are bound together by the following rule (or axiom): in quantum mechanics, modalities are at- tributed jointly to the system and the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It means that the quantum properties of a system do not “belong” to the system alone, but to the system within a context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In order to give an operational content to CSM, we need a second axiom called Quantization Principle: (i) For each well-defined system and context, there is a discrete number N of mutually exclusive modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This number N depends on the system, but does not depend on any particular context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (ii) Modalities, when defined in different contexts, are generally not mutually exclusive, and they are said to be “incompatible”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' CSM is based on a physically realistic point of view, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' physics is applied to objects which exist independently from any observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' However, the “object” for CSM is a system within a context, which makes it highly non- classical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' As it can be shown on Figure 2(c), in CSM the observer is outside of the context, illustrating again that the (objective) state of the context must be taken into account in defining the modality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Such a “contextual objectivity” [8] is quite different from the classical “abso- lute objectivity” of Figure 2(a), but it fully agrees with quantum reality as deduced from empirical evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Now, coming back to the original problem, CSM was hidden so far but in fact already there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In order to define systems and contexts according to CSM, we have to avoid mixing notations between agents, labs and experimental set ups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' First, as it was pointed out before, 6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Graphic representations of different ontologies: (a) Classical ontology: the observer can know the “real” phys- ical properties of the system, and the context is only used as an auxiliary tool for measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (b) Usual quantum on- tology: through successive “entangling” interactions and uni- tary evolution, the system will include the context, and also (ultimately) the observer or “agent”, whose status may be problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (c) CSM ontology: the context appears always between the system and the observer, and definite values of the relevant physical properties (modalities) are attributed jointly to the system and the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (o) Naive way to see Wigner’s friends thought ex- periment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Such a picture is impossible for CSM, because a (quantum) system cannot include a (classical) context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (i) Case where F and F are agents making quantum measure- ments on systems with their “own” classical contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (ii) Second option where F and F are considered as systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' there is only one ultimate reality which imposes that a context cannot be included in a system and vice versa (see Figure 3 (o)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' For consistency, different agents must agree on the definition of systems and contexts which is exactly the purpose of assumption (A), formulated according to CSM as: (A) All agents must agree on the definition of the system and context to which they apply assumption (Q);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' as a consequence, no agent should be included in what another agent considers as the measured system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Again, several cases are possible, corresponding e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' to point (i) and (ii) of Section IV, and are drawn in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In case (i), F and F perform quantum measurements on their systems within their respective contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then W and W cannot make quantum measurements on them (composite systems in yellow and orange dash lines of Figure 3), and the F&R reasoning does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In case (ii), F and F are considered as systems so W and W can perform quantum measurements on those systems in two different contexts on each side (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' projecting F or F in superposed or non-superposed states).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The modalities defined in these different contexts are incompatible and thus not simultaneously true, no contradiction can arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' To conclude, we have shown that within the CSM in- terpretation, the F&R contradiction is removed without additional assumption because CSM is already an “con- textually objective” theory [8], where agents cannot be- come systems for other agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' CONCLUSION To conclude, we have presented several ways to escape the “no-go theorem” introduced by F&R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Our arguments can be summed up by “Contextually objective quan- tum mechanics can describe the use of itself”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This statement does not allow every single world inter- pretation of quantum mechanics to be self-consistent, but only those which rely on some form of objectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' A con- sequence is that the (single world) quantum rules must introduce a clear distinction between agents and systems, embedded in the additional assumption (A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then we have shown that in the framework of CSM approach, no F&R contradiction can arise since CSM already contains (A) as a theorem, deduced from the central concept of contextual objectivity [8] which governs quantum mea- surements in the CSM framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' APPENDIX 1: ABOUT THE TIME EVOLUTION OF THE EXPERIMENT In their article [1], F&R insist on the temporal order of measurements made by successive agents, associated to changing the status of F and F between system and context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In the CSM interpretation, changing the agents status in a same experiment cannot occur, therefore the chronology is not relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It could be if we had adopted Everett’s point of view also called “multi-world”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' but this interpretation is in conflict with assumption (S), so the F&R no-go theorem also does not apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 7 More precisely, through the usual quantum or CSM point of view, an ideal measurement takes place as fol- lows: (a) entanglement of the system with the pointer (also quantum) and then (b) reading of the pointer, which brings the result at the single classical context level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' From the Everett’s point of view, there is no single classical context level but many possible results which are associated to differents universe branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then it is, in principle, possible to reverse the evolution of these branches, rewriting the history as if no measurement were done, and to make another different measurement, cre- ating again new branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' So in Everett’s point of view, temporal order makes sense to describe first a measure- ment by F, and then its “erasure” by W, followed by a new measurement in the (OK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' fail) basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In CSM, the measurement can be reversed only if it has not reached the context level, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' between steps (a) and (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' When the measurement is over (step b), the result is macroscopic and unique and the modalities cor- responding to other results in other contexts cannot co- exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Explicitly, if F and F are superposable systems, we can measure them in superposed bases S = {OK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' fail}, S = {OK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' fail} or in non superposed ones N = {heads;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' tails}, N = {up;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' down}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The four situations we have discussed correspond to four combined measurements (N, N), (N, S), (S, N), (S, S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In that case, temporal order is not relevant since only one of these four measurements can be made, as in Hardy’s paradox, such that there is a unique objective macro- scopic world in which QM is consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' We note also that the CSM point of view makes a clear distinction between the usual “pre-measurement” stage, that is entangling the system with a probe in a reversible way, and the actual irreversible measurement that brings the result to the context level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' It can be told that the F&R paradox fails because it mixes these two stages in an inappropriate way, as explained in details in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' APPENDIX 2: ADDING A HIDDEN QUBIT Another approach to the F&R contradiction can be found in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' This point of view stipulates that defining agents is equivalent to define where projective measure- ments are done, that is to say, where mathematically the state is projected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' For instance, without any projection, the state of the total system after “measurements” by F, F, W and W is |Ψ⟩ = 1 √ 12 ��OK � ��W : OK � |OK⟩ |W : OK⟩ − 1 √ 12 ��OK � ��W : OK � |fail⟩ |W : fail⟩ + 1 √ 12 ��fail � ��W : fail � |OK⟩ |W : OK⟩ + √ 3 2 ��fail � ��W : fail � |fail⟩ |W : fail⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (25) In this state, all observers are entangled as if we had considered Everett’s multi-world interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then all possibilities can be investigated for the pro- jections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' First, we consider F and F as agent (point (i) of Section IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore, they have to project states in agreement with their measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' According to F, two states are available |Ψ⟩tails = |t⟩ ��F : t � 1 √ 2 � |↓⟩ + |↑⟩ � , (26) |Ψ⟩heads = |h⟩ ��F : h � |↓⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (27) If then we consider F’s projections which lead to many cases depending of the result she gets but also of F’s results,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' we have the states |Ψ↓⟩tails = |t⟩ ��F : t � |↓⟩ |F : ↓⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (28) |Ψ↑⟩tails = |t⟩ ��F : t � |↑⟩ |F : ↑⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (29) |Ψ↓⟩heads = |h⟩ ��F : h � |↓⟩ |F : ↓⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (30) or equivalently written in the other bases |Ψ↓⟩tails = 1 2 � ��fail � − ��OK � �� |fail⟩ + |OK⟩ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (31) |Ψ↑⟩tails = 1 2 � ��fail � − ��OK � �� |fail⟩ − |OK⟩ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (32) |Ψ↓⟩heads = 1 2 � ��fail � + ��OK � �� |fail⟩ − |OK⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (33) Here we see that all these states are products;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' whatever W and W measure, they cannot obtain informations on spin state or coin state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore, statements [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] and [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] of Section III are wrong and no contradiction can appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' The second option is to consider F and F as systems, and W and W as agents (point (ii) of Section IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Be- fore they perform measurements, the system is in state (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Then, two outcomes are possible for W and give the states |Ψ⟩OK = − |↑⟩ |F : ↑⟩ ��OK � ��W : OK � = 1 √ 2 � |OK⟩ − |fail⟩ � ��OK � ��W : OK � , (34) |Ψ⟩fail = � 2 |↓⟩ |F : ↓⟩ + |↑⟩ |F : ↑⟩ � ��fail � ��W : fail � = � 3 √ 2 |fail⟩ |W : fail⟩ + 1 √ 2 |OK⟩ |W : OK⟩ � ⊗ ��fail � ��W : fail � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (35) 8 We see again, that the result OK is only correlated to spin up, and that W cannot predict anything on W’s measurement since both results OK and fail are still available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' In the second option where W gets fail, no predictions can be obtained about the spin state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' If we furthemore add the projection made by W we obtain |ΨOK⟩OK = |OK⟩ |W : OK⟩ ��OK � ��W : OK � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (36) |Ψfail⟩OK = − |fail⟩ |W : fail⟩ ��OK � ��W : OK � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (37) |ΨOK⟩fail = |OK⟩ |W : OK⟩ ��fail � ��W : fail � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (38) |Ψfail⟩fail = |fail⟩ |W : fail⟩ ��fail � ��W : fail � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (39) or equivalently expressed in F and F basis |ΨOK⟩OK = 1 2 � |h⟩ − |t⟩ �� |↓⟩ − |↑⟩ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (40) |Ψfail⟩OK = 1 2 � |h⟩ + |t⟩ �� |↑⟩ − |↓⟩ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (41) |ΨOK⟩fail = 1 2 � |h⟩ − |t⟩ �� |↓⟩ + |↑⟩ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (42) |Ψfail⟩fail = 1 2 � |h⟩ + |t⟩ �� |↓⟩ + |↑⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' (43) Again, since every state is a product state, statements [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='B] and [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='C] cannot be true and the contradiction dis- appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Therefore this way to define agents and to write states after measurements, also erases the contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Frauchiger and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Renner, “Quantum theory cannot consistently describe the use of itself” Nature Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 9, 3711 (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' a previous version is “Single-world inter- pretations of quantum theory cannot be self-consistent”, arXiv:1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='07422v1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Wigner, “Symmetries and Reflections”, chapter Re- marks on the Mind-Body Question, pages 171-184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Indi- ana University Press, 1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [3] A search on arxiv in December 2022 gives more than 50 articles commenting or criticizing [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Bub, “In a defense of a “Single World” interpretation of quantum mechanics”, arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='03267v1 (2018) [5] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Hardy, “Quantum Mechanics, Local Realistic Theo- ries, and Lorentz-Invariant Realistic Theories.”, Physical Review Letters 68, 2981 2984 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [6] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Lalo¨e, “Can quantum mechanics be considered con- sistent?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' a discussion of Frauchiger and Renner’s argu- ment.”, arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='06396v2 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Bell, On the Einstein-Podolski-Rosen paradox, Physics 1, 195 (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Grangier, “Contextual objectivity: a realistic inter- pretation of quantum mechanics”, European Journal of Physics 23:3, 331 (2002) [arXiv: quant-ph/0012122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Auff`eves and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Grangier, “Contexts, Systems and Modalities: a new ontology for quantum mechanics”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 46, 121 (2016), eprint arXiv:1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='2120 [quant-ph] (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Auff`eves and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Grangier “Deriving Born’s rule from an Inference to the Best Explanation”, Found Phys 50, 1781 (2020) [arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='13738 quant-ph] [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Grangier, “Revisiting Quantum Mysteries”, https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='org/abs/2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content='14448 [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Zukowski and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Markiewicz, “Physics and Meta- physics of Wigner’s Friends: Even Performed Premea- surements Have No Results”, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} +page_content=' 126, 130402 (2021)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE1T4oBgHgl3EQfOgOc/content/2301.03016v1.pdf'} diff --git a/ptE4T4oBgHgl3EQfUQxX/content/2301.05014v1.pdf b/ptE4T4oBgHgl3EQfUQxX/content/2301.05014v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0ea4965748b9b9d498c167acf2524c211ac80ca5 --- /dev/null +++ b/ptE4T4oBgHgl3EQfUQxX/content/2301.05014v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c34e16d1ba84bc23cfaf194b0966245e55eca76594e873929b427fd3ae453e8d +size 1230164 diff --git a/q9AyT4oBgHgl3EQfzvm4/content/2301.00707v1.pdf b/q9AyT4oBgHgl3EQfzvm4/content/2301.00707v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1ffe944f7d5b217b578af51d4659bc4fab825323 --- /dev/null +++ b/q9AyT4oBgHgl3EQfzvm4/content/2301.00707v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1b7e0d34c83d58ab6a20a5593ab35b520132db7c5a132121c65fa00ebcab37fc +size 756267 diff --git a/qNAyT4oBgHgl3EQfzfnr/vector_store/index.faiss b/qNAyT4oBgHgl3EQfzfnr/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..328ef526b68de3c4fb2ec2a50ac2b9a6465e466d --- /dev/null +++ b/qNAyT4oBgHgl3EQfzfnr/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:197d215563cc02e1ba221aec052f5c33542a1b8f025c3fc4fa4a0c31e514b105 +size 6160429 diff --git a/qNAyT4oBgHgl3EQfzfnr/vector_store/index.pkl b/qNAyT4oBgHgl3EQfzfnr/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..d09e6253369993132881ba63bfe2fd46c6606d04 --- /dev/null +++ b/qNAyT4oBgHgl3EQfzfnr/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1e77cd26a11a2576aa36ceec85afb454d02420925328c7fc41b12f3266987fb4 +size 205039 diff --git a/qNE5T4oBgHgl3EQflA99/content/2301.05667v1.pdf b/qNE5T4oBgHgl3EQflA99/content/2301.05667v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8dbdb9e4584424b9186db6ec3daf33c6fe1bc313 --- /dev/null +++ b/qNE5T4oBgHgl3EQflA99/content/2301.05667v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:215869430e252deeb0654714e26f31aa15e9daf9b45cc126b3c4552f0d077ae2 +size 1462368 diff --git a/qNE5T4oBgHgl3EQflA99/vector_store/index.pkl b/qNE5T4oBgHgl3EQflA99/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..73bdaf362fed1e5e2859bd1e9b655e7251fb9ef7 --- /dev/null +++ b/qNE5T4oBgHgl3EQflA99/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:867e334b611c6458206f95df1696745d93b684fed6209a7bdede732f36c7ed26 +size 188999 diff --git a/vtAzT4oBgHgl3EQfB_rN/vector_store/index.faiss b/vtAzT4oBgHgl3EQfB_rN/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..dacf008d4b3167d474a9e135a00a8249494644be --- /dev/null +++ b/vtAzT4oBgHgl3EQfB_rN/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:04063bfeba95500c0d3273315b275fc75540da4ba0e807921e55b6d9dc844db6 +size 5898285 diff --git a/vtFAT4oBgHgl3EQfih2j/content/2301.08600v1.pdf b/vtFAT4oBgHgl3EQfih2j/content/2301.08600v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6c7cce1f2388c00ab1f02f0a62c4cf88acc89d09 --- /dev/null +++ b/vtFAT4oBgHgl3EQfih2j/content/2301.08600v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e78f103cf43305385c990b5e15c2d38da857e32f491383e40b94b2d3a1928239 +size 394855 diff --git a/vtFAT4oBgHgl3EQfih2j/vector_store/index.pkl b/vtFAT4oBgHgl3EQfih2j/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..96cb2ad984c06cf649a8877425294ece12abc9c0 --- /dev/null +++ b/vtFAT4oBgHgl3EQfih2j/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2c774b0f9e9316128b64a87496759dc136e72a7bff2373a71441ed59750564fd +size 86477 diff --git a/w9FQT4oBgHgl3EQfwTaN/content/2301.13401v1.pdf b/w9FQT4oBgHgl3EQfwTaN/content/2301.13401v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..18219a6b998529643c741782d0b736853512dfcc --- /dev/null +++ b/w9FQT4oBgHgl3EQfwTaN/content/2301.13401v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a88a4302ac961cb9bc533fa988d3cf03d74ad6ea887272104dbc4f0413da262d +size 619618 diff --git a/w9FQT4oBgHgl3EQfwTaN/vector_store/index.pkl b/w9FQT4oBgHgl3EQfwTaN/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..d0dcfadec0a2f68c91ca4c509d56dc36792c9bb1 --- /dev/null +++ b/w9FQT4oBgHgl3EQfwTaN/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5668f1dc2ad4babd8273759c3778ecfdcd7a8606c57b21c8a9d0ce546635abf9 +size 71967 diff --git a/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/2301.00487v1.pdf.txt b/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/2301.00487v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d076a8e2645d3d4ac6b5f4882dcde52675d3f347 --- /dev/null +++ b/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/2301.00487v1.pdf.txt @@ -0,0 +1,2859 @@ +Springer Nature 2021 LATEX template +Vacuum Stability and Radiative Symmetry Breaking of the +Scale-Invariant Singlet Extension of Type II Seesaw Model +Bayu Dirgantara1, Kristjan Kannike2 and Warintorn Sreethawong1* +1*School of Physics and Center of Excellence in High Energy Physics & Astrophysics, +Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand. +2Laboratory of High Energy and Computational Physics, NICPB, R¨avala, Tallinn, 10143, +Estonia. +*Corresponding author(s). E-mail(s): warintorn.s@g.sut.ac.th; +Contributing authors: bayuquarkquantum@yahoo.com; kristjan.kannike@cern.ch; +Abstract +The questions of the origin of electroweak symmetry breaking and neutrino mass are two major puz- +zles in particle physics. Neutrino mass generation requires new physics beyond the Standard Model +and also suggests reconsideration of physics of symmetry breaking. The aim of this paper is to +study radiative symmetry breaking in the singlet scalar extension of type II seesaw neutrino mass +model. We derive bounded-from-below conditions for the scalar potential of the model in full gen- +erality for the first time. The Gildener-Weinberg approach is utilised in minimising the multiscalar +potential. Upon imposing the bounded-from-below and perturbativity conditions, as well as experi- +mental constraints from colliders, we find the parameter space of scalar quartic couplings that can +radiatively realise electroweak symmetry breaking at one-loop level. To satisfy all the constraints, +the masses of the heavy triplet-like Higgs bosons must be nearly degenerate. The evolution of the +Higgs doublet quartic coupling λH can be prevented from being negative up to the Planck scale. +Keywords: type II seesaw, Coleman-Weinberg, scale-invariant, orbit space, vacuum stability +1 Introduction +The Standard Model (SM) has achieved astound- +ing success in describing fundamental interactions +of particles, and its predictions have been per- +sistently tested to high precision. The discovery +of a Higgs boson with mass mh ≃ 125 GeV at +the Large Hadron Collider (LHC) [1, 2] seems to +provide the last missing piece of the SM. Never- +theless, unanswered puzzles such as the origin of +electroweak symmetry breaking (EWSB), the sta- +bility of the Higgs mass scale, the existence of dark +matter, and nonzero neutrino masses motivate us +to seek new physics beyond the SM (BSM). +In the SM, the electroweak symmetry is spon- +taneously broken due to the presence of a negative +mass term in the Higgs potential. This is the only +dimensionful parameter in the theory. New physi- +cal states that couple to the Higgs boson can occur +anywhere between the electroweak and the Planck +scale. Their tree-level and loop-level contributions +to the Higgs mass would have to cancel to tremen- +dous accuracy to uphold the hierarchy. Various +1 +arXiv:2301.00487v1 [hep-ph] 1 Jan 2023 + +Springer Nature 2021 LATEX template +2 +Scale-Invariant Type II Seesaw Model +extensions of the SM aiming to unravel this hier- +archy problem involve extra dimensions [3–6] or a +new symmetry such as supersymmetry [7]. +An attractive class of models addressing the +hierarchy problem stems from inspiring guidance +proposed by Bardeen [8]. If the Higgs mass param- +eter in the SM is forbidden by classical scale invari- +ance, which is broken only by quantum anomalies, +the hierarchy problem can be alleviated. (Besides +that, if we assume that physics at the Planck +scale – quantum gravity – behaves differently +from usual quantum field theory, there should +be no intermediate scale between the electroweak +scale and the Planck scale, and no instability +or Landau pole before the Planck scale [9].) In +this way, a mass scale can be dynamically gener- +ated in model with classical scale symmetry via +dimensional transmutation as first demonstrated +in a seminal paper by S. Coleman and E. Wein- +berg [10]. Unfortunately, the radiative EWSB via +the Coleman-Weinberg (CW) mechanism can not +be realized in classically scale-invariant SM since +the top quark renders the one-loop Higgs poten- +tial unbounded from below [11]. Nevertheless, a +plethora of proposals have been putting forward a +scale invariance with extended scalar sector as a +possible solution to the hierarchy problem [12–21]. +In the case of multi-field potentials, the minimum +direction can be found by the Gildener-Weinberg +(GW) method [22]. +On the other hand, the discovery of neutrino +oscillations have provided us the solid evidence +of massive neutrino [23–26]. One of the appeal- +ing BSM extensions that can naturally induce the +tiny neutrino masses is the type II seesaw model +[27–31], in which the Higgs sector is extended +by an SU(2)L Higgs triplet. A trilinear interac- +tion between the doublet and triplet Higgs plays +an important role in generating Majorana neu- +trino masses and is the source of lepton number +violation in the model. However if classical scale +invariance is imposed, this trilinear term is for- +bidden and a global lepton number symmetry will +be spontaneously broken after the triplet develops +nonzero vacuum expectation value (VEV). This +results in the emergence of a massless Goldstone +boson, a majoron [32]. Since a triplet majoron has +SU(2)L and UY (1) gauge interactions, it affects +the invisible decay width of the Z boson and has +already been ruled out [33]. A majoron that arises +predominantly from a singlet [34], however, is still +allowed. +In this work, we consider a scalar singlet exten- +sion of the type II seesaw model with a classical +scale-invariant scalar potential. This model was +originally proposed in Ref. [35] without classical +scale symmetry, and its collider phenomenology +was studied in [36, 37]. With the aid of the orbit +space of scalar quartic gauge invariants – in par- +ticular the P-matrix method [38–40] – we derive +vacuum stability constraints and study the radia- +tive EWSB along the flat direction of the tree-level +scalar potential. We find a range of VEVs and +particle masses that realises the EWSB and is +compatible with all theoretical and experimental +constraints. +This paper is organised as follows. In Sec. 2 +we briefly review the type II seesaw model and +introduce its scale-invariant singlet extension. In +Sec. 3, we determine the orbit space of the model. +In Sec. 4 we study the sufficient and necessary +conditions for the scalar potential to be bounded +from below with details given in Appendix A. In +Sec. 5, the effective potential is minimised via GW +method. We show the available parameter space +in Sec. 6 and present our conclusions in Sec. 7. +2 Scale-Invariant Extension of +the Type II Seesaw Model +Considering the SM as an effective field theory, +one can add higher-dimensional operators which +encode the effect of heavy degrees of freedom in +UV-complete theory to low energy physics. The +Weinberg operator LLHH is a unique dimension- +5 operator that can generate neutrino mass after +spontaneous symmetry breaking. The tree-level +realisations of this operator are classified into +three types of canonical seesaw models [41]. +Among the seesaw model variants, the type II see- +saw model offers a rich phenomenology to study. +However, it fails to be a scale-invariant model that +could address the hierarchy problem. In addition +to the SM-Higgs doublet mass term, there are +two additional dimensionful parameters entering +scalar potential of type II seesaw: the triplet mass +term and the trilinear coupling between doublet + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +3 +and triplet fields: +V = µ2 +HH†H + µ2 +∆ Tr +� +∆†∆ +� ++ λH(H†H)2 ++ λ∆ Tr +� +∆†∆ +�2 + λ′ +∆ Tr +� +∆†∆∆†∆ +� ++ λH∆H†H Tr +� +∆†∆ +� ++ λ′ +H∆H†∆∆†H ++ 1 +2(µHT ε∆†H + h.c.), +(1) +where H is the SM Higgs doublet with hyper- +charge Y = 1 and lepton number L = 0 and ∆ +is an SU(2) triplet with hypercharge Y = 2 and +L = −2. Notice that the presence of the trilin- +ear coupling µ explicitly breaks the lepton number +invariance. +In order to construct a classically scale- +invariant model of type II seesaw, we consider, +besides H and ∆, a complex singlet S with L = +−2. Then, the dimensionful terms in the poten- +tial can be generated when a scalar singlet S gets +a VEV. This model was originally proposed in +Ref. [35] without classical scale symmetry, its col- +lider phenomenology was studied in Refs. [36, 37] +and a recent review is given by Ref. [42]. +We parametrise the Higgs fields around the +neutral electroweak minimum as +S = +1 +√ +2(vs + SR + iSI), +(2) +H = +� +h+ +vh+φh+iχh +√ +2 +� +, +(3) +∆ ≡ ⃗σ +√ +2 · ⃗∆ = +� +δ+/ +√ +2 +δ++ +vδ+φδ+iχδ +√ +2 +−δ+/ +√ +2 +� +, +(4) +where vs, vh and vδ are the VEVs of the singlet, +doublet and triplet, respectively, and ⃗σ are the +Pauli matrices. +With classical scale invariance, the most gen- +eral renormalisable scalar potential takes the form +V = λH(H†H)2 + λS(S†S)2 ++ λ∆ Tr +� +∆†∆ +�2 + λ′ +∆ Tr +� +∆†∆∆†∆ +� ++ λH∆H†H Tr +� +∆†∆ +� ++ λ′ +H∆H†∆∆†H ++ λHSH†HS†S + λS∆S†S Tr +� +∆†∆ +� ++ 1 +2(λSH∆SHT ε∆†H + h.c.), +(5) +where all the couplings are real except λSH∆, +which we make real as well by a phase rota- +tion without loss of generality. The scale-invariant +potential (5) also respects lepton number. (See +ref. [43] for the scale-invariant type II seesaw +model with the extended gauge group U(1)B−L). +After S and ∆ develop VEVs, the global lepton +number symmetry will be spontaneously broken, +resulting in an emergence of massless Goldstone +boson – the majoron. In this case, a majoron is +mainly singlet under the SM gauge interactions. +All in all, the physical mass eigenstates comprise +the charged scalars H±± ≡ δ±± and H±, the +neutral CP-even scalars ϕ, h, H and the CP-odd +scalars J and A. The mass spectrum and mixing +matrices are given in Sec. 5.2. +3 Orbit Space +We now turn our attention to the constraints on +scalar quartic couplings required by the vacuum +stability of the scalar potential. To ensure a finite +minimum, the potential must be bounded from +below (BfB) in all possible directions of the field +space as the fields become large. In multi-scalar +theories, finding vacuum stability conditions or +potential minima is a non-trivial task. +A powerful method to deal with this is to write +the scalar potential in terms of gauge invariant +variables: the norms of fields (or their ratios) and +angular variables known as orbit space parameters +[39, 40, 44, 45]. The physical region of orbit param- +eters is called the orbit space. An elegance of +this method is that it contains all the information +needed to determine the minimum of potential. +More interestingly, when potential is monotonous +function of orbit space parameters, its minimum +is located on the boundary of the orbit space. +3.1 Orbit Space and Its Boundary +The components of a constant scalar field config- +uration φ (such as a VEV) will rotate amongst +themselves under a gauge transformation T(θ) +through a gauge orbit: φ → φθ = T(θ)φ. The value +of the scalar potential V (φ) or any other gauge- +invariant function, on the other hand, remains the +same. In particular, for a unitary group all the +states φθ have the same norm φ∗ +i φi. +For a compact group, all gauge-invariant poly- +nomials constructed of scalar fields can be given + +Springer Nature 2021 LATEX template +4 +Scale-Invariant Type II Seesaw Model +as combinations of elements of a finite polyno- +mial basis (minimal integrity basis) of the orbit +space: pa with a = 1, . . . , q. In particular, we can +write the scalar potential in terms of this basis, +whose elements comprise a finite number of gauge +invariants including the norms of fields. Because +the basis does not change under gauge transforma- +tions, a gauge orbit corresponds to a single point +in the orbit space. +The orbit space of a compact group is a +closed connected subset of Rq with q the num- +ber of the polynomials in the minimal basis. It +can be described by a finite number of polyno- +mial equations or inequalities. It is useful to reduce +the orbit space to unit norms of fields by defining +dimensionless ratios of the or orbit space variables +such as +α = fijklφ∗ +i φjφ∗ +kφl +(φ∗mφm)2 +, +(6) +where f a +ijkl denotes a gauge contraction [46–48]. +In this way, we can write the scalar potential in +terms of field norms φ∗ +mφm and the orbit space +variables. Below, it will be clear from the context +whether we mean by the orbit space the space of +the basis polynomials or the reduced space of the +dimensionless orbit variables. +Each subgroup of the full gauge group G is +the isotropy subgroup Gφ of some field configu- +ration φ. Moreover, all the transformed states φθ +have the same isotropy subgroup Gφ. The set of +orbits that respects the same isotropy subgroup is +called the stratum of the isotropy subgroup. The +VEV φ of the potential that breaks the full gauge +group G to Gφ therefore lies in the stratum of Gφ. +In the main stratum – corresponding to a general +field configuration – the gauge symmetry is com- +pletely broken, while the lower-dimensional strata +that form the orbit space boundary correspond +to more symmetrical field configurations invari- +ant under larger isotropy subgroups Gφ. The orbit +space thus consists of strata of different dimen- +sions: vertices, edges, . . . , up to the main stratum +whose dimension is given by the number of orbit +space variables. For three orbit space variables, as +in our case, the main stratum is three-dimensional +and the boundary of the orbit space has two- +dimensional faces bordered by edges which end at +the vertices of the orbit space. +We derive the boundary of the orbit space +using two methods. First of all, in a conventional +approach, the set of equations describing the +boundary of orbit space can be obtained by trial +and error by taking particular field components to +zero. +A more powerful approach is the so-called P- +matrix method [38–40]. The P-matrix is a q × +q symmetric and positive semi-definite matrix +with elements constructed from gradients of basis +invariants pa, given by +Pab = ∂pa +∂φ† +i +∂pb +∂φi +, +(7) +where φi run over the field components. Essen- +tially it is the Hermitian square of the Jacobian +matrix. It can be shown that elements of the +P-matrix can be given in terms of the minimal +integrity basis pa. +The P-matrix is positive-definite only inside +the orbit space. For that reason, the boundary of +the orbit space is obtained by solving det P = 0, +which is a polynomial equation in the basis ele- +ments pa. In particular, the orbit space vertices are +found by requiring that all the one-by-one prin- +cipal minors of the P-matrix vanish; the edges, +by requiring that the two-by-two principal minors +vanish (with the one-by-one principal minors pos- +itive); etc. When the orbit space has more than +three dimensions, then the P-matrix approach is +much more efficient. +We hope that this necessarily very cursory +overview of the orbit space may be enough for +an intuitive understanding of the next subsections +and refer the interested reader for details to the +original references [38–40]. +3.2 Orbit Space Parameters +Through the gauge invariants present in the +potential (5), we define the orbit space parameters +s, h, δ, ζ, ξ, η, α as follows1 +H†H ≡ h2, +(8) +S†S ≡ s2, +(9) +Tr +� +∆†∆ +�2 ≡ δ2, +(10) +1In Sec. 5, we denote by h the usual physical Higgs boson, +as will be clear from the context. + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +5 +(Tr ∆†∆)2 ≡ ζ Tr +� +∆†∆ +�2 , +(11) +H†∆∆†H ≡ ξ (H†H) Tr +� +∆†∆ +� +, +(12) +SHT ϵ∆†H ≡ ηeiα H†H +√ +S†S +� +Tr(∆†∆). +(13) +By considering simplest field configurations, with +most of the field components set to zero, the +ranges of these orbit parameters are found to be +0 ≤ h, +0 ≤ s, +0 ≤ δ, +1/2 ≤ ζ ≤ 1, +0 ≤ ξ ≤ 1, +0 ≤ η ≤ 1, +0 ≤ α < 2π. +(14) +In terms of orbit space parameters, the poten- +tial (5) reads +V = λHh4 + λSs4 + (λ∆ + λ′ +∆ζ)δ4 ++ (λH∆ + λ′ +H∆ξ)h2δ2 + λHSh2s2 ++ λS∆s2δ2 + |λSH∆|ηsδh2 cos α. +(15) +Because the potential (15) is linear in ξ, ζ +and η, the potential minimum is on the bound- +ary of the orbit space – more precisely, on the +intersection of the orbit space with its convex hull +[44, 49, 50]. Note that one does not have to sep- +arately minimise the potential over any flat or +concave regions of the orbit space, since such a +region is already accounted for in the convex hull +by its edges. For shortness, we will denote a vector +of the three orbit space parameters as ⃗ρ = (ξ, ζ, η). +The last term of the potential (15) satisfies +min |λSH∆|ηsδh2 cos α = −|λSH∆|ηsδh2 +(16) +in the potential minimum, so the three parameters +in ⃗ρ suffice. +In the conventional approach, we obtain four +non-trivial boundary solutions by taking all possi- +ble pairs of fields to be zero. As an example, if one +consider the direction where δ+ and h+ vanish, +one gets +lim +δ+,h+→0 η = +� +ξ, +(17) +lim +δ+,h+→0 ζ = 2η4 − 2η2 + 1. +(18) +The first boundary solution is then expressed in +parametric form as +⃗ρI = (ξ, 2ξ2 − 2ξ + 1, +� +ξ), +0 ≤ ξ ≤ 1. +(19) +The curve ⃗ρI is an edge of the orbit space. The +remaining three edges can be obtained in similar +fashion: +⃗ρII = (ξ, 1 − 2ξ2, 0), +0 ≤ ξ ≤ 1/2, +(20) +⃗ρIII = (ξ, 1, ξ), +0 ≤ ξ ≤ 1, +(21) +⃗ρIV = (1/2, 1/2, η), +0 ≤ η ≤ 1/ +√ +2. +(22) +3.3 P -matrix Approach +We will now determine the whole orbit space via +the P-matrix approach. We define gauge invariant +polynomials p1 to p6 that enter the scalar potential +as +p1 = S†S ≡ s2, +(23) +p2 = H†H ≡ h2, +(24) +p3 = tr +� +∆†∆ +� +≡ δ2, +(25) +p4 = H†∆∆†H ≡ ξh2δ2, +(26) +p5 = tr +� +∆†∆∆†∆ +� +≡ ζδ4, +(27) +p6R + ip6I = SHT ϵ∆†H ≡ ηeiαsδh2, +(28) +where the parameters ξ, ζ, η and α are the same +as in Eqs. (11)-(13). Thanks to Eq. (16), we can +consider the absolute value of p6 +|p6|2 = p2 +6R + p2 +6I = +��SHT ε∆†H +��2 += η2s2δ2h4 +(29) +instead of separate p6R and p6I. We calculate +the elements of the P-matrix defined in Eq. (7) +where pa are given by p1 to p5 and |p6|2. In gen- +eral, the P-matrix elements are gauge-invariant +quantities, and can be expressed in terms of +the gauge invariant polynomials. For the present +model, unfortunately, our polynomial basis is not +complete. To complete the basis would necessi- +tate introducing higher-order (d > 4) invariants +which would complicate things considerably. How- +ever, we can find an equation for the boundary +of the orbit space directly in terms of field com- +ponents. In this approach, we express the SU(2) +triplet as a complex traceless matrix of the form +∆ = +⃗σ +√ +2 · ⃗∆. We can use an SU(2) gauge rotation +to get rid of three real components of the triplet, +and parametrise the remaining components as +∆1 = x, +∆2 = iy, +∆3 = z, +(30) + +Springer Nature 2021 LATEX template +6 +Scale-Invariant Type II Seesaw Model +so that the norm of ∆ is given by δ2 = x2+y2+z2. +It is easy to show that the orbit space parame- +ters can in principle only depend on the difference +of the phases of the two components h1 and h2 +of the Higgs doublet. Real solutions for real com- +ponents of the fields, however, are only obtained +when the phase difference is zero. For that reason, +we take h1 and h2 to be real on the orbit space +boundary without loss of generality. The orbit +space parameters on the orbit space boundary are +given by +ξ = 1 +2 + y(h2 +1x − h2 +2x − 2h1h2z) +(h2 +1 + h2 +2)(x2 + y2 + z2), +(31) +ζ = 1 +2 + +2y2(x2 + z2) +(x2 + y2 + z2)2 , +(32) +η = +��h2 +2(y − x) + h2 +1(x + y) − 2h1h2z +�� +√ +2 +� +x2 + y2 + z2(h2 +1 + h2 +2) +. +(33) +The equation det P = 0 for the boundary of +the orbit space is then given by +y(x2 − y2 + z2) (4x2 + 4z2 + h2 +1 + h2 +2) +× [2xh1h2 + z(h2 +1 − h2 +2)] +× [(x + y)h2 +1 − 2zh1h2 + (y − x)h2 +2] = 0. +(34) +The boundary equation (34) has 8 real solutions. +Some of them are different parametrisations of the +same strata; in the end, four distinct edges are +obtained, coinciding with the results (19), (20), +(21), and (22) obtained from conventional method. +The orbit space has three vertices at the ends +of the edges: +⃗ρA = (1, 1, 1), ⃗ρB = ( 1 +2, 1 +2, 0), ⃗ρC = (0, 1, 0). (35) +The h1 = h2 → 0 limit solution gives the two- +dimensional surface of the orbit space. If we take +a section of this surface at constant ζ, we obtain a +triangle on the ξη-plane whose vertices are given +by the intersection points of the ζ = const plane +with the edge I (in two places) and edge II. The +two straight edges III and IV are the degenerate +limiting cases of this triangle at extremal values +of ζ. The vertices of the triangle at a given ζ are +given by +⃗ρ0 = +� 1 +√ +2 +� +1 − ζ, ζ, 0 +� +, +(36) +⃗ρ± = +� +1 ± √2ζ − 1 +2 +, ζ, +� +1 ± √2ζ − 1 +2 +� +, (37) +of which the triangle vertex (36) is the intersection +point of edge II, and the triangle vertices (37) are +the two crossings of edge I with the constant ζ +plane. Two-dimensional projections of the orbit +space on the ξζ-, ξη- and ζη-planes are shown in +Fig. 1. +The minimum of the potential occurs on the +convex hull of the orbit space [44, 49, 50]. Because +the cross section of the orbit space is given by a +triangle (the surface of the orbit space is a ruled +surface), the convex hull is determined by the +vertices and curved edges of the orbit space. +Only the neutral components of the Higgs +doublet and triplet should obtain VEVs. Insert- +ing these VEVs into the orbit space parameters, +we find we must require that the global mini- +mum be in the vertex ⃗ρA = (1, 1, 1) of the orbit +space. Electromagnetism is broken in the rest of +the orbit space. For example, the charge-breaking +extremum with vh/ +√ +2 = vh+, vδ++ = −vδ, and +vδ+ = 0 considered in Ref. [47] is given by ⃗ρ = +(1/2, 1/2, 1/ +√ +2) which lies on the end of edge +IV where it meets edge I (but is not a vertex). +Any extrema on other vertices and edges must +have greater potential energy than that in vertex +A. Moreover, because the edges III and IV are +straight line segments, it is not necessary to con- +sider them separately in the minimisation of the +potential. They are automatically included in the +convex hull of the orbit space by their end points. +4 Bounded-from-Below +Conditions +It is known that if quartic terms in the scalar +potential have a biquadratic λijφ2 +i φ2 +j form of real +fields or gauge orbit variables, the potential is +bounded from below if the λij matrix is copos- +itive (positive on non-negative vectors) [51–53]. +However, for our potential in (5), a complica- +tion arises due to the last term which is not +biquadratic. Note, though, that the constraints +obtained neglecting the λSH∆ are necessary con- +ditions for the potential to be BfB. +In this work, we derive the BfB conditions in a +scale-invariant singlet extention of type II seesaw +model for the first time. They cannot be given in + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +7 +0 +0.25 +0.5 +0.75 +1 +ξ +0 +0.25 +0.5 +0.75 +1 +ζ +0 +0.25 +0.5 +0.75 +1 +ξ +0 +0.25 +0.5 +0.75 +1 +η +0 +0.25 +0.5 +0.75 +1 +ζ +0 +0.25 +0.5 +0.75 +1 +η +Fig. 1 Two-dimensional projections of the orbit space on the ξζ-, ξη- and ζη-planes, respectively. Boundary solutions I, +II, III, and IV are shown in blue, green, yellow and red, respectively. The middle panel also shows the constant ζ = 2 +3 +triangular slice of the orbit space in gray. The projection on the ξη-plane is the union of such slices. The vertex A that +yields physical EWSB is projected to the upper-right corner of each plot. +a fully analytical form, but can be found semi- +numerically by solving the minimisation equations +for the fields on a sphere, the Lagrange multiplier +λ enforcing that condition, and the orbit space +variables. The details of the derivation and the +necessary and sufficient conditions on the Higgs +quartic couplings are given by in Appendix A. +5 Radiative Symmetry +Breaking +In multi-scalar theories, the treatment of radia- +tive symmetry breaking requires a special care and +general minimisation of the effective potential is a +difficult task. A method of analysing the minimum +of multi-scalar potential is devised by E. Gildener +and S. Weinberg [22]. Since scalar couplings evolve +with energy scale governed by their corresponding +renormalisation group equations (RGEs), the cen- +tral idea of Gildener-Weinberg (GW) method is +to choose a renormalisation scale µGW such that +the tree-level potential develops a continuous line +of degenerate non-trivial minima. Along this flat +direction, even small loop corrections can change +the shape of potential by developing a small cur- +vature in the radial direction. In this sense, the +GW method ensures a successful application of the +Coleman-Weinberg radiative symmetry breaking +mechanism in multi-scalar models. +5.1 Gildener-Weinberg Approach +We now apply the Gildener-Weinberg method to +our model. In the symmetry breaking vertex ⃗ρA = +(1, 1, 1) of the orbit space, the tree-level potential +(15) reads +V = λHh4 + (λH∆ + λ′ +H∆)δ2h2 ++ λHSs2h2 + λSs4 + λS∆s2δ2 ++ (λ∆ + λ′ +∆)δ4 − λSH∆sδh2. +(38) +We now set all but the components that will get +VEVs to zero, so the field norms are given by +h2 = φ2 +h +2 , +s2 = S2 +R +2 , +δ2 = φ2 +δ +2 , +(39) +and parametrise the fields as +φh = ϕ Nh, +SR = ϕ Ns, +φδ = ϕ Nδ. +(40) +where ϕ is the radial coordinate and Ni has unit +norm. At the scale µGW, the tree-level potential +admits a flat direction defined by Ni = ni. The +condition for the flat direction being a station- +ary line is given by considering the minimum with +V = 0 on the unit sphere of fields, given by the +stationary point equations +0 = λHn3 +h + 1 +2 +� +(λH∆ + λ′ +H∆)n2 +δ + λHSn2 +s +� +nh +− λSH∆ +2 +nsnδnh, +(41) +0 = (λ∆ + λ′ +∆)n3 +δ + 1 +2 +� +(λH∆ + λ′ +H∆)n2 +h ++λS∆n2 +s +� +nδ − λSH∆ +4 +nsn2 +h, +(42) +0 = λSn3 +s + 1 +2 +� +λS∆n2 +δ + λHSn2 +h +� +ns + +Springer Nature 2021 LATEX template +8 +Scale-Invariant Type II Seesaw Model +− λSH∆ +4 +nδn2 +h, +(43) +1 = n2 +h + n2 +δ + n2 +s. +(44) +Along the flat direction, a non-trivial mini- +mum can be obtained by minimising the one-loop +effective potential +Veff(ϕ) = A(⃗n)ϕ4 + B(⃗n)ϕ4 log ϕ2 +µ2 +GW +. +(45) +In the MS scheme, the dimensionless parameters +A(⃗n) and B(⃗n) read +A(⃗n) = +1 +64π2v4ϕ +� +6M 4 +W +� +log M 2 +W +v2ϕ +− 5 +6 +� ++3M 4 +Z +� +log M 2 +Z +v2ϕ +− 5 +6 +� ++ +� +i +niM 4 +Hi +� +log M 2 +Hi +v2ϕ +− 3 +2 +� +−12M 4 +t +� +log M 2 +t +v2ϕ +− 3 +2 +�� +, +(46) +B(⃗n) = +1 +64π2v4ϕ +� +6M 4 +W + 3M 4 +Z ++ +� +i +niM 4 +Hi − 12M 4 +t +� +, +(47) +where the sum runs over the number of scalar mass +eigenstates with ni = 2 for charged scalar and +ni = 1 for neutral scalar. The scalar Higgs mass +spectrum after EWSB is provided in Section 5.2. +5.2 Mass Spectrum +We calculate the scalar mass matrices and their +mixing matrices. Note that in the end the mix- +ing angles are completely determined by the flat +direction components ns, nh and nδ. +5.2.1 Mass of the neutral CP-even +Higgs +The mass-squared matrix M2 +R of the neutral CP- +even Higgs in the weak basis (SR, φh, φδ) is given +by +(M2 +R)11 = +� +2λSn2 +s + λSH∆ +4 +n2 +h +nδ +ns +� +v2 +ϕ, +(48) +(M2 +R)12 = +� +λHSnhns − λSH∆ +2 +nhnδ +� +v2 +ϕ, +(49) +(M2 +R)13 = +� +λS∆nsnδ − λSH∆ +4 +n2 +h +� +v2 +ϕ, +(50) +(M2 +R)22 = 2λHn2 +hv2 +ϕ, +(51) +(M2 +R)23 = +� +(λH∆ + λ′ +H∆)nhnδ +− λSH∆ +2 +nhnδ +� +v2 +ϕ, +(52) +(M2 +R)33 = +� +2(λ∆ + λ′ +∆)n2 +δ ++ λSH∆ +4 +n2 +h +ns +nδ +� +v2 +ϕ. +(53) +The matrix M2 +R can be diagonalised by +OR M2 +R OT +R = diag +� +m2 +ϕ, m2 +h, m2 +H +� +. +(54) +The mixing matrix OR is quite complicated, +except for its first row that is given by the flat +direction: +(OR)1 = (ns, nh, nδ). +(55) +The mass and weak eigenstates are related by +� +� +ϕ +h +H +� +� = OR +� +� +SR +φh +φδ +� +� . +(56) +5.2.2 Mass of the neutral CP-odd +Higgs +The mass-squared matrix of the neutral CP-odd +Higgs in the weak basis (SI, χh, χδ) is, after the +minimum conditions are applied, given by +M2 +I = λSH∆ +2 +v2 +ϕ +� +� +� +� +� +� +� +n2 +h +2 +nδ +ns +nhnδ +− n2 +h +2 +nhnδ 2nsnδ −nhns +− n2 +h +2 +−nhns +n2 +h +2 +ns +nδ +� +� +� +� +� +� +� +. (57) +The matrix rank of M2 +I is one and the null space +of this matrix is two-dimensional. Hence, there +are two massless fields: the unphysical Goldstone +boson G which will become the longitudinal com- +ponent of the Z boson, and the physical majoron +J. The matrix M2 +I can be diagonalised by +OI M2 +I OT +I = diag +� +0, 0, m2 +A +� +, +(58) + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +9 +where +OI = +� +� +−CI1ns(n2 +h + 4n2 +δ) CI1 2nhn2 +δ −CI1n2 +hnδ +0 +CI2 nh +CI2 2nδ +−CI3 +nδ +ns +−CI3 +2nδ +nh +CI3 +� +� +(59) +with +C−1 +I1 = +� +(n2 +h + 4n2 +δ) +× +� +(4n2sn2 +δ + n2 +h(n2s + n2 +δ)), +(60) +C−1 +I2 = +� +n2 +h + 4n2 +δ, +(61) +C−1 +I3 = +� +1 + +� 4 +n2 +h ++ 1 +n2s +� +n2 +δ. +(62) +The mass and weak eigenstates are related by +� +� +J +G +A +� +� = OI +� +� +SI +χh +χδ +� +� . +(63) +5.2.3 Mass of the singly-charged Higgs +The mass-squared matrix of the singly-charged +Higgs is +M2 +± = v2 +ϕ +4 (λSH∆nsnh − λ′ +H∆nδnh) +× +� +� +2 nδ +nh − +√ +2 +− +√ +2 +nh +nδ +� +� +(64) +in the weak basis (h±, δ±). The zero eigenvalue of +M2 +± corresponds to the charged Goldstone boson +absorbed by W ±. This mass matrix can be diag- +onalised by the orthogonal matrix O± such that +O±M2 +±OT +± = diag(mH±, 0), where +O± = +1 +� +n2 +h + 2n2 +δ +�√ +2nδ −nh +nh +√ +2nδ +� +, +(65) +and the physical charged Higgs mass is +m2 +H± = v2 +ϕ +4 (λSH∆nsnh − λ′ +H∆nhnδ) n2 +h + 2n2 +δ +nhnδ +. +(66) +5.2.4 Mass of doubly charged Higgs +Applying the tadpole condition, the mass squared +of the doubly-charged Higgs takes the form +m2 +H±± = v2 +ϕ +�λSH∆ +4 +ns +nδ +n2 +h − λ′ +∆n2 +δ − λ′ +H∆ +2 +n2 +h +� +. +(67) +5.3 Parametrisation via VEVs and +Masses +We now parametrise the quartic couplings via the +VEVs of fields and the masses of particles. The +scalar potential (5) has nine free parameters; in +addition, the flat direction component ns can be +given via other ones. On the other hand, we have +eight nonzero independent VEVs and masses: vϕ, +nh, nδ, mA, mh, mH, mH± and mH±±. +We consider the tree-level mass hierarchy +mϕ < mh < mH of the CP-even mass eigen- +states. We identify h with the SM-like Higgs with +mh = 125.25 GeV. The mass of the dilaton ϕ +is zero at tree level (note that at one-loop level, +the dilaton can become heavier than the SM-like +Higgs). +We solve the Eqs. (41), (42), (43) and (44) +together with +m2 +h + m2 +H = tr M2 +R, +(68) +m2 +hm2 +H = 1 +2 +� +(tr M2 +R)2 +− tr +� +M2 +R +�2� +, +(69) +m2 +A = tr M2 +I, +(70) +m2 +H± = tr M2 +±, +(71) +m2 +H±± = M2 +±±, +(72) +where we taken into account that the dilaton +mass is zero at tree level and that M2 +I and M2 +± +also contain zero eigenvalues – Goldstone masses.2 +Note that the equations det M2 +R = det M2 +I = +det M2 +± = 0 do not provide further constraints on +quartic couplings. +Considering, without loss of generality, only +ns > 0, the system of equations has two solutions, +2We use the three invariants of a 3 × 3 matrix M2 in +terms of its eigenvalues m2 +i , i.e. tr M2 = m2 +1 + m2 +2 + m2 +3, +tr +� +adj M2� += +1 +2 [(tr M2)2 − tr +� +M2�2] = m2 +1m2 +2 + m2 +1m2 +3 + +m2 +2m2 +3 and det M2 = m2 +1m2 +2m2 +3. + +Springer Nature 2021 LATEX template +10 +Scale-Invariant Type II Seesaw Model +of which we pick the one that tends to give per- +turbative values to quartic couplings. Because we +have nine free parameters in the potential, but +eight VEVs and masses, we have to specify the +value of one of the quartic couplings. For this we +choose λ∆, because it is more convenient to remain +within perturbativity bounds in this way. Unfor- +tunately the solutions to the above equations are +too lengthy to present explicitly. The solutions for +λ′ +∆ and λH∆ are sensitive to the value of the triplet +VEV and their expansion in Taylor series results +in inaccurate expressions. +The dilaton mass mϕ arises at one-loop level +via +mϕ = 8B(⃗n) +(73) +with B(⃗n) given by Eq. (47). All the mixing angles +of the mass matrices are also determined by the +VEVs and masses. In particular, since ϕ is the +scalon, the first row of the CP-even scalar mixing +matrix is given by the flat direction unit vector ⃗n. +6 Numerical Study +In this section, we show representative examples +of the parameter space with radiative symmetry +breaking that results in the electroweak vacuum +together with various theoretical and experimen- +tal constraints. +We fix the doublet and triplet Higgs VEVs to +the combination v ≡ +� +v2 +h + 2v2 +δ = 246.22 GeV +and the SM-like Higgs mass mh = 125.25 GeV. +For the triplet self-coupling λ∆, we use the value +λ∆ = 0.1 which is sufficient to ensure vacuum +stability but not too large so as not to run +non-perturbative at a low scale. +We consider the following experimental and +theoretical constraints on the parameter space: +• The ρ parameter; +• Electroweak precision parameters; +• Collider bounds on H++; +• Energy loss from red giants via Majorons; +• Mixing of the Higgs boson with other scalars; +• Higgs-to-Majoron decay h → JJ; +• Higgs-to-dilaton decay h → ϕϕ; +• Bounded-from-below conditions (??); +• Perturbativity of the quartic couplings in the +minimum; +• Perturbativity of couplings at the Planck scale. +As usual with a mostly singlet majoron, the Z → +ϕJ decay is negligible and does not constrain the +parameter space. +Because in the type II seesaw model the triplet +component masses commonly lie near a common +mass scale, we define as usual +δm1 = mH± −mH, +δm2 = mH±± −mH±. (74) +The triplet VEV contributes to the ρ parame- +ter ρ ≡ m2 +W /(m2 +Zc2 +W ), where cW is the cosine +of the Weinberg angle. Comparing the value ρ = +1.00038 ± 0.00020 from a global fit [54] with ρ ≈ +1 − v2 +δ/v2 from the type II seesaw, one obtains +the bound vδ ≤ 2.6 GeV at the 3σ C.L. [42]. The +mass differences of the triplet components cannot +be arbitrarily large due to constraints from the +electroweak precision parameters [55, 56]. From a +global fit on the S and T parameter (with U = 0) +[54], one obtains |δm1| ≈ |δm2| ≤ 45.5 GeV at +90% C.L. [42]. In our examples, we take δm1 = +δm2 = δm and mA = mH. +The doubly-charged scalar decays predomi- +nantly into gauge bosons for vδ > 10−4 GeV, +giving the bound on its mass mH++ ≥ 220 GeV, +while for vδ < 10−4 GeV, one has mH++ +≥ +870 GeV since then it will decay predominantly +into leptons [57]. +A strong constraint on the pseudoscalar mixing +comes from the energy loss from red giant stars via +the process γ+e− → e−+J, since the Majoron can +escape the star [58–61]. This restricts the coupling +g¯eeJ = ye +√ +2(OI)12 ≈ +√ +2me +v2 +h +v2 +δ +vs +(75) +to be within g¯eeJ ≤ 10−10 to 10−12. Since the g¯eeJ +coupling is suppressed by v2 +δ, this constraint only +requires vδ ≤ 10−1 GeV in order to be satisfied. +The mixing of the Higgs boson with other CP- +even fields, given by the |(OR)22| element of the +CP-even mixing matrix, is constrained by global +fits of the Higgs couplings and by the LEP data +[62]. +If the dilaton mass is less than mh/2, then the +SM-like Higgs boson can decay into dilatons. with +the decay width +Γh→ϕϕ = +g2 +hϕϕ +32πmh +� +1 − 4m2ϕ +m2 +h +. +(76) + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +11 +510 +25 +50 +100 +150 +200 250300350 +vφ = 1000 GeV, vδ = 0.1 GeV +500 +1000 +1500 +2000 +mH/GeV +0 +0.1 +0.2 +0.3 +|δm|/GeV +1 2.5 5 +10 +25 +50 +vφ = 5000 GeV, vδ = 0.1 GeV +500 +1000 +1500 +2000 +mH/GeV +0 +0.1 +0.2 +0.3 +|δm|/GeV +Fig. 2 The parameter space on the |δm| vs. mH plane with vδ = 0.1 GeV and λ∆ = 0.1. In the left panel, vϕ = 1000 GeV; +in the right panel, vϕ = 5000 GeV. The black lines are contours of the dilaton mass mϕ/GeV. The couplings are non- +perturbative in the red region (not perturbative up to the Planck scale in the red dotted region) and the potential is not +bounded from below in the yellow region. The blue region is forbidden by the mixing of the Higgs boson with the other fields. +If the branching ratio BRh→ϕϕ is large enough, +this significantly constrains the mixing [63]. In our +case, however, BRh→ϕϕ is small in larger part of +the parameter space, and the Higgs mixing is less +constrained. +The h → JJ decay will contribute to the Higgs +invisible width. The decay width is given by +Γh→JJ = +1 +32π +g2 +hJJ +mh +, +(77) +while the SM Higgs width is Γh→SM = 3.2 × +10−3 GeV [64]. The Higgs invisible branching ratio +is given by +BRh→inv = Γh→JJ + Γh→ϕϕBR2 +ϕ→JJ +Γh→SM + Γh→ϕϕ + Γh→JJ +, +(78) +where +BRϕ→JJ = +Γϕ→JJ +Γh→SM(mϕ)(OR)2 +12 + Γϕ→JJ +. (79) +We have (OR)12 = nh and Γh→SM(mϕ) is obtained +from [65].3 Latest measurements by the CMS +3Numerically, the second term in the numerator of Eq. (78) +is negligible. We also neglect the contribution of the triplet +experiment at the LHC find BRh→inv < 0.18 [66], +while the ATLAS experiment finds BRh→inv < +0.145 [67]; we require the latter constraint. +We have also identified the parameter space in +which the couplings remain perturbative up to the +Planck scale, by calculating the RG running with +the RGEs given in Appendix B. As initial values of +gauge couplings and top Yukawa coupling, we use +gY (Mt) = 0.35745, g2(Mt) = 0.64779, g3(Mt) = +1.1666, yt(Mt) = 0.93690 [68]. +We also comment on the fate of the Higgs dou- +blet quartic coupling from weak scale to Planck +scale. As is well known that RGE running of quar- +tic coupling in SM crosses zero around 1010 GeV +due to the strong negative contribution from the +top Yukawa term [68, 69]. The situation can be +dramatically changed with positive contributions +from additional bosons. In the case of singlet +extension of type II seesaw, there are new contri- +butions to the the Higgs quartic β-function from +the portal couplings λH∆, λ′ +H∆, and λHS. It can +be seen that in this model, the λH can remain +positive up to the Planck scale signaling that the +vacuum will be stable. +component of the dilaton to the decay with into the SM, since +it is proportional to n2 +δ. + +Springer Nature 2021 LATEX template +12 +Scale-Invariant Type II Seesaw Model +1 +2.5 +5 +10 +25 +50 +100 +250 +500 +1000 +500 +1000 +1500 +2000 +mH/GeV +1000 +2000 +3000 +4000 +5000 +vφ/GeV +Fig. 3 The parameter space on the vϕ vs. mH plane with +δm = 0 GeV. The black lines are contours of the dilaton +mass mϕ/GeV. The couplings are non-perturbative in the +red region (not perturbative up to the Planck scale in the +red dotted region). The blue region is forbidden by the +mixing of other scalars with the Higgs boson and the violet +region by the Higgs invisible width from Higgs decay into +majorons. +The parameter space in the |δm| vs. mH plane +is shown in Figure 2.4 The couplings are non- +perturbative at the weak scale in the red region +and not perturbative up to the Planck scale in the +dotted red region (in this region, a Landau pole +arises at the scale 108 GeV at the highest). The +potential is not bounded from below in the yel- +low region. Both the BfB and non-perturbativity +bounds arise from λ′ +∆ that becomes large and neg- +ative with larger |δm|. The BfB bound is mostly +due to violation of the λ∆ + λ′ +∆ > 0 condi- +tion in Eq. (??). The blue region is forbidden +by the mixing of Higgs and other scalars [62]. +The left panel of Figure 2 shows the parameter +space for vϕ = 1000 GeV; in the right panel, +vϕ = 5000 GeV, while vδ = 0.1 GeV in both cases. +For vϕ = 1000 GeV, only the lower-left corner of +the plot presents parameter space that satisfies all +the constraints. For the larger vϕ = 5000 GeV, the +Higgs-dilaton mixing is not constraining and the +couplings remain perturbative up to the Planck +scale in a larger region. +4The parameter space is practically symmetric in δm for the +range of parameters we show, so we only show positive |δm|; +in larger regions this may not hold. +Because in most cases, as we see, the mass +difference δm has to be very small, it is interest- +ing to study separately the parameter space with +δm = 0. This is shown in Fig. 3 in the vϕ vs. mH +plane with contours of the dilaton mass mϕ (black +lines). This plot is valid for any small value of vδ. +The quartic couplings are non-perturbative in the +solid red region and have a Landau pole Λ < mP +in the dotted red region. The blue region is forbid- +den by the mixing of other scalars with the Higgs +boson and the violet region by the Higgs invisible +branching ratio Eq. (78). Satisfying other con- +straints (except perturbativity up to the Planck +scale), with vϕ = 600 GeV, the Higgs quartic can +be down to 83% of its SM value. When pertur- +bativity up to the Planck scale is required, the +value differs from the SM value up to 5%. The +Higgs quartic remains positive up to the Planck +scale in the same region in which couplings remain +perturbative up to the Planck scale. +As an example, the values of quartic couplings +for three benchmark points that satisfy all con- +straints are listed in Table 1. Point A is chosen +with a small mH = 225 GeV in the region where a +vϕ = 1 TeV is allowed: in this point, λH = 0.122 is +smaller than its SM value. In points B and C, we +choose a larger vϕ = 5 TeV and the Higgs quartic +coupling is practically the same as in the SM. + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +13 +Table 1 A few benchmark points with δm = 0 GeV, vδ = 0.1 GeV and λδ = 0.1 that satisfy all constraints. +BP +mH/GeV +vϕ/GeV +vδ +λH +λ′ +∆ +λS +λHS +λH∆ +λ′ +H∆ +λS∆ +λSH∆ +A +225 +1000 +0.1 +0.122 +0.054 +5.0 × 10−4 +−0.0157 +0.338 +−1.14 × 10−8 +0.086 +3.4 × 10−4 +B +225 +5000 +0.1 +0.129 +0.0020 +7.6 × 10−7 +−6.28 × 10−4 +0.325 +−1.10 × 10−8 +0.0033 +6.6 × 10−5 +C +1000 +5000 +0.1 +0.129 +0.040 +7.6 × 10−7 +−6.28 × 10−4 +0.329 +−2.18 × 10−7 +0.0079 +1.3 × 10−3 +7 Conclusions +In this paper, we have considered the singlet +extension of type II seesaw possessing classical +scale invariance. A new scalar singlet has been +introduced, whose VEV spontaneously breaks the +global lepton number symmetry. Consequently, +the majoron – the Goldstone boson of lepton +number breaking – is mostly singlet-like. This +framework is interesting in three aspects. First, +the triplet Yukawa coupling of type II seesaw, +together with spontaneous breaking of the lep- +ton number, addresses the neutrino mass problem. +Second, a classical scale-invariant theory paves +the way to the origin of the electroweak potential +which also allows us to cure the hierarchy problem. +Last, the incorporation of a new bosonic degree of +freedom can save the vacuum of the theory from +being unstable. +In order to minimise a complicated scalar +potential, we determine and use the gauge orbit +space of the model. A full set of sufficient and +necessary conditions for the scalar potential to be +bounded from below is derived in Appendix A. +The multi-scalar potential is minimised with the +Gildener-Weinberg method. The quartic couplings +are parametrised in terms of VEVs and masses. +We showed that the perturbativity of quartic +couplings and the stability of electroweak vac- +uum can be maintained all the way up to the +Planck scale with the new contributions coming +from the singlet and triplet scalars. In particu- +lar, the evolution of λH with the energy scale +can be prevented from crossing zero value at high +energy due to sizeable contributions from λH∆ +and λ′ +H∆. In the allowed parameter space, demon- +strated in Figures 2 and 3, the mass splittings +between triplet-like states have to be almost zero. +In conclusion, we have shown in this work that +radiative symmetry breaking can be realised in the +scale-invariant singlet extension of type II seesaw +model, taking into account restrictions from col- +lider experiments and astrophysics. Due to new +scalar fields, the model has rich phenomenology. +Acknowledgments. +BD and WS acknowledge +support from Suranaree University of Technology +(SUT). BD was supported by Thailand Science +Research and Innovation and Suranaree Univer- +sity of Technology through SUT-Ph.D. Scholar- +ship Program for ASEAN. KK was supported by +the Estonian Research Council grant PRG434, by +the European Regional Development Fund and +the programme Mobilitas Pluss grant MOBTT5, +and by the EU through the European Regional +Development Fund CoE program TK133 “The +Dark Side of the Universe”. +Appendix A +Derivation of +Bounded-from- +Below +Conditions +We derive the necessary and sufficient bounded- +from-below conditions for the scalar potential. +Because the potential (15) is linear in the orbit +space variables, its minimum with respect to them +lies on the boundary of the orbit space, more pre- +cisely on the intersection of the boundary and its +convex hull. As discussed at the end of Sec. (3), it +is enough to give the conditions at the vertices A, +B and C (35) and at the edges I (19) and II (20) of +the orbit space. Notice that the end points of edge +I are vertices A and C, and the end points of edge +II are vertices B and C. If there are no physical +solution inside an edge, then the edge minimum is +at an end point. +The vertex A is already accounted for, because +we require the flat direction of the potential to lie +there. At vertices B and C and edge II, the orbit +space parameter η = 0 which makes the potential +biquadratic there. Therefore at B and C we can +derive BfB conditions by requiring copositivity of + +Springer Nature 2021 LATEX template +14 +Scale-Invariant Type II Seesaw Model +the quartic coupling matrix [70]: +Λ = +� +� +λH +1 +2(λH∆ + ξλ′ +H∆) 1 +2λHS +1 +2(λH∆ + ξλ′ +H∆) +λ∆ + ζλ′ +∆ +1 +2λS∆ +1 +2λHS +1 +2λS∆ +λS +� +� . +(A1) +The copositivity conditions for the matrix (A1) +read +λH > 0, +λ∆ + ζλ′ +∆ > 0, +λS > 0, +¯λH∆ ≡ 1 +2(λH∆ + ξλ′ +H∆) ++ +� +λH(λ∆ + ζλ′ +∆) > 0, +¯λHS ≡1 +2λHS + +� +λHλS > 0, +¯λS∆ ≡ 1 +2λS∆ + +� +λS(λ∆ + ζλ′ +∆), +� +λH(λ∆ + ζλ′ +∆)λS + 1 +2λS∆ +� +λH ++ 1 +2λHS +� +λ∆ + ζλ′ +∆ ++ 1 +2(λH∆ + ξλ′ +H∆) +� +λS ++ +� +2¯λH∆¯λHS¯λS∆ > 0. +(A2) +These conditions must hold true for the values of +orbit space variables ξ and ζ at both vertices B +and C (35). +On edge II, we can minimise the potential +(15) on a unit sphere of fields together with the +orbit variable ξ parametrising the edge and the +Lagrange multiplier λ by solving +2λs = s (2λHSh2 + 4λSs2 + 2λS∆δ2), +2λh = h [2λHSs2 + 4λHh2 ++ 2(λH∆ + ξλ′ +H∆)δ2], +2λδ = δ[2λS∆s2 + 2(λH∆ + ξλ′ +H∆)h2 ++ 4(λ∆ + (1 − 2ξ2)λ′ +∆)δ2], +0 = λ′ +H∆h2δ2 − 4ξλ′ +∆δ4, +1 = h2 + s2 + δ2. +(A3) +These equations can be solved analytically. For +each solution, one has to check whether the vari- +ables are in the physically allowed range and if +they are, check that the Lagrange parameter λ, +proportional to the potential V for this solution, +is greater than zero: +0 < h2 < 1 ∧ 0 ≤ s2 < 1 ∧ 0 < δ2 < 1 +∧ 0 < ξ < 1 +2 =⇒ V > 0. +(A4) +Notice that p =⇒ q is equivalent to ¬p ∨ q and +also that λ ∝ V for each solution. +On edge I, the minimisation equations for the +fields on a unit sphere, ξ and λ are given by +2λs = s (2λHSh2 + 4λSs2 + 2λS∆δ2) +− +� +ξ|λSH∆|h2δ, +2λh = h [2λHSs2 + 4λHh2 ++ 2(λH∆ + ξλ′ +H∆)δ2 − 2 +� +ξ|λSH∆|sδ], +2λδ = δ[2λS∆s2 + 2(λH∆ + ξλ′ +H∆)h2 ++ 4(λ∆ + (1 − 2ξ + 2ξ2)λ′ +∆)δ2] +− +� +ξ|λSH∆|h2s, +0 = h2 +� +λ′ +H∆δ2 − |λSH∆|sδ +2√ξ +� ++ 2(2ξ − 1)λ′ +∆δ4, +1 = h2 + s2 + δ2. +(A5) +These equations can only be solved numerically.5 +Similarly to the case of Eq. (A4) for edge II, one +has to check that the solutions are in the physi- +cal range before checking that V > 0 with these +arguments: +0 ≤ h < 1 ∧ 0 ≤ s < 1 ∧ 0 ≤ δ < 1 +∧ 0 < ξ < 1 =⇒ V > 0. +(A6) +Altogether, since vertex A is accounted for by the +requirement of a flat direction, the BfB conditions +can be written as +V |B > 0 ∧ V |C > 0 ∧ V |II > 0 ∧ V |I > 0, +(A7) +where the first two conditions are given by Eq. +(A2) with, respectively, the values of the orbit +variables at vertices B and C inserted, and the last +two conditions are given by Eq. (A4) which has to +be satisfied for each solution of Eq. (A3) and (A6) +which has to be satisfied for each solution of Eq. +(A5). +5Because usually λSH∆ is very small, good necessary condi- +tions are obtained by setting it to zero in Eq. (A5). + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +15 +Appendix B +RGEs of quartic +couplings +We use the PyR@TE package [71] to calculate +the beta-functions of all scalar quartic couplings, +gauge couplings and the top Yukawa coupling at +two-loop level (we have ignored all other Yukawa +couplings). For conciseness, we only provide the +one-loop results here, while in our numerical study +we use the two-loop beta-functions. The beta- +functions are given by +dλH +dt += +1 +16π2 +� +24λ2 +H + 1 +2λ2 +SH∆ + 3λ2 +H∆ ++ λ2 +HS + 3λH∆λ′ +H∆ + 5 +4λ′2 +H∆ ++3 +8g4 +1 + 9 +8g4 +2 + 3 +4g2 +1g2 +2 − (3g2 +1 + 9g2 +2)λH +− 6y4 +t + 12λHy2 +t +� +, +(B8) +dλ∆ +dt += +1 +16π2 +� +28λ2 +∆ + 24λ∆λ′ +∆ + 6λ′2 +∆ + 2λ2 +H∆ ++ 2λH∆λ′ +H∆ + λ2 +S∆ + 6g4 +1 + 15g4 +2 +−12g2 +1g2 +2 − +� +12g2 +1 + 24g2 +2 +� +λ∆ +� +, +(B9) +dλ′ +∆ +dt += +1 +16π2 +� +18λ′2 +∆ + 24λ∆λ′ +∆ + λ′2 +H∆ − 6g4 +2 ++ 24g2 +1g2 +2 − +� +12g2 +1 + 24g2 +2 +� +λ′ +∆ +� +, +(B10) +dλS +dt = +1 +16π2 +� +20λ2 +S + 2λ2 +HS + 3λ2 +S∆ +� +, +(B11) +dλH∆ +dt += +1 +16π2 +� +3g4 +1 + 6g4 +2 − 6g2 +1g2 +2 + 6λH∆y2 +t +− +�15 +2 g2 +1 + 33 +2 g2 +2 +� +λH∆ + 12λHλH∆ ++ 4λHλ′ +H∆ + 4λ2 +H∆ + 16λ∆λH∆ ++ 12λ′ +∆λH∆ + λ′2 +H∆ + 6λ∆λ′ +H∆ ++2λ′ +∆λ′ +H∆ + 2λHSλS∆ +� +, +(B12) +dλ′ +H∆ +dt += +1 +16π2 +� +12g2 +1g2 +2 − +�15 +2 g2 +1 + 33 +2 g2 +2 +� +λ′ +H∆ ++ 4λHλ′ +H∆ + 8λH∆λ′ +H∆ + 4λ′2 +H∆ ++ 4λ∆λ′ +H∆ + 8λ′ +∆λ′ +H∆ + 2λ2 +SH∆ ++ 6λ′ +H∆y2 +t +� +, +(B13) +dλHS +dt += +1 +16π2 +� +4λ2 +HS + 8λHSλS + 12λHλHS ++ 6λS∆λH∆ + 3λS∆λ′ +H∆ + 3λ2 +SH∆ +− +�3 +2g2 +1 + 9 +2g2 +2 +� +λHS + 6λHSy2 +t +� +, (B14) +dλS∆ +dt += +1 +16π2 +� +4λ2 +S∆ + λHS(4λH∆ + 2λ′ +H∆) ++ λS∆(16λ∆ + 12λ′ +∆ + 8λS) + λ2 +SH∆ +−(6g2 +1 + 12g2 +2)λS∆ +� +, +(B15) +dλSH∆ +dt += +1 +16π2 +� +4λH + 4λH∆ + 6λ′ +H∆ ++ 4λHS + 2λS∆ + 6y2 +t − 9 +2g2 +1 +− 21 +2 g2 +2 +� +λSH∆, +(B16) +where g1, g2, g3 are the gauge coupling of U(1)Y , +SU(2)L, and SU(3)c, respectively. + +Springer Nature 2021 LATEX template +16 +Scale-Invariant Type II Seesaw Model +References +[1] Aad, G., et al.: Observation of a new par- +ticle in the search for the Standard Model +Higgs boson with the ATLAS detector at +the LHC. Phys. Lett. B 716, 1–29 (2012) +arXiv:1207.7214 [hep-ex]. https://doi.org/10. +1016/j.physletb.2012.08.020 +[2] Chatrchyan, S., et al.: Observation of a New +Boson at a Mass of 125 GeV with the CMS +Experiment at the LHC. Phys. Lett. B 716, +30–61 (2012) arXiv:1207.7235 [hep-ex]. https: +//doi.org/10.1016/j.physletb.2012.08.021 +[3] Arkani-Hamed, N., Dimopoulos, S., Dvali, +G.R.: The Hierarchy problem and new dimen- +sions at a millimeter. Phys. Lett. B 429, +263–272 (1998) arXiv:hep-ph/9803315. https: +//doi.org/10.1016/S0370-2693(98)00466-3 +[4] Arkani-Hamed, +N., +Dimopoulos, +S., +Dvali, G.R.: Phenomenology, astrophysics +and +cosmology +of +theories +with +sub- +millimeter +dimensions +and +TeV +scale +quantum gravity. Phys. Rev. D 59, 086004 +(1999) +arXiv:hep-ph/9807344. +https: +//doi.org/10.1103/PhysRevD.59.086004 +[5] Randall, L., Sundrum, R.: A Large mass +hierarchy +from +a +small +extra +dimen- +sion. +Phys. +Rev. +Lett. +83, +3370–3373 +(1999) +arXiv:hep-ph/9905221. +https: +//doi.org/10.1103/PhysRevLett.83.3370 +[6] Randall, L., Sundrum, R.: An Alternative to +compactification. Phys. Rev. Lett. 83, 4690– +4693 (1999) arXiv:hep-th/9906064. https:// +doi.org/10.1103/PhysRevLett.83.4690 +[7] Martin, S.P.: A Supersymmetry primer. Adv. +Ser. Direct. High Energy Phys. 18, 1–98 +(1998) +arXiv:hep-ph/9709356. +https://doi. +org/10.1142/9789812839657 0001 +[8] Bardeen, W.A.: On naturalness in the stan- +dard model. In: Ontake Summer Institute on +Particle Physics (1995) +[9] Meissner, K.A., Nicolai, H.: Effective action, +conformal anomaly and the issue of quadratic +divergences. Phys. Lett. B 660, 260–266 +(2008) arXiv:0710.2840 [hep-th]. https://doi. +org/10.1016/j.physletb.2007.12.035 +[10] Coleman, S.R., Weinberg, E.J.: Radiative +Corrections as the Origin of Spontaneous +Symmetry +Breaking. +Phys. +Rev. +D +7, +1888–1910 (1973). https://doi.org/10.1103/ +PhysRevD.7.1888 +[11] Fujikawa, K.: Heavy Fermions in the Stan- +dard Sequential Scheme. Prog. Theor. Phys. +61, 1186 (1979). https://doi.org/10.1143/ +PTP.61.1186 +[12] Foot, R., Kobakhidze, A., Volkas, R.R.: Elec- +troweak Higgs as a pseudo-Goldstone boson +of broken scale invariance. Phys. Lett. B +655, 156–161 (2007) arXiv:0704.1165 [hep- +ph]. https://doi.org/10.1016/j.physletb.2007. +06.084 +[13] Espinosa, J.R., Quiros, M.: Novel Effects +in +Electroweak +Breaking +from +a +Hid- +den +Sector. +Phys. +Rev. +D +76, +076004 +(2007) +arXiv:hep-ph/0701145. +https://doi. +org/10.1103/PhysRevD.76.076004 +[14] Foot, R., Kobakhidze, A., McDonald, K.L., +Volkas, R.R.: A Solution to the hierarchy +problem from an almost decoupled hidden +sector within a classically scale invariant +theory. Phys. Rev. D 77, 035006 (2008) +arXiv:0709.2750 +[hep-ph]. +https://doi.org/ +10.1103/PhysRevD.77.035006 +[15] Iso, S., Okada, N., Orikasa, Y.: Classi- +cally conformal B− L extended Standard +Model. Phys. Lett. B 676, 81–87 (2009) +arXiv:0902.4050 +[hep-ph]. +https://doi.org/ +10.1016/j.physletb.2009.04.046 +[16] Foot, R., Kobakhidze, A., Volkas, R.R.: +Stable mass hierarchies and dark matter +from hidden sectors in the scale-invariant +standard model. Phys. Rev. D 82, 035005 +(2010) arXiv:1006.0131 [hep-ph]. https://doi. +org/10.1103/PhysRevD.82.035005 +[17] Alexander-Nunneley, L., Pilaftsis, A.: The +Minimal Scale Invariant Extension of the +Standard +Model. +JHEP +09, +021 +(2010) +arXiv:1006.5916 +[hep-ph]. +https://doi.org/ + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +17 +10.1007/JHEP09(2010)021 +[18] Farzinnia, A., He, H.-J., Ren, J.: Natural +Electroweak Symmetry Breaking from Scale +Invariant Higgs Mechanism. Phys. Lett. B +727, 141–150 (2013) arXiv:1308.0295 [hep- +ph]. https://doi.org/10.1016/j.physletb.2013. +09.060 +[19] Heikinheimo, +M., +Racioppi, +A., +Raidal, +M., +Spethmann, +C., +Tuominen, +K.: +Physical +Naturalness +and +Dynamical +Breaking +of +Classical +Scale +Invari- +ance. +Mod. +Phys. +Lett. +A +29, +1450077 +(2014) +arXiv:1304.7006 +[hep-ph]. +https: +//doi.org/10.1142/S0217732314500771 +[20] Karam, A., Tamvakis, K.: Dark matter and +neutrino masses from a scale-invariant multi- +Higgs portal. Phys. Rev. D 92(7), 075010 +(2015) arXiv:1508.03031 [hep-ph]. https:// +doi.org/10.1103/PhysRevD.92.075010 +[21] Ghorbani, P.H.: Electroweak phase tran- +sition +in +the +scale +invariant +standard +model. Phys. Rev. D 98(11), 115016 (2018) +arXiv:1711.11541 [hep-ph]. https://doi.org/ +10.1103/PhysRevD.98.115016 +[22] Gildener, E., Weinberg, S.: Symmetry Break- +ing and Scalar Bosons. Phys. Rev. D 13, 3333 +(1976). +https://doi.org/10.1103/PhysRevD. +13.3333 +[23] Ahmad, Q.R., et al.: Measurement of the rate +of νe + d → p + p + e− interactions pro- +duced by 8B solar neutrinos at the Sudbury +Neutrino Observatory. Phys. Rev. Lett. 87, +071301 (2001) arXiv:nucl-ex/0106015. https: +//doi.org/10.1103/PhysRevLett.87.071301 +[24] Ahmad, Q.R., et al.: Direct evidence for +neutrino flavor transformation from neutral +current interactions in the Sudbury Neutrino +Observatory. Phys. Rev. Lett. 89, 011301 +(2002) arXiv:nucl-ex/0204008. https://doi. +org/10.1103/PhysRevLett.89.011301 +[25] Ahn, +M.H., +et +al.: +Measurement +of +Neutrino +Oscillation +by +the +K2K +Experiment. +Phys. +Rev. +D +74, +072003 +(2006) +arXiv:hep-ex/0606032. +https: +//doi.org/10.1103/PhysRevD.74.072003 +[26] Eguchi, K., et al.: First results from Kam- +LAND: Evidence for reactor anti-neutrino +disappearance. Phys. Rev. Lett. 90, 021802 +(2003) +arXiv:hep-ex/0212021. +https://doi. +org/10.1103/PhysRevLett.90.021802 +[27] Magg, M., Wetterich, C.: Neutrino Mass +Problem and Gauge Hierarchy. Phys. Lett. +B 94, 61–64 (1980). https://doi.org/10.1016/ +0370-2693(80)90825-4 +[28] Schechter, J., Valle, J.W.F.: Neutrino Masses +in SU(2) x U(1) Theories. Phys. Rev. D +22, 2227 (1980). https://doi.org/10.1103/ +PhysRevD.22.2227 +[29] Cheng, T.P., Li, L.-F.: Neutrino Masses, Mix- +ings and Oscillations in SU(2) x U(1) Mod- +els of Electroweak Interactions. Phys. Rev. +D 22, 2860 (1980). https://doi.org/10.1103/ +PhysRevD.22.2860 +[30] Lazarides, +G., +Shafi, +Q., +Wetterich, +C.: +Proton Lifetime and Fermion Masses in +an +SO(10) +Model. +Nucl. +Phys. +B +181, +287–300 +(1981). +https://doi.org/10.1016/ +0550-3213(81)90354-0 +[31] Mohapatra, R.N., Senjanovic, G.: Neutrino +Masses and Mixings in Gauge Models with +Spontaneous Parity Violation. Phys. Rev. +D 23, 165 (1981). https://doi.org/10.1103/ +PhysRevD.23.165 +[32] Chikashige, Y., Mohapatra, R.N., Peccei, +R.D.: Are There Real Goldstone Bosons +Associated with Broken Lepton Number? +Phys. Lett. B 98, 265–268 (1981). https:// +doi.org/10.1016/0370-2693(81)90011-3 +[33] Gonzalez-Garcia, M.C., Nir, Y.: Implica- +tions +of +a +Precise +Measurement +of +the +Z +Width +on +the +Spontaneous +Break- +ing of Global Symmetries. Phys. Lett. B +232, +383–386 +(1989). +https://doi.org/10. +1016/0370-2693(89)90761-2 +[34] Masiero, A., Valle, J.W.F.: A Model for +Spontaneous R Parity Breaking. Phys. Lett. +B 251, 273–278 (1990). https://doi.org/10. + +Springer Nature 2021 LATEX template +18 +Scale-Invariant Type II Seesaw Model +1016/0370-2693(90)90935-Y +[35] Schechter, J., Valle, J.W.F.: Neutrino Decay +and Spontaneous Violation of Lepton Num- +ber. Phys. Rev. D 25, 774 (1982). https: +//doi.org/10.1103/PhysRevD.25.774 +[36] Diaz, M.A., Garcia-Jareno, M.A., Restrepo, +D.A., Valle, J.W.F.: Seesaw Majoron model +of neutrino mass and novel signals in Higgs +boson production at LEP. Nucl. Phys. B 527, +44–60 (1998) arXiv:hep-ph/9803362. https:// +doi.org/10.1016/S0550-3213(98)00434-9 +[37] Bonilla, C., Rom˜ao, J.C., Valle, J.W.F.: Elec- +troweak breaking and neutrino mass: ‘invis- +ible’ Higgs decays at the LHC (type II see- +saw). New J. Phys. 18(3), 033033 (2016) +arXiv:1511.07351 [hep-ph]. https://doi.org/ +10.1088/1367-2630/18/3/033033 +[38] Talamini, +V.: +Affine-P-matrices +in +orbit +spaces and invariant theory. J. Phys. Conf. +Ser. 30, 30 (2006) arXiv:hep-th/0607165. +https://doi.org/10.1088/1742-6596/30/1/ +005 +[39] Abud, M., Sartori, G.: The Geometry of +Spontaneous Symmetry Breaking. Annals +Phys. 150, 307 (1983). https://doi.org/10. +1016/0003-4916(83)90017-9 +[40] Abud, +M., +Sartori, +G.: +The +Geometry +of Orbit Space and Natural Minima of +Higgs +Potentials. +Phys. +Lett. +B +104, +147–152 +(1981). +https://doi.org/10.1016/ +0370-2693(81)90578-5 +[41] Ma, E.: Pathways to naturally small neu- +trino masses. Phys. Rev. Lett. 81, 1171– +1174 (1998) arXiv:hep-ph/9805219. https:// +doi.org/10.1103/PhysRevLett.81.1171 +[42] Mandal, S., Miranda, O.G., Sanchez Gar- +cia, G., Valle, J.W.F., Xu, X.-J.: Toward +deconstructing the simplest seesaw mecha- +nism. Phys. Rev. D 105(9), 095020 (2022) +arXiv:2203.06362 [hep-ph]. https://doi.org/ +10.1103/PhysRevD.105.095020 +[43] Okada, H., Orikasa, Y., Yagyu, K.: Higgs +Triplet Model with Classically Conformal +Invariance (2015) arXiv:1510.00799 [hep-ph] +[44] Kim, +J.: +General +Method +for +Analyz- +ing Higgs Potentials. Nucl. Phys. B 196, +285–300 +(1982). +https://doi.org/10.1016/ +0550-3213(82)90040-2 +[45] Kim, J.S.: Orbit Spaces of Low Dimensional +Representations of Simple Compact Con- +nected Lie Groups and Extrema of a Group +Invariant Scalar Potential. J. Math. Phys. +25, 1694 (1984). https://doi.org/10.1063/1. +526347 +[46] El Kaffas, A.W., Khater, W., Ogreid, O.M., +Osland, P.: Consistency of the two Higgs +doublet model and CP violation in top pro- +duction at the LHC. Nucl. Phys. B 775, +45–77 (2007) arXiv:hep-ph/0605142. https: +//doi.org/10.1016/j.nuclphysb.2007.03.041 +[47] Arhrib, A., Benbrik, R., Chabab, M., Moul- +taka, +G., +Peyranere, +M.C., +Rahili, +L., +Ramadan, J.: The Higgs Potential in the +Type +II +Seesaw +Model. +Phys. +Rev. +D +84, 095005 (2011) arXiv:1105.1925 [hep- +ph]. +https://doi.org/10.1103/PhysRevD.84. +095005 +[48] Bonilla, C., Fonseca, R.M., Valle, J.W.F.: +Consistency of the triplet seesaw model revis- +ited. Phys. Rev. D 92(7), 075028 (2015) +arXiv:1508.02323 [hep-ph]. https://doi.org/ +10.1103/PhysRevD.92.075028 +[49] Degee, A., Ivanov, I.P., Keus, V.: Geometric +minimization of highly symmetric potentials. +JHEP 02, 125 (2013) arXiv:1211.4989 [hep- +ph]. https://doi.org/10.1007/JHEP02(2013) +125 +[50] Heikinheimo, +M., +Kannike, +K., +Lyonnet, +F., Raidal, M., Tuominen, K., Veerm¨ae, +H.: Vacuum Stability and Perturbativity +of SU(3) Scalars. JHEP 10, 014 (2017) +arXiv:1707.08980 [hep-ph]. https://doi.org/ +10.1007/JHEP10(2017)014 +[51] Cottle, R.W., Habetler, G.J., Lemke, C.E.: +On +classes +of +copositive +matrices. +Lin- +ear +Algebra +and +its +Applications +3(3), +295–310 +(1970). +https://doi.org/10.1016/ + +Springer Nature 2021 LATEX template +Scale-Invariant Type II Seesaw Model +19 +0024-3795(70)90002-9 +[52] Kaplan, W.: A test for copositive matrices. +Linear Algebra and its Applications 313(1– +3), 203–206 (2000) +[53] Kannike, +K.: +Vacuum +Stability +of +a +General +Scalar +Potential +of +a +Few +Fields. +Eur. +Phys. +J. +C +76(6), +324 +(2016) +arXiv:1603.02680 +[hep-ph]. +https: +//doi.org/10.1140/epjc/s10052-016-4160-3. +[Erratum: Eur.Phys.J.C 78, 355 (2018)] +[54] Zyla, P.A., et al.: Review of Particle Physics. +PTEP 2020(8), 083–01 (2020). https://doi. +org/10.1093/ptep/ptaa104 +[55] Peskin, M.E., Takeuchi, T.: Estimation of +oblique electroweak corrections. Phys. Rev. D +46, 381–409 (1992). https://doi.org/10.1103/ +PhysRevD.46.381 +[56] Peskin, M.E., Takeuchi, T.: A New constraint +on a strongly interacting Higgs sector. Phys. +Rev. Lett. 65, 964–967 (1990). https://doi. +org/10.1103/PhysRevLett.65.964 +[57] Melfo, A., Nemevsek, M., Nesti, F., Sen- +janovic, G., Zhang, Y.: Type II Seesaw +at +LHC: +The +Roadmap. +Phys. +Rev. +D +85, 055018 (2012) arXiv:1108.4416 [hep- +ph]. +https://doi.org/10.1103/PhysRevD.85. +055018 +[58] Georgi, H.M., Glashow, S.L., Nussinov, S.: +Unconventional Model of Neutrino Masses. +Nucl. Phys. B 193, 297–316 (1981). https: +//doi.org/10.1016/0550-3213(81)90336-9 +[59] Choi, K., Santamaria, A.: Majorons and +Supernova +Cooling. +Phys. +Rev. +D +42, +293–306 +(1990). +https://doi.org/10.1103/ +PhysRevD.42.293 +[60] Montero, J.C., Sanchez-Vega, B.L.: Neutrino +masses and the scalar sector of a B-L exten- +sion of the standard model. Phys. Rev. +D 84, 053006 (2011) arXiv:1102.0321 [hep- +ph]. +https://doi.org/10.1103/PhysRevD.84. +053006 +[61] S´anchez-Vega, B.L., Montero, J.C., Schmitz, +E.R.: +Complex +Scalar +DM +in +a +B-L +Model. Phys. Rev. D 90(5), 055022 (2014) +arXiv:1404.5973 +[hep-ph]. +https://doi.org/ +10.1103/PhysRevD.90.055022 +[62] Robens, +T., +Stefaniak, +T.: +LHC +Bench- +mark +Scenarios +for +the +Real +Higgs +Singlet +Extension +of +the +Standard +Model. +Eur. +Phys. +J. +C +76(5), +268 +(2016) +arXiv:1601.07880 +[hep-ph]. +https: +//doi.org/10.1140/epjc/s10052-016-4115-8 +[63] Robens, T., Stefaniak, T.: Status of the Higgs +Singlet Extension of the Standard Model +after LHC Run 1. Eur. Phys. J. C 75, 104 +(2015) arXiv:1501.02234 [hep-ph]. https:// +doi.org/10.1140/epjc/s10052-015-3323-y +[64] Workman, R.L., Others: Review of Particle +Physics. PTEP 2022, 083–01 (2022). https: +//doi.org/10.1093/ptep/ptac097 +[65] Gomez-Bock, M., Mondragon, M., Muhlleit- +ner, M., Spira, M., Zerwas, P.M.: Concepts of +Electroweak Symmetry Breaking and Higgs +Physics. In: 4th CERN-CLAF School of High- +Energy Physics, pp. 177–238 (2007) +[66] Tumasyan, A., et al.: Search for invisible +decays of the Higgs boson produced via vec- +tor boson fusion in proton-proton collisions +at √s = 13 TeV. Phys. Rev. D 105, 092007 +(2022) arXiv:2201.11585 [hep-ex]. https:// +doi.org/10.1103/PhysRevD.105.092007 +[67] Aad, +G., +et +al.: +Search +for +invisi- +ble +Higgs-boson +decays +in +events +with +vector-boson +fusion +signatures +using +139 +fb−1 +of +proton-proton +data +recorded +by +the +ATLAS +experiment. +JHEP +08, +104 +(2022) +arXiv:2202.07953 +[hep-ex]. +https://doi.org/10.1007/JHEP08(2022)104 +[68] Buttazzo, D., Degrassi, G., Giardino, P.P., +Giudice, G.F., Sala, F., Salvio, A., Stru- +mia, A.: Investigating the near-criticality +of the Higgs boson. JHEP 12, 089 (2013) +arXiv:1307.3536 +[hep-ph]. +https://doi.org/ +10.1007/JHEP12(2013)089 +[69] Degrassi, G., Di Vita, S., Elias-Miro, J., +Espinosa, J.R., Giudice, G.F., Isidori, G., + +Springer Nature 2021 LATEX template +20 +Scale-Invariant Type II Seesaw Model +Strumia, A.: Higgs mass and vacuum stability +in the Standard Model at NNLO. JHEP 08, +098 (2012) arXiv:1205.6497 [hep-ph]. https: +//doi.org/10.1007/JHEP08(2012)098 +[70] Kannike, K.: Vacuum Stability Conditions +From +Copositivity +Criteria. +Eur. +Phys. +J. +C +72, +2093 +(2012) +arXiv:1205.3781 +[hep-ph]. +https://doi.org/10.1140/epjc/ +s10052-012-2093-z +[71] Sartore, L., Schienbein, I.: PyR@TE 3. Com- +put. Phys. Commun. 261, 107819 (2021) +arXiv:2007.12700 [hep-ph]. https://doi.org/ +10.1016/j.cpc.2020.107819 + diff --git a/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/load_file.txt b/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..76994269d71f05bf885baf298c4c333762338671 --- /dev/null +++ b/wNAyT4oBgHgl3EQfnPjX/content/tmp_files/load_file.txt @@ -0,0 +1,1300 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf,len=1299 +page_content='Springer Nature 2021 LATEX template Vacuum Stability and Radiative Symmetry Breaking of the Scale-Invariant Singlet Extension of Type II Seesaw Model Bayu Dirgantara1, Kristjan Kannike2 and Warintorn Sreethawong1* 1*School of Physics and Center of Excellence in High Energy Physics & Astrophysics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 2Laboratory of High Energy and Computational Physics, NICPB, R¨avala, Tallinn, 10143, Estonia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Corresponding author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' E-mail(s): warintorn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='s@g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='sut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='th;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Contributing authors: bayuquarkquantum@yahoo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='com;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' kristjan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='kannike@cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='ch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Abstract The questions of the origin of electroweak symmetry breaking and neutrino mass are two major puz- zles in particle physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Neutrino mass generation requires new physics beyond the Standard Model and also suggests reconsideration of physics of symmetry breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The aim of this paper is to study radiative symmetry breaking in the singlet scalar extension of type II seesaw neutrino mass model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We derive bounded-from-below conditions for the scalar potential of the model in full gen- erality for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The Gildener-Weinberg approach is utilised in minimising the multiscalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Upon imposing the bounded-from-below and perturbativity conditions, as well as experi- mental constraints from colliders, we find the parameter space of scalar quartic couplings that can radiatively realise electroweak symmetry breaking at one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' To satisfy all the constraints, the masses of the heavy triplet-like Higgs bosons must be nearly degenerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The evolution of the Higgs doublet quartic coupling λH can be prevented from being negative up to the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Keywords: type II seesaw, Coleman-Weinberg, scale-invariant, orbit space, vacuum stability 1 Introduction The Standard Model (SM) has achieved astound- ing success in describing fundamental interactions of particles, and its predictions have been per- sistently tested to high precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The discovery of a Higgs boson with mass mh ≃ 125 GeV at the Large Hadron Collider (LHC) [1, 2] seems to provide the last missing piece of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Never- theless, unanswered puzzles such as the origin of electroweak symmetry breaking (EWSB), the sta- bility of the Higgs mass scale, the existence of dark matter, and nonzero neutrino masses motivate us to seek new physics beyond the SM (BSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the SM, the electroweak symmetry is spon- taneously broken due to the presence of a negative mass term in the Higgs potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This is the only dimensionful parameter in the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' New physi- cal states that couple to the Higgs boson can occur anywhere between the electroweak and the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Their tree-level and loop-level contributions to the Higgs mass would have to cancel to tremen- dous accuracy to uphold the hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Various 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='00487v1 [hep-ph] 1 Jan 2023 Springer Nature 2021 LATEX template 2 Scale-Invariant Type II Seesaw Model extensions of the SM aiming to unravel this hier- archy problem involve extra dimensions [3–6] or a new symmetry such as supersymmetry [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' An attractive class of models addressing the hierarchy problem stems from inspiring guidance proposed by Bardeen [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' If the Higgs mass param- eter in the SM is forbidden by classical scale invari- ance, which is broken only by quantum anomalies, the hierarchy problem can be alleviated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (Besides that, if we assume that physics at the Planck scale – quantum gravity – behaves differently from usual quantum field theory, there should be no intermediate scale between the electroweak scale and the Planck scale, and no instability or Landau pole before the Planck scale [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=') In this way, a mass scale can be dynamically gener- ated in model with classical scale symmetry via dimensional transmutation as first demonstrated in a seminal paper by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Coleman and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Wein- berg [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Unfortunately, the radiative EWSB via the Coleman-Weinberg (CW) mechanism can not be realized in classically scale-invariant SM since the top quark renders the one-loop Higgs poten- tial unbounded from below [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nevertheless, a plethora of proposals have been putting forward a scale invariance with extended scalar sector as a possible solution to the hierarchy problem [12–21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the case of multi-field potentials, the minimum direction can be found by the Gildener-Weinberg (GW) method [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' On the other hand, the discovery of neutrino oscillations have provided us the solid evidence of massive neutrino [23–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' One of the appeal- ing BSM extensions that can naturally induce the tiny neutrino masses is the type II seesaw model [27–31], in which the Higgs sector is extended by an SU(2)L Higgs triplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A trilinear interac- tion between the doublet and triplet Higgs plays an important role in generating Majorana neu- trino masses and is the source of lepton number violation in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' However if classical scale invariance is imposed, this trilinear term is for- bidden and a global lepton number symmetry will be spontaneously broken after the triplet develops nonzero vacuum expectation value (VEV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This results in the emergence of a massless Goldstone boson, a majoron [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Since a triplet majoron has SU(2)L and UY (1) gauge interactions, it affects the invisible decay width of the Z boson and has already been ruled out [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A majoron that arises predominantly from a singlet [34], however, is still allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this work, we consider a scalar singlet exten- sion of the type II seesaw model with a classical scale-invariant scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This model was originally proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [35] without classical scale symmetry, and its collider phenomenology was studied in [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' With the aid of the orbit space of scalar quartic gauge invariants – in par- ticular the P-matrix method [38–40] – we derive vacuum stability constraints and study the radia- tive EWSB along the flat direction of the tree-level scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We find a range of VEVs and particle masses that realises the EWSB and is compatible with all theoretical and experimental constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 2 we briefly review the type II seesaw model and introduce its scale-invariant singlet extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3, we determine the orbit space of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 4 we study the sufficient and necessary conditions for the scalar potential to be bounded from below with details given in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5, the effective potential is minimised via GW method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We show the available parameter space in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 6 and present our conclusions in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 2 Scale-Invariant Extension of the Type II Seesaw Model Considering the SM as an effective field theory, one can add higher-dimensional operators which encode the effect of heavy degrees of freedom in UV-complete theory to low energy physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The Weinberg operator LLHH is a unique dimension- 5 operator that can generate neutrino mass after spontaneous symmetry breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The tree-level realisations of this operator are classified into three types of canonical seesaw models [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Among the seesaw model variants, the type II see- saw model offers a rich phenomenology to study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' However, it fails to be a scale-invariant model that could address the hierarchy problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In addition to the SM-Higgs doublet mass term, there are two additional dimensionful parameters entering scalar potential of type II seesaw: the triplet mass term and the trilinear coupling between doublet Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 3 and triplet fields: V = µ2 HH†H + µ2 ∆ Tr � ∆†∆ � + λH(H†H)2 + λ∆ Tr � ∆†∆ �2 + λ′ ∆ Tr � ∆†∆∆†∆ � + λH∆H†H Tr � ∆†∆ � + λ′ H∆H†∆∆†H + 1 2(µHT ε∆†H + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='), (1) where H is the SM Higgs doublet with hyper- charge Y = 1 and lepton number L = 0 and ∆ is an SU(2) triplet with hypercharge Y = 2 and L = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Notice that the presence of the trilin- ear coupling µ explicitly breaks the lepton number invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In order to construct a classically scale- invariant model of type II seesaw, we consider, besides H and ∆, a complex singlet S with L = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Then, the dimensionful terms in the poten- tial can be generated when a scalar singlet S gets a VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This model was originally proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [35] without classical scale symmetry, its col- lider phenomenology was studied in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [36, 37] and a recent review is given by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We parametrise the Higgs fields around the neutral electroweak minimum as S = 1 √ 2(vs + SR + iSI), (2) H = � h+ vh+φh+iχh √ 2 � , (3) ∆ ≡ ⃗σ √ 2 · ⃗∆ = � δ+/ √ 2 δ++ vδ+φδ+iχδ √ 2 −δ+/ √ 2 � , (4) where vs, vh and vδ are the VEVs of the singlet, doublet and triplet, respectively, and ⃗σ are the Pauli matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' With classical scale invariance, the most gen- eral renormalisable scalar potential takes the form V = λH(H†H)2 + λS(S†S)2 + λ∆ Tr � ∆†∆ �2 + λ′ ∆ Tr � ∆†∆∆†∆ � + λH∆H†H Tr � ∆†∆ � + λ′ H∆H†∆∆†H + λHSH†HS†S + λS∆S†S Tr � ∆†∆ � + 1 2(λSH∆SHT ε∆†H + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='), (5) where all the couplings are real except λSH∆, which we make real as well by a phase rota- tion without loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The scale-invariant potential (5) also respects lepton number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (See ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [43] for the scale-invariant type II seesaw model with the extended gauge group U(1)B−L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' After S and ∆ develop VEVs, the global lepton number symmetry will be spontaneously broken, resulting in an emergence of massless Goldstone boson – the majoron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this case, a majoron is mainly singlet under the SM gauge interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' All in all, the physical mass eigenstates comprise the charged scalars H±± ≡ δ±± and H±, the neutral CP-even scalars ϕ, h, H and the CP-odd scalars J and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The mass spectrum and mixing matrices are given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3 Orbit Space We now turn our attention to the constraints on scalar quartic couplings required by the vacuum stability of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' To ensure a finite minimum, the potential must be bounded from below (BfB) in all possible directions of the field space as the fields become large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In multi-scalar theories, finding vacuum stability conditions or potential minima is a non-trivial task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A powerful method to deal with this is to write the scalar potential in terms of gauge invariant variables: the norms of fields (or their ratios) and angular variables known as orbit space parameters [39, 40, 44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The physical region of orbit param- eters is called the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' An elegance of this method is that it contains all the information needed to determine the minimum of potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' More interestingly, when potential is monotonous function of orbit space parameters, its minimum is located on the boundary of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 Orbit Space and Its Boundary The components of a constant scalar field config- uration φ (such as a VEV) will rotate amongst themselves under a gauge transformation T(θ) through a gauge orbit: φ → φθ = T(θ)φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The value of the scalar potential V (φ) or any other gauge- invariant function, on the other hand, remains the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In particular, for a unitary group all the states φθ have the same norm φ∗ i φi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For a compact group, all gauge-invariant poly- nomials constructed of scalar fields can be given Springer Nature 2021 LATEX template 4 Scale-Invariant Type II Seesaw Model as combinations of elements of a finite polyno- mial basis (minimal integrity basis) of the orbit space: pa with a = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' , q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In particular, we can write the scalar potential in terms of this basis, whose elements comprise a finite number of gauge invariants including the norms of fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because the basis does not change under gauge transforma- tions, a gauge orbit corresponds to a single point in the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The orbit space of a compact group is a closed connected subset of Rq with q the num- ber of the polynomials in the minimal basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' It can be described by a finite number of polyno- mial equations or inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' It is useful to reduce the orbit space to unit norms of fields by defining dimensionless ratios of the or orbit space variables such as α = fijklφ∗ i φjφ∗ kφl (φ∗mφm)2 , (6) where f a ijkl denotes a gauge contraction [46–48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this way, we can write the scalar potential in terms of field norms φ∗ mφm and the orbit space variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Below, it will be clear from the context whether we mean by the orbit space the space of the basis polynomials or the reduced space of the dimensionless orbit variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Each subgroup of the full gauge group G is the isotropy subgroup Gφ of some field configu- ration φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Moreover, all the transformed states φθ have the same isotropy subgroup Gφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The set of orbits that respects the same isotropy subgroup is called the stratum of the isotropy subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The VEV φ of the potential that breaks the full gauge group G to Gφ therefore lies in the stratum of Gφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the main stratum – corresponding to a general field configuration – the gauge symmetry is com- pletely broken, while the lower-dimensional strata that form the orbit space boundary correspond to more symmetrical field configurations invari- ant under larger isotropy subgroups Gφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The orbit space thus consists of strata of different dimen- sions: vertices, edges, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' , up to the main stratum whose dimension is given by the number of orbit space variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For three orbit space variables, as in our case, the main stratum is three-dimensional and the boundary of the orbit space has two- dimensional faces bordered by edges which end at the vertices of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We derive the boundary of the orbit space using two methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' First of all, in a conventional approach, the set of equations describing the boundary of orbit space can be obtained by trial and error by taking particular field components to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A more powerful approach is the so-called P- matrix method [38–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The P-matrix is a q × q symmetric and positive semi-definite matrix with elements constructed from gradients of basis invariants pa, given by Pab = ∂pa ∂φ† i ∂pb ∂φi , (7) where φi run over the field components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Essen- tially it is the Hermitian square of the Jacobian matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' It can be shown that elements of the P-matrix can be given in terms of the minimal integrity basis pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The P-matrix is positive-definite only inside the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For that reason, the boundary of the orbit space is obtained by solving det P = 0, which is a polynomial equation in the basis ele- ments pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In particular, the orbit space vertices are found by requiring that all the one-by-one prin- cipal minors of the P-matrix vanish;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' the edges, by requiring that the two-by-two principal minors vanish (with the one-by-one principal minors pos- itive);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' When the orbit space has more than three dimensions, then the P-matrix approach is much more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We hope that this necessarily very cursory overview of the orbit space may be enough for an intuitive understanding of the next subsections and refer the interested reader for details to the original references [38–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 Orbit Space Parameters Through the gauge invariants present in the potential (5), we define the orbit space parameters s, h, δ, ζ, ξ, η, α as follows1 H†H ≡ h2, (8) S†S ≡ s2, (9) Tr � ∆†∆ �2 ≡ δ2, (10) 1In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5, we denote by h the usual physical Higgs boson, as will be clear from the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 5 (Tr ∆†∆)2 ≡ ζ Tr � ∆†∆ �2 , (11) H†∆∆†H ≡ ξ (H†H) Tr � ∆†∆ � , (12) SHT ϵ∆†H ≡ ηeiα H†H √ S†S � Tr(∆†∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (13) By considering simplest field configurations, with most of the field components set to zero, the ranges of these orbit parameters are found to be 0 ≤ h, 0 ≤ s, 0 ≤ δ, 1/2 ≤ ζ ≤ 1, 0 ≤ ξ ≤ 1, 0 ≤ η ≤ 1, 0 ≤ α < 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (14) In terms of orbit space parameters, the poten- tial (5) reads V = λHh4 + λSs4 + (λ∆ + λ′ ∆ζ)δ4 + (λH∆ + λ′ H∆ξ)h2δ2 + λHSh2s2 + λS∆s2δ2 + |λSH∆|ηsδh2 cos α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (15) Because the potential (15) is linear in ξ, ζ and η, the potential minimum is on the bound- ary of the orbit space – more precisely, on the intersection of the orbit space with its convex hull [44, 49, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Note that one does not have to sep- arately minimise the potential over any flat or concave regions of the orbit space, since such a region is already accounted for in the convex hull by its edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For shortness, we will denote a vector of the three orbit space parameters as ⃗ρ = (ξ, ζ, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The last term of the potential (15) satisfies min |λSH∆|ηsδh2 cos α = −|λSH∆|ηsδh2 (16) in the potential minimum, so the three parameters in ⃗ρ suffice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the conventional approach, we obtain four non-trivial boundary solutions by taking all possi- ble pairs of fields to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As an example, if one consider the direction where δ+ and h+ vanish, one gets lim δ+,h+→0 η = � ξ, (17) lim δ+,h+→0 ζ = 2η4 − 2η2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (18) The first boundary solution is then expressed in parametric form as ⃗ρI = (ξ, 2ξ2 − 2ξ + 1, � ξ), 0 ≤ ξ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (19) The curve ⃗ρI is an edge of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The remaining three edges can be obtained in similar fashion: ⃗ρII = (ξ, 1 − 2ξ2, 0), 0 ≤ ξ ≤ 1/2, (20) ⃗ρIII = (ξ, 1, ξ), 0 ≤ ξ ≤ 1, (21) ⃗ρIV = (1/2, 1/2, η), 0 ≤ η ≤ 1/ √ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (22) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 P -matrix Approach We will now determine the whole orbit space via the P-matrix approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We define gauge invariant polynomials p1 to p6 that enter the scalar potential as p1 = S†S ≡ s2, (23) p2 = H†H ≡ h2, (24) p3 = tr � ∆†∆ � ≡ δ2, (25) p4 = H†∆∆†H ≡ ξh2δ2, (26) p5 = tr � ∆†∆∆†∆ � ≡ ζδ4, (27) p6R + ip6I = SHT ϵ∆†H ≡ ηeiαsδh2, (28) where the parameters ξ, ζ, η and α are the same as in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (11)-(13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Thanks to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (16), we can consider the absolute value of p6 |p6|2 = p2 6R + p2 6I = ��SHT ε∆†H ��2 = η2s2δ2h4 (29) instead of separate p6R and p6I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We calculate the elements of the P-matrix defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (7) where pa are given by p1 to p5 and |p6|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In gen- eral, the P-matrix elements are gauge-invariant quantities, and can be expressed in terms of the gauge invariant polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For the present model, unfortunately, our polynomial basis is not complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' To complete the basis would necessi- tate introducing higher-order (d > 4) invariants which would complicate things considerably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' How- ever, we can find an equation for the boundary of the orbit space directly in terms of field com- ponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this approach, we express the SU(2) triplet as a complex traceless matrix of the form ∆ = ⃗σ √ 2 · ⃗∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We can use an SU(2) gauge rotation to get rid of three real components of the triplet, and parametrise the remaining components as ∆1 = x, ∆2 = iy, ∆3 = z, (30) Springer Nature 2021 LATEX template 6 Scale-Invariant Type II Seesaw Model so that the norm of ∆ is given by δ2 = x2+y2+z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' It is easy to show that the orbit space parame- ters can in principle only depend on the difference of the phases of the two components h1 and h2 of the Higgs doublet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Real solutions for real com- ponents of the fields, however, are only obtained when the phase difference is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For that reason, we take h1 and h2 to be real on the orbit space boundary without loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The orbit space parameters on the orbit space boundary are given by ξ = 1 2 + y(h2 1x − h2 2x − 2h1h2z) (h2 1 + h2 2)(x2 + y2 + z2), (31) ζ = 1 2 + 2y2(x2 + z2) (x2 + y2 + z2)2 , (32) η = ��h2 2(y − x) + h2 1(x + y) − 2h1h2z �� √ 2 � x2 + y2 + z2(h2 1 + h2 2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (33) The equation det P = 0 for the boundary of the orbit space is then given by y(x2 − y2 + z2) (4x2 + 4z2 + h2 1 + h2 2) × [2xh1h2 + z(h2 1 − h2 2)] × [(x + y)h2 1 − 2zh1h2 + (y − x)h2 2] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (34) The boundary equation (34) has 8 real solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Some of them are different parametrisations of the same strata;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' in the end, four distinct edges are obtained, coinciding with the results (19), (20), (21), and (22) obtained from conventional method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The orbit space has three vertices at the ends of the edges: ⃗ρA = (1, 1, 1), ⃗ρB = ( 1 2, 1 2, 0), ⃗ρC = (0, 1, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (35) The h1 = h2 → 0 limit solution gives the two- dimensional surface of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' If we take a section of this surface at constant ζ, we obtain a triangle on the ξη-plane whose vertices are given by the intersection points of the ζ = const plane with the edge I (in two places) and edge II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The two straight edges III and IV are the degenerate limiting cases of this triangle at extremal values of ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The vertices of the triangle at a given ζ are given by ⃗ρ0 = � 1 √ 2 � 1 − ζ, ζ, 0 � , (36) ⃗ρ± = � 1 ± √2ζ − 1 2 , ζ, � 1 ± √2ζ − 1 2 � , (37) of which the triangle vertex (36) is the intersection point of edge II, and the triangle vertices (37) are the two crossings of edge I with the constant ζ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Two-dimensional projections of the orbit space on the ξζ-, ξη- and ζη-planes are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The minimum of the potential occurs on the convex hull of the orbit space [44, 49, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because the cross section of the orbit space is given by a triangle (the surface of the orbit space is a ruled surface), the convex hull is determined by the vertices and curved edges of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Only the neutral components of the Higgs doublet and triplet should obtain VEVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Insert- ing these VEVs into the orbit space parameters, we find we must require that the global mini- mum be in the vertex ⃗ρA = (1, 1, 1) of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Electromagnetism is broken in the rest of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For example, the charge-breaking extremum with vh/ √ 2 = vh+, vδ++ = −vδ, and vδ+ = 0 considered in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [47] is given by ⃗ρ = (1/2, 1/2, 1/ √ 2) which lies on the end of edge IV where it meets edge I (but is not a vertex).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Any extrema on other vertices and edges must have greater potential energy than that in vertex A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Moreover, because the edges III and IV are straight line segments, it is not necessary to con- sider them separately in the minimisation of the potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' They are automatically included in the convex hull of the orbit space by their end points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 4 Bounded-from-Below Conditions It is known that if quartic terms in the scalar potential have a biquadratic λijφ2 i φ2 j form of real fields or gauge orbit variables, the potential is bounded from below if the λij matrix is copos- itive (positive on non-negative vectors) [51–53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' However, for our potential in (5), a complica- tion arises due to the last term which is not biquadratic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Note, though, that the constraints obtained neglecting the λSH∆ are necessary con- ditions for the potential to be BfB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this work, we derive the BfB conditions in a scale-invariant singlet extention of type II seesaw model for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' They cannot be given in Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 7 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 ξ 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 ζ 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 ξ 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 η 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 ζ 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='75 1 η Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 1 Two-dimensional projections of the orbit space on the ξζ-, ξη- and ζη-planes, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Boundary solutions I, II, III, and IV are shown in blue, green, yellow and red, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The middle panel also shows the constant ζ = 2 3 triangular slice of the orbit space in gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The projection on the ξη-plane is the union of such slices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The vertex A that yields physical EWSB is projected to the upper-right corner of each plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' a fully analytical form, but can be found semi- numerically by solving the minimisation equations for the fields on a sphere, the Lagrange multiplier λ enforcing that condition, and the orbit space variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The details of the derivation and the necessary and sufficient conditions on the Higgs quartic couplings are given by in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5 Radiative Symmetry Breaking In multi-scalar theories, the treatment of radia- tive symmetry breaking requires a special care and general minimisation of the effective potential is a difficult task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A method of analysing the minimum of multi-scalar potential is devised by E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Gildener and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Weinberg [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Since scalar couplings evolve with energy scale governed by their corresponding renormalisation group equations (RGEs), the cen- tral idea of Gildener-Weinberg (GW) method is to choose a renormalisation scale µGW such that the tree-level potential develops a continuous line of degenerate non-trivial minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Along this flat direction, even small loop corrections can change the shape of potential by developing a small cur- vature in the radial direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In this sense, the GW method ensures a successful application of the Coleman-Weinberg radiative symmetry breaking mechanism in multi-scalar models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 Gildener-Weinberg Approach We now apply the Gildener-Weinberg method to our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the symmetry breaking vertex ⃗ρA = (1, 1, 1) of the orbit space, the tree-level potential (15) reads V = λHh4 + (λH∆ + λ′ H∆)δ2h2 + λHSs2h2 + λSs4 + λS∆s2δ2 + (λ∆ + λ′ ∆)δ4 − λSH∆sδh2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (38) We now set all but the components that will get VEVs to zero, so the field norms are given by h2 = φ2 h 2 , s2 = S2 R 2 , δ2 = φ2 δ 2 , (39) and parametrise the fields as φh = ϕ Nh, SR = ϕ Ns, φδ = ϕ Nδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (40) where ϕ is the radial coordinate and Ni has unit norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' At the scale µGW, the tree-level potential admits a flat direction defined by Ni = ni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The condition for the flat direction being a station- ary line is given by considering the minimum with V = 0 on the unit sphere of fields,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' given by the stationary point equations 0 = λHn3 h + 1 2 � (λH∆ + λ′ H∆)n2 δ + λHSn2 s � nh − λSH∆ 2 nsnδnh,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (41) 0 = (λ∆ + λ′ ∆)n3 δ + 1 2 � (λH∆ + λ′ H∆)n2 h +λS∆n2 s � nδ − λSH∆ 4 nsn2 h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (42) 0 = λSn3 s + 1 2 � λS∆n2 δ + λHSn2 h � ns Springer Nature 2021 LATEX template 8 Scale-Invariant Type II Seesaw Model − λSH∆ 4 nδn2 h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (43) 1 = n2 h + n2 δ + n2 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (44) Along the flat direction, a non-trivial mini- mum can be obtained by minimising the one-loop effective potential Veff(ϕ) = A(⃗n)ϕ4 + B(⃗n)ϕ4 log ϕ2 µ2 GW .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (45) In the MS scheme, the dimensionless parameters A(⃗n) and B(⃗n) read A(⃗n) = 1 64π2v4ϕ � 6M 4 W � log M 2 W v2ϕ − 5 6 � +3M 4 Z � log M 2 Z v2ϕ − 5 6 � + � i niM 4 Hi � log M 2 Hi v2ϕ − 3 2 � −12M 4 t � log M 2 t v2ϕ − 3 2 �� , (46) B(⃗n) = 1 64π2v4ϕ � 6M 4 W + 3M 4 Z + � i niM 4 Hi − 12M 4 t � , (47) where the sum runs over the number of scalar mass eigenstates with ni = 2 for charged scalar and ni = 1 for neutral scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The scalar Higgs mass spectrum after EWSB is provided in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 Mass Spectrum We calculate the scalar mass matrices and their mixing matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Note that in the end the mix- ing angles are completely determined by the flat direction components ns, nh and nδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 Mass of the neutral CP-even Higgs The mass-squared matrix M2 R of the neutral CP- even Higgs in the weak basis (SR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' φh,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' φδ) is given by (M2 R)11 = � 2λSn2 s + λSH∆ 4 n2 h nδ ns � v2 ϕ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (48) (M2 R)12 = � λHSnhns − λSH∆ 2 nhnδ � v2 ϕ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (49) (M2 R)13 = � λS∆nsnδ − λSH∆ 4 n2 h � v2 ϕ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (50) (M2 R)22 = 2λHn2 hv2 ϕ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (51) (M2 R)23 = � (λH∆ + λ′ H∆)nhnδ − λSH∆ 2 nhnδ � v2 ϕ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (52) (M2 R)33 = � 2(λ∆ + λ′ ∆)n2 δ + λSH∆ 4 n2 h ns nδ � v2 ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (53) The matrix M2 R can be diagonalised by OR M2 R OT R = diag � m2 ϕ, m2 h, m2 H � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (54) The mixing matrix OR is quite complicated, except for its first row that is given by the flat direction: (OR)1 = (ns, nh, nδ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (55) The mass and weak eigenstates are related by � � ϕ h H � � = OR � � SR φh φδ � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (56) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 Mass of the neutral CP-odd Higgs The mass-squared matrix of the neutral CP-odd Higgs in the weak basis (SI, χh, χδ) is, after the minimum conditions are applied, given by M2 I = λSH∆ 2 v2 ϕ � � � � � � � n2 h 2 nδ ns nhnδ − n2 h 2 nhnδ 2nsnδ −nhns − n2 h 2 −nhns n2 h 2 ns nδ � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (57) The matrix rank of M2 I is one and the null space of this matrix is two-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Hence, there are two massless fields: the unphysical Goldstone boson G which will become the longitudinal com- ponent of the Z boson, and the physical majoron J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The matrix M2 I can be diagonalised by OI M2 I OT I = diag � 0, 0, m2 A � , (58) Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 9 where OI = � � −CI1ns(n2 h + 4n2 δ) CI1 2nhn2 δ −CI1n2 hnδ 0 CI2 nh CI2 2nδ −CI3 nδ ns −CI3 2nδ nh CI3 � � (59) with C−1 I1 = � (n2 h + 4n2 δ) × � (4n2sn2 δ + n2 h(n2s + n2 δ)), (60) C−1 I2 = � n2 h + 4n2 δ, (61) C−1 I3 = � 1 + � 4 n2 h + 1 n2s � n2 δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (62) The mass and weak eigenstates are related by � � J G A � � = OI � � SI χh χδ � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (63) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 Mass of the singly-charged Higgs The mass-squared matrix of the singly-charged Higgs is M2 ± = v2 ϕ 4 (λSH∆nsnh − λ′ H∆nδnh) × � � 2 nδ nh − √ 2 − √ 2 nh nδ � � (64) in the weak basis (h±, δ±).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The zero eigenvalue of M2 ± corresponds to the charged Goldstone boson absorbed by W ±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This mass matrix can be diag- onalised by the orthogonal matrix O± such that O±M2 ±OT ± = diag(mH±, 0), where O± = 1 � n2 h + 2n2 δ �√ 2nδ −nh nh √ 2nδ � , (65) and the physical charged Higgs mass is m2 H± = v2 ϕ 4 (λSH∆nsnh − λ′ H∆nhnδ) n2 h + 2n2 δ nhnδ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (66) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4 Mass of doubly charged Higgs Applying the tadpole condition, the mass squared of the doubly-charged Higgs takes the form m2 H±± = v2 ϕ �λSH∆ 4 ns nδ n2 h − λ′ ∆n2 δ − λ′ H∆ 2 n2 h � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (67) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 Parametrisation via VEVs and Masses We now parametrise the quartic couplings via the VEVs of fields and the masses of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The scalar potential (5) has nine free parameters;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' in addition, the flat direction component ns can be given via other ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' On the other hand, we have eight nonzero independent VEVs and masses: vϕ, nh, nδ, mA, mh, mH, mH± and mH±±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We consider the tree-level mass hierarchy mϕ < mh < mH of the CP-even mass eigen- states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We identify h with the SM-like Higgs with mh = 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The mass of the dilaton ϕ is zero at tree level (note that at one-loop level, the dilaton can become heavier than the SM-like Higgs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We solve the Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (41), (42), (43) and (44) together with m2 h + m2 H = tr M2 R, (68) m2 hm2 H = 1 2 � (tr M2 R)2 − tr � M2 R �2� , (69) m2 A = tr M2 I, (70) m2 H± = tr M2 ±, (71) m2 H±± = M2 ±±, (72) where we taken into account that the dilaton mass is zero at tree level and that M2 I and M2 ± also contain zero eigenvalues – Goldstone masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 Note that the equations det M2 R = det M2 I = det M2 ± = 0 do not provide further constraints on quartic couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Considering, without loss of generality, only ns > 0, the system of equations has two solutions, 2We use the three invariants of a 3 × 3 matrix M2 in terms of its eigenvalues m2 i , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' tr M2 = m2 1 + m2 2 + m2 3, tr � adj M2� = 1 2 [(tr M2)2 − tr � M2�2] = m2 1m2 2 + m2 1m2 3 + m2 2m2 3 and det M2 = m2 1m2 2m2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template 10 Scale-Invariant Type II Seesaw Model of which we pick the one that tends to give per- turbative values to quartic couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because we have nine free parameters in the potential, but eight VEVs and masses, we have to specify the value of one of the quartic couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For this we choose λ∆, because it is more convenient to remain within perturbativity bounds in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Unfor- tunately the solutions to the above equations are too lengthy to present explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The solutions for λ′ ∆ and λH∆ are sensitive to the value of the triplet VEV and their expansion in Taylor series results in inaccurate expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The dilaton mass mϕ arises at one-loop level via mϕ = 8B(⃗n) (73) with B(⃗n) given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' All the mixing angles of the mass matrices are also determined by the VEVs and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In particular, since ϕ is the scalon, the first row of the CP-even scalar mixing matrix is given by the flat direction unit vector ⃗n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 6 Numerical Study In this section, we show representative examples of the parameter space with radiative symmetry breaking that results in the electroweak vacuum together with various theoretical and experimen- tal constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We fix the doublet and triplet Higgs VEVs to the combination v ≡ � v2 h + 2v2 δ = 246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='22 GeV and the SM-like Higgs mass mh = 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For the triplet self-coupling λ∆, we use the value λ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 which is sufficient to ensure vacuum stability but not too large so as not to run non-perturbative at a low scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We consider the following experimental and theoretical constraints on the parameter space: The ρ parameter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Electroweak precision parameters;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Collider bounds on H++;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Energy loss from red giants via Majorons;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Mixing of the Higgs boson with other scalars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Higgs-to-Majoron decay h → JJ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Higgs-to-dilaton decay h → ϕϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Bounded-from-below conditions (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Perturbativity of the quartic couplings in the minimum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Perturbativity of couplings at the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As usual with a mostly singlet majoron, the Z → ϕJ decay is negligible and does not constrain the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because in the type II seesaw model the triplet component masses commonly lie near a common mass scale, we define as usual δm1 = mH± −mH, δm2 = mH±± −mH±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (74) The triplet VEV contributes to the ρ parame- ter ρ ≡ m2 W /(m2 Zc2 W ), where cW is the cosine of the Weinberg angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Comparing the value ρ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='00038 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='00020 from a global fit [54] with ρ ≈ 1 − v2 δ/v2 from the type II seesaw, one obtains the bound vδ ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='6 GeV at the 3σ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The mass differences of the triplet components cannot be arbitrarily large due to constraints from the electroweak precision parameters [55, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' From a global fit on the S and T parameter (with U = 0) [54], one obtains |δm1| ≈ |δm2| ≤ 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 GeV at 90% C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In our examples, we take δm1 = δm2 = δm and mA = mH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The doubly-charged scalar decays predomi- nantly into gauge bosons for vδ > 10−4 GeV, giving the bound on its mass mH++ ≥ 220 GeV, while for vδ < 10−4 GeV, one has mH++ ≥ 870 GeV since then it will decay predominantly into leptons [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A strong constraint on the pseudoscalar mixing comes from the energy loss from red giant stars via the process γ+e− → e−+J, since the Majoron can escape the star [58–61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This restricts the coupling g¯eeJ = ye √ 2(OI)12 ≈ √ 2me v2 h v2 δ vs (75) to be within g¯eeJ ≤ 10−10 to 10−12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Since the g¯eeJ coupling is suppressed by v2 δ, this constraint only requires vδ ≤ 10−1 GeV in order to be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The mixing of the Higgs boson with other CP- even fields, given by the |(OR)22| element of the CP-even mixing matrix, is constrained by global fits of the Higgs couplings and by the LEP data [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' If the dilaton mass is less than mh/2, then the SM-like Higgs boson can decay into dilatons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' with the decay width Γh→ϕϕ = g2 hϕϕ 32πmh � 1 − 4m2ϕ m2 h .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (76) Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 11 510 25 50 100 150 200 250300350 vφ = 1000 GeV, vδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 GeV 500 1000 1500 2000 mH/GeV 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 |δm|/GeV 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 5 10 25 50 vφ = 5000 GeV, vδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 GeV 500 1000 1500 2000 mH/GeV 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 |δm|/GeV Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 2 The parameter space on the |δm| vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' mH plane with vδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 GeV and λ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the left panel, vϕ = 1000 GeV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' in the right panel, vϕ = 5000 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The black lines are contours of the dilaton mass mϕ/GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The couplings are non- perturbative in the red region (not perturbative up to the Planck scale in the red dotted region) and the potential is not bounded from below in the yellow region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The blue region is forbidden by the mixing of the Higgs boson with the other fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' If the branching ratio BRh→ϕϕ is large enough, this significantly constrains the mixing [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In our case, however, BRh→ϕϕ is small in larger part of the parameter space, and the Higgs mixing is less constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The h → JJ decay will contribute to the Higgs invisible width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The decay width is given by Γh→JJ = 1 32π g2 hJJ mh , (77) while the SM Higgs width is Γh→SM = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2 × 10−3 GeV [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The Higgs invisible branching ratio is given by BRh→inv = Γh→JJ + Γh→ϕϕBR2 ϕ→JJ Γh→SM + Γh→ϕϕ + Γh→JJ , (78) where BRϕ→JJ = Γϕ→JJ Γh→SM(mϕ)(OR)2 12 + Γϕ→JJ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (79) We have (OR)12 = nh and Γh→SM(mϕ) is obtained from [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 Latest measurements by the CMS 3Numerically, the second term in the numerator of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (78) is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We also neglect the contribution of the triplet experiment at the LHC find BRh→inv < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='18 [66], while the ATLAS experiment finds BRh→inv < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='145 [67];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' we require the latter constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We have also identified the parameter space in which the couplings remain perturbative up to the Planck scale, by calculating the RG running with the RGEs given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As initial values of gauge couplings and top Yukawa coupling, we use gY (Mt) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='35745, g2(Mt) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='64779, g3(Mt) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1666, yt(Mt) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='93690 [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We also comment on the fate of the Higgs dou- blet quartic coupling from weak scale to Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As is well known that RGE running of quar- tic coupling in SM crosses zero around 1010 GeV due to the strong negative contribution from the top Yukawa term [68, 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The situation can be dramatically changed with positive contributions from additional bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the case of singlet extension of type II seesaw, there are new contri- butions to the the Higgs quartic β-function from the portal couplings λH∆, λ′ H∆, and λHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' It can be seen that in this model, the λH can remain positive up to the Planck scale signaling that the vacuum will be stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' component of the dilaton to the decay with into the SM, since it is proportional to n2 δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template 12 Scale-Invariant Type II Seesaw Model 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 5 10 25 50 100 250 500 1000 500 1000 1500 2000 mH/GeV 1000 2000 3000 4000 5000 vφ/GeV Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3 The parameter space on the vϕ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' mH plane with δm = 0 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The black lines are contours of the dilaton mass mϕ/GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The couplings are non-perturbative in the red region (not perturbative up to the Planck scale in the red dotted region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The blue region is forbidden by the mixing of other scalars with the Higgs boson and the violet region by the Higgs invisible width from Higgs decay into majorons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The parameter space in the |δm| vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' mH plane is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4 The couplings are non- perturbative at the weak scale in the red region and not perturbative up to the Planck scale in the dotted red region (in this region, a Landau pole arises at the scale 108 GeV at the highest).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The potential is not bounded from below in the yel- low region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Both the BfB and non-perturbativity bounds arise from λ′ ∆ that becomes large and neg- ative with larger |δm|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The BfB bound is mostly due to violation of the λ∆ + λ′ ∆ > 0 condi- tion in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The blue region is forbidden by the mixing of Higgs and other scalars [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The left panel of Figure 2 shows the parameter space for vϕ = 1000 GeV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' in the right panel, vϕ = 5000 GeV, while vδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 GeV in both cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For vϕ = 1000 GeV, only the lower-left corner of the plot presents parameter space that satisfies all the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For the larger vϕ = 5000 GeV, the Higgs-dilaton mixing is not constraining and the couplings remain perturbative up to the Planck scale in a larger region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 4The parameter space is practically symmetric in δm for the range of parameters we show, so we only show positive |δm|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' in larger regions this may not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because in most cases, as we see, the mass difference δm has to be very small, it is interest- ing to study separately the parameter space with δm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 3 in the vϕ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' mH plane with contours of the dilaton mass mϕ (black lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This plot is valid for any small value of vδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The quartic couplings are non-perturbative in the solid red region and have a Landau pole Λ < mP in the dotted red region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The blue region is forbid- den by the mixing of other scalars with the Higgs boson and the violet region by the Higgs invisible branching ratio Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Satisfying other con- straints (except perturbativity up to the Planck scale), with vϕ = 600 GeV, the Higgs quartic can be down to 83% of its SM value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' When pertur- bativity up to the Planck scale is required, the value differs from the SM value up to 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The Higgs quartic remains positive up to the Planck scale in the same region in which couplings remain perturbative up to the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As an example, the values of quartic couplings for three benchmark points that satisfy all con- straints are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Point A is chosen with a small mH = 225 GeV in the region where a vϕ = 1 TeV is allowed: in this point, λH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='122 is smaller than its SM value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In points B and C, we choose a larger vϕ = 5 TeV and the Higgs quartic coupling is practically the same as in the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 13 Table 1 A few benchmark points with δm = 0 GeV, vδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 GeV and λδ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 that satisfy all constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' BP mH/GeV vϕ/GeV vδ λH λ′ ∆ λS λHS λH∆ λ′ H∆ λS∆ λSH∆ A 225 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='122 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='054 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0 × 10−4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0157 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='338 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='14 × 10−8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='086 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4 × 10−4 B 225 5000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='129 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0020 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='6 × 10−7 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='28 × 10−4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='325 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='10 × 10−8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0033 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='6 × 10−5 C 1000 5000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='129 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='040 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='6 × 10−7 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='28 × 10−4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='329 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='18 × 10−7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0079 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3 × 10−3 7 Conclusions In this paper, we have considered the singlet extension of type II seesaw possessing classical scale invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A new scalar singlet has been introduced, whose VEV spontaneously breaks the global lepton number symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Consequently, the majoron – the Goldstone boson of lepton number breaking – is mostly singlet-like.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' This framework is interesting in three aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' First, the triplet Yukawa coupling of type II seesaw, together with spontaneous breaking of the lep- ton number, addresses the neutrino mass problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Second, a classical scale-invariant theory paves the way to the origin of the electroweak potential which also allows us to cure the hierarchy problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Last, the incorporation of a new bosonic degree of freedom can save the vacuum of the theory from being unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In order to minimise a complicated scalar potential, we determine and use the gauge orbit space of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A full set of sufficient and necessary conditions for the scalar potential to be bounded from below is derived in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The multi-scalar potential is minimised with the Gildener-Weinberg method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The quartic couplings are parametrised in terms of VEVs and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' We showed that the perturbativity of quartic couplings and the stability of electroweak vac- uum can be maintained all the way up to the Planck scale with the new contributions coming from the singlet and triplet scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In particu- lar, the evolution of λH with the energy scale can be prevented from crossing zero value at high energy due to sizeable contributions from λH∆ and λ′ H∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In the allowed parameter space, demon- strated in Figures 2 and 3, the mass splittings between triplet-like states have to be almost zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In conclusion, we have shown in this work that radiative symmetry breaking can be realised in the scale-invariant singlet extension of type II seesaw model, taking into account restrictions from col- lider experiments and astrophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Due to new scalar fields, the model has rich phenomenology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' BD and WS acknowledge support from Suranaree University of Technology (SUT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' BD was supported by Thailand Science Research and Innovation and Suranaree Univer- sity of Technology through SUT-Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Scholar- ship Program for ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' KK was supported by the Estonian Research Council grant PRG434, by the European Regional Development Fund and the programme Mobilitas Pluss grant MOBTT5, and by the EU through the European Regional Development Fund CoE program TK133 “The Dark Side of the Universe”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Appendix A Derivation of Bounded-from- Below Conditions We derive the necessary and sufficient bounded- from-below conditions for the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Because the potential (15) is linear in the orbit space variables, its minimum with respect to them lies on the boundary of the orbit space, more pre- cisely on the intersection of the boundary and its convex hull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' As discussed at the end of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (3), it is enough to give the conditions at the vertices A, B and C (35) and at the edges I (19) and II (20) of the orbit space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Notice that the end points of edge I are vertices A and C, and the end points of edge II are vertices B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' If there are no physical solution inside an edge, then the edge minimum is at an end point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The vertex A is already accounted for, because we require the flat direction of the potential to lie there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' At vertices B and C and edge II, the orbit space parameter η = 0 which makes the potential biquadratic there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Therefore at B and C we can derive BfB conditions by requiring copositivity of Springer Nature 2021 LATEX template 14 Scale-Invariant Type II Seesaw Model the quartic coupling matrix [70]: Λ = � � λH 1 2(λH∆ + ξλ′ H∆) 1 2λHS 1 2(λH∆ + ξλ′ H∆) λ∆ + ζλ′ ∆ 1 2λS∆ 1 2λHS 1 2λS∆ λS � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A1) The copositivity conditions for the matrix (A1) read λH > 0, λ∆ + ζλ′ ∆ > 0, λS > 0, ¯λH∆ ≡ 1 2(λH∆ + ξλ′ H∆) + � λH(λ∆ + ζλ′ ∆) > 0, ¯λHS ≡1 2λHS + � λHλS > 0, ¯λS∆ ≡ 1 2λS∆ + � λS(λ∆ + ζλ′ ∆), � λH(λ∆ + ζλ′ ∆)λS + 1 2λS∆ � λH + 1 2λHS � λ∆ + ζλ′ ∆ + 1 2(λH∆ + ξλ′ H∆) � λS + � 2¯λH∆¯λHS¯λS∆ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A2) These conditions must hold true for the values of orbit space variables ξ and ζ at both vertices B and C (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' On edge II, we can minimise the potential (15) on a unit sphere of fields together with the orbit variable ξ parametrising the edge and the Lagrange multiplier λ by solving 2λs = s (2λHSh2 + 4λSs2 + 2λS∆δ2), 2λh = h [2λHSs2 + 4λHh2 + 2(λH∆ + ξλ′ H∆)δ2], 2λδ = δ[2λS∆s2 + 2(λH∆ + ξλ′ H∆)h2 + 4(λ∆ + (1 − 2ξ2)λ′ ∆)δ2], 0 = λ′ H∆h2δ2 − 4ξλ′ ∆δ4, 1 = h2 + s2 + δ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A3) These equations can be solved analytically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For each solution, one has to check whether the vari- ables are in the physically allowed range and if they are, check that the Lagrange parameter λ, proportional to the potential V for this solution, is greater than zero: 0 < h2 < 1 ∧ 0 ≤ s2 < 1 ∧ 0 < δ2 < 1 ∧ 0 < ξ < 1 2 =⇒ V > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A4) Notice that p =⇒ q is equivalent to ¬p ∨ q and also that λ ∝ V for each solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' On edge I, the minimisation equations for the fields on a unit sphere, ξ and λ are given by 2λs = s (2λHSh2 + 4λSs2 + 2λS∆δ2) − � ξ|λSH∆|h2δ, 2λh = h [2λHSs2 + 4λHh2 + 2(λH∆ + ξλ′ H∆)δ2 − 2 � ξ|λSH∆|sδ], 2λδ = δ[2λS∆s2 + 2(λH∆ + ξλ′ H∆)h2 + 4(λ∆ + (1 − 2ξ + 2ξ2)λ′ ∆)δ2] − � ξ|λSH∆|h2s, 0 = h2 � λ′ H∆δ2 − |λSH∆|sδ 2√ξ � + 2(2ξ − 1)λ′ ∆δ4, 1 = h2 + s2 + δ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A5) These equations can only be solved numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5 Similarly to the case of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A4) for edge II, one has to check that the solutions are in the physi- cal range before checking that V > 0 with these arguments: 0 ≤ h < 1 ∧ 0 ≤ s < 1 ∧ 0 ≤ δ < 1 ∧ 0 < ξ < 1 =⇒ V > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A6) Altogether, since vertex A is accounted for by the requirement of a flat direction, the BfB conditions can be written as V |B > 0 ∧ V |C > 0 ∧ V |II > 0 ∧ V |I > 0, (A7) where the first two conditions are given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A2) with, respectively, the values of the orbit variables at vertices B and C inserted, and the last two conditions are given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A4) which has to be satisfied for each solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A3) and (A6) which has to be satisfied for each solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 5Because usually λSH∆ is very small, good necessary condi- tions are obtained by setting it to zero in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (A5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 15 Appendix B RGEs of quartic couplings We use the PyR@TE package [71] to calculate the beta-functions of all scalar quartic couplings, gauge couplings and the top Yukawa coupling at two-loop level (we have ignored all other Yukawa couplings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' For conciseness, we only provide the one-loop results here, while in our numerical study we use the two-loop beta-functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' The beta- functions are given by dλH dt = 1 16π2 � 24λ2 H + 1 2λ2 SH∆ + 3λ2 H∆ + λ2 HS + 3λH∆λ′ H∆ + 5 4λ′2 H∆ +3 8g4 1 + 9 8g4 2 + 3 4g2 1g2 2 − (3g2 1 + 9g2 2)λH − 6y4 t + 12λHy2 t � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B8) dλ∆ dt = 1 16π2 � 28λ2 ∆ + 24λ∆λ′ ∆ + 6λ′2 ∆ + 2λ2 H∆ + 2λH∆λ′ H∆ + λ2 S∆ + 6g4 1 + 15g4 2 −12g2 1g2 2 − � 12g2 1 + 24g2 2 � λ∆ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B9) dλ′ ∆ dt = 1 16π2 � 18λ′2 ∆ + 24λ∆λ′ ∆ + λ′2 H∆ − 6g4 2 + 24g2 1g2 2 − � 12g2 1 + 24g2 2 � λ′ ∆ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B10) dλS dt = 1 16π2 � 20λ2 S + 2λ2 HS + 3λ2 S∆ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B11) dλH∆ dt = 1 16π2 � 3g4 1 + 6g4 2 − 6g2 1g2 2 + 6λH∆y2 t − �15 2 g2 1 + 33 2 g2 2 � λH∆ + 12λHλH∆ + 4λHλ′ H∆ + 4λ2 H∆ + 16λ∆λH∆ + 12λ′ ∆λH∆ + λ′2 H∆ + 6λ∆λ′ H∆ +2λ′ ∆λ′ H∆ + 2λHSλS∆ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B12) dλ′ H∆ dt = 1 16π2 � 12g2 1g2 2 − �15 2 g2 1 + 33 2 g2 2 � λ′ H∆ + 4λHλ′ H∆ + 8λH∆λ′ H∆ + 4λ′2 H∆ + 4λ∆λ′ H∆ + 8λ′ ∆λ′ H∆ + 2λ2 SH∆ + 6λ′ H∆y2 t � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B13) dλHS dt = 1 16π2 � 4λ2 HS + 8λHSλS + 12λHλHS + 6λS∆λH∆ + 3λS∆λ′ H∆ + 3λ2 SH∆ − �3 2g2 1 + 9 2g2 2 � λHS + 6λHSy2 t � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B14) dλS∆ dt = 1 16π2 � 4λ2 S∆ + λHS(4λH∆ + 2λ′ H∆) + λS∆(16λ∆ + 12λ′ ∆ + 8λS) + λ2 SH∆ −(6g2 1 + 12g2 2)λS∆ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B15) dλSH∆ dt = 1 16π2 � 4λH + 4λH∆ + 6λ′ H∆ + 4λHS + 2λS∆ + 6y2 t − 9 2g2 1 − 21 2 g2 2 � λSH∆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' (B16) where g1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' g2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' g3 are the gauge coupling of U(1)Y ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' SU(2)L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' and SU(3)c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template 16 Scale-Invariant Type II Seesaw Model References [1] Aad, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Observation of a new par- ticle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 716, 1–29 (2012) arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='7214 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='020 [2] Chatrchyan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 716, 30–61 (2012) arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='7235 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='021 [3] Arkani-Hamed, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Dimopoulos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Dvali, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : The Hierarchy problem and new dimen- sions at a millimeter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 429, 263–272 (1998) arXiv:hep-ph/9803315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/S0370-2693(98)00466-3 [4] Arkani-Hamed, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Dimopoulos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Dvali, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Phenomenology, astrophysics and cosmology of theories with sub- millimeter dimensions and TeV scale quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 59, 086004 (1999) arXiv:hep-ph/9807344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='086004 [5] Randall, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sundrum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': A Large mass hierarchy from a small extra dimen- sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 83, 3370–3373 (1999) arXiv:hep-ph/9905221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3370 [6] Randall, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sundrum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': An Alternative to compactification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 83, 4690– 4693 (1999) arXiv:hep-th/9906064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4690 [7] Martin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : A Supersymmetry primer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Direct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 18, 1–98 (1998) arXiv:hep-ph/9709356.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1142/9789812839657 0001 [8] Bardeen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : On naturalness in the stan- dard model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In: Ontake Summer Institute on Particle Physics (1995) [9] Meissner, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Nicolai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Effective action, conformal anomaly and the issue of quadratic divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 660, 260–266 (2008) arXiv:0710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2840 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='035 [10] Coleman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Weinberg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Radiative Corrections as the Origin of Spontaneous Symmetry Breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 7, 1888–1910 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1888 [11] Fujikawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Heavy Fermions in the Stan- dard Sequential Scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 61, 1186 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1143/ PTP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1186 [12] Foot, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Kobakhidze, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Volkas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Elec- troweak Higgs as a pseudo-Goldstone boson of broken scale invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 655, 156–161 (2007) arXiv:0704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1165 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='084 [13] Espinosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Quiros, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Novel Effects in Electroweak Breaking from a Hid- den Sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 76, 076004 (2007) arXiv:hep-ph/0701145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='076004 [14] Foot, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Kobakhidze, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', McDonald, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Volkas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : A Solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 77, 035006 (2008) arXiv:0709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2750 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='035006 [15] Iso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Okada, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Orikasa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Classi- cally conformal B− L extended Standard Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 676, 81–87 (2009) arXiv:0902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4050 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='046 [16] Foot, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Kobakhidze, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Volkas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Stable mass hierarchies and dark matter from hidden sectors in the scale-invariant standard model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 82, 035005 (2010) arXiv:1006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0131 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='035005 [17] Alexander-Nunneley, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Pilaftsis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': The Minimal Scale Invariant Extension of the Standard Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 09, 021 (2010) arXiv:1006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5916 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 17 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP09(2010)021 [18] Farzinnia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 727, 141–150 (2013) arXiv:1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0295 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='060 [19] Heikinheimo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Racioppi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Raidal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Spethmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Tuominen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Physical Naturalness and Dynamical Breaking of Classical Scale Invari- ance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' A 29, 1450077 (2014) arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='7006 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1142/S0217732314500771 [20] Karam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Tamvakis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Dark matter and neutrino masses from a scale-invariant multi- Higgs portal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 92(7), 075010 (2015) arXiv:1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='03031 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='075010 [21] Ghorbani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Electroweak phase tran- sition in the scale invariant standard model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 98(11), 115016 (2018) arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='11541 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='115016 [22] Gildener, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Weinberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Symmetry Break- ing and Scalar Bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 13, 3333 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3333 [23] Ahmad, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Measurement of the rate of νe + d → p + p + e− interactions pro- duced by 8B solar neutrinos at the Sudbury Neutrino Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 87, 071301 (2001) arXiv:nucl-ex/0106015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='071301 [24] Ahmad, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 89, 011301 (2002) arXiv:nucl-ex/0204008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='011301 [25] Ahn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Measurement of Neutrino Oscillation by the K2K Experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 74, 072003 (2006) arXiv:hep-ex/0606032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='072003 [26] Eguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : First results from Kam- LAND: Evidence for reactor anti-neutrino disappearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 90, 021802 (2003) arXiv:hep-ex/0212021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='021802 [27] Magg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Wetterich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Neutrino Mass Problem and Gauge Hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 94, 61–64 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/ 0370-2693(80)90825-4 [28] Schechter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Neutrino Masses in SU(2) x U(1) Theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 22, 2227 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2227 [29] Cheng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Neutrino Masses, Mix- ings and Oscillations in SU(2) x U(1) Mod- els of Electroweak Interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 22, 2860 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2860 [30] Lazarides, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Shafi, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Wetterich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Proton Lifetime and Fermion Masses in an SO(10) Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 181, 287–300 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/ 0550-3213(81)90354-0 [31] Mohapatra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Senjanovic, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 23, 165 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='165 [32] Chikashige, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Mohapatra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Peccei, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Are There Real Goldstone Bosons Associated with Broken Lepton Number?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 98, 265–268 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/0370-2693(81)90011-3 [33] Gonzalez-Garcia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Nir, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Implica- tions of a Precise Measurement of the Z Width on the Spontaneous Break- ing of Global Symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 232, 383–386 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 1016/0370-2693(89)90761-2 [34] Masiero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : A Model for Spontaneous R Parity Breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 251, 273–278 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Springer Nature 2021 LATEX template 18 Scale-Invariant Type II Seesaw Model 1016/0370-2693(90)90935-Y [35] Schechter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Neutrino Decay and Spontaneous Violation of Lepton Num- ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 25, 774 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='774 [36] Diaz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Garcia-Jareno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Restrepo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Seesaw Majoron model of neutrino mass and novel signals in Higgs boson production at LEP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 527, 44–60 (1998) arXiv:hep-ph/9803362.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/S0550-3213(98)00434-9 [37] Bonilla, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Rom˜ao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Elec- troweak breaking and neutrino mass: ‘invis- ible’ Higgs decays at the LHC (type II see- saw).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 18(3), 033033 (2016) arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='07351 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1088/1367-2630/18/3/033033 [38] Talamini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Affine-P-matrices in orbit spaces and invariant theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 30, 30 (2006) arXiv:hep-th/0607165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1088/1742-6596/30/1/ 005 [39] Abud, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sartori, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': The Geometry of Spontaneous Symmetry Breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 150, 307 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 1016/0003-4916(83)90017-9 [40] Abud, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sartori, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': The Geometry of Orbit Space and Natural Minima of Higgs Potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 104, 147–152 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/ 0370-2693(81)90578-5 [41] Ma, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Pathways to naturally small neu- trino masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 81, 1171– 1174 (1998) arXiv:hep-ph/9805219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1171 [42] Mandal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Miranda, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sanchez Gar- cia, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Toward deconstructing the simplest seesaw mecha- nism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 105(9), 095020 (2022) arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='06362 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='095020 [43] Okada, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Orikasa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Yagyu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Higgs Triplet Model with Classically Conformal Invariance (2015) arXiv:1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='00799 [hep-ph] [44] Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': General Method for Analyz- ing Higgs Potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 196, 285–300 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/ 0550-3213(82)90040-2 [45] Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Orbit Spaces of Low Dimensional Representations of Simple Compact Con- nected Lie Groups and Extrema of a Group Invariant Scalar Potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 25, 1694 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 526347 [46] El Kaffas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Khater, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Ogreid, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Osland, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Consistency of the two Higgs doublet model and CP violation in top pro- duction at the LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 775, 45–77 (2007) arXiv:hep-ph/0605142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='nuclphysb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='041 [47] Arhrib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Benbrik, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Chabab, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Moul- taka, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Peyranere, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Rahili, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Ramadan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': The Higgs Potential in the Type II Seesaw Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 84, 095005 (2011) arXiv:1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1925 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 095005 [48] Bonilla, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Fonseca, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Valle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Consistency of the triplet seesaw model revis- ited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 92(7), 075028 (2015) arXiv:1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='02323 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='075028 [49] Degee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Ivanov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Keus, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Geometric minimization of highly symmetric potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 02, 125 (2013) arXiv:1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4989 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP02(2013) 125 [50] Heikinheimo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Kannike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Lyonnet, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Raidal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Tuominen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Veerm¨ae, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Vacuum Stability and Perturbativity of SU(3) Scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 10, 014 (2017) arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='08980 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP10(2017)014 [51] Cottle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Habetler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Lemke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : On classes of copositive matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lin- ear Algebra and its Applications 3(3), 295–310 (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/ Springer Nature 2021 LATEX template Scale-Invariant Type II Seesaw Model 19 0024-3795(70)90002-9 [52] Kaplan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': A test for copositive matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Linear Algebra and its Applications 313(1– 3), 203–206 (2000) [53] Kannike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Vacuum Stability of a General Scalar Potential of a Few Fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' C 76(6), 324 (2016) arXiv:1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='02680 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1140/epjc/s10052-016-4160-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' [Erratum: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C 78, 355 (2018)] [54] Zyla, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Review of Particle Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' PTEP 2020(8), 083–01 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1093/ptep/ptaa104 [55] Peskin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Takeuchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Estimation of oblique electroweak corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 46, 381–409 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='381 [56] Peskin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Takeuchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': A New constraint on a strongly interacting Higgs sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 65, 964–967 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='964 [57] Melfo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Nemevsek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Nesti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sen- janovic, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Type II Seesaw at LHC: The Roadmap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 85, 055018 (2012) arXiv:1108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='4416 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 055018 [58] Georgi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Glashow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Nussinov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Unconventional Model of Neutrino Masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' B 193, 297–316 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/0550-3213(81)90336-9 [59] Choi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Santamaria, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Majorons and Supernova Cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 42, 293–306 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/ PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='293 [60] Montero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sanchez-Vega, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Neutrino masses and the scalar sector of a B-L exten- sion of the standard model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 84, 053006 (2011) arXiv:1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='0321 [hep- ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 053006 [61] S´anchez-Vega, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Montero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Schmitz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Complex Scalar DM in a B-L Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 90(5), 055022 (2014) arXiv:1404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='5973 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='055022 [62] Robens, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Stefaniak, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': LHC Bench- mark Scenarios for the Real Higgs Singlet Extension of the Standard Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' C 76(5), 268 (2016) arXiv:1601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='07880 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1140/epjc/s10052-016-4115-8 [63] Robens, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Stefaniak, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Status of the Higgs Singlet Extension of the Standard Model after LHC Run 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' C 75, 104 (2015) arXiv:1501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='02234 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1140/epjc/s10052-015-3323-y [64] Workman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Others: Review of Particle Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' PTEP 2022, 083–01 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1093/ptep/ptac097 [65] Gomez-Bock, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Mondragon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Muhlleit- ner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Spira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Zerwas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Concepts of Electroweak Symmetry Breaking and Higgs Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' In: 4th CERN-CLAF School of High- Energy Physics, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 177–238 (2007) [66] Tumasyan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Search for invisible decays of the Higgs boson produced via vec- tor boson fusion in proton-proton collisions at √s = 13 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' D 105, 092007 (2022) arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='11585 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='092007 [67] Aad, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' : Search for invisi- ble Higgs-boson decays in events with vector-boson fusion signatures using 139 fb−1 of proton-proton data recorded by the ATLAS experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 08, 104 (2022) arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='07953 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP08(2022)104 [68] Buttazzo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Degrassi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Giardino, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Giudice, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Sala, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Salvio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Stru- mia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Investigating the near-criticality of the Higgs boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 12, 089 (2013) arXiv:1307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3536 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP12(2013)089 [69] Degrassi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Di Vita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Elias-Miro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Espinosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Giudice, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Isidori, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Springer Nature 2021 LATEX template 20 Scale-Invariant Type II Seesaw Model Strumia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Higgs mass and vacuum stability in the Standard Model at NNLO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' JHEP 08, 098 (2012) arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='6497 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1007/JHEP08(2012)098 [70] Kannike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': Vacuum Stability Conditions From Copositivity Criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' C 72, 2093 (2012) arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='3781 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1140/epjc/ s10052-012-2093-z [71] Sartore, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=', Schienbein, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=': PyR@TE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Com- put.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' 261, 107819 (2021) arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='12700 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='cpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} +page_content='107819' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNAyT4oBgHgl3EQfnPjX/content/2301.00487v1.pdf'} diff --git a/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/2301.00961v1.pdf.txt b/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/2301.00961v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..29e2170383158ad880d956e866b05a0aa56dd8b1 --- /dev/null +++ b/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/2301.00961v1.pdf.txt @@ -0,0 +1,2252 @@ +arXiv:2301.00961v1 [math.AG] 3 Jan 2023 +Some Properties of Internal Locale Morphisms Externalised +J. L. Wrigley∗ +January 4, 2023 +Abstract +We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales +and their morphisms as, respectively, fibred pre-orders and natural transformations. We characterise +those morphisms of internal locales that induce surjective geometric morphisms, open geometric mor- +phisms and geometric embeddings, and we demonstrate that surjections and embeddings can be computed +‘point-wise’ on the components of the underlying natural transformations. Internal nuclei on an internal +locale are then introduced, as a generalisation of nuclei on a locale, in order to study subtoposes of the +topos of internal sheaves on an internal locale. We show that the frame operations on the frame of inter- +nal nuclei, and therefore the co-frame operations on the co-frame of subtoposes, can also be computed +‘point-wise’ via the frame of nuclei on the locale of each fibre. +Contents +1 +Introduction +1 +2 +Morphisms and Comorphisms of Sites +3 +3 +Internal Locales +7 +3.1 +Over a Non-Cartesian Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +8 +3.2 +Gluing Internal Locales +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +11 +3.3 +Internal Locales of Sheaf Toposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +13 +4 +Internal Locale Morphisms +14 +4.1 +Internal Locale Morphisms and Geometric Morphisms . . . . . . . . . . . . . . . . . . . . . . +15 +4.2 +Surjective Internal Locale Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +18 +4.3 +Open Internal Locale Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +19 +5 +Internal Embeddings and Nuclei +21 +5.1 +Internal Nuclei +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +22 +5.2 +Geometric Embeddings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +24 +5.3 +The Frame of Internal Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +26 +1 +Introduction +By and large, the topologically interesting data of a space X (respectively, a continuous map f : X → Y ) +is contained in the algebra of open subsets O(X) (resp., the inverse image map f −1 : O(Y ) → O(X)). +This prompted the shift to ‘point-free’ topology, as exposited in [11]. +The notions of frame and frame +homomorphism capture these algebraic aspects of topology. +∗Universit`a degli Studi dell’Insubria, Via Valleggio n. 11, 22100 Como CO, email: jwrigley@uninsubria.it +1 + +Definition 1.1. A frame L is a complete lattice satisfying, for each { Ui | i ∈ I } ⊆ L and V ∈ L, the +infinite distributivity law +V ∧ +� +i∈I +Ui = +� +i∈I +V ∧ Ui. +A frame homomorphism is any map between frames that preserves arbitrary joins and finite meets. We +denote the resultant category by Frm. +Our motivating examples, the algebra of opens O(X) of a topological space X and the inverse image +map f −1 : O(Y ) → O(X) of a continuous map f : X → Y , are both examples of, respectively, a frame and a +frame homomorphism. To strengthen the analogy with topological spaces, one often works with the category +of locales Loc ≃ Frmop instead. +Notation 1.2. For a locale morphism f : L → K, we will use f −1 : K → L to denote the corresponding +frame homomorphism. Additionally, each frame homomorphism f −1 : K → L has a right adjoint f∗ : L → K, +since K is complete. +Since a topos E comes equipped with a rich internal language, we can consider internal locales of E, +which are structured objects that behave, according to the internal language of E, as a locale (equivalently, +a complete Heyting algebra, see [16, Proposition 7.3.2, Appendix I]). +Examples 1.3. +(i) Unsurprisingly, the internal locales of Sets, the topos of sets, are just locales. +(ii) For any topos E, the subobject classifier ΩE is an internal locale of E (that ΩE is an internal Heyting +algebra is shown in [15, Theorem IV.8.1], and that ΩE is internally complete is shown in [12, Examples +B2.3.8(a)]). In fact, we will see in Corollary 4.5 that ΩE is the terminal internal locale in E. +The development of a study of internal locales has coincided with profound advances in topos theory as +evidenced by Joyal and Tierney’s landmark work [13]. Internal locales can be understood both internally +and externally. When E is a Grothendieck topos with a presenting site (C, J), an external treatment of +the internal locales of E involves working explicitly with those J-sheaves L: Cop → Sets that define locales +internal to E. Examples of external accounts of internal locale theory can be found in §VI [13], §C1.6 [12] and +§4-5 [3]. Neglecting an external treatment could hamper calculating with internal locales for applications +outside of topos theory. +In this paper, we will study, externally, internal locale morphisms and some of their properties in the +style of the treatment given for localic toposes and their morphisms in §IX [15]. In doing so, we will show +that many important properties and constructions on internal locales can be computed ‘point-wise’. +We begin, in §2, by recalling some site-theoretic notions, principally morphisms and comorphisms of sites, +that will frequently appear in our treatment. Additionally, in Lemma 2.5 we prove a result, that we will +need in subsequent sections, regarding the commutativity of the geometric morphisms induced by a mixed +diagram of morphisms and comorphisms of sites. +In §3, a review is given of the classification of internal locales for the Grothendieck topos Sh(C, J) +as established in Proposition VI.2.2 [13] (see also [12, Lemma C1.6.9 & Corollary C1.6.10]), when C is +assumed to be a cartesian category, and in Proposition 5.10 [3] for an arbitrary category C. We recall that +an internal locale of Sh(C, J) is defined by a J-sheaf L: Cop → Sets that factors through Frmopen, the +category of frames and open frame homomorphisms (see [13, Definition V.1]), and which satisfies the relative +Beck-Chevalley condition (see [3, Definition 5.1(e)(i)]; in the case when C is cartesian, this is equivalent to +the Beck-Chevalley condition). We also review the construction of the relative topos of internal sheaves +Sh(L) → E on an internal locale L of E as described in [12, Examples C2.5.8(c)] and [3, Definition 5.2]. In +§3.2 we prove a result regarding the ‘gluing’ of internal locales together, which allows the easy identification +of examples (and non-examples) of functors L: Cop → Frmopen that define internal locales of the topos +SetsCop, for certain, potentially non-cartesian, categories C. +Our study of internal locale morphisms begins in §4. It is well-known (see [15, Proposition IX.5.2]) that, +given two locales X, Y , there is a bijective correspondence between locale morphisms X → Y and geometric +morphisms Sh(X) → Sh(Y ) between the respective sheaf toposes. By an analogous internalised account +(cf. [13, §VI.5] or [9, §2]), given internal locales L and L′ of a Grothendieck topos E ≃ Sh(C, J), there is an +2 + +equivalence between internal locale morphisms f: L → L′ and geometric morphisms g for which the diagram +Sh(L) +Sh(L′) +E +g +commutes, as fully shown in [3, Corollary 3.5]. +Our first task, undertaken in §4.1, is to demonstrate +this equivalence with internal locale morphisms as natural transformations between the underlying sheaves +L, L′ : Cop → Sets as defined in §VI.2 of [13]. It is further shown, in §4.2 and §4.3, that the geometric mor- +phism Sh(f) induced by an internal locale morphism f: L → L′ is surjective if and only if each component +f−1 +c +: L′(c) → L(c), for c ∈ C, is a surjective frame homomorphism, and open if and only if each component +f−1 +c +: L′(c) → L(c) is open frame homomorphism and the respective left adjoints ∃fc are natural in c. +Those internal locale morphisms that induce embeddings of subtoposes are the subject of the final section +§5, where it is shown that such internal locale embeddings coincide with ‘point-wise’ locale embeddings. We +also introduce, in §5.1, the notion of an internal nucleus on an internal locale L: Cop → Frmopen of Sh(C, J), +in order to study the co-frame Sub(Sh(L)) of subtoposes of Sh(L) (shown to be a co-frame in [12, §A4.5], +cf. also [1, §4]). In addition to demonstrating a correspondence between the internal nuclei on L, its internal +sublocales and the subtoposes Sub(Sh(L)), we show in §5.3 that the co-frame operations of Sub(Sh(L)) can +be computed ‘point-wise’ via the co-frame operations on SubLoc(L(c)), the co-frame of sublocales of L(c), +for each c ∈ C. +2 +Morphisms and Comorphisms of Sites +Familiarity with introductory topos theory, such as can be found in [15], is assumed. In this section, we +recall some site-theoretic notions, found in [15, §VII.10] and studied in detail in [2], that will make frequent +appearances in our treatment. Two notions will be central to our development: comorphisms of sites and +morphisms of sites. +Definition 2.1. Let (C, J) and (D, K) be sites. A comorphism of sites F : (C, J) → (D, K) is a functor +F : C → D with the cover lifting property: for each object c of C and K-covering sieve S on F(c), there exists +a J-covering sieve R on c such that F(R) ⊆ S. +A comorphism of sites F : (C, J) → (D, K) induces a geometric morphism CF : Sh(C, J) → Sh(D, K) +(see [15, Theorem VII.10.5]) for which the inverse image C∗ +F is given by aJ(− ◦ F). +The composite of +two comorphisms of sites F and G is still a comorphism of sites whose induced geometric morphism is the +composite CF ◦G = CF ◦ CG since aJ(− ◦ F ◦ G) = aJ(aK(− ◦ F) ◦ G). +Definition 2.2 (cf. Definition 3.2 [2]). Let (C, J) and (D, K) be sites. A morphism of sites +F : (C, J) → (D, K) +is a functor F : C → D satisfying the following conditions. +(i) If S is a J-covering sieve on c ∈ C, then F(S) is a K-covering family of morphisms on F(c). +(ii) Every object d of D admits a K-covering sieve { di → d | i ∈ I } such that each di, for i ∈ I, has a +morphism di → F(ci) to the image of some ci ∈ C. +(iii) For any pair of objects c1, c2 of C and any pair of morphisms +g1 : d → F(c1), g2 : d → F(c2) +of D, there exists a K-covering family +{ hi : di → d | i ∈ I } +of morphisms in D, a pair of families +{ f 1 +i : ci → c1 | i ∈ I }, { f 2 +i : ci → c2 | i ∈ I } +3 + +of morphisms in C, and, for each i ∈ I, a morphism ki : di → F(c′ +i) such that the squares +di +d +di +d +F(ci) +F(c1) +F(ci) +F(c2) +hi +ki +g1 +hi +ki +g2 +F (f 1 +i ) +F (f 2 +i ) +commute. +(iv) For any pair of parrallel arrows f1, f2 : c′ → c of C, and any arrow g : d → F(c′) of D such that +F(f1) ◦ g = F(f2) ◦ g, there exists a K-covering family +{ hi : di → d | i ∈ I } +of morphisms of D, a family of morphisms +{ ei : ci → c′ | i ∈ I } +of C such that f1 ◦ ei = f2 ◦ ei for all i ∈ I, and, for each i ∈ I, a morphism ki : di → F(ci) such that +the square +di +d +F(ci) +F(c′) +hi +ki +g +F (ei) +commutes for each i ∈ I. +A morphism of sites F : (C, J) → (D, K) induces a geometric morphism Sh(F): Sh(D, K) → Sh(C, J) +(see [15, Theorem VII.10.2]), for which the direct image Sh(F)∗ sends a sheaf P : Dop → Sets of Sh(D, K) +to P ◦ F op. A functor F : C → D is a morphism of sites F : (C, J) → (D, K) if and only if there exists a +geometric morphism f : Sh(D, K) → Sh(C, J) such that the square +C +D +Sh(C, J) +Sh(D, K) +ℓ +F +ℓ′ +f ∗ +commutes (see [2, §3.2]), and therefore it follows that the composite of two morphisms of sites is still a +morphism of sites. We observe that, just as with comorphisms of sites, Sh(F ◦ G) = Sh(G) ◦ Sh(F) for any +two morphisms of sites F and G. +Given a site (D, K), under certain conditions, the inclusion of a subcategory C ֒→ D can induce an +equivalence of toposes. This is the familiar Comparison Lemma (see [14, §2] or [12, Theorem C2.2.3]). +Definition 2.3. A subcategory C ⊆ D of a site (D, K) is dense for K if: +(i) for every d ∈ D, there is a covering family S ∈ K(d) generated by morphisms whose domains are in C, +(ii) for every arrow c +g−→ d ∈ D with d ∈ C, there is a covering family S ∈ K(c) generated by morphisms +b +f−→ c such that g ◦ f is in C. +Lemma 2.4 (The Comparison Lemma). Let (D, K) be a site and let C be a K-dense subcategory. There is +an equivalence Sh(D, K) ≃ Sh(C, K|C), where a sieve in C is K|C-covering if and only if the same family of +arrows is K-covering in D. +Let (D, K) be a site and let C be a dense subcategory. The equivalence Sh(D, K) ≃ Sh(C, K|C) is induced +by the inclusion functor ⊆: C → D acting as both a comorphism and a morpism of sites (C, K|C) → (D, K). +4 + +A mixed diagram of morphisms and comorphisms of sites. +We complete this section with a result +regarding the commutativity of a certain diagram of geometric morphisms induced by morphisms and co- +morphisms of sites. Recall from [12, Definition B1.3.4] that a fibration A: C → E is a functor such that, for +each object c of C and an arrow e +f−→ A(c), there exists a cartesian lifting d +g−→ c of f, that is an arrow of C +such that A(g) = f and, for any arrows d′ +h−→ c of C and A(d′) +k−→ A(d) of E for which +A(d′) +A(d) +A(c) +k +A(h) +A(g) +commutes, there exists an arrow d′ +k′ +−→ d of C such that A(k′) = k (note that we are using the terminology +‘cartesian arrow’ where Johnstone uses ‘prone’). Recall also that, given a pair of fibrations A: C → E and +B : D → F, a morphism of the fibrations A → B consists of a pair of functors F : C → D and G: E → F +such that the square +C +D +E +F +F +A +B +G +commutes and, if d +g−→ c ∈ C is cartesian, so too is F(d) +F (g) +−−−→ F(c). +Lemma 2.5. Let (C, J), (D, K), (E, L) and (F, M) be sites. Let A: C → E and B : D → F both be fibrations +and let F : C → D and G: E → F be functors such that the square +C +D +E +F +F +A +B +G +(1) +is a morphism of fibrations. Suppose that the functors A and B yield comorphisms of sites A: (C, J) → (E, L) +and B : (D, K) → (F, M), and that the functors F and G yield morphisms of sites F : (C, J) → (D, K) and +G: (E, L) → (F, M), then the induced square of geometric morphisms +Sh(C, J) +Sh(D, K) +Sh(E, L) +Sh(F, M) +CA +Sh(F ) +CB +Sh(G) +also commutes. +Proof. By [2, Theorem 3.16], we are able to transform the morphism of sites F : (C, J) → (D, K) into a +comorphism of sites thusly: there are functors +C +(1D ↓F) +D +iF +πC +πD +where +(i) (1D ↓ F) is the comma category whose objects are triples (d, c, a: d → F(c)) of objects d ∈ D, c ∈ C, +and an arrow α: d → F(c) in D; +(ii) πC and πD are the respective projection functors; +(iii) iF : C → (1D ↓F) is the functor that sends c ∈ C to (F(c), c, idF (c) : F(c) → F(c)). +Moreover, when the category (1D ↓F) is endowed with the Grothendieck topology ˜K, whose covering sieves +are precisely those that are sent by πD to K-covering sieves, we have that +5 + +(i) πC : ((1D ↓F), ˜K) → (C, J) is a comorphism of sites, +(ii) iF : (C, J) → ((1D ↓F), ˜K) is a morphism of sites, +(iii) πD : ((1D ↓F), ˜K) → (D, K) is both a morphism and comorphism of sites and induces an equivalence +of toposes Sh((1D ↓F), ˜K) ≃ Sh(D, K), +and also that Sh(F) = CπC ◦ Sh(πD), and CπD is an inverse to Sh(πD). Similarly, there are functors +E +(1F ↓G) +F +iG +πE +πF +with analogous properties, in particular Sh(G) = CπE ◦ Sh(πF) and CπF is an inverse for Sh(πF). +We construct a comorphism of sites H : ((1D ↓F), ˜K) → ((1F ↓G), ˜ +M) such that the diagram +C +(1D ↓F) +D +E +(1F ↓G) +F +A +πC +H +πD +B +πE +πF +(2) +commutes. Define the functor H as sending an object (d, c, α: d → F(c)) to +(B(d), A(c), B(α): B(d) → B(F(c))) = (B(d), A(c), B(α): B(d) → G(A(c))), +and similarly an arrow (g, h): (d′, c′, α′ : d′ → F(c′)) → (d, c, a: d → F(c)) is sent to (B(g), A(h)). The +functor H clearly makes the diagram (2) commute. It remains to show that H is cover lifting. Let +S = +� +(fi, ei, β : fi → G(ei)) +(gi,hi) +−−−−→ (B(d), A(c), B(α): B(d) → G(A(c))) | i ∈ I +� +be a +˜ +M-covering sieve, i.e. +πF(S) is M-covering. +As A is a fibration, there exists, for each i ∈ I, a +cartesian lifting of hi : ei → A(c) to an arrow h′ : c′ → c in C. +Since (1) is a morphism of fibrations, +F(h′): F(c′) → F(c) is also cartesian. As B has the cover lifting property, there exists a K-covering sieve R +on d such that B(R) ⊆ πF(S), that is, for each k: d′ → d in R, there exists an i ∈ I such that B(k) factors +as +B(d′) +fi +B(d) +B(F(c′)) +B(F(c)) = G(A(c)). +B(k) +β +gi +B(α) +B(F (h′)) +As F(h′) is cartesian, there is a unique arrow γ : d′ → F(c′) making the square +d′ +d +F(c′) +F(c) +k +γ +α +F (h′) +commute. Hence, { (d′, c′, γ : d → F(c′)) +(k,h′) +−−−−→ (d, c, α: d → F(c)) | k ∈ R } is a K-covering lifting of S. +By the commutation of (2), we deduce that the induced diagram of geometric morphisms +Sh(C, J) +Sh((1D ↓F), ˜K) +Sh(D, K) +Sh(E, L) +Sh((1F ↓G), ˜ +M) +Sh(F, M) +CA +CπC +CH +CπD +CB +CπE +CπF +6 + +commutes. Thereby, we conclude that +CA ◦ Sh(F) = CA ◦ CπC ◦ Sh(πD), += CπE ◦ CH ◦ Sh(πD), += CπE ◦ Sh(πF) ◦ CπF ◦ CH ◦ Sh(πD), += Sh(G) ◦ CB ◦ CπD ◦ Sh(πD), += Sh(G) ◦ CB +as desired. +We will be exclusively concerned with faithful fibrations. Let P : Eop → PreOrd be a functor (also +known as a fibred pre-order over E). By E ⋊ P we denote the Grothendieck construction (see [12, Definition +B1.3.1] for the general definiton), the category which has: +(i) as objects, pairs (e, x) where e is an object of E and x is an element of P(e), +(ii) and an arrow f : (e, x) → (d, y) for each arrow f : e → d in E such that x ⩽ P(f)(y). +The evident projection functor pP : E ⋊ P → E is faithful and a fibration; in fact – assuming the axiom of +choice – every faithful fibration is of the form E ⋊ P for some P (see [12, §B1.3]). +3 +Internal Locales +We devote this section to a review of the internal locale theory of Grothendieck toposes. We will require an +externalisation of internal locales: that is, given a Grothendieck topos E with a site of definition (C, J), a +classification for which J-sheaves L: Cop → Sets correspond to internal locales of E ≃ Sh(C, J). +An externalised treatment of internal locales can be found in §VI [13] and §C1.6 [12] for the special +case when C is cartesian (i.e. C has all finite limits). When C is non-cartesian, Section 5 [3] establishes a +classification of internal locales of Sh(C, J), which we recall in §3.1. +We proceed as follows. +• The statement of the classification from §VI [13] and §C1.6 [12] for internal locales of the presheaf +topos SetsCop, when C is assumed to be cartesian, is recalled below in Theorem 3.2. +• An overview of the classification of internal locales of SetsCop, where C is an arbitrary category, as +calculated in §5 [3], is given in §3.1. +• In §3.2 we prove a corollary of the classification established in [3] useful in calculating examples and +identifying non-examples of internal locales. +• Finally, §3.3 demonstrates how a classification of the internal locales of SetsCop yields a classification +of the internal locales of Sh(C, J). +Notation 3.1. By Frmopen we denote the category of frames and open frame homomorphisms. Recall from +[13, Definition V.1] that a frame homomorphism f −1 : L → K is open if there exists a left adjoint ∃f : K → L +which satisfies the Frobenius condition: that for all U ∈ L and V ∈ K, +U ∧ ∃f(V ) = ∃f(f −1(U) ∧ V ). +Equivalently, f is open if it is a morphism of complete Heyting algebras (see [13, Proposition V.1.1]). +Given a functor L: Cop → Frmopen, an object c and an arrow g of C, when there is no confusion we will +use the shorthand Lc for L(c), g−1 for L(g) and ∃g for the left adjoint to L(g). +Theorem 3.2 (Proposition VI.2.2 [13] & Lemma C1.6.9 [12]). Let C be a category with all finite limits. The +internal locales of SetsCop are precisely those functors L: Cop → Frmopen which satisfy the Beck-Chevalley +condition: for each pullback square +c ×e d +d +c +e +k +g +h +f +7 + +of C, the square +Lc×ed +Ld +Lc +Le +∃g +∃f +k−1 +h−1 +commutes. +As observed in [3, Corollary 5.4], the classification presented in the following section, of internal locales +of SetsCop for an arbitrary category C, coincides with the classification of Proposition VI.2.2 [13] and Lemma +C1.6.9 [12] when C is cartesian. In fact, not all finite limits are needed: we will observe that only pullbacks +are required for the Beck-Chevalley condition to be a necessary and sufficient condition for when a functor +L: Cop → Frmopen defines an internal locale of the topos SetsCop. +3.1 +Over a Non-Cartesian Category +We now give an overview of the classification of internal locales of SetsCop for an arbitrary category C as +can be found in §5 [3]. +Localic geometric morphisms. +The keystone property used in the classification of internal locales is the +connection between internal locales and localic geometric morphisms. +Definition 3.3. A geometric morphism f : F → E is localic if every object F of F is a subquotient of f ∗(E) +for some E ∈ E, i.e. there exists F ′ ∈ F and a diagram +F +F ′ +f ∗(E). +As remarked in [12, Definition A4.6.1], this is equivalent to saying that 1F is a bound (see [12, Definition +B3.1.7]) for F over E. Localic geometric morphisms f : F → E correspond bijectively (up to isomorphism) +to internal locales of E via the following result. +Theorem 3.4 (Theorem 5.37 [7] or Lemma 1.2 [9], cf. also Proposition 4.2 [3]). For a geometric morphism +f : F → E, the following are equivalent: +(i) f is a localic geometric morphism, +(ii) F is the topos of internal sheaves on an internal locale of E, and moreover this internal locale can be +taken as f∗(ΩF). +This bijection can be visualised with the ‘bridge’ diagram: +F ≃ Sh(C, J) +E +localic morphism +f∗(ΩF) +direct image of +subobject classifier +L ∈ E +internal locale. +f +Let L be an internal locale of E ≃ Sh(C, J). It appears as the direct image of the subobject classifier +f∗(ΩF) ∼= L for some localic geometric morphism f : F → E. Considered as a sheaf f∗(ΩF): Eop → Sets on +the canonical site (E, Jcan) for E, there is the chain of isomorphisms +f∗(ΩF) ∼= HomE(−, f∗(ΩF)), +∼= HomF(f ∗(−), ΩF), +∼= SubF(f ∗(−)) +8 + +(here, the first isomorphism is by the Yoneda lemma). Hence, by composing with the canonical morphism +ℓ: C → Sh(C, J) (that is, the Yoneda embedding followed by sheafification), we obtain the isomorphism of +J-sheaves: +L ∼= SubF(f ∗ ◦ ℓ(−)): Cop → Sets. +(3) +Thus, we can observe some basic facts about the internal locale L: +(i) for each object c of C, L(c) is a complete Heyting algebra, or frame, by [15, Proposition III.8.1]; +(ii) for each arrow f : c → d of C, by [15, Proposition III.8.2], L(f): L(d) → L(c) is an open frame +homomorphism. +Although not every such functor L′ : Cop → Frmopen will yield an internal locale, even when L′ satisfies the +Beck-Chevalley condition for those pullbacks that exist in C (an example is given in Example 3.12), it is +possible to characterise when they do. +The topos of internal sheaves. +Let f : F → E be a geometric morphism. There exists a canonical +relative site ((1F ↓ f ∗), Jf) for the topos F (see [2, Theorem 3.16]), where: +(i) (1F ↓ f ∗) is the comma category whose objects are triples (F, E, F +a−→ f ∗(E)) consisting of objects +F ∈ F, E ∈ E, and an arrow F +a−→ f ∗(E) in E; +(ii) Jf is the Grothendieck topology on (1F ↓ f ∗) whose covering sieves are precisely those whose image +under the projection πF : (1F ↓ f ∗) → F are jointly epimorphic, +such that the projection πE : (1F ↓ f ∗) → E defines a comorphism of sites πE : ((1F ↓ f ∗), Jf) → (E, Jcan) +for which CπE ∼= f. Suppose further that f : F → E is localic, then the full subcategory +E ⋊ SubF(f ∗(−)) ⊆ (1F ↓ f ∗) +(denoted by (1F ↓Sub f ∗) in [3]) on objects (F, E, F ֌ f ∗(E)), where F is a subobject of f ∗(E), is a +Jf-dense subcategory (see [3, Proposition 4.1]). +Suppose that E is the presheaf topos SetsCop, and let L: Cop → Frmopen be an internal locale of E. +By f : F → E denote the associated localic geometric morphism, so that L ∼= SubF(f ∗ ◦ よ(−)) (where +よ: C → SetsCop denotes the Yoneda embedding). We immediately have that the subcategory +C ⋊ L ≃ C ⋊ SubF(f ∗ ◦ よ(−)) ⊆ E ⋊ SubF(f ∗(−)) ⊆ (1F ↓ f ∗), +where an object (c, V ) ∈ C ⋊ L is associated with the object (V, よ(c), V ֌ f ∗(よ(c))) ∈ (1F ↓ f ∗), yields the +inclusion of a Jf-dense subcategory C ⋊ L ⊆ (1F ↓ f ∗), and so, by the comparison lemma, +F ≃ Sh(C ⋊ L, Jf|C⋊L). +Moreover, since there is a commuting square +(C ⋊ L, Jf|C⋊L) +((1F ↓ f ∗), Jf) +(C, Jtriv) +(E, Jcan) +pL +πE +よ +of comorphisms of sites (the Yoneda embedding is a comorphism of sites, see [2, §3.3]) where both horizon- +tal arrows induce equivalences of toposes, we obtain that CpL ∼= f via the diagram of induced geometric +morphisms: +Sh(C ⋊ L, Jf|C⋊L) +Sh((1F ↓ f ∗), Jf) ≃ F +SetsCop +Sh(E, Jcan) ≃ E. +CpL +∼ +CπE ∼ +=f +∼ +9 + +Definition 3.5 (Theorem 5.1 [3]). Let L be an internal locale of SetsCop. The relative topos +CpL : Sh(C ⋊ L, Jf|C⋊L) → SetsCop +constructed above is called the topos of internal sheaves (or just topos of sheaves) on L. We will use KL to +denote the Grothendieck topology Jf|C⋊L, and will also sometimes denote the topos Sh(C ⋊ L, KL) by just +Sh(L). A sieve S in C ⋊ L is KL-covering if and only if S contains a small family { (ci, Ui) +fi +−→ (d, V ) | i ∈ I } +in C ⋊ L such that +V = +� +i∈I +∃fiUi. +In [3], this is called the existential topology. +Remark 3.6. Let L be an internal locale of SetsCop. The projection pL : C ⋊ L → C has a right adjoint +tL : C → C ⋊ L that sends each object c ∈ C to (c, ⊤c). Therefore, by the description of the direct image +functor CpL∗ found in [15, Theorem VII.10.4], for each c ∈ C, there is an isomorphism of frames +{ V ∈ Lc | V ⩽ ⊤c } ∼= Lc ∼= CpL ∗ +� +ΩSh(L) +� +(c) ∼= ΩSh(L)(c, ⊤c). +It is not hard to recognise that this isomorphism can be extended so that, for each object (c, U) of C ⋊ L, +there is an isomorphism +{ V ∈ Lc | V ⩽ U } ∼= ΩSh(L)(c, U), +and that, for each morphism (c, U) +f−→ (d, W) of C ⋊ L, the transition map +ΩSh(L)(f): ΩSh(L)(d, W) → ΩSh(L)(c, U) +sends V ∈ ΩSh(L)(d, W) to g−1(V ) ∧ U ∈ ΩSh(L)(c, U). +Internal locales as existential fibred sites. +Given any functor L: Cop → Frmopen, we are still able +to define KL as the function that assigns to each object (d, V ) of C ⋊ L the collection KL(c) of sieves +{ (ci, Ui) +fi +−→ (d, V ) | i ∈ I } in C⋊L such that V = � +i∈I ∃fiUi. However, KL is not necessarily a Grothendieck +topology on C⋊L (see [15, Definition III.2.1]): KL clearly satisfies the maximality and transitivity conditions, +but KL does not always satisfy the stability condition. When KL does define a Grothendieck topology, it +coincides with the existential topology on L as defined in [3, Theorem 5.1], and so (C ⋊L, KL) is an existential +fibred site over C in the sense of Definition 5.1 [3]. In fact, as L(g), for each arrow g of C, satisfies the Frobenius +condition, (C ⋊ L, KL) is an existential site (i.e. KL is stable) if and only if the relative Beck-Chevalley +condition is satisfied (see Theorem 5.1 [3]). +Definition 3.7 (Definition 5.1.(e)(i) [3]). A functor L: Cop → Frmopen is said to satisfy the relative Beck- +Chevalley condition if, given an arrow e +h−→ d of C, and a sieve S of C ⋊ L on the object (d, V ) for which +V = � +f∈S ∃fU, then +h−1(V ) = +� +g∈h∗(S) +∃gW, +where h∗(S) is the sieve on (e, h−1(V )) given by those arrows (c, W) +g−→ (e, h−1(V )) such that the composite +(c, W) +g−→ (e, h−1(V )) +h−→ (d, V ) is in S. +If KL does define a Grothendieck topology on the category C ⋊ L, then the topos Sh(C ⋊ L, KL) (called +the existential topos for L in [3, Definition 5.2]) is also definable. The geometric morphism +CpL : Sh(C ⋊ L, KL) → SetsCop, +induced by the projection pL : C ⋊ L → C considered as a comorphism of sites +pL : (C ⋊ L, KL) → (C, Jtriv), +is localic by Examples A4.6.2(a) & (c) in [12] (alternatively, by [2, Proposition 7.11] alone). Subsequently, +one can calculate that L ∼= CpL ∗(ΩSh(C⋊L,KL)). Thus, we arrive at the classification of internal locales in the +topos SetsCop found in §5 of [3]. +10 + +Theorem 3.8 (Proposition 5.10 [3]). Let L: Cop → Frmopen be a functor. The following are equivalent: +(i) L is an internal locale of SetsCop, +(ii) L satisfies the relative Beck-Chevalley condition, +(iii) KL is a Grothendieck topology on C ⋊ L. +The classification of internal locales of SetsCop, when C is cartesian, established by Joyal and Tierney in +[13, Proposition VI.2.2], can be recovered via the classification of [3, Proposition 5.10] by noting, as is done +in [3, Proposition 5.3], that the Beck-Chevalley and relative Beck-Chevalley conditions coincide when C has +all finite limits (in fact, a study of the proof of [3, Proposition 5.3] reveals that only pullbacks are necessary). +Corollary 3.9 (Proposition 5.3 & Corollary 5.4 [3]). Let C be a category with all pullbacks. +A functor +L: Cop → Frmopen satisfies the relative Beck-Chevalley condition, and thus defines an internal locale of +SetsCop, if and only if L satisfies the Beck-Chevalley condition. +We complete this subsection with some observations of the Grothendieck topology KL. +Proposition 3.10 (cf. Remark 5.1 [3]). Let L be an internal locale of SetsCop. The Grothendieck topology +KL on C ⋊ L is generated by the following two species of covering families: +(A) +� +(c, U) +f−→ (d, ∃fU) +� +for each arrow c +f−→ d of C and U ∈ O(Lc), +(B) +� +(c, Ui) +idc +−−→ +� +c, � +i∈I Ui +� +| i ∈ I +� +for object c of C and family of opens Ui ∈ O(Lc), for i ∈ I. +Proof. We immediately have that both species are KL-covering. For the converse, note that, given a KL- +covering sieve S on (d, V ), each morphism (c, U) +f−→ (d, V ) of S can be written as the composite +(c, U) +(d, ∃fU) +� +d, � +f∈S ∃fU +� += (d, V ). +f +idd +Hence, any Grothendieck topology J for which both species (A) and (B) are J-covering contains the +Grothendieck topology KL. +Remark 3.11. Let L be an internal locale of SetsCop. We have refrained from naming the Grothendieck +topology KL the ‘canonical topology’ to avoid confusion, despite it being a generalisation of the canonical +topology on a locale. Unlike a locale L of Sets, the Grothendieck topology KL is not necessarily a subcanoni- +cal topology (defined on p. 126 of [15, §III.4]). Recall from [12, p. 542-3, §C1.2] that a Grothendieck topology +J on a category D is subcanonical only if every J-covering sieve S on an object D is effective-epimorphic, in +the sense that D is the colimit of the (potentially large) diagram +S +D/D +D, +U +where U : D/D → D is the forgetful functor. Observe, however, that the sieve generated by a KL-covering +family +� +(c, U) +f−→ (d, ∃fU) +� +of species (A) is not effective-epimorphic for any non-invertible arrow f of C +since the colimit in C ⋊ L is given by (c, U). +3.2 +Gluing Internal Locales +What can prevent a functor L: Cop → Frmopen from being an internal locale? What goes wrong when KL +is not stable? We give an example of such a functor, over a category C without all pullbacks, which is not +an internal locale, despite L satisfying the Beck-Chevalley condition for those pullbacks in C that do exist. +Inspired by this counterexample, we develop in Corollary 3.13 a method for identifying the internal locales +of the presheaf topos SetsDop when D is obtained by ‘gluing’ certain constituent subcategories together. +11 + +Example 3.12. Let L be any locale in Sets. For any category C with pullbacks, the constant functor +L: Cop → Frmopen for L, i.e. L(c) = L and L(f) = idL for all objects c and arrows f of C, satisfies the +Beck-Chevalley condition and so defines an internal locale of SetsCop. +Now consider the category +•1 +•2 +•3 +id1 +f +id2 +g +id3 +with all arrows displayed (we will refer to it as • → • ← •), which clearly lacks a pullback for the diagram +•3 +•1 +•2. +g +f +The constant functor +L: (• → • ← •)op → Frmopen +for a non-trivial locale L is not an internal locale of Sets(•→•←•)op since, for instance, the set +S = +� +(•1, U) +f−→ (•2, ⊤•2) | U ∈ O(L) +� +is a sieve of (• → • ← •) ⋊ L on (•2, ⊤•2) such that ⊤•2 = � +S U but where ⊤•3 ̸= � +g∗(S) U as g∗(S) is +empty (here ⊤•i denotes the top element in L•i). +The subobject classifier ΩSets(•→•←•)op is, of course, an internal locale of the presheaf topos Sets(•→•←•)op. +Recall from [15, §III.7] that the subobject classifier ΩSetsCop : Cop → Sets of a presheaf topos SetsCop acts +by sending an object c of C to the set of sieves on c while, for each arrow d +f−→ c of C, the transition map +ΩSetsCop (f): ΩSetsCop (c) → ΩSetsCop(d) sends a sieve S on c to the sieve f ∗(S) = { g | f ◦ g ∈ S } on d. +Hence, considered as a diagram of shape • → • ← • in Locopen (the category of locales and open local +morphisms, i.e. Frmop +open), ΩSets(•→•←•)op is given by +2 +2 + 2 +2, +i1 +i2 +where 2 denotes the 2 element locale (i.e. the terminal locale) and 2 + 2 is the coproduct in Loc, because +there are two sieves, ∅ and { id1 }, on •1, etc. Observe that the arrows i1 and i2 are disjoint open embeddings +of locales, by which we mean the following are satisfied, for all V ∈ 2: +i−1 +1 ∃i1V = V, +i−1 +2 ∃i2V = ⊥, +i−1 +2 ∃i2V = V, +i−1 +1 ∃i2V = ⊥, +where ⊥ represents the bottom element of 2. We show that the locale morphisms L(f) and L(g) being +disjoint open embeddings characterises internal locales of Sets(•→•←•)op. We present this as a consequence +of a wider theory regarding ‘gluing’ internal locales together. +Corollary 3.13. Let { Ci | i ∈ I } be a set of categories where, for each i ∈ I, Ci has a terminal object 1i. +Let D be the category obtained from the disjoint union � +i∈I Ci by freely adding a new terminal object 1. For +each i ∈ I, we denote by fi : 1i → 1 the newly added morphism. A functor L: Dop → Frmopen defines an +internal locale of SetsDop if and only if +(i) for all i ∈ I, +L|Ci : Ci +op ֒→ Dop +L−→ Frmopen +is an internal locale of SetsCop +i , +12 + +(ii) and, for each pair i, j ∈ I with i ̸= j, the locale morphisms +L1i +L1 +L1j +L(fi) +L(fj) +are disjoint open embeddings of locales, by which we mean that, for all V ∈ L1i, V ′ ∈ L1j, +f −1 +i +∃fiV = V, +f −1 +j +∃fiV = ⊥i, +f −1 +j +∃fjV ′ = V ′, +f −1 +i +∃fjV ′ = ⊥i, +where ⊥i (respectively ⊥j) represents the bottom element of L1i (resp. L1j). +Proof. For each object (d, V ) of D ⋊ L, with d being an object of Cj say, a sieve S on (d, V ) consists only of +morphisms contained in Cj ⋊ L|Cj ⊆ D ⋊ L, and any arrow e +h−→ d of D is also contained in the subcategory +Cj ⊆ D. Therefore h−1(V ) = � +g∈h∗(S) ∃gU for each such V , S and h if and only if L|Cj satisfies the relative +Beck-Chevalley condition. We can thus limit our attention to the second criterion of the corollary and sieves +on objects of the form (1, V ) ∈ D ⋊ L. +Suppose that L satisfies the relative Beck-Chevalley condition. For each i ∈ I and U ∈ L1i, the principle +sieve S generated by the arrow (1i, U) +fi +−→ (1, ∃fiU) is KL-covering. Therefore +f −1 +i +∃fiU = +� +g∈f ∗ +i (S) +∃gW = U, +and so fi is an open embedding. For each j ∈ I with i ̸= j, we have that f −1 +j +∃fiU = � +g∈f ∗ +j (S) ∃gW, which, +as f ∗ +j (S) is empty, is equal to ⊥i as required. +Conversely, suppose that L|Ci is an internal locale of SetsCiop, for each i ∈ I, and that L(fi) and L(fj) +are disjoint open embeddings for each pair i, j ∈ I with i ̸= j. It remains to show that, if S is a sieve on +(1, V ) for which V = � +g∈S ∃gU, then +h−1(V ) = +� +g∈h∗(S) +∃g′U ′ +for any arrow e +h−→ 1 of D. It suffices to consider the case when h = fj : 1j → 1, for some j ∈ I, and S is +generated by arrows of the form (1i, U) +fi +−→ (1, V ), as any arrow h′ can be factored as e → 1j +fj +−→ 1 and any +such sieve S can be rewritten as { (c, U) +g−→ (1i, ∃gU) +fi +−→ (1, V ) | fi ∈ T } where T generates a KL-covering +sieve of the desired form. But now the thesis follows since L(fi) and L(fj) are disjoint open embeddings for +each pair i, j ∈ I with i ̸= j. +Example 3.14. Using Corollary 3.13, we are instantly able to recognise that a functor +L: (• → • ← •)op → Frmopen +defines an internal locale of the topos Sets(•→•←•)op if and only if the diagram in Loc +L•1 +L•2 +L•3 +f +g +is a pair of disjoint open embeddings, and thus confirm using Corollary 3.13 that the constant functor +L: (• → • ← •)op → Frmopen considered in Example 3.12 does not define an internal locale of Sets(•→•←•)op. +3.3 +Internal Locales of Sheaf Toposes +Let (C, J) be a Grothendieck site. The embedding Sh(C, J) ֌ SetsCop is a localic geometric morphism +(see [12, Example A4.6.2(a)]), and thus, for any localic geometric morphism F → Sh(C, J), the composite +F → Sh(C, J) ֌ SetsCop is still localic (see [9, Lemma 1.1]). Thus, our understanding of the internal locales +of the presheaf topos SetsCop can be leveraged to describe the internal locales of Sh(C, J). +Recall, from [6, §2] or [4, Definition 2.11.1], that, given a fibration A: D → C and a Grothendieck topology +J on C, the Giraud topology JA is the smallest topology on D making A a comorphism of sites. +13 + +Lemma 3.15 (cf. +Proposition 5.10 [3] & Corollary C1.6.10 [12]). Let L: Cop → Frmopen be a functor +indexed over a category C with a Grothendieck topology J. The following are equivalent: +(i) L is an internal locale of Sh(C, J), +(ii) L is an internal locale of SetsCop and a J-sheaf, +(iii) KL is stable and contains the Giraud topology JpL, +(iv) KL is stable and there exists a factorisation +Sh(C ⋊ L, KL) +Sh(C, J) +SetsCop. +CpL +The equivalence of statements (i) and (ii) is a consequence of the fact that the direct image functor of any +geometric morphism (in this case the inclusion Sh(C, J) ֒→ SetsCop) preserves internal locales (see p. 528 +[12, §C1.6], cf. [12, Corollary C1.6.10] as well). The equivalence of (ii) and (iii) is proved in [3, Proposition +5.10] (cf. Remark 5.3(b) [3] too). The final equivalence of (iii) and (iv) follows by definition of the Giraud +topology. +4 +Internal Locale Morphisms +In this section we study the morphisms of internal locales. We aim to provide a parallel to the treatment of +locale morphisms and the geometric morphisms between localic toposes that is found in Chapter IX [15]. In +[15, Proposition IX.5.2], it is shown that, given two locales X, Y (of Sets), there is an equivalence +Loc(X, Y ) ≃ Geom(Sh(X), Sh(Y )) +between the category of locale morphisms X → Y and the category of geometric morphisms Sh(X) → Sh(Y ) +and their respective natural transformations. Our first aim in this section is to extend this result to internal +locales of an arbitrary Grothendieck topos Sh(C, J), as is done in [3, Corollary 3.5]. Our method differs +slightly from that of [3] as we never leave our site of definition (C, J) and establish an equivalence between +the morphisms f: L1 → L2 of internal locales of Sh(C, J) and the morphisms of sites +˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) +that are also morphisms of fibrations (cf. [3, Theorem 3.3]). Morphisms of internal locales over a cartesian +base category first appear in §VI.2 of [13]. Our definition is identical. +Definition 4.1 (Proposition VI.2.1 [13]). An internal locale morphism f: L1 → L2, between internal locales +L1, L2 : Cop → Frmopen of the topos Sh(C, J), is a natural transformation f−1 : L2 → L1 such that, for each +object c of C, f−1 +c +: L2(c) → L1(c) is a frame homomorphism and, for each morphism g : c → d of C, the +diagram +L2(d) +L2(c) +L1(d) +L1(c) +f−1 +d +L2(g) +∃L2(g) +f−1 +c +L1(g) +∃L1(g) +is a morphism of adjunctions: that is, L1(g) ◦ f−1 +d += f−1 +c +◦ L2(g) and ∃L1(g) ◦ f−1 +c += f−1 +d +◦ ∃L2(g). +We will show in §4.1 that internal locale morphisms f: L1 → L2 correspond bijectively to morphisms of +sites +˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) +14 + +for which the triangle +C ⋊ L2 +C ⋊ L1 +C +˘f +CpL2 +CpL1 +commutes, and also to geometric morphisms f : Sh(L1) → Sh(L2) for which the triangle +Sh(L1) +Sh(L2) +Sh(C, J) +f +CpL1 +CpL2 +(4) +commutes, thereby recovering [3, Corollary 3.5] that there is an equivalence of 2-categories +Loc (Sh(C, J)) ≃ Loc/Sh(C, J). +(5) +Here Loc (Sh(C, J)) denotes the 2-category of internal locales of Sh(C, J), their internal locale morphisms +and natural transformations between these. By Loc/Sh(C, J) we denote the 2-category whose objects are +localic geometric morphisms f : E → Sh(C, J), whose 1-cells are commuting geometric morphisms +E +E′ +Sh(C, J), +g +f +f ′ +(the geometric morphism g is also localic by [9, Lemma 1.1(ii)]) and whose 2-cells are natural transformations +between these. +Having related internal locale morphisms and arrows in Loc/Sh(C, J), we will then study in §4.2 and +§4.3 some select properties of internal locale morphisms and relate them to properties of the corresponding +geometric morphisms. +We will extend, to the to internal setting, the results [15, Proposition IX.5.5(i) +& Proposition IX.7.2], which state that a locale morphism f : L → K is an surjective locale morphism +(respectively open) if and only if the corresponding geometric morphism Sh(f): Sh(L) → Sh(K) between +localic toposes is an surjective (resp. open). +4.1 +Internal Locale Morphisms and Geometric Morphisms +We first demonstrate two constructions: that each morphism of internal locales induces a geometric morphism +that makes the triangle (4) commute, and, vice versa, each geometric morphism as in (4) induces a morphism +of internal locales. Using this, we then demonstrate the equivalence (5). +Proposition 4.2. Let L1, L2 : Cop → Frmopen be internal locales of Sh(C, J). Each internal locale morphism +f: L1 → L2 induces a morphism of sites +˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1). +Moreover, the induced geometric morphism Sh(˘f) makes the triangle +Sh(C ⋊ L1, KL1) +Sh(C ⋊ L2, KL2) +Sh(C, J) +Sh(˘f) +CpL1 +CpL2 +(6) +commute. +15 + +Proof. We define a functor ˘f: C ⋊ L2 → C ⋊ L1 by sending an object (c, U) of C ⋊ L2 to the object (c, f−1 +c (U)) +and a morphism g : (c, U) → (d, V ) of C ⋊ L2 to g : (c, f−1 +c (U)) → (d, f−1 +d (V )). We claim that +˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) +is a morphism of sites. +We check that the four conditions of Definition 2.2 are satisfied. +(i) It suffices to show that the two generating species of KL2-covering families identified in Proposition +3.10 are sent by ˘f to KL1-covering families. Let { g : (c, U) → (c, ∃L2(g)U) } be a KL2-covering family +of species (A). The family +˘f({ g : (c, U) → (c, ∃L2(g)U) }) = { g : (c, f−1 +c (U)) → (c, f−1 +d (∃L2(g)U)) } +is KL1-covering as f−1 +d (∃L2(g)U) = ∃L1(g)f−1 +c (U). Let { idc : (c, Ui) → (c, � +i∈I Ui) | i ∈ I } be a KL2- +covering family of species (B). The family +˘f +�� +idc : (c, Ui) → +� +c, +� +i∈I +Ui +� +| i ∈ I +�� += +� +idc : (c, f−1 +c (Ui)) → +� +c, f−1 +c +�� +i∈I +Ui +�� +| i ∈ I +� +is KL1-covering since f−1 +c +is a frame homomorphism. +(ii) Each object (c, U) of C ⋊ L1 has an arrow idc : (c, U) → (c, ⊤) = (c, f−1 +c (⊤)). +(iii) Given a pair of arrows +g1 : (d, V ) → (c1, f−1 +c1 (U1)), g2 : (d, V ) → (c2, f−1 +c2 (U2)) +of C ⋊ L2, we have that +V ⩽ L2(g)(f−1 +c1 (U1)) ∧ L2(g)(f−1 +c2 (U2)), += f−1 +d (L1(g)(U1) ∧ L1(g)(U2)). +Hence, there are the commutative triangles +(d, V ) +(d, f−1 +d (L1(g)(U1) ∧ L1(g)(U2))) +(c1, f−1 +c1 (U1)), +(d, V ) +(d, f−1 +d (L1(g)(U1) ∧ L1(g)(U2))) +(c2, f−1 +c2 (U2)). +idd +g1 +g1 +idd +g2 +g2 +(iv) Let f1, f2 : (c′, U ′) → (c, U) be a pair of parallel morphisms of C ⋊ L2. If g : (d, V ) → (c′, f−1 +c′ (U ′)) is a +morphism of C ⋊ L1 such that ˘f(f1) ◦ g = ˘f(f2) ◦ g, then g : (d, V ) → (c′, f−1 +c′ (U ′)) factors through the +morphism g : (d, L1(g)(f−1 +c′ (U ′))) → (c′, f−1 +c′ (U ′)), which is of the form +˘f(g): (d, f−1 +d (L2(g)(U ′))) → (c′, f−1 +c′ (U ′)). +Finally, the triangle (6) commutes by Lemma 2.5. +Let L1, L2 be internal locales of Sh(C, J) with an internal locale morphism f: L1 → L2. We will write +Sh(f): Sh(L1) → Sh(L2) for the geometric morphism Sh(˘f) induced as above. By [9, Lemma 1.2(ii)], Sh(f) +is also a localic geometric morphism. +16 + +Proposition 4.3. Let L1, L2 : Cop → Frmopen be internal locales of Sh(C, J). Each geometric morphism +f : Sh(L1) → Sh(L2), +for which the triangle +Sh(L1) +Sh(L2) +Sh(C, J) +f +CpL1 +CpL2 +(7) +commutes induces an internal locale morphism f: L1 → L2 for which Sh(f) = f. +Proof. For each object E of Sh(L2), the map that sends a subobject U ֌ E to f ∗(U) ֌ f ∗(E) is a frame +homomorphism +f ∗ +E : SubSh(L2)(E) → SubSh(L1)(f ∗(E)) +and moreover, for each arrow g : E → E′ of Sh(L2), the diagram +SubSh(L2)(E) +SubSh(L2)(E′) +SubSh(L1)(f ∗(E)) +SubSh(L1)(f ∗(E′)) +g−1 +f ∗ +E +∃g +f ∗ +E′ +f ∗(g)−1 +∃f∗(g) +commutes (see [15, p. 496-8]). +Since (7) commutes, f ∗ ◦ C∗ +pL2 = C∗ +pL1 ; in particular, for each object c of C, we have that +f ∗ ◦ C∗ +pL2 (l(c)) = C∗ +pL1 (l(c)), +where l denotes the canonical functor l: C → Sh(C, J). We observed in (3) that +L1 ∼= SubSh(L1)(C∗ +pL1 ◦ l(−)): Cop → Frmopen, +and similarly for L2. Hence, the frame homomorphisms +f ∗ +C∗ +pL2 (l(c)) : SubSh(L2)(C∗ +pL2 (l(c))) → SubSh(L1)(C∗ +pL1 (l(c))), +for each object c of C, collectively define an internal locale morphism f: L1 → L2 where f−1 +c (U) = f ∗(U) for +each subobject U ֌ C∗ +pL2 (l(c)). +Finally, that Sh(f) = f follows from the description of the inverse image Sh(f)∗ of a geometric morphism +induced by a morphism of sites found in [15, Theorem VII.10.2]: for each U ∈ O(L2(c)), we have that +Sh(f)∗(ℓ(c, U)) = ℓ′(c, f−1 +c (U)) = ℓ′(c, f ∗(U)) = f ∗(U) +(where ℓ and ℓ′ denote the canonical functors ℓ: C ⋊L2 → Sh(C ⋊L2, KL2) and ℓ′ : C ⋊L1 → Sh(C ⋊L1, KL1) +respectively). +Thus we obtain our bijective correspondence between between: +• the internal locale morphisms f: L1 → L2, +• the morphisms of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) for which the triangle +C ⋊ L2 +C ⋊ L1 +C +pL2 +˘f +pL1 +commutes, +17 + +• the geometric morphisms f : Sh(L1) → Sh(L2) for which the triangle +Sh(L1) +Sh(L2) +Sh(C, J) +f +CpL1 +CpL2 +commutes. +We now use this bijective correspondence to establish the equivalence (5). +Theorem 4.4 (Corollary 3.5 [3]). There is an equivalence of 2-categories: +Loc(Sh(C, J)) ≃ Loc/Sh(C, J). +Proof. By L: Loc/Sh(C, J) → Loc (Sh(C, J)) denote the (1-)functor that sends a localic geometric morphism +f : E → Sh(C, J) to the internal locale f∗(ΩE) and a commuting geometric morphism +E +E′ +Sh(C, J) +g +f +f ′ +to the internal locale morphism g: f∗(ΩE) → f ′ +∗(ΩE′) induced by Proposition 4.3. +By T: Loc (Sh(C, J)) → Loc/Sh(C, J) denote the functor that sends an internal locale L to the localic +geometric morphism CpL : Sh(C ⋊ L, KL) → Sh(C, J) and an internal locale morphism f: L → L′ to Sh(f). +By the isomorphism L ∼= CpL∗ +� +ΩSh(L) +� +and Proposition 4.3, the functors L and T are mutually inverse. +This 1-equivalence extends to a 2-equivalence. One direction of the equivalence +HomLoc(Sh(C,J))(L, L′) ≃ HomLoc/Sh(C,J)(Sh(L), Sh(L′)) +follows from [12, Remark C2.3.5], the other by noting that a natural transformation of inverse image functors +Sh(L) +Sh(L′), +Sh(f)∗ +Sh(f′)∗ +α +for two internal locale morphisms f, f′ : L → L′, induces a natural transformation +SubSh(L)(−) +SubSh(L′)(−). +Sh(f)∗ +Sh(f′)∗ +α +Corollary 4.5. The subobject classifier ΩE of a topos is the terminal object of Loc(E). +Proof. The identity idE : E → E is the terminal object of Loc/E . +4.2 +Surjective Internal Locale Morphisms +Recall (from [12, Lemma A4.2.6] say) that a geometric morphism f : F → E is a surjection if the inverse +image functor f ∗ : E → F is faithful. Recall from [15, Definition IX.4.1] that a locale morphism f : L → K +is a surjection if the corresponding frame homomorphism f −1 : K → L is injective. In [15, Proposition +X.5.5(i)], it is shown that a locale morphism f : L → K is surjective if and only if the corresponding +geometric morphism Sh(f): Sh(L) → Sh(K) is surjective. We show that surjections of internal locales can +be characterised ‘point-wise’. +18 + +Definition 4.6. Let f: L1 → L2 be an internal locale morphism of SetsCop. We say that f is a surjective +internal locale morphism if, for each c ∈ C, f−1 +c +: L2(c) → L1(c) is injective. +Proposition 4.7. Let f: L1 → L2 be an internal locale morphism of Sh(C, J). The following are equivalent: +(i) the geometric morphism Sh(f) is a surjective geometric morphism, +(ii) f is a surjective internal locale morphism. +Proof. By [2, Theorem 6.3], the geometric morphism Sh(f) is surjective if and only if the corresponding +morphism of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) is cover reflecting. Suppose each f−1 +d +is injective. Let S +be sieve of C ⋊ L2 on (d, V ) such that ˘f(S) is KL1-covering, i.e. f−1 +d (V ) = � +g∈S ∃L1(g)f−1 +c (U). We have that +f−1 +d (V ) = +� +g∈S +∃L1(g)f−1 +c (U), += +� +g∈S +f−1 +d ∃L2(g)U, += f−1 +d + + � +g∈S +∃L2(g)U + + . +Thus, V = � +g∈S ∃L2(g)U and so S is KL2-covering. Conversely, if ˘f is cover reflecting and f−1 +c (U) = f−1 +c (V ) +for a pair U, V ∈ L2(c), then ˘f reflects the maximal cover and so U = V . +4.3 +Open Internal Locale Morphisms +Recall from [8, Definition 1.1] that a geometric morphism f : F → E is open if, for each object E ∈ E, the +canonical arrow +ϕE : f ∗ � +ΩE +E +� +→ Ωf ∗(E) +F +is a monomorphism or, equivalently by [8, Theorem 3.2], the canonical arrow l: ΩE → f∗(ΩF) has an internal +left adjoint, by which we mean a natural transformation m: f∗(ΩF) → ΩE where, for each c ∈ C, there is +an adjunction mc ⊣ lc, where (C, J) is a site of definition for E. +Where the inverse image functor of a +geometric morphism preserves only the interpretation of geometric logic, open geometric morphisms, like +open locale morphisms, preserve the interpretation of all infinitary first-order logic, and this property also +characterises open geometric morphisms (see [8, Theorem 3.2 & Corollary 3.3]). In [15, Proposition IX.7.2], +it is shown that a locale morphism f : X → Y is open if and only if the corresponding geometric morphism +Sh(f): Sh(X) → Sh(Y ) is open. +Definition 4.8. Let f: L1 → L2 be an internal locale morphism of SetsCop. We say that f is an open internal +locale morphism if, for each c ∈ C, f−1 +c +: L2(c) → L1(c) is open and, for each morphism g : c → d, the square +L2(d) +L2(c) +L1(d) +L1(c) +L2(g) +∃fd +L1(g) +∃fc +commutes, where ∃fc is the left adjoint to f−1 +c . +Proposition 4.9. Let f: L1 → L2 be an internal locale morphism of SetsCop. The following are equivalent: +(i) the geometric morphism Sh(f) is an open geometric morphism, +(ii) f is an open internal locale morphism. +19 + +Proof. From Remark 3.6, we know that, for each object (c, U) of C ⋊ L2, +ΩSh(L2)(c, U) = { V ∈ L2(c) | V ⩽ U } +and, by extension, +Sh(f)∗(ΩSh(L1))(c, U) = ΩSh(L1) ◦˘f(c, U), += ΩSh(L1)(c, f−1 +c (U)), += { V ′ ∈ L1(c) | V ′ ⩽ f−1 +c (U) }. +Thus, for each object (c, U) of C ⋊ L2, the component +l(c,U) : { V ∈ L2(c) | V ⩽ U } → { V ′ ∈ L1(c) | V ′ ⩽ f−1 +c (U) } +of the natural transformation l: ΩSh(L2) → Sh(f)∗(ΩSh(L1)) acts by V �→ f−1 +c (V ). +If f−1 +c +is open for each object c of C, there is an external left adjoint +(∃f)(c,U) : Sh(f)∗(ΩSh(L1))(c, U) → ΩSh(L2)(c, U) +given by V ′ �→ ∃fcV ′. It remains to show that the maps (∃f)(c,U) together define a natural transformation +∃f : Sh(f)∗(ΩSh(L1)) → ΩSh(L2). +Let g : (c, U) → (d, V ) be an arrow of C ⋊ L2. We observe that the diagram +Sh(f)∗(ΩSh(L1))(d, V ) +Sh(f)∗(ΩSh(L1))(c, L2(g)(V )) +Sh(f)∗(ΩSh(L1))(c, U) +ΩSh(L2)(d, V ) +ΩSh(L2)(c, L2(g)(V )) +ΩSh(L2)(c, U) +(∃f)(d,V ) +(∃f)(c,L2(g)(V )) +(∃f)(c,U) +commutes. The left hand square commutes since +L2(d) +L2(c) +L1(d) +L1(c) +L2(g) +∃fd +L1(g) +∃fc +commutes. The right hand square commutes since (∃fcV ′)∧U = ∃fc(V ′∧f−1 +c (U)) for each V ′ ⩽ f−1 +c (L2(g)(V )). +Conversely, if l: ΩSh(L2) → Sh(f)∗(ΩSh(L1)) has an internal left adjoint m, then, for each object c of C, +as the map +l(c,⊤): ΩSh(L2)(c, ⊤) → Sh(f)∗(ΩSh(L1))(c, ⊤), +is isomorphic to f−1 +c +: L2(c) → L1(c), we obtain a left adjoint ∃fc to f−1 +c , isomorphic to m(c,⊤), which is +natural in the sense that the square +L2(d) +L2(c) +L1(d) +L1(c) +L2(g) +∃fd +L1(g) +∃fc +commutes. +It remains to show that ∃fc satisfies the Frobenius condition. +This follows since, for each +U ∈ L1(c), the square +Sh(f)∗(ΩSh(L2))(c, ⊤) +ΩSh(L1)(c, ⊤) +Sh(f)∗(ΩSh(L2))(c, U) +ΩSh(L1)(c, U) +m(c,⊤) +m(c,U) +20 + +commutes and so m(c,⊤)(V ) ∧ U = m(c,U)(V ∧ f−1 +c (U)) for each V ∈ O(L2(c)). Hence, by following the same +argument of [15, p. 504, Proposition IX.7.2], we conclude that +m(c,⊤)(V ) ∧ U = m(c,U)(V ∧ f−1 +c (U)), += m(c,U)(V ∧ f−1 +c (U) ∧ f−1 +c (U)), += m(c,⊤)(V ∧ f−1 +c (U)) ∧ U, += m(c,⊤)(V ∧ f−1 +c (U)). +Thus, as m(c,⊤) ∼= ∃fc, we have that f−1 +c +is an open frame homomorphism for each c ∈ C. +5 +Internal Embeddings and Nuclei +This final section is dedicated to the study of internal locale embeddings. Recall from [15, Definition IX.4.1] +that a locale morphism f : K → L is said to be an embedding if the corresponding frame homomorphism +f −1 : L → K is surjective. +Just as with surjective internal locale morphisms, we define internal locale +embeddings as the ‘point-wise’ generalisation. +Definition 5.1. Let f: L1 → L2 be an internal locale morphism of SetsCop. We say that f is an internal +locale embedding if, for each c ∈ C, f−1 +c +: L2(c) → L1(c) is surjective. We will also refer to L1 as an internal +sublocale of L2 and as f as the inclusion of this internal sublocale. +Recall (from [15, §VII.4] say) that a geometric morphism f : F → E is said to be a geometric embedding +(and F a subtopos of E) if the direct image functor f∗ is full and faithful. Recall also, from [15, Proposition +IX.5.4], that geometric embeddings generalise embeddings of sublocales in the sense that, given a locale +morphism f : K → L, the induced geometric morphism Sh(f): Sh(K) → Sh(L) between the toposes of +sheaves is a geometric embedding if and only if f is an embedding of locales. The aim of this section is +to prove an analogous result for embeddings of internal locales: that, given a morphism of internal locales +f: L′ → L of Sh(C, J), the geometric morpism Sh(f) is an embedding if and only if f is an internal locale +embedding. One direction is easily achieved by applying results from §6 [2]. Demonstrating the converse to +Proposition 5.2 below is postponed to Theorem 5.7. +Proposition 5.2. If f: L1 → L2 is an internal locale embedding of Sh(C, J), then Sh(f) is a geometric +embedding. +Proof. Let (D, J) be a site and E a Grothendieck topos. By [2, Corollary 6.4], a J-continuous flat functor +G: D → E yields a geometric embedding if and only if: +(i) each object E of E is covered by objects of the form G(d), for d ∈ D, +(ii) for each pair of objects d, d′ of D and arrow g : G(d) → G(d′) of E, there exists a family of morphisms +S = { hi : ei → d | i ∈ I } such that G(S) is jointly epimorhic in E and, for each i ∈ I, g ◦G(hi) = G(ki) +for some arrow ki : ei → d′ in D. +The canonical functor ℓ: C ⋊ L1 → Sh(L) is a KL1-continuous flat functor that induces an equivalence +of toposes, hence an inclusion, and so satisfies both conditions of [2, Corollary 6.4]. The KL2-flat functor +Sh(f)∗ ◦ ℓ′ : C ⋊ L2 → Sh(L) that defines the geometric morphism Sh(f): Sh(L1) → Sh(L2) factors as +C ⋊ L2 +C ⋊ L1 +Sh(L). +˘f +Sh(f)∗◦ℓ′ +ℓ +If f−1 +c +is surjective for each c ∈ C, then ˘f: C ⋊ L2 → C ⋊ L1 is surjective on both objects and arrows. Thus, as +ℓ satisfies the conditions of [2, Corollary 6.4], so too does Sh(f)∗ ◦ ℓ′. Hence, Sh(f) is a geometric embedding +as desired. +21 + +Let L be an internal locale of Sh(C, J). Since every geometric embedding is localic (see [12, Example +A4.6.2(a)]), every subtopos of Sh(L) is obtained by a morphism of internal locales L′ → L. Therefore, we +can understand the subtoposes of Sh(L) by leveraging a study of the internal sublocales of L. In particular, +we will reprove the well-known result (see [12, §A4.5]) that the poset Sub(Sh(L)) of subtoposes of Sh(L) is +a co-frame. +To do so, we will develop a study of internal nuclei, the internal generalisation of a nucleus on a locale. +We proceed as follows. +• In §5.1, internal nuclei on an internal locale are introduced and it is shown that internal nuclei corre- +spond bijectively with internal locale embeddings. +• In §5.2, it is shown that internal nuclei on L, and thus by extension internal sublocales of L, correspond +bijectively with subtoposes of Sh(L). +• Finally, §5.3 is dedicated to proving that Sub(Sh(L)) is a co-frame. By using an internal generalisation +of pre-nuclei, we observe that the co-frame operations on Sub(Sh(L)) can be computed ‘point-wise’ +via the co-frame operations on SubLoc(Lc). +5.1 +Internal Nuclei +Recall from [10, §II.2] that a nucleus on a locale L is a function j : L → L satisfying, for all x, y ∈ L, +x ⩽ j(x), +j(j(x)) ⩽ j(x), +j(x ∧ y) = j(x) ∧ j(y). +These properties are referred to as j being, respectively, inflationary, idempotent, and meet-preserving. Any +function satisfying these properties must also be monotone. +It is well-known (see [10, Theorem II.2.3]) that there is a bijective correspondence between nuclei on +L and sublocales of L. In one direction, the nucleus associated to a sublocale f : K ֌ L is given by the +function f∗f −1 : L → L (here f∗ denotes the right adjoint to f −1, see Notation 1.2). Conversely, given a +nucleus j : L → L, the image of j as a subset of L, which we denote by Lj, can be given the structure of a +frame. The meets are computed as they are in L while the join of a subset { Ui | i ∈ I } ⊆ Lj is computed +as j +�� +i∈I Ui +� +, where � +i∈I Ui is the join in L. It is then clear that j : L → Lj constitutes a surjective frame +homomorphism (see [10, Lemma II.2.2] or [15, Proposition IX.4.3]). +Nuclei are a useful tool when studying sublocales since many properties of sublocales are more readily +proven using nuclei than directly. In particular, that the sublocales of a locale L form a co-frame is often +proved via nuclei, as discussed in §5.3 below. Our aim in this subsection is to generalise the notion of nucleus +to the internal setting and thereby develop a nucleic study of internal sublocales, and therefore subtoposes +of sheaves on an internal locale. +Definition 5.3. Let L: Cop → Frmopen be an internal locale of Sh(C, J). An internal nucleus is a natural +transformation j : L → L (as a functor into Sets) such that each component jc : Lc → Lc, for c ∈ C, is a +nucleus on the locale Lc. +When the subobject classifier ΩSh(C,J) of Sh(C, J) is considered as an internal locale, the definition of an +internal nucleus j : ΩSh(C,J) → ΩSh(C,J) coincides with that of a Lawvere-Tierney topology (see [12, Definition +A4.4.1]). Let f : F → E be a localic geometric morphism. We will observe below in §5.2 that internal nuclei +on f∗(ΩF) correspond bijectively with Lawvere-Tierney topologies on ΩF. +Let L be an internal locale of Sh(C, J). In the following results we establish a bijective correspondence +between internal nuclei on L and internal sublocales of L that generalises the bijective correspondence for +locales found in [10, Theorem II.2.3]. +Lemma 5.4. Let j : L → L be a nucleus. For each subset { Ui | i ∈ I } ⊆ L, we have that: +j +�� +i∈I +Ui +� += j +�� +i∈I +jUi +� +. +Proof. The first inequality j +�� +i∈I Ui +� +⩽ j +�� +i∈I jUi +� +is a consequence of j being inflationary as Ui ⩽ jUi +for each i ∈ I. The converse inequality is achieved by applying j to both sides of the canonical inequality +� +i∈I jUi ⩽ j +�� +i∈I Ui +� +. +22 + +Proposition 5.5. Each internal nucleus j on an internal locale L of Sh(C, J) defines an embedding of +internal locales Lj ֒→ L. +Proof. By the above discussion, for each object c of C, the nucleus jc : Lc → Lc induces a sublocale Lj +c of +Lc. As j is a natural transformation, for each arrow c +g−→ d of C, g−1 : Ld → Lc restricts to a function +g−1 : Lj +d → Lj +c which, by the definition of meets and joins in Lj +d and Lj +c, can easily be shown to be a frame +homomorphism. We must therefore show that each g−1 : Lj +d → Lj +c is open. A left adjoint is given by jd∃L(g) +since, for each U ∈ Lj +c and V ∈ Lj +d, +jd∃L(g)U ⩽ V = jd(V ) ⇐⇒ ∃L(g)U ⩽ V ⇐⇒ U ⩽ g−1(V ), +and furthermore the Frobenius condition is satisfied: +jd∃L(g)U ∧ V = jd∃L(g)U ∧ jdV = jd((∃L(g)U) ∧ V ) = jd∃L(g)(U ∧ g−1(V )). +We thus conclude that each internal nucleus j induces a functor Lj : Cop → Frmopen. +Moreover, we observe that the square +Lc +Ld +Ljc +c +Ljd +d +jc +∃g +jd +jd∃g +commutes. For each U ∈ Lc, U ⩽ jc(U) and so jd∃gU ⩽ jd∃gjc(U). Conversely, as U ⩽ g−1∃gU, it follows +that +jd(U) ⩽ jd ◦ g−1 ◦ ∃g(U) =⇒ jd(U) ⩽ g−1 ◦ jc ◦ ∃g(U), +=⇒ ∃g ◦ jd(U) ⩽ jc ◦ ∃g(U), +=⇒ jc ◦ ∃g ◦ jd(U) ⩽ jc ◦ ∃g(U). +Therefore, we have a natural transformation j : L → Lj where each component is a surjective frame homo- +morphism for which jd∃gjc = jd∃g for each arrow d +g−→ c of C, and hence j would define an embedding of +internal locales if Lj were also an internal locale of SetsCop. +It remains only to show that functor Lj satisfies the relative Beck-Chevalley condition. Let S be a sieve +on (d, V ) ∈ C ⋊ Lj such that +V = jd + + � +g∈S +jd∃L(g)U + + , +which, by Lemma 5.4, is equal to jd +�� +g∈S ∃L(g)U +� +, and let e +h−→ d be an arrow of C. Let W = � +g∈S ∃L(g)U. +Since L is an internal locale of Sh(C, J), +h−1(W) = +� +g∈h∗(S) +∃L(g)U. +Thus, by Lemma 5.4, we have the desired equality +h−1(V ) = h−1(jd(W)) = je(h−1(W)) = je + + +� +g∈h∗(S) +∃L(g)U + + = je + + +� +g∈h∗(S) +je∃L(g)U + + , +and therefore Lj is an internal locale of SetsCop (and since Sh(Lj) → SetsCop factors as +Sh(Lj) +Sh(L) +Sh(C, J) +Sh(C, J), +we conclude that Lj is an internal locale of Sh(C, J) too). +23 + +Corollary 5.6. Let L: Cop → Frmopen be an internal locale of Sh(C, J). There is a bijective correspondence +between internal sublocales of L and internal nuclei on L. +Proof. By the theory of standard locales, there is a bijective correspondence between collections of nuclei +{ jc : Lc → Lc | c ∈ C } and collections of sublocales { fc: L′ +c ֌ Lc | c ∈ C }, where both are indexed by the +objects of C. Our bijection will be a restriction of this correspondence. We have already seen in Proposition +5.5 that if the collection { jc: Lc → Lc | c ∈ C } of nuclei is natural in c, i.e. it defines an internal nucleus, +then the corresponding collection of sublocales yields an internal sublocale embedding. It remains to show +the other direction: that if { fc: L′ +c ֌ Lc | c ∈ C } are the components of an internal sublocale embedding, +then the corresponding collection of nuclei is natural. +Let f: L′ → L be an embedding of an internal sublocale. Since each component f−1 +c +: L′(c) → L(c) is +surjective, it induces a nucleus f∗cf−1 +c +: L(c) → L(c), for each object c of C. We wish to show that, for each +arrow c +g−→ d of C, the square +Ld +Lc +Ld +Lc +f∗df−1 +d +g−1 +f∗cf−1 +c +g−1 +commutes. Since the square +Ld +Lc +Ld +Lc, +f−1 +d +g−1 +∃g +f−1 +c +g−1 +∃g +is a morphism of fibrations, so is the square of right adjoints +Ld +Lc +Ld +Lc. +g−1 +g∗ +f∗d +g−1 +f∗c +g∗ +Hence we have the desired equality +f∗cf−1 +c g−1 = f∗cg−1f−1 +d += g−1f∗df−1 +d . +5.2 +Geometric Embeddings +We now establish a bijective correspondence between internal nuclei and Lawvere-Tierney topologies, and +hence between internal sublocales and subtoposes. Let F be a Grothendieck topos. Recall from [12, Definition +A4.4.1] that a Lawvere-Tierney topology is a endomorphism j : ΩF → ΩF on the subobject classifier of the +topos F such that the diagrams +1 +ΩF +ΩF +ΩF +ΩF × ΩF +ΩF +ΩF, +ΩF, +ΩF × ΩF +ΩF +⊤ +⊤ +j +j +j +j +j×j +∧ +j +∧ +commute. Recall also, from [12, Theorem A4.4.8] that there is a bijection between Lawvere-Tierney topolo- +gies and subtoposes of F. As observed in [15, Corollary IX.6.6], given a locale L, there is a bijection between +Lawevere-Tierney topologies on ΩSh(L) (and hence subtoposes of Sh(L)) and nuclei on L (and hence sublo- +cales of L). The following result extends this bijection to the internal setting. +24 + +Theorem 5.7. Let L: Cop → Frmopen be an internal locale of E ≃ Sh(C, J). There is a bijective correspon- +dence between the following: +(i) the subtoposes of F ≃ Sh(L); +(ii) internal nuclei on L; +(iii) internal sublocales of L. +In particular, if f: L′ → L is an internal locale morphism, Sh(f) is a geometric embedding if and only if f is +an internal locale embedding. +Proof. The bijective correspondence between internal nuclei and internal sublocales was shown in Corollary +5.6. We now demonstrate a bijective correspondence between subtoposes of F ≃ Sh(L) and internal nuclei +on L. We rely on the characterisation of subtoposes of Sh(L) in terms of Lawvere-Tierney topologies. +Let j : ΩSh(L) → ΩSh(L) be a Lawvere-Tierney topology and let f : Sh(L) → SetsCop be the localic +geometric morphism such that f∗(ΩSh(L)) ∼= L (i.e. f = CpL). By now applying the direct image functor +f∗ : Sh(L) → SetsCop, we obtain an endomorphism +f∗j : f∗(ΩSh(L)) ∼= L → f∗(ΩSh(L)) ∼= L +(by the description of CpL ∗ afforded by [15, Theorem VII.10.2], (f∗j)c = j(c,⊤)). We claim that f∗j is an +internal nucleus. Since j was a Lawvere-Tierney topology, makes the following diagrams commute: +L +L +L × L +L +L, +L × L +L. +f∗j +f∗j +f∗j +f∗j×f∗j +∧ +f∗j +∧ +Thus, f∗j : L → L is a natural transformation such that (f∗j)c : Lc → Lc is idempotent and preserves binary +meets, for each c ∈ C. It remains to show that (f∗j)c is inflationary. +Let U ∈ Lc ∼= f∗(ΩSh(L))(c) ∼= SubSh(L)(f ∗よ(c)). We consider the subobject classifier ΩSh(L) as a sheaf +on the canonical site (Sh(L), Jcan). As j is a Lawvere-Tierney topology and natural, there is a commutative +diagram of sets +1(U) +SubSh(L)(U) +SubSh(L)(f ∗よ(c)) +SubSh(L)(U) +SubSh(L)(f ∗よ(c)) +⊤U +⊤U +jU +(f∗j)c +where ⊤U picks out the top element U ∈ SubSh(L)(U) and the map SubSh(L)(f ∗よ(c)) → SubSh(L)(U) is +induced by pulling back subobjects along the monomorphism U ֌ f ∗(よ(c)). In other words, it sends a sub- +object V ∈ SubSh(L)(f ∗よ(c)) to U ∧ V ∈ SubSh(L)(U). Thus, by chasing the element U ∈ SubSh(L)(f ∗よ(c)) +through the diagram, we observe that U ∧ (f∗j)c(U) = jU(U) = U. Thus, U ⩽ (f∗j)c(U) as desired. +Conversely, given an internal nucleus k: L ∼= f∗(ΩSh(L)) → L ∼= f∗(ΩSh(L)), we define an endomorphism +kf on the subobject classifier ΩSh(L), viewed as a sheaf +ΩSh(L) : (C ⋊ L)op → Sets, +by setting kf +(c,U)(V ) as kc(V ) ∧ U, for each (c, U) ∈ C ⋊ L and V ∈ ΩSh(L)(c, U) = { V ∈ O(Lc) | V ⩽ U }. +We now demonstrate that kf is an Lawvere-Tierney topology. +As k is an internal nucleus, it is clear that, for each (c, U) ∈ C ⋊ L, the diagrams +1(c, U) +ΩSh(L)(c, U) +ΩSh(L)(c, U) +ΩSh(L)(c, U) +ΩSh(L)(c, U), +ΩSh(L)(c, U), +⊤(c,U) +⊤(c,U) +kf +(c,U) +kf +(c,U) +kf +(c,U) +kf +(c,U) +25 + +ΩSh(L) × ΩSh(L)(c, U) +ΩSh(L)(c, U) +ΩSh(L) × ΩSh(L)(c, U) +ΩSh(L)(c, U) +∧ +kf +(c,U)×kf +(c,U) +kf +(c,U) +∧ +all commute. It remains to observe that kf is natural. For each arrow (c, U) +g−→ (d, V ) of C ⋊ L, the diagram +ΩSh(L)(d, V ) +ΩSh(L)(c, g−1(V )) +ΩSh(L)(c, U) +ΩSh(L)(d, V ) +ΩSh(L)(d, g−1(V )) +ΩSh(L)(c, U) +kf +(d,V ) +kf +(c,g−1(V )) +kf +(c,U) +commutes. The left-hand square commutes since, for each W ∈ Ld with W ⩽ V , +kc(g−1(W)) ∧ g−1(V ) = g−1(kd(W)) ∧ g−1(V ) = g−1(kd(W) ∧ V ). +Meanwhile, the right-hand square commutes since kc(W ∧ U) ∧ U = kc(W) ∧ U for each W ∈ Lc with +W ⩽ g−1(V ). +Finally, the bijection is completed by noting that, for each c ∈ C and U, V ∈ Lc, +(f∗kf)c(V ) = kf +(c,⊤)(V ) = kc(V ) ∧ ⊤ = jc(V ) +and +(f∗j)f +(c,U)(V ) = j(c,⊤)(V ) ∧ U = j(c,U)(V ), +for each internal nucleus k on L and each Lawvere-Tierney topology j on ΩSh(L). +5.3 +The Frame of Internal Nuclei +In this final subsection, we consider the poset of internal nuclei on an internal locale, and demonstrate that +it forms a frame whose frame operations can be computed ‘point-wise’. +Let L be a locale and let N(L) denote the set of nuclei on L. We can order N(L) by setting j ⩽ k if +j(U) ⩽ k(U) for all U ∈ O(L). Recall, from [10, Proposition II.2.5] say, that so ordered N(L) is a frame. +The set of sublocales of L, written as SubLoc(L), can also be ordered with [K ֌ L] ⩽ [K′ ֌ L] if and only +if there is a factorisation +K +K′ +L. +Under the bijection between nuclei and sublocales, this is precisely the order dual N(L) ∼= SubLoc(L)op, and +hence SubLoc(L) is a co-frame. +Definitions 5.8. Let L: Cop → Frmopen be an internal locale of Sh(C, J) and let E be a topos. +(i) By N(L) we denote the poset of internal nuclei on L ordered by j ⩽ k if and only if, for each c ∈ C +and U ∈ Lc, jc(U) ⩽ kc(U) for each pair of internal nulcei on L. +(ii) By LT(E) we denote the poset of Lawvere-Tierney topologies for E, ordered by j ⩽ k if and only if +j = j ∧ k, given two Lawvere-Tierney topologies j, k: ΩE → ΩE (this poset is denoted as Lop(E) in +[12, §A.5]). +(iii) By Sub(E) we denote the poset of subtoposes of E ordered by [F′ ֌ E] ⩽ [F ֌ E] if and only if there +is a factorisation of geometric morphisms +F′ +F +E. +26 + +(iv) By SubLoc(Sh(C,J))(L) we denote the poset of internal sublocales of L ordered by [L′ ֌ L] ⩽ [L′′ ֌ L] +if and only if there is a factorisation of internal locale morphisms +L′ +L′′ +L. +Under the bijections established in Theorem 5.7, there is an isomorphism of posets: +N(L) ∼= LT(Sh(L)) ∼= Sub(Sh(L))op ∼= SubLoc(Sh(C,J))(L)op +(where the latter two posets are the order duals of Sub(Sh(L)) and SubLoc(Sh(C,J))(L) respectively). We +know already, from [12, §A4.5] say, that Sub(Sh(L)) is a complete co-Heyting algebra, i.e. a co-frame. We +will give an alternative proof using internal nuclei that N(L) is a frame. +Moreover, we will show that the frame operations of N(L) can be computed ‘point-wise’. That is, for +each subset { ji | i ∈ I } ⊆ N(L) and each object c of C, there are equalities +�� +i∈I +ji +� +c += +� +i∈I +ji +c, +�� +i∈I +ji +� +c += +� +i∈I +ji +c, +where � +i∈I ji +c and � +i∈I ji +c are computed as in N(Lc). The first of these equalities is easily shown. +Lemma 5.9. The meet of a subset { ji | i ∈ I } ⊆ N(L) is given by +�� +i∈I +ji +� +c +(U) = +� +i∈I +ji +c(U), +(8) +for each c ∈ C and U ∈ Lc. +Proof. If (8) defines a valid internal nucleus on L, it must clearly be the meet of { ji | i ∈ I } ⊆ N(L). Recall +from [10, Proposition II.2.5] that � +i∈I ji +c yields a nucleus on Lc. As g−1 : O(Ld) → O(Lc) is open, for an +arrow c +g−→ d of C, it preserves all meets and so +g−1 +�� +i∈I +ji +d(U) +� += +� +i∈I +g−1ji +d(U) = +� +i∈I +ji +cg−1(U). +Thus, � +i∈I ji defines an internal nucleus on L. +We will demonstrate that N(L) is a frame by generalising the notion of a pre-nucleus on a locale, recalled +below, to the internal setting. +We give some justification as to why the frame operations can be computed ‘point-wise’ as described in +Theorem 5.13 below. Recall that the suptoposes of Sh(C, J) correspond to Grothendieck topologies J′ on C +that contain J. In the case of a Grothendieck topology J on C ⋊ L that contains KL, we observe that the +added data is generated by new covering families on the fibres Lc. Specifically, adding a new covering family +{ (ci, Ui) +fi +−→ (c, U) | i ∈ I } to KL is equivalent to requiring that the family { (c, ∃fiUi) +idc +−−→ (c, U) | i ∈ I } is +covering. +Pre-nuclei of Locales. +There are many proofs of the fact that, for each locale L, N(L) is a frame. For +example, the proof found in [10, Proposition II.2.5] shows that N(L) is a complete Heyting algebra by +defining the Heyting operation. Alternative approaches using pre-nuclei are considered in [17] and [5]. We +will follow the argument of [17] when developing our internal generalisation. We briefly repeat the argument +for locales below. +Recall from [17, §2] that a pre-nucleus on a locale L is a (necessarily monotone) map p: L → L that is +inflationary and finite-meet-preserving: that is, for all U, V ∈ L, +U ⩽ p(U), +p(U ∧ V ) = p(U) ∧ p(V ). +27 + +Thus, a nucleus on L is simply an idempotent pre-nucleus. +Unlike nuclei, pre-nuclei are closed under +composition. +We denote by PN(L) the poset of pre-nuclei on L ordered by p ⩽ q if p(U) ⩽ q(U) for all U ∈ L. It is +clear that PN(L) is a complete lattice: for each subset { pi | i ∈ I } ⊆ PN(L) and U ∈ L, +�� +i∈I +pi +� +(U) = +� +i∈I +pi(U), +�� +i∈I +pi +� +(U) = +� +i∈I +pi(U), +where � +i∈I pi(U) and � +i∈I pi(U) are calculated as in L. It follows by the infinite distributive law for L that +PN(L) is also a frame. +In [5, Lemma 2.1] it is shown that the inclusion of nuclei into pre-nuclei N(L) ֒→ PN(L) has a left +adjoint (−)∞ : PN(L) → N(L), which we call the nucleation (the nuclear reflection in [5] and idempotent +closure in [17]), constructed as follows. For each ordinal α and limit ordinal λ, we define inductively: +p0(U) = U, +pα+1(U) = p(pα(U)), +pλ(U) = +� +α<λ +pα(U). +At each stage, the resultant map pκ : L → L is a pre-nucleus. Necessarily, as L is small, there is a sufficiently +large ordinal κ such that pκ is idempotent and therefore a nucleus. We label this p∞. We observe that if +p ⩽ q then p∞ ⩽ q∞, that p ⩽ p∞, and if j is a nucleus then j = j∞. That is, nucleation is functorial, and +has units and counits yielding the adjunction +N(L) +PN(L) +(−)∞ +⊥ +witnessing N(L) as a reflective subcategory of PN(L). +Thus, N(L), in addition to the meets constructed in Lemma 5.9, has all joins: for a subset +{ ji | i ∈ I } ⊆ N(L), +the join in N(L) is given by +�� +i∈I ji�∞. The infinite distributive law for N(L), and hence the fact that +N(L) is a frame, is a consequence of Lemma 5.10 below. +Lemma 5.10 (cf. Lemma 3.1 [17]). Let L be a locale, n a nucleus on L, and let { pi | i ∈ I } be a collection +of pre-nuclei on L. The infinite distributive law +� +n ∧ +� +i∈I +pi +�∞ += n ∧ +�� +i∈I +pi +�∞ +holds. +Proof. We will show that +� +n ∧ � +i∈I pi�κ = n ∧ +�� +i∈I pi�κ, for each ordinal κ, and thereby deduce the result. +The base case +� +n ∧ +� +i∈I +pi +�0 += idL = n ∧ +�� +i∈I +pi +�0 +is trivial. +Suppose that +� +n ∧ � +i∈I pi�α = n ∧ +�� +i∈I pi�α, then: +� +n ∧ +� +i∈I +pi +�α+1 += +� +n ∧ +� +i∈I +pi +� � +n ∧ +� +i∈I +pi +�α +, += n +�� +n ∧ +� +i∈I +pi +�α� +∧ +� +i∈I +pi +�� +n ∧ +� +i∈I +pi +�α� +, += n ∧ n +��� +i∈I +pi +�α� +∧ +� +i∈I +pin ∧ pi +��� +i∈I +pi +�α� +. +28 + +Using that n ⩽ n +��� +i∈I pi�α� +, and n ⩽ pin, for all i, we have that: +� +n ∧ +� +i∈I +pi +�α+1 += n ∧ +� +i∈I +pin ∧ pi +��� +i∈I +pi +�α� +, += +� +i∈I +n ∧ pin ∧ pi +��� +i∈I +pi +�α� +, += +� +i∈I +n ∧ pi +��� +i∈I +pi +�α� +, += n ∧ +�� +i∈I +pi +�α+1 +. +Finally, if λ is a limit ordinal such that +� +n ∧ � +i∈I pi�α = n ∧ +�� +i∈I pi�α for each ordinal α < λ, then: +� +n ∧ +� +i∈I +pi +�λ += +� +α<λ +� +n ∧ +� +i∈I +pi +�α +, += +� +α<λ +n ∧ +�� +i∈I +pi +�α +, += n ∧ +�� +i∈I +pi +�λ +. +Internal Pre-nuclei. +We now extend the theory of pre-nuclei and nucleation to the internal context. In +doing so we will observe that N(L) is a frame for every internal locale. +Definition 5.11. Let L be an internal locale of Sh(C, J). An internal pre-nucleus is a natural transformation +p: L → L such that, for each c ∈ C, pc: Lc → Lc is a pre-nucleus. The set of internal pre-nuclei, denoted by +PN(L), can be ordered by p ⩽ q if pc(U) ⩽ qc(U) for all c ∈ C and U ∈ Lc. +The poset of internal pre-nuclei PN(L) on an internal locale L of Sh(C, J) has all meets and all joins, +which are computed ‘point-wise’. Thus, by the infinite distributivity law for Lc, for each c ∈ C, PN(L) is a +frame. We show that an internal nucleation can be performed ‘point-wise’. +Lemma 5.12. Let p: L → L be an internal pre-nucleus on an internal locale L, fibred over a category C. +The pointwise nucleations p∞ +c : L → Lc of each component pc of p are the components of an internal nucleus. +Proof. For each object c ∈ C, the nucleation p∞ +c : Lc → Lc of pc is a nucleus, so it remains only show that +they are natural in c. This is easily shown by induction. We will perform the case for a limit ordinal λ. Let +g : c → d be an arrow of C. If, for all α < λ, the square +Ld +Lc +Ld +Lc +g−1 +pα +d +pα +c +g−1 +commutes, then we have the desired equality +g−1 +� � +α<λ +pα +d +� += +� +α<λ +g−1pα +d = +� +α<λ +pα +c g−1. +29 + +As a result, we obtain a left adjoint to the inclusion N(L) ֒→ PN(L), +N(L) +PN(L), +(−)∞ +⊥ +just as we did for locales. +The functor (−)∞ : PN(L) → N(L), the internal nucleation, sends internal +pre-nuclei to their point-wise nucleation. +Theorem 5.13. Let L be an internal locale of Sh(C, J). The poset N(L) of internal nuclei is a frame whose +frame operations can be computed ‘point-wise’ in that, for each subset { ji | i ∈ I } ⊆ N(L) and each object +c of C, there are equalities +�� +i∈I +ji +� +c += +� +i∈I +ji +c, +�� +i∈I +ji +� +c += +� +i∈I +ji +c, +(9) +where � +i∈I ji +c and � +i∈I ji +c are computed as in N(Lc). +Proof. We saw in Lemma 5.5 that N(L) has all meets and that these are computed pointwise. The join of +{ ji | i ∈ I } ⊆ N(L) is the nucleation of the join of { ji | i ∈ I } as internal pre-nuclei. Since the nucleation +of internal pre-nuclei is computed pointwise, as are joins in PN(L), the joins in N(L) are also computed +pointwise in the sense of (9). Finally, as N(Lc) satisfies the infinite distributivity law for each c ∈ C, we +obtain the infinite distributivity law for N(L). +Remark 5.14. Let L: Cop → Frmopen be an internal locale of Sh(C, J). Since the frame operations of +N(L) are computed ‘point-wise’, for each object c of C, the projection πc : N(L) → N(Lc) that sends an +internal nucleus j : L → L to its component jc : Lc → Lc at c preserves all joins and meets. Therefore, +πc : N(L) → N(Lc) is an open frame homomorphism. +Corollary 5.15 (§A4.5 [12]). The poset of subtoposes of a Grothendieck topos is a co-frame. +Proof. Every Grothendieck topos E is the topos of sheaves Sh(L) for some internal locale L (see, for example, +[13, Proposition VII.3.1]). The result follows as Sub(E) ∼= N(L)op. +Acknowledgements +I thank the support of my supervisor Olivia Caramello, and acknowledge the financial support of the Insubria- +Huawei studentship into “Grothendieck toposes for information and computation”. +References +[1] +O. Caramello, Theories, sites, toposes: relating and studying mathematical theories through topos- +theoretic ‘bridges’. Oxford University press, 2018. +[2] +——, “Denseness conditions, morphisms and equivalences of toposes,” 2020. arXiv: 1906.08737 [math.CT]. +[3] +——, “Fibred sites and existential toposes,” 2022. arXiv: 2212.11693 [math.AG]. +[4] +O. Caramello and R. Zanfa, “Relative topos theory via stacks,” 2021. arXiv: 2107.04417 [math.AG]. +[5] +M. Escard´o, “Joins in the frame of nuclei,” Applied Categorical Structures, vol. 11, pp. 117–124, 2003. +[6] +J. Giraud, “Classifying topos,” in Toposes, Algebraic Geometry and Logic, F. W. Lawvere, Ed., Berlin, +Heidelberg: Springer Berlin Heidelberg, 1972, pp. 43–56. +[7] +P. T. Johnstone, Topos Theory. Academic Press, 1977. +[8] +——, “Open maps of toposes,” Manuscripta mathematica, vol. 31, pp. 217–248, 1980. +[9] +——, “Factorization theorems for geometric morphisms, I,” Cahiers de Topologie et G´eom´etrie Diff´erentielle +Cat´egoriques, vol. 22, no. 1, pp. 3–17, 1981. +30 + +[10] +——, Stone Spaces, ser. Cambridge Studies in Advanced Mathematics. Cambridge University Press, +1982. +[11] +——, “The point of pointless topology,” Bulletin (New Series) of the American Mathematical Society, +vol. 8, no. 1, pp. 41–53, 1983. +[12] +——, Sketches of an Elephant: A topos theoretic compendium, Vol. 1 and 2. Oxford University Press, +2002. +[13] +A. Joyal and M. Tierney, “An extension of the Galois theory of Grothendieck,” Memoirs of the Amer- +ican Mathematical Society, vol. 51, 1984. +[14] +A. Kock and I. Moerdijk, “Presentations of ´etendues,” Cahiers de Topologie et G´eom´etrie Diff´erentielle +Cat´egoriques, vol. 32, no. 2, pp. 145–164, 1991. +[15] +S. MacLane and I. Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory. +Springer New York, 1994. +[16] +J. Picado and A. Pultr, Frames and Locales: Topology without points. Springer Basel, 2012. +[17] +H. Simmons, “Near-discreteness of modules and spaces as measured by Gabriel and Cantor,” Journal +of Pure and Applied Algebra, vol. 56, no. 2, pp. 119–162, 1989. +31 + diff --git a/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/load_file.txt b/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..85933df6ca7acc32b39d32c1463b9e8c2ef66222 --- /dev/null +++ b/xtAzT4oBgHgl3EQfCfq3/content/tmp_files/load_file.txt @@ -0,0 +1,1313 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf,len=1312 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='00961v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='AG] 3 Jan 2023 Some Properties of Internal Locale Morphisms Externalised J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Wrigley∗ January 4, 2023 Abstract We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as, respectively, fibred pre-orders and natural transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We characterise those morphisms of internal locales that induce surjective geometric morphisms, open geometric mor- phisms and geometric embeddings, and we demonstrate that surjections and embeddings can be computed ‘point-wise’ on the components of the underlying natural transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Internal nuclei on an internal locale are then introduced, as a generalisation of nuclei on a locale, in order to study subtoposes of the topos of internal sheaves on an internal locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We show that the frame operations on the frame of inter- nal nuclei, and therefore the co-frame operations on the co-frame of subtoposes, can also be computed ‘point-wise’ via the frame of nuclei on the locale of each fibre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Contents 1 Introduction 1 2 Morphisms and Comorphisms of Sites 3 3 Internal Locales 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Over a Non-Cartesian Category .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Gluing Internal Locales .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 Internal Locales of Sheaf Toposes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 13 4 Internal Locale Morphisms 14 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Internal Locale Morphisms and Geometric Morphisms .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 15 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Surjective Internal Locale Morphisms .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 18 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 Open Internal Locale Morphisms .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 19 5 Internal Embeddings and Nuclei 21 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Internal Nuclei .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 22 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Geometric Embeddings .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 24 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 The Frame of Internal Nuclei .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 26 1 Introduction By and large, the topologically interesting data of a space X (respectively, a continuous map f : X → Y ) is contained in the algebra of open subsets O(X) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=', the inverse image map f −1 : O(Y ) → O(X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This prompted the shift to ‘point-free’ topology, as exposited in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The notions of frame and frame homomorphism capture these algebraic aspects of topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ∗Universit`a degli Studi dell’Insubria, Via Valleggio n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 11, 22100 Como CO, email: jwrigley@uninsubria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='it 1 Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A frame L is a complete lattice satisfying, for each { Ui | i ∈ I } ⊆ L and V ∈ L, the infinite distributivity law V ∧ � i∈I Ui = � i∈I V ∧ Ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A frame homomorphism is any map between frames that preserves arbitrary joins and finite meets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We denote the resultant category by Frm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our motivating examples, the algebra of opens O(X) of a topological space X and the inverse image map f −1 : O(Y ) → O(X) of a continuous map f : X → Y , are both examples of, respectively, a frame and a frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' To strengthen the analogy with topological spaces, one often works with the category of locales Loc ≃ Frmop instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Notation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For a locale morphism f : L → K, we will use f −1 : K → L to denote the corresponding frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Additionally, each frame homomorphism f −1 : K → L has a right adjoint f∗ : L → K, since K is complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since a topos E comes equipped with a rich internal language, we can consider internal locales of E, which are structured objects that behave, according to the internal language of E, as a locale (equivalently, a complete Heyting algebra, see [16, Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2, Appendix I]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Examples 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (i) Unsurprisingly, the internal locales of Sets, the topos of sets, are just locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) For any topos E, the subobject classifier ΩE is an internal locale of E (that ΩE is an internal Heyting algebra is shown in [15, Theorem IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1], and that ΩE is internally complete is shown in [12, Examples B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8(a)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In fact, we will see in Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 that ΩE is the terminal internal locale in E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The development of a study of internal locales has coincided with profound advances in topos theory as evidenced by Joyal and Tierney’s landmark work [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Internal locales can be understood both internally and externally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' When E is a Grothendieck topos with a presenting site (C, J), an external treatment of the internal locales of E involves working explicitly with those J-sheaves L: Cop → Sets that define locales internal to E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Examples of external accounts of internal locale theory can be found in §VI [13], §C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6 [12] and §4-5 [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Neglecting an external treatment could hamper calculating with internal locales for applications outside of topos theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In this paper, we will study, externally, internal locale morphisms and some of their properties in the style of the treatment given for localic toposes and their morphisms in §IX [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In doing so, we will show that many important properties and constructions on internal locales can be computed ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We begin, in §2, by recalling some site-theoretic notions, principally morphisms and comorphisms of sites, that will frequently appear in our treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Additionally, in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 we prove a result, that we will need in subsequent sections, regarding the commutativity of the geometric morphisms induced by a mixed diagram of morphisms and comorphisms of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In §3, a review is given of the classification of internal locales for the Grothendieck topos Sh(C, J) as established in Proposition VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [13] (see also [12, Lemma C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9 & Corollary C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10]), when C is assumed to be a cartesian category, and in Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 [3] for an arbitrary category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We recall that an internal locale of Sh(C, J) is defined by a J-sheaf L: Cop → Sets that factors through Frmopen, the category of frames and open frame homomorphisms (see [13, Definition V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]), and which satisfies the relative Beck-Chevalley condition (see [3, Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1(e)(i)];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' in the case when C is cartesian, this is equivalent to the Beck-Chevalley condition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We also review the construction of the relative topos of internal sheaves Sh(L) → E on an internal locale L of E as described in [12, Examples C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8(c)] and [3, Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 we prove a result regarding the ‘gluing’ of internal locales together, which allows the easy identification of examples (and non-examples) of functors L: Cop → Frmopen that define internal locales of the topos SetsCop, for certain, potentially non-cartesian, categories C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our study of internal locale morphisms begins in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is well-known (see [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2]) that, given two locales X, Y , there is a bijective correspondence between locale morphisms X → Y and geometric morphisms Sh(X) → Sh(Y ) between the respective sheaf toposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By an analogous internalised account (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [13, §VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] or [9, §2]), given internal locales L and L′ of a Grothendieck topos E ≃ Sh(C, J), there is an 2 equivalence between internal locale morphisms f: L → L′ and geometric morphisms g for which the diagram Sh(L) Sh(L′) E g commutes, as fully shown in [3, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our first task, undertaken in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1, is to demonstrate this equivalence with internal locale morphisms as natural transformations between the underlying sheaves L, L′ : Cop → Sets as defined in §VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 of [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is further shown, in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 and §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3, that the geometric mor- phism Sh(f) induced by an internal locale morphism f: L → L′ is surjective if and only if each component f−1 c : L′(c) → L(c), for c ∈ C, is a surjective frame homomorphism, and open if and only if each component f−1 c : L′(c) → L(c) is open frame homomorphism and the respective left adjoints ∃fc are natural in c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Those internal locale morphisms that induce embeddings of subtoposes are the subject of the final section §5, where it is shown that such internal locale embeddings coincide with ‘point-wise’ locale embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We also introduce, in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1, the notion of an internal nucleus on an internal locale L: Cop → Frmopen of Sh(C, J), in order to study the co-frame Sub(Sh(L)) of subtoposes of Sh(L) (shown to be a co-frame in [12, §A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5], cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' also [1, §4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In addition to demonstrating a correspondence between the internal nuclei on L, its internal sublocales and the subtoposes Sub(Sh(L)), we show in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 that the co-frame operations of Sub(Sh(L)) can be computed ‘point-wise’ via the co-frame operations on SubLoc(L(c)), the co-frame of sublocales of L(c), for each c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 2 Morphisms and Comorphisms of Sites Familiarity with introductory topos theory, such as can be found in [15], is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In this section, we recall some site-theoretic notions, found in [15, §VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10] and studied in detail in [2], that will make frequent appearances in our treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Two notions will be central to our development: comorphisms of sites and morphisms of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (C, J) and (D, K) be sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A comorphism of sites F : (C, J) → (D, K) is a functor F : C → D with the cover lifting property: for each object c of C and K-covering sieve S on F(c), there exists a J-covering sieve R on c such that F(R) ⊆ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A comorphism of sites F : (C, J) → (D, K) induces a geometric morphism CF : Sh(C, J) → Sh(D, K) (see [15, Theorem VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5]) for which the inverse image C∗ F is given by aJ(− ◦ F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The composite of two comorphisms of sites F and G is still a comorphism of sites whose induced geometric morphism is the composite CF ◦G = CF ◦ CG since aJ(− ◦ F ◦ G) = aJ(aK(− ◦ F) ◦ G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (C, J) and (D, K) be sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A morphism of sites F : (C, J) → (D, K) is a functor F : C → D satisfying the following conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (i) If S is a J-covering sieve on c ∈ C, then F(S) is a K-covering family of morphisms on F(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) Every object d of D admits a K-covering sieve { di → d | i ∈ I } such that each di, for i ∈ I, has a morphism di → F(ci) to the image of some ci ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) For any pair of objects c1, c2 of C and any pair of morphisms g1 : d → F(c1), g2 : d → F(c2) of D, there exists a K-covering family { hi : di → d | i ∈ I } of morphisms in D, a pair of families { f 1 i : ci → c1 | i ∈ I }, { f 2 i : ci → c2 | i ∈ I } 3 of morphisms in C, and, for each i ∈ I, a morphism ki : di → F(c′ i) such that the squares di d di d F(ci) F(c1) F(ci) F(c2) hi ki g1 hi ki g2 F (f 1 i ) F (f 2 i ) commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iv) For any pair of parrallel arrows f1, f2 : c′ → c of C, and any arrow g : d → F(c′) of D such that F(f1) ◦ g = F(f2) ◦ g, there exists a K-covering family { hi : di → d | i ∈ I } of morphisms of D, a family of morphisms { ei : ci → c′ | i ∈ I } of C such that f1 ◦ ei = f2 ◦ ei for all i ∈ I, and, for each i ∈ I, a morphism ki : di → F(ci) such that the square di d F(ci) F(c′) hi ki g F (ei) commutes for each i ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A morphism of sites F : (C, J) → (D, K) induces a geometric morphism Sh(F): Sh(D, K) → Sh(C, J) (see [15, Theorem VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2]), for which the direct image Sh(F)∗ sends a sheaf P : Dop → Sets of Sh(D, K) to P ◦ F op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A functor F : C → D is a morphism of sites F : (C, J) → (D, K) if and only if there exists a geometric morphism f : Sh(D, K) → Sh(C, J) such that the square C D Sh(C, J) Sh(D, K) ℓ F ℓ′ f ∗ commutes (see [2, §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2]), and therefore it follows that the composite of two morphisms of sites is still a morphism of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We observe that, just as with comorphisms of sites, Sh(F ◦ G) = Sh(G) ◦ Sh(F) for any two morphisms of sites F and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Given a site (D, K), under certain conditions, the inclusion of a subcategory C ֒→ D can induce an equivalence of toposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This is the familiar Comparison Lemma (see [14, §2] or [12, Theorem C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A subcategory C ⊆ D of a site (D, K) is dense for K if: (i) for every d ∈ D, there is a covering family S ∈ K(d) generated by morphisms whose domains are in C, (ii) for every arrow c g−→ d ∈ D with d ∈ C, there is a covering family S ∈ K(c) generated by morphisms b f−→ c such that g ◦ f is in C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4 (The Comparison Lemma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (D, K) be a site and let C be a K-dense subcategory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There is an equivalence Sh(D, K) ≃ Sh(C, K|C), where a sieve in C is K|C-covering if and only if the same family of arrows is K-covering in D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (D, K) be a site and let C be a dense subcategory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The equivalence Sh(D, K) ≃ Sh(C, K|C) is induced by the inclusion functor ⊆: C → D acting as both a comorphism and a morpism of sites (C, K|C) → (D, K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 4 A mixed diagram of morphisms and comorphisms of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We complete this section with a result regarding the commutativity of a certain diagram of geometric morphisms induced by morphisms and co- morphisms of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [12, Definition B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4] that a fibration A: C → E is a functor such that, for each object c of C and an arrow e f−→ A(c), there exists a cartesian lifting d g−→ c of f, that is an arrow of C such that A(g) = f and, for any arrows d′ h−→ c of C and A(d′) k−→ A(d) of E for which A(d′) A(d) A(c) k A(h) A(g) commutes, there exists an arrow d′ k′ −→ d of C such that A(k′) = k (note that we are using the terminology ‘cartesian arrow’ where Johnstone uses ‘prone’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall also that, given a pair of fibrations A: C → E and B : D → F, a morphism of the fibrations A → B consists of a pair of functors F : C → D and G: E → F such that the square C D E F F A B G commutes and, if d g−→ c ∈ C is cartesian, so too is F(d) F (g) −−−→ F(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (C, J), (D, K), (E, L) and (F, M) be sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let A: C → E and B : D → F both be fibrations and let F : C → D and G: E → F be functors such that the square C D E F F A B G (1) is a morphism of fibrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose that the functors A and B yield comorphisms of sites A: (C, J) → (E, L) and B : (D, K) → (F, M), and that the functors F and G yield morphisms of sites F : (C, J) → (D, K) and G: (E, L) → (F, M), then the induced square of geometric morphisms Sh(C, J) Sh(D, K) Sh(E, L) Sh(F, M) CA Sh(F ) CB Sh(G) also commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By [2, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='16], we are able to transform the morphism of sites F : (C, J) → (D, K) into a comorphism of sites thusly: there are functors C (1D ↓F) D iF πC πD where (i) (1D ↓ F) is the comma category whose objects are triples (d, c, a: d → F(c)) of objects d ∈ D, c ∈ C, and an arrow α: d → F(c) in D;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) πC and πD are the respective projection functors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) iF : C → (1D ↓F) is the functor that sends c ∈ C to (F(c), c, idF (c) : F(c) → F(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moreover,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' when the category (1D ↓F) is endowed with the Grothendieck topology ˜K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' whose covering sieves are precisely those that are sent by πD to K-covering sieves,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' we have that 5 (i) πC : ((1D ↓F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ˜K) → (C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' J) is a comorphism of sites,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) iF : (C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' J) → ((1D ↓F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ˜K) is a morphism of sites,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) πD : ((1D ↓F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ˜K) → (D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' K) is both a morphism and comorphism of sites and induces an equivalence of toposes Sh((1D ↓F),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ˜K) ≃ Sh(D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' K),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' and also that Sh(F) = CπC ◦ Sh(πD),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' and CπD is an inverse to Sh(πD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Similarly, there are functors E (1F ↓G) F iG πE πF with analogous properties, in particular Sh(G) = CπE ◦ Sh(πF) and CπF is an inverse for Sh(πF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We construct a comorphism of sites H : ((1D ↓F), ˜K) → ((1F ↓G), ˜ M) such that the diagram C (1D ↓F) D E (1F ↓G) F A πC H πD B πE πF (2) commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Define the functor H as sending an object (d, c, α: d → F(c)) to (B(d), A(c), B(α): B(d) → B(F(c))) = (B(d), A(c), B(α): B(d) → G(A(c))), and similarly an arrow (g, h): (d′, c′, α′ : d′ → F(c′)) → (d, c, a: d → F(c)) is sent to (B(g), A(h)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The functor H clearly makes the diagram (2) commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show that H is cover lifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let S = � (fi, ei, β : fi → G(ei)) (gi,hi) −−−−→ (B(d), A(c), B(α): B(d) → G(A(c))) | i ∈ I � be a ˜ M-covering sieve, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' πF(S) is M-covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As A is a fibration, there exists, for each i ∈ I, a cartesian lifting of hi : ei → A(c) to an arrow h′ : c′ → c in C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since (1) is a morphism of fibrations, F(h′): F(c′) → F(c) is also cartesian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As B has the cover lifting property, there exists a K-covering sieve R on d such that B(R) ⊆ πF(S), that is, for each k: d′ → d in R, there exists an i ∈ I such that B(k) factors as B(d′) fi B(d) B(F(c′)) B(F(c)) = G(A(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' B(k) β gi B(α) B(F (h′)) As F(h′) is cartesian, there is a unique arrow γ : d′ → F(c′) making the square d′ d F(c′) F(c) k γ α F (h′) commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, { (d′, c′, γ : d → F(c′)) (k,h′) −−−−→ (d, c, α: d → F(c)) | k ∈ R } is a K-covering lifting of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By the commutation of (2), we deduce that the induced diagram of geometric morphisms Sh(C, J) Sh((1D ↓F), ˜K) Sh(D, K) Sh(E, L) Sh((1F ↓G), ˜ M) Sh(F, M) CA CπC CH CπD CB CπE CπF 6 commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thereby, we conclude that CA ◦ Sh(F) = CA ◦ CπC ◦ Sh(πD), = CπE ◦ CH ◦ Sh(πD), = CπE ◦ Sh(πF) ◦ CπF ◦ CH ◦ Sh(πD), = Sh(G) ◦ CB ◦ CπD ◦ Sh(πD), = Sh(G) ◦ CB as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will be exclusively concerned with faithful fibrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let P : Eop → PreOrd be a functor (also known as a fibred pre-order over E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By E ⋊ P we denote the Grothendieck construction (see [12, Definition B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] for the general definiton), the category which has: (i) as objects, pairs (e, x) where e is an object of E and x is an element of P(e), (ii) and an arrow f : (e, x) → (d, y) for each arrow f : e → d in E such that x ⩽ P(f)(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The evident projection functor pP : E ⋊ P → E is faithful and a fibration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' in fact – assuming the axiom of choice – every faithful fibration is of the form E ⋊ P for some P (see [12, §B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 3 Internal Locales We devote this section to a review of the internal locale theory of Grothendieck toposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will require an externalisation of internal locales: that is, given a Grothendieck topos E with a site of definition (C, J), a classification for which J-sheaves L: Cop → Sets correspond to internal locales of E ≃ Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' An externalised treatment of internal locales can be found in §VI [13] and §C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6 [12] for the special case when C is cartesian (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' C has all finite limits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' When C is non-cartesian, Section 5 [3] establishes a classification of internal locales of Sh(C, J), which we recall in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The statement of the classification from §VI [13] and §C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6 [12] for internal locales of the presheaf topos SetsCop, when C is assumed to be cartesian, is recalled below in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' An overview of the classification of internal locales of SetsCop, where C is an arbitrary category, as calculated in §5 [3], is given in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 we prove a corollary of the classification established in [3] useful in calculating examples and identifying non-examples of internal locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 demonstrates how a classification of the internal locales of SetsCop yields a classification of the internal locales of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Notation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By Frmopen we denote the category of frames and open frame homomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [13, Definition V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] that a frame homomorphism f −1 : L → K is open if there exists a left adjoint ∃f : K → L which satisfies the Frobenius condition: that for all U ∈ L and V ∈ K, U ∧ ∃f(V ) = ∃f(f −1(U) ∧ V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Equivalently, f is open if it is a morphism of complete Heyting algebras (see [13, Proposition V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Given a functor L: Cop → Frmopen, an object c and an arrow g of C, when there is no confusion we will use the shorthand Lc for L(c), g−1 for L(g) and ∃g for the left adjoint to L(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 (Proposition VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [13] & Lemma C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9 [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let C be a category with all finite limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The internal locales of SetsCop are precisely those functors L: Cop → Frmopen which satisfy the Beck-Chevalley condition: for each pullback square c ×e d d c e k g h f 7 of C, the square Lc×ed Ld Lc Le ∃g ∃f k−1 h−1 commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As observed in [3, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4], the classification presented in the following section, of internal locales of SetsCop for an arbitrary category C, coincides with the classification of Proposition VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [13] and Lemma C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9 [12] when C is cartesian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In fact, not all finite limits are needed: we will observe that only pullbacks are required for the Beck-Chevalley condition to be a necessary and sufficient condition for when a functor L: Cop → Frmopen defines an internal locale of the topos SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Over a Non-Cartesian Category We now give an overview of the classification of internal locales of SetsCop for an arbitrary category C as can be found in §5 [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Localic geometric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The keystone property used in the classification of internal locales is the connection between internal locales and localic geometric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A geometric morphism f : F → E is localic if every object F of F is a subquotient of f ∗(E) for some E ∈ E, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' there exists F ′ ∈ F and a diagram F F ′ f ∗(E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As remarked in [12, Definition A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1], this is equivalent to saying that 1F is a bound (see [12, Definition B3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7]) for F over E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Localic geometric morphisms f : F → E correspond bijectively (up to isomorphism) to internal locales of E via the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4 (Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='37 [7] or Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [9], cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' also Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For a geometric morphism f : F → E, the following are equivalent: (i) f is a localic geometric morphism, (ii) F is the topos of internal sheaves on an internal locale of E, and moreover this internal locale can be taken as f∗(ΩF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This bijection can be visualised with the ‘bridge’ diagram: F ≃ Sh(C, J) E localic morphism f∗(ΩF) direct image of subobject classifier L ∈ E internal locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f Let L be an internal locale of E ≃ Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It appears as the direct image of the subobject classifier f∗(ΩF) ∼= L for some localic geometric morphism f : F → E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Considered as a sheaf f∗(ΩF): Eop → Sets on the canonical site (E, Jcan) for E, there is the chain of isomorphisms f∗(ΩF) ∼= HomE(−, f∗(ΩF)), ∼= HomF(f ∗(−), ΩF), ∼= SubF(f ∗(−)) 8 (here, the first isomorphism is by the Yoneda lemma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, by composing with the canonical morphism ℓ: C → Sh(C, J) (that is, the Yoneda embedding followed by sheafification), we obtain the isomorphism of J-sheaves: L ∼= SubF(f ∗ ◦ ℓ(−)): Cop → Sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (3) Thus, we can observe some basic facts about the internal locale L: (i) for each object c of C, L(c) is a complete Heyting algebra, or frame, by [15, Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) for each arrow f : c → d of C, by [15, Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], L(f): L(d) → L(c) is an open frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Although not every such functor L′ : Cop → Frmopen will yield an internal locale, even when L′ satisfies the Beck-Chevalley condition for those pullbacks that exist in C (an example is given in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='12), it is possible to characterise when they do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The topos of internal sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f : F → E be a geometric morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There exists a canonical relative site ((1F ↓ f ∗), Jf) for the topos F (see [2, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='16]), where: (i) (1F ↓ f ∗) is the comma category whose objects are triples (F, E, F a−→ f ∗(E)) consisting of objects F ∈ F, E ∈ E, and an arrow F a−→ f ∗(E) in E;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) Jf is the Grothendieck topology on (1F ↓ f ∗) whose covering sieves are precisely those whose image under the projection πF : (1F ↓ f ∗) → F are jointly epimorphic, such that the projection πE : (1F ↓ f ∗) → E defines a comorphism of sites πE : ((1F ↓ f ∗), Jf) → (E, Jcan) for which CπE ∼= f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose further that f : F → E is localic, then the full subcategory E ⋊ SubF(f ∗(−)) ⊆ (1F ↓ f ∗) (denoted by (1F ↓Sub f ∗) in [3]) on objects (F, E, F \u058c f ∗(E)), where F is a subobject of f ∗(E), is a Jf-dense subcategory (see [3, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose that E is the presheaf topos SetsCop, and let L: Cop → Frmopen be an internal locale of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By f : F → E denote the associated localic geometric morphism, so that L ∼= SubF(f ∗ ◦ よ(−)) (where よ: C → SetsCop denotes the Yoneda embedding).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We immediately have that the subcategory C ⋊ L ≃ C ⋊ SubF(f ∗ ◦ よ(−)) ⊆ E ⋊ SubF(f ∗(−)) ⊆ (1F ↓ f ∗), where an object (c, V ) ∈ C ⋊ L is associated with the object (V, よ(c), V \u058c f ∗(よ(c))) ∈ (1F ↓ f ∗), yields the inclusion of a Jf-dense subcategory C ⋊ L ⊆ (1F ↓ f ∗), and so, by the comparison lemma, F ≃ Sh(C ⋊ L, Jf|C⋊L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moreover, since there is a commuting square (C ⋊ L, Jf|C⋊L) ((1F ↓ f ∗), Jf) (C, Jtriv) (E, Jcan) pL πE よ of comorphisms of sites (the Yoneda embedding is a comorphism of sites, see [2, §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]) where both horizon- tal arrows induce equivalences of toposes, we obtain that CpL ∼= f via the diagram of induced geometric morphisms: Sh(C ⋊ L, Jf|C⋊L) Sh((1F ↓ f ∗), Jf) ≃ F SetsCop Sh(E, Jcan) ≃ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' CpL ∼ CπE ∼ =f ∼ 9 Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 (Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The relative topos CpL : Sh(C ⋊ L, Jf|C⋊L) → SetsCop constructed above is called the topos of internal sheaves (or just topos of sheaves) on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will use KL to denote the Grothendieck topology Jf|C⋊L, and will also sometimes denote the topos Sh(C ⋊ L, KL) by just Sh(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A sieve S in C ⋊ L is KL-covering if and only if S contains a small family { (ci, Ui) fi −→ (d, V ) | i ∈ I } in C ⋊ L such that V = � i∈I ∃fiUi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In [3], this is called the existential topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The projection pL : C ⋊ L → C has a right adjoint tL : C → C ⋊ L that sends each object c ∈ C to (c, ⊤c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore, by the description of the direct image functor CpL∗ found in [15, Theorem VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4], for each c ∈ C, there is an isomorphism of frames { V ∈ Lc | V ⩽ ⊤c } ∼= Lc ∼= CpL ∗ � ΩSh(L) � (c) ∼= ΩSh(L)(c, ⊤c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is not hard to recognise that this isomorphism can be extended so that, for each object (c, U) of C ⋊ L, there is an isomorphism { V ∈ Lc | V ⩽ U } ∼= ΩSh(L)(c, U), and that, for each morphism (c, U) f−→ (d, W) of C ⋊ L, the transition map ΩSh(L)(f): ΩSh(L)(d, W) → ΩSh(L)(c, U) sends V ∈ ΩSh(L)(d, W) to g−1(V ) ∧ U ∈ ΩSh(L)(c, U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Internal locales as existential fibred sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Given any functor L: Cop → Frmopen, we are still able to define KL as the function that assigns to each object (d, V ) of C ⋊ L the collection KL(c) of sieves { (ci, Ui) fi −→ (d, V ) | i ∈ I } in C⋊L such that V = � i∈I ∃fiUi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' However, KL is not necessarily a Grothendieck topology on C⋊L (see [15, Definition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]): KL clearly satisfies the maximality and transitivity conditions, but KL does not always satisfy the stability condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' When KL does define a Grothendieck topology, it coincides with the existential topology on L as defined in [3, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1], and so (C ⋊L, KL) is an existential fibred site over C in the sense of Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In fact, as L(g), for each arrow g of C, satisfies the Frobenius condition, (C ⋊ L, KL) is an existential site (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' KL is stable) if and only if the relative Beck-Chevalley condition is satisfied (see Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7 (Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (e)(i) [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A functor L: Cop → Frmopen is said to satisfy the relative Beck- Chevalley condition if, given an arrow e h−→ d of C, and a sieve S of C ⋊ L on the object (d, V ) for which V = � f∈S ∃fU, then h−1(V ) = � g∈h∗(S) ∃gW, where h∗(S) is the sieve on (e, h−1(V )) given by those arrows (c, W) g−→ (e, h−1(V )) such that the composite (c, W) g−→ (e, h−1(V )) h−→ (d, V ) is in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If KL does define a Grothendieck topology on the category C ⋊ L, then the topos Sh(C ⋊ L, KL) (called the existential topos for L in [3, Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2]) is also definable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The geometric morphism CpL : Sh(C ⋊ L, KL) → SetsCop, induced by the projection pL : C ⋊ L → C considered as a comorphism of sites pL : (C ⋊ L, KL) → (C, Jtriv), is localic by Examples A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2(a) & (c) in [12] (alternatively, by [2, Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='11] alone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Subsequently, one can calculate that L ∼= CpL ∗(ΩSh(C⋊L,KL)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, we arrive at the classification of internal locales in the topos SetsCop found in §5 of [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 10 Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8 (Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be a functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The following are equivalent: (i) L is an internal locale of SetsCop, (ii) L satisfies the relative Beck-Chevalley condition, (iii) KL is a Grothendieck topology on C ⋊ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The classification of internal locales of SetsCop, when C is cartesian, established by Joyal and Tierney in [13, Proposition VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], can be recovered via the classification of [3, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10] by noting, as is done in [3, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3], that the Beck-Chevalley and relative Beck-Chevalley conditions coincide when C has all finite limits (in fact, a study of the proof of [3, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3] reveals that only pullbacks are necessary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9 (Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 & Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let C be a category with all pullbacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A functor L: Cop → Frmopen satisfies the relative Beck-Chevalley condition, and thus defines an internal locale of SetsCop, if and only if L satisfies the Beck-Chevalley condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We complete this subsection with some observations of the Grothendieck topology KL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The Grothendieck topology KL on C ⋊ L is generated by the following two species of covering families: (A) � (c, U) f−→ (d, ∃fU) � for each arrow c f−→ d of C and U ∈ O(Lc), (B) � (c, Ui) idc −−→ � c, � i∈I Ui � | i ∈ I � for object c of C and family of opens Ui ∈ O(Lc), for i ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We immediately have that both species are KL-covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For the converse, note that, given a KL- covering sieve S on (d, V ), each morphism (c, U) f−→ (d, V ) of S can be written as the composite (c, U) (d, ∃fU) � d, � f∈S ∃fU � = (d, V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f idd Hence, any Grothendieck topology J for which both species (A) and (B) are J-covering contains the Grothendieck topology KL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We have refrained from naming the Grothendieck topology KL the ‘canonical topology’ to avoid confusion, despite it being a generalisation of the canonical topology on a locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Unlike a locale L of Sets, the Grothendieck topology KL is not necessarily a subcanoni- cal topology (defined on p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 126 of [15, §III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 542-3, §C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2] that a Grothendieck topology J on a category D is subcanonical only if every J-covering sieve S on an object D is effective-epimorphic, in the sense that D is the colimit of the (potentially large) diagram S D/D D, U where U : D/D → D is the forgetful functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Observe, however, that the sieve generated by a KL-covering family � (c, U) f−→ (d, ∃fU) � of species (A) is not effective-epimorphic for any non-invertible arrow f of C since the colimit in C ⋊ L is given by (c, U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Gluing Internal Locales What can prevent a functor L: Cop → Frmopen from being an internal locale?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' What goes wrong when KL is not stable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We give an example of such a functor, over a category C without all pullbacks, which is not an internal locale, despite L satisfying the Beck-Chevalley condition for those pullbacks in C that do exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Inspired by this counterexample, we develop in Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13 a method for identifying the internal locales of the presheaf topos SetsDop when D is obtained by ‘gluing’ certain constituent subcategories together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 11 Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be any locale in Sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For any category C with pullbacks, the constant functor L: Cop → Frmopen for L, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' L(c) = L and L(f) = idL for all objects c and arrows f of C, satisfies the Beck-Chevalley condition and so defines an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Now consider the category 1 2 3 id1 f id2 g id3 with all arrows displayed (we will refer to it as • → • ← •), which clearly lacks a pullback for the diagram 3 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' g f The constant functor L: (• → • ← •)op → Frmopen for a non-trivial locale L is not an internal locale of Sets(•→•←•)op since, for instance, the set S = � (•1, U) f−→ (•2, ⊤•2) | U ∈ O(L) � is a sieve of (• → • ← •) ⋊ L on (•2, ⊤•2) such that ⊤•2 = � S U but where ⊤•3 ̸= � g∗(S) U as g∗(S) is empty (here ⊤•i denotes the top element in L•i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The subobject classifier ΩSets(•→•←•)op is, of course, an internal locale of the presheaf topos Sets(•→•←•)op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [15, §III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7] that the subobject classifier ΩSetsCop : Cop → Sets of a presheaf topos SetsCop acts by sending an object c of C to the set of sieves on c while, for each arrow d f−→ c of C, the transition map ΩSetsCop (f): ΩSetsCop (c) → ΩSetsCop(d) sends a sieve S on c to the sieve f ∗(S) = { g | f ◦ g ∈ S } on d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, considered as a diagram of shape • → • ← • in Locopen (the category of locales and open local morphisms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Frmop open), ΩSets(•→•←•)op is given by 2 2 + 2 2, i1 i2 where 2 denotes the 2 element locale (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' the terminal locale) and 2 + 2 is the coproduct in Loc, because there are two sieves, ∅ and { id1 }, on •1, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Observe that the arrows i1 and i2 are disjoint open embeddings of locales, by which we mean the following are satisfied, for all V ∈ 2: i−1 1 ∃i1V = V, i−1 2 ∃i2V = ⊥, i−1 2 ∃i2V = V, i−1 1 ∃i2V = ⊥, where ⊥ represents the bottom element of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We show that the locale morphisms L(f) and L(g) being disjoint open embeddings characterises internal locales of Sets(•→•←•)op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We present this as a consequence of a wider theory regarding ‘gluing’ internal locales together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let { Ci | i ∈ I } be a set of categories where, for each i ∈ I, Ci has a terminal object 1i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let D be the category obtained from the disjoint union � i∈I Ci by freely adding a new terminal object 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each i ∈ I, we denote by fi : 1i → 1 the newly added morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A functor L: Dop → Frmopen defines an internal locale of SetsDop if and only if (i) for all i ∈ I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' L|Ci : Ci op ֒→ Dop L−→ Frmopen is an internal locale of SetsCop i ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 12 (ii) and,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' for each pair i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' j ∈ I with i ̸= j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' the locale morphisms L1i L1 L1j L(fi) L(fj) are disjoint open embeddings of locales,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' by which we mean that,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' for all V ∈ L1i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' V ′ ∈ L1j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f −1 i ∃fiV = V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f −1 j ∃fiV = ⊥i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f −1 j ∃fjV ′ = V ′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f −1 i ∃fjV ′ = ⊥i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' where ⊥i (respectively ⊥j) represents the bottom element of L1i (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' L1j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each object (d, V ) of D ⋊ L, with d being an object of Cj say, a sieve S on (d, V ) consists only of morphisms contained in Cj ⋊ L|Cj ⊆ D ⋊ L, and any arrow e h−→ d of D is also contained in the subcategory Cj ⊆ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore h−1(V ) = � g∈h∗(S) ∃gU for each such V , S and h if and only if L|Cj satisfies the relative Beck-Chevalley condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We can thus limit our attention to the second criterion of the corollary and sieves on objects of the form (1, V ) ∈ D ⋊ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose that L satisfies the relative Beck-Chevalley condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each i ∈ I and U ∈ L1i, the principle sieve S generated by the arrow (1i, U) fi −→ (1, ∃fiU) is KL-covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore f −1 i ∃fiU = � g∈f ∗ i (S) ∃gW = U, and so fi is an open embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each j ∈ I with i ̸= j, we have that f −1 j ∃fiU = � g∈f ∗ j (S) ∃gW, which, as f ∗ j (S) is empty, is equal to ⊥i as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, suppose that L|Ci is an internal locale of SetsCiop, for each i ∈ I, and that L(fi) and L(fj) are disjoint open embeddings for each pair i, j ∈ I with i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show that, if S is a sieve on (1, V ) for which V = � g∈S ∃gU, then h−1(V ) = � g∈h∗(S) ∃g′U ′ for any arrow e h−→ 1 of D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It suffices to consider the case when h = fj : 1j → 1, for some j ∈ I, and S is generated by arrows of the form (1i, U) fi −→ (1, V ), as any arrow h′ can be factored as e → 1j fj −→ 1 and any such sieve S can be rewritten as { (c, U) g−→ (1i, ∃gU) fi −→ (1, V ) | fi ∈ T } where T generates a KL-covering sieve of the desired form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' But now the thesis follows since L(fi) and L(fj) are disjoint open embeddings for each pair i, j ∈ I with i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Using Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13, we are instantly able to recognise that a functor L: (• → • ← •)op → Frmopen defines an internal locale of the topos Sets(•→•←•)op if and only if the diagram in Loc L•1 L•2 L•3 f g is a pair of disjoint open embeddings, and thus confirm using Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13 that the constant functor L: (• → • ← •)op → Frmopen considered in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='12 does not define an internal locale of Sets(•→•←•)op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 Internal Locales of Sheaf Toposes Let (C, J) be a Grothendieck site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The embedding Sh(C, J) \u058c SetsCop is a localic geometric morphism (see [12, Example A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2(a)]), and thus, for any localic geometric morphism F → Sh(C, J), the composite F → Sh(C, J) \u058c SetsCop is still localic (see [9, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, our understanding of the internal locales of the presheaf topos SetsCop can be leveraged to describe the internal locales of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall, from [6, §2] or [4, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1], that, given a fibration A: D → C and a Grothendieck topology J on C, the Giraud topology JA is the smallest topology on D making A a comorphism of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 13 Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='15 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 [3] & Corollary C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be a functor indexed over a category C with a Grothendieck topology J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The following are equivalent: (i) L is an internal locale of Sh(C, J), (ii) L is an internal locale of SetsCop and a J-sheaf, (iii) KL is stable and contains the Giraud topology JpL, (iv) KL is stable and there exists a factorisation Sh(C ⋊ L, KL) Sh(C, J) SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' CpL The equivalence of statements (i) and (ii) is a consequence of the fact that the direct image functor of any geometric morphism (in this case the inclusion Sh(C, J) ֒→ SetsCop) preserves internal locales (see p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 528 [12, §C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6], cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [12, Corollary C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10] as well).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The equivalence of (ii) and (iii) is proved in [3, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10] (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3(b) [3] too).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The final equivalence of (iii) and (iv) follows by definition of the Giraud topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 4 Internal Locale Morphisms In this section we study the morphisms of internal locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We aim to provide a parallel to the treatment of locale morphisms and the geometric morphisms between localic toposes that is found in Chapter IX [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], it is shown that, given two locales X, Y (of Sets), there is an equivalence Loc(X, Y ) ≃ Geom(Sh(X), Sh(Y )) between the category of locale morphisms X → Y and the category of geometric morphisms Sh(X) → Sh(Y ) and their respective natural transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our first aim in this section is to extend this result to internal locales of an arbitrary Grothendieck topos Sh(C, J), as is done in [3, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our method differs slightly from that of [3] as we never leave our site of definition (C, J) and establish an equivalence between the morphisms f: L1 → L2 of internal locales of Sh(C, J) and the morphisms of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) that are also morphisms of fibrations (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [3, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Morphisms of internal locales over a cartesian base category first appear in §VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 of [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our definition is identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 (Proposition VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' An internal locale morphism f: L1 → L2, between internal locales L1, L2 : Cop → Frmopen of the topos Sh(C, J), is a natural transformation f−1 : L2 → L1 such that, for each object c of C, f−1 c : L2(c) → L1(c) is a frame homomorphism and, for each morphism g : c → d of C, the diagram L2(d) L2(c) L1(d) L1(c) f−1 d L2(g) ∃L2(g) f−1 c L1(g) ∃L1(g) is a morphism of adjunctions: that is, L1(g) ◦ f−1 d = f−1 c L2(g) and ∃L1(g) ◦ f−1 c = f−1 d ∃L2(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will show in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 that internal locale morphisms f: L1 → L2 correspond bijectively to morphisms of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) 14 for which the triangle C ⋊ L2 C ⋊ L1 C ˘f CpL2 CpL1 commutes, and also to geometric morphisms f : Sh(L1) → Sh(L2) for which the triangle Sh(L1) Sh(L2) Sh(C, J) f CpL1 CpL2 (4) commutes, thereby recovering [3, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] that there is an equivalence of 2-categories Loc (Sh(C, J)) ≃ Loc/Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (5) Here Loc (Sh(C, J)) denotes the 2-category of internal locales of Sh(C, J), their internal locale morphisms and natural transformations between these.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By Loc/Sh(C, J) we denote the 2-category whose objects are localic geometric morphisms f : E → Sh(C, J), whose 1-cells are commuting geometric morphisms E E′ Sh(C, J), g f f ′ (the geometric morphism g is also localic by [9, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1(ii)]) and whose 2-cells are natural transformations between these.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Having related internal locale morphisms and arrows in Loc/Sh(C, J), we will then study in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 and §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 some select properties of internal locale morphisms and relate them to properties of the corresponding geometric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will extend, to the to internal setting, the results [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5(i) & Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], which state that a locale morphism f : L → K is an surjective locale morphism (respectively open) if and only if the corresponding geometric morphism Sh(f): Sh(L) → Sh(K) between localic toposes is an surjective (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' open).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Internal Locale Morphisms and Geometric Morphisms We first demonstrate two constructions: that each morphism of internal locales induces a geometric morphism that makes the triangle (4) commute, and, vice versa, each geometric morphism as in (4) induces a morphism of internal locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Using this, we then demonstrate the equivalence (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L1, L2 : Cop → Frmopen be internal locales of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Each internal locale morphism f: L1 → L2 induces a morphism of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moreover, the induced geometric morphism Sh(˘f) makes the triangle Sh(C ⋊ L1, KL1) Sh(C ⋊ L2, KL2) Sh(C, J) Sh(˘f) CpL1 CpL2 (6) commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 15 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We define a functor ˘f: C ⋊ L2 → C ⋊ L1 by sending an object (c, U) of C ⋊ L2 to the object (c, f−1 c (U)) and a morphism g : (c, U) → (d, V ) of C ⋊ L2 to g : (c, f−1 c (U)) → (d, f−1 d (V )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We claim that ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) is a morphism of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We check that the four conditions of Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (i) It suffices to show that the two generating species of KL2-covering families identified in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 are sent by ˘f to KL1-covering families.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let { g : (c, U) → (c, ∃L2(g)U) } be a KL2-covering family of species (A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The family ˘f({ g : (c, U) → (c, ∃L2(g)U) }) = { g : (c, f−1 c (U)) → (c, f−1 d (∃L2(g)U)) } is KL1-covering as f−1 d (∃L2(g)U) = ∃L1(g)f−1 c (U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let { idc : (c, Ui) → (c, � i∈I Ui) | i ∈ I } be a KL2- covering family of species (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The family ˘f �� idc : (c, Ui) → � c, � i∈I Ui � | i ∈ I �� = � idc : (c, f−1 c (Ui)) → � c, f−1 c �� i∈I Ui �� | i ∈ I � is KL1-covering since f−1 c is a frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) Each object (c, U) of C ⋊ L1 has an arrow idc : (c, U) → (c, ⊤) = (c, f−1 c (⊤)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) Given a pair of arrows g1 : (d, V ) → (c1, f−1 c1 (U1)), g2 : (d, V ) → (c2, f−1 c2 (U2)) of C ⋊ L2, we have that V ⩽ L2(g)(f−1 c1 (U1)) ∧ L2(g)(f−1 c2 (U2)), = f−1 d (L1(g)(U1) ∧ L1(g)(U2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, there are the commutative triangles (d, V ) (d, f−1 d (L1(g)(U1) ∧ L1(g)(U2))) (c1, f−1 c1 (U1)), (d, V ) (d, f−1 d (L1(g)(U1) ∧ L1(g)(U2))) (c2, f−1 c2 (U2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' idd g1 g1 idd g2 g2 (iv) Let f1, f2 : (c′, U ′) → (c, U) be a pair of parallel morphisms of C ⋊ L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If g : (d, V ) → (c′, f−1 c′ (U ′)) is a morphism of C ⋊ L1 such that ˘f(f1) ◦ g = ˘f(f2) ◦ g, then g : (d, V ) → (c′, f−1 c′ (U ′)) factors through the morphism g : (d, L1(g)(f−1 c′ (U ′))) → (c′, f−1 c′ (U ′)), which is of the form ˘f(g): (d, f−1 d (L2(g)(U ′))) → (c′, f−1 c′ (U ′)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, the triangle (6) commutes by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L1, L2 be internal locales of Sh(C, J) with an internal locale morphism f: L1 → L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will write Sh(f): Sh(L1) → Sh(L2) for the geometric morphism Sh(˘f) induced as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By [9, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2(ii)], Sh(f) is also a localic geometric morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 16 Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L1, L2 : Cop → Frmopen be internal locales of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Each geometric morphism f : Sh(L1) → Sh(L2), for which the triangle Sh(L1) Sh(L2) Sh(C, J) f CpL1 CpL2 (7) commutes induces an internal locale morphism f: L1 → L2 for which Sh(f) = f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each object E of Sh(L2), the map that sends a subobject U \u058c E to f ∗(U) \u058c f ∗(E) is a frame homomorphism f ∗ E : SubSh(L2)(E) → SubSh(L1)(f ∗(E)) and moreover, for each arrow g : E → E′ of Sh(L2), the diagram SubSh(L2)(E) SubSh(L2)(E′) SubSh(L1)(f ∗(E)) SubSh(L1)(f ∗(E′)) g−1 f ∗ E ∃g f ∗ E′ f ∗(g)−1 ∃f∗(g) commutes (see [15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 496-8]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since (7) commutes, f ∗ ◦ C∗ pL2 = C∗ pL1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' in particular, for each object c of C, we have that f ∗ ◦ C∗ pL2 (l(c)) = C∗ pL1 (l(c)), where l denotes the canonical functor l: C → Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We observed in (3) that L1 ∼= SubSh(L1)(C∗ pL1 ◦ l(−)): Cop → Frmopen, and similarly for L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, the frame homomorphisms f ∗ C∗ pL2 (l(c)) : SubSh(L2)(C∗ pL2 (l(c))) → SubSh(L1)(C∗ pL1 (l(c))), for each object c of C, collectively define an internal locale morphism f: L1 → L2 where f−1 c (U) = f ∗(U) for each subobject U \u058c C∗ pL2 (l(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, that Sh(f) = f follows from the description of the inverse image Sh(f)∗ of a geometric morphism induced by a morphism of sites found in [15, Theorem VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2]: for each U ∈ O(L2(c)), we have that Sh(f)∗(ℓ(c, U)) = ℓ′(c, f−1 c (U)) = ℓ′(c, f ∗(U)) = f ∗(U) (where ℓ and ℓ′ denote the canonical functors ℓ: C ⋊L2 → Sh(C ⋊L2, KL2) and ℓ′ : C ⋊L1 → Sh(C ⋊L1, KL1) respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus we obtain our bijective correspondence between between: the internal locale morphisms f: L1 → L2, the morphisms of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) for which the triangle C ⋊ L2 C ⋊ L1 C pL2 ˘f pL1 commutes, 17 the geometric morphisms f : Sh(L1) → Sh(L2) for which the triangle Sh(L1) Sh(L2) Sh(C, J) f CpL1 CpL2 commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We now use this bijective correspondence to establish the equivalence (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4 (Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There is an equivalence of 2-categories: Loc(Sh(C, J)) ≃ Loc/Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By L: Loc/Sh(C, J) → Loc (Sh(C, J)) denote the (1-)functor that sends a localic geometric morphism f : E → Sh(C, J) to the internal locale f∗(ΩE) and a commuting geometric morphism E E′ Sh(C, J) g f f ′ to the internal locale morphism g: f∗(ΩE) → f ′ ∗(ΩE′) induced by Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By T: Loc (Sh(C, J)) → Loc/Sh(C, J) denote the functor that sends an internal locale L to the localic geometric morphism CpL : Sh(C ⋊ L, KL) → Sh(C, J) and an internal locale morphism f: L → L′ to Sh(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By the isomorphism L ∼= CpL∗ � ΩSh(L) � and Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3, the functors L and T are mutually inverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This 1-equivalence extends to a 2-equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' One direction of the equivalence HomLoc(Sh(C,J))(L, L′) ≃ HomLoc/Sh(C,J)(Sh(L), Sh(L′)) follows from [12, Remark C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5], the other by noting that a natural transformation of inverse image functors Sh(L) Sh(L′), Sh(f)∗ Sh(f′)∗ α for two internal locale morphisms f, f′ : L → L′, induces a natural transformation SubSh(L)(−) SubSh(L′)(−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Sh(f)∗ Sh(f′)∗ α Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The subobject classifier ΩE of a topos is the terminal object of Loc(E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The identity idE : E → E is the terminal object of Loc/E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Surjective Internal Locale Morphisms Recall (from [12, Lemma A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6] say) that a geometric morphism f : F → E is a surjection if the inverse image functor f ∗ : E → F is faithful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [15, Definition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] that a locale morphism f : L → K is a surjection if the corresponding frame homomorphism f −1 : K → L is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In [15, Proposition X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5(i)], it is shown that a locale morphism f : L → K is surjective if and only if the corresponding geometric morphism Sh(f): Sh(L) → Sh(K) is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We show that surjections of internal locales can be characterised ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 18 Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L1 → L2 be an internal locale morphism of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We say that f is a surjective internal locale morphism if, for each c ∈ C, f−1 c : L2(c) → L1(c) is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L1 → L2 be an internal locale morphism of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The following are equivalent: (i) the geometric morphism Sh(f) is a surjective geometric morphism, (ii) f is a surjective internal locale morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By [2, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3], the geometric morphism Sh(f) is surjective if and only if the corresponding morphism of sites ˘f: (C ⋊ L2, KL2) → (C ⋊ L1, KL1) is cover reflecting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose each f−1 d is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let S be sieve of C ⋊ L2 on (d, V ) such that ˘f(S) is KL1-covering, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f−1 d (V ) = � g∈S ∃L1(g)f−1 c (U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We have that f−1 d (V ) = � g∈S ∃L1(g)f−1 c (U), = � g∈S f−1 d ∃L2(g)U, = f−1 d \uf8eb \uf8ed � g∈S ∃L2(g)U \uf8f6 \uf8f8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, V = � g∈S ∃L2(g)U and so S is KL2-covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, if ˘f is cover reflecting and f−1 c (U) = f−1 c (V ) for a pair U, V ∈ L2(c), then ˘f reflects the maximal cover and so U = V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 Open Internal Locale Morphisms Recall from [8, Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] that a geometric morphism f : F → E is open if, for each object E ∈ E, the canonical arrow ϕE : f ∗ � ΩE E � → Ωf ∗(E) F is a monomorphism or, equivalently by [8, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], the canonical arrow l: ΩE → f∗(ΩF) has an internal left adjoint, by which we mean a natural transformation m: f∗(ΩF) → ΩE where, for each c ∈ C, there is an adjunction mc ⊣ lc, where (C, J) is a site of definition for E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Where the inverse image functor of a geometric morphism preserves only the interpretation of geometric logic, open geometric morphisms, like open locale morphisms, preserve the interpretation of all infinitary first-order logic, and this property also characterises open geometric morphisms (see [8, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 & Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], it is shown that a locale morphism f : X → Y is open if and only if the corresponding geometric morphism Sh(f): Sh(X) → Sh(Y ) is open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L1 → L2 be an internal locale morphism of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We say that f is an open internal locale morphism if, for each c ∈ C, f−1 c : L2(c) → L1(c) is open and, for each morphism g : c → d, the square L2(d) L2(c) L1(d) L1(c) L2(g) ∃fd L1(g) ∃fc commutes, where ∃fc is the left adjoint to f−1 c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L1 → L2 be an internal locale morphism of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The following are equivalent: (i) the geometric morphism Sh(f) is an open geometric morphism, (ii) f is an open internal locale morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 19 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' From Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6, we know that, for each object (c, U) of C ⋊ L2, ΩSh(L2)(c, U) = { V ∈ L2(c) | V ⩽ U } and, by extension, Sh(f)∗(ΩSh(L1))(c, U) = ΩSh(L1) ◦˘f(c, U), = ΩSh(L1)(c, f−1 c (U)), = { V ′ ∈ L1(c) | V ′ ⩽ f−1 c (U) }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, for each object (c, U) of C ⋊ L2, the component l(c,U) : { V ∈ L2(c) | V ⩽ U } → { V ′ ∈ L1(c) | V ′ ⩽ f−1 c (U) } of the natural transformation l: ΩSh(L2) → Sh(f)∗(ΩSh(L1)) acts by V �→ f−1 c (V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If f−1 c is open for each object c of C, there is an external left adjoint (∃f)(c,U) : Sh(f)∗(ΩSh(L1))(c, U) → ΩSh(L2)(c, U) given by V ′ �→ ∃fcV ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show that the maps (∃f)(c,U) together define a natural transformation ∃f : Sh(f)∗(ΩSh(L1)) → ΩSh(L2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let g : (c, U) → (d, V ) be an arrow of C ⋊ L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We observe that the diagram Sh(f)∗(ΩSh(L1))(d, V ) Sh(f)∗(ΩSh(L1))(c, L2(g)(V )) Sh(f)∗(ΩSh(L1))(c, U) ΩSh(L2)(d, V ) ΩSh(L2)(c, L2(g)(V )) ΩSh(L2)(c, U) (∃f)(d,V ) (∃f)(c,L2(g)(V )) (∃f)(c,U) commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The left hand square commutes since L2(d) L2(c) L1(d) L1(c) L2(g) ∃fd L1(g) ∃fc commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The right hand square commutes since (∃fcV ′)∧U = ∃fc(V ′∧f−1 c (U)) for each V ′ ⩽ f−1 c (L2(g)(V )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, if l: ΩSh(L2) → Sh(f)∗(ΩSh(L1)) has an internal left adjoint m, then, for each object c of C, as the map l(c,⊤): ΩSh(L2)(c, ⊤) → Sh(f)∗(ΩSh(L1))(c, ⊤), is isomorphic to f−1 c : L2(c) → L1(c), we obtain a left adjoint ∃fc to f−1 c , isomorphic to m(c,⊤), which is natural in the sense that the square L2(d) L2(c) L1(d) L1(c) L2(g) ∃fd L1(g) ∃fc commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show that ∃fc satisfies the Frobenius condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This follows since, for each U ∈ L1(c), the square Sh(f)∗(ΩSh(L2))(c, ⊤) ΩSh(L1)(c, ⊤) Sh(f)∗(ΩSh(L2))(c, U) ΩSh(L1)(c, U) m(c,⊤) m(c,U) 20 commutes and so m(c,⊤)(V ) ∧ U = m(c,U)(V ∧ f−1 c (U)) for each V ∈ O(L2(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, by following the same argument of [15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 504, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], we conclude that m(c,⊤)(V ) ∧ U = m(c,U)(V ∧ f−1 c (U)), = m(c,U)(V ∧ f−1 c (U) ∧ f−1 c (U)), = m(c,⊤)(V ∧ f−1 c (U)) ∧ U, = m(c,⊤)(V ∧ f−1 c (U)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, as m(c,⊤) ∼= ∃fc, we have that f−1 c is an open frame homomorphism for each c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 5 Internal Embeddings and Nuclei This final section is dedicated to the study of internal locale embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [15, Definition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] that a locale morphism f : K → L is said to be an embedding if the corresponding frame homomorphism f −1 : L → K is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Just as with surjective internal locale morphisms, we define internal locale embeddings as the ‘point-wise’ generalisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L1 → L2 be an internal locale morphism of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We say that f is an internal locale embedding if, for each c ∈ C, f−1 c : L2(c) → L1(c) is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will also refer to L1 as an internal sublocale of L2 and as f as the inclusion of this internal sublocale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall (from [15, §VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4] say) that a geometric morphism f : F → E is said to be a geometric embedding (and F a subtopos of E) if the direct image functor f∗ is full and faithful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall also, from [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4], that geometric embeddings generalise embeddings of sublocales in the sense that, given a locale morphism f : K → L, the induced geometric morphism Sh(f): Sh(K) → Sh(L) between the toposes of sheaves is a geometric embedding if and only if f is an embedding of locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The aim of this section is to prove an analogous result for embeddings of internal locales: that, given a morphism of internal locales f: L′ → L of Sh(C, J), the geometric morpism Sh(f) is an embedding if and only if f is an internal locale embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' One direction is easily achieved by applying results from §6 [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Demonstrating the converse to Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 below is postponed to Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If f: L1 → L2 is an internal locale embedding of Sh(C, J), then Sh(f) is a geometric embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let (D, J) be a site and E a Grothendieck topos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By [2, Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4], a J-continuous flat functor G: D → E yields a geometric embedding if and only if: (i) each object E of E is covered by objects of the form G(d), for d ∈ D, (ii) for each pair of objects d, d′ of D and arrow g : G(d) → G(d′) of E, there exists a family of morphisms S = { hi : ei → d | i ∈ I } such that G(S) is jointly epimorhic in E and, for each i ∈ I, g ◦G(hi) = G(ki) for some arrow ki : ei → d′ in D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The canonical functor ℓ: C ⋊ L1 → Sh(L) is a KL1-continuous flat functor that induces an equivalence of toposes, hence an inclusion, and so satisfies both conditions of [2, Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The KL2-flat functor Sh(f)∗ ◦ ℓ′ : C ⋊ L2 → Sh(L) that defines the geometric morphism Sh(f): Sh(L1) → Sh(L2) factors as C ⋊ L2 C ⋊ L1 Sh(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' ˘f Sh(f)∗◦ℓ′ ℓ If f−1 c is surjective for each c ∈ C, then ˘f: C ⋊ L2 → C ⋊ L1 is surjective on both objects and arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, as ℓ satisfies the conditions of [2, Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4], so too does Sh(f)∗ ◦ ℓ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Hence, Sh(f) is a geometric embedding as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 21 Let L be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since every geometric embedding is localic (see [12, Example A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2(a)]), every subtopos of Sh(L) is obtained by a morphism of internal locales L′ → L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore, we can understand the subtoposes of Sh(L) by leveraging a study of the internal sublocales of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In particular, we will reprove the well-known result (see [12, §A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5]) that the poset Sub(Sh(L)) of subtoposes of Sh(L) is a co-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' To do so, we will develop a study of internal nuclei, the internal generalisation of a nucleus on a locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1, internal nuclei on an internal locale are introduced and it is shown that internal nuclei corre- spond bijectively with internal locale embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2, it is shown that internal nuclei on L, and thus by extension internal sublocales of L, correspond bijectively with subtoposes of Sh(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 is dedicated to proving that Sub(Sh(L)) is a co-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By using an internal generalisation of pre-nuclei, we observe that the co-frame operations on Sub(Sh(L)) can be computed ‘point-wise’ via the co-frame operations on SubLoc(Lc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 Internal Nuclei Recall from [10, §II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2] that a nucleus on a locale L is a function j : L → L satisfying, for all x, y ∈ L, x ⩽ j(x), j(j(x)) ⩽ j(x), j(x ∧ y) = j(x) ∧ j(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' These properties are referred to as j being, respectively, inflationary, idempotent, and meet-preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Any function satisfying these properties must also be monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is well-known (see [10, Theorem II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]) that there is a bijective correspondence between nuclei on L and sublocales of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In one direction, the nucleus associated to a sublocale f : K \u058c L is given by the function f∗f −1 : L → L (here f∗ denotes the right adjoint to f −1, see Notation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, given a nucleus j : L → L, the image of j as a subset of L, which we denote by Lj, can be given the structure of a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The meets are computed as they are in L while the join of a subset { Ui | i ∈ I } ⊆ Lj is computed as j �� i∈I Ui � , where � i∈I Ui is the join in L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is then clear that j : L → Lj constitutes a surjective frame homomorphism (see [10, Lemma II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2] or [15, Proposition IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Nuclei are a useful tool when studying sublocales since many properties of sublocales are more readily proven using nuclei than directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In particular, that the sublocales of a locale L form a co-frame is often proved via nuclei, as discussed in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our aim in this subsection is to generalise the notion of nucleus to the internal setting and thereby develop a nucleic study of internal sublocales, and therefore subtoposes of sheaves on an internal locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' An internal nucleus is a natural transformation j : L → L (as a functor into Sets) such that each component jc : Lc → Lc, for c ∈ C, is a nucleus on the locale Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' When the subobject classifier ΩSh(C,J) of Sh(C, J) is considered as an internal locale, the definition of an internal nucleus j : ΩSh(C,J) → ΩSh(C,J) coincides with that of a Lawvere-Tierney topology (see [12, Definition A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f : F → E be a localic geometric morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will observe below in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 that internal nuclei on f∗(ΩF) correspond bijectively with Lawvere-Tierney topologies on ΩF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In the following results we establish a bijective correspondence between internal nuclei on L and internal sublocales of L that generalises the bijective correspondence for locales found in [10, Theorem II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let j : L → L be a nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each subset { Ui | i ∈ I } ⊆ L, we have that: j �� i∈I Ui � = j �� i∈I jUi � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The first inequality j �� i∈I Ui � ⩽ j �� i∈I jUi � is a consequence of j being inflationary as Ui ⩽ jUi for each i ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The converse inequality is achieved by applying j to both sides of the canonical inequality � i∈I jUi ⩽ j �� i∈I Ui � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 22 Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Each internal nucleus j on an internal locale L of Sh(C, J) defines an embedding of internal locales Lj ֒→ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By the above discussion, for each object c of C, the nucleus jc : Lc → Lc induces a sublocale Lj c of Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As j is a natural transformation, for each arrow c g−→ d of C, g−1 : Ld → Lc restricts to a function g−1 : Lj d → Lj c which, by the definition of meets and joins in Lj d and Lj c, can easily be shown to be a frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We must therefore show that each g−1 : Lj d → Lj c is open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' A left adjoint is given by jd∃L(g) since, for each U ∈ Lj c and V ∈ Lj d, jd∃L(g)U ⩽ V = jd(V ) ⇐⇒ ∃L(g)U ⩽ V ⇐⇒ U ⩽ g−1(V ), and furthermore the Frobenius condition is satisfied: jd∃L(g)U ∧ V = jd∃L(g)U ∧ jdV = jd((∃L(g)U) ∧ V ) = jd∃L(g)(U ∧ g−1(V )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We thus conclude that each internal nucleus j induces a functor Lj : Cop → Frmopen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moreover, we observe that the square Lc Ld Ljc c Ljd d jc ∃g jd jd∃g commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each U ∈ Lc, U ⩽ jc(U) and so jd∃gU ⩽ jd∃gjc(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, as U ⩽ g−1∃gU, it follows that jd(U) ⩽ jd ◦ g−1 ◦ ∃g(U) =⇒ jd(U) ⩽ g−1 ◦ jc ◦ ∃g(U), =⇒ ∃g ◦ jd(U) ⩽ jc ◦ ∃g(U), =⇒ jc ◦ ∃g ◦ jd(U) ⩽ jc ◦ ∃g(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore, we have a natural transformation j : L → Lj where each component is a surjective frame homo- morphism for which jd∃gjc = jd∃g for each arrow d g−→ c of C, and hence j would define an embedding of internal locales if Lj were also an internal locale of SetsCop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains only to show that functor Lj satisfies the relative Beck-Chevalley condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let S be a sieve on (d, V ) ∈ C ⋊ Lj such that V = jd \uf8eb \uf8ed � g∈S jd∃L(g)U \uf8f6 \uf8f8 , which, by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4, is equal to jd �� g∈S ∃L(g)U � , and let e h−→ d be an arrow of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let W = � g∈S ∃L(g)U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since L is an internal locale of Sh(C, J), h−1(W) = � g∈h∗(S) ∃L(g)U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4, we have the desired equality h−1(V ) = h−1(jd(W)) = je(h−1(W)) = je \uf8eb \uf8ed � g∈h∗(S) ∃L(g)U \uf8f6 \uf8f8 = je \uf8eb \uf8ed � g∈h∗(S) je∃L(g)U \uf8f6 \uf8f8 , and therefore Lj is an internal locale of SetsCop (and since Sh(Lj) → SetsCop factors as Sh(Lj) Sh(L) Sh(C, J) Sh(C, J), we conclude that Lj is an internal locale of Sh(C, J) too).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 23 Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There is a bijective correspondence between internal sublocales of L and internal nuclei on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By the theory of standard locales, there is a bijective correspondence between collections of nuclei { jc : Lc → Lc | c ∈ C } and collections of sublocales { fc: L′ c \u058c Lc | c ∈ C }, where both are indexed by the objects of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Our bijection will be a restriction of this correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We have already seen in Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 that if the collection { jc: Lc → Lc | c ∈ C } of nuclei is natural in c, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' it defines an internal nucleus, then the corresponding collection of sublocales yields an internal sublocale embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show the other direction: that if { fc: L′ c \u058c Lc | c ∈ C } are the components of an internal sublocale embedding, then the corresponding collection of nuclei is natural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let f: L′ → L be an embedding of an internal sublocale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since each component f−1 c : L′(c) → L(c) is surjective, it induces a nucleus f∗cf−1 c : L(c) → L(c), for each object c of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We wish to show that, for each arrow c g−→ d of C, the square Ld Lc Ld Lc f∗df−1 d g−1 f∗cf−1 c g−1 commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since the square Ld Lc Ld Lc, f−1 d g−1 ∃g f−1 c g−1 ∃g is a morphism of fibrations, so is the square of right adjoints Ld Lc Ld Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' g−1 g∗ f∗d g−1 f∗c g∗ Hence we have the desired equality f∗cf−1 c g−1 = f∗cg−1f−1 d = g−1f∗df−1 d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2 Geometric Embeddings We now establish a bijective correspondence between internal nuclei and Lawvere-Tierney topologies, and hence between internal sublocales and subtoposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let F be a Grothendieck topos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [12, Definition A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] that a Lawvere-Tierney topology is a endomorphism j : ΩF → ΩF on the subobject classifier of the topos F such that the diagrams 1 ΩF ΩF ΩF ΩF × ΩF ΩF ΩF, ΩF, ΩF × ΩF ΩF ⊤ ⊤ j j j j j×j ∧ j ∧ commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall also, from [12, Theorem A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8] that there is a bijection between Lawvere-Tierney topolo- gies and subtoposes of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As observed in [15, Corollary IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6], given a locale L, there is a bijection between Lawevere-Tierney topologies on ΩSh(L) (and hence subtoposes of Sh(L)) and nuclei on L (and hence sublo- cales of L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The following result extends this bijection to the internal setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 24 Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be an internal locale of E ≃ Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There is a bijective correspon- dence between the following: (i) the subtoposes of F ≃ Sh(L);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) internal nuclei on L;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) internal sublocales of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In particular, if f: L′ → L is an internal locale morphism, Sh(f) is a geometric embedding if and only if f is an internal locale embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The bijective correspondence between internal nuclei and internal sublocales was shown in Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We now demonstrate a bijective correspondence between subtoposes of F ≃ Sh(L) and internal nuclei on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We rely on the characterisation of subtoposes of Sh(L) in terms of Lawvere-Tierney topologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let j : ΩSh(L) → ΩSh(L) be a Lawvere-Tierney topology and let f : Sh(L) → SetsCop be the localic geometric morphism such that f∗(ΩSh(L)) ∼= L (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f = CpL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' By now applying the direct image functor f∗ : Sh(L) → SetsCop, we obtain an endomorphism f∗j : f∗(ΩSh(L)) ∼= L → f∗(ΩSh(L)) ∼= L (by the description of CpL ∗ afforded by [15, Theorem VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2], (f∗j)c = j(c,⊤)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We claim that f∗j is an internal nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since j was a Lawvere-Tierney topology, makes the following diagrams commute: L L L × L L L, L × L L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' f∗j f∗j f∗j f∗j×f∗j ∧ f∗j ∧ Thus, f∗j : L → L is a natural transformation such that (f∗j)c : Lc → Lc is idempotent and preserves binary meets, for each c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to show that (f∗j)c is inflationary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let U ∈ Lc ∼= f∗(ΩSh(L))(c) ∼= SubSh(L)(f ∗よ(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We consider the subobject classifier ΩSh(L) as a sheaf on the canonical site (Sh(L), Jcan).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As j is a Lawvere-Tierney topology and natural, there is a commutative diagram of sets 1(U) SubSh(L)(U) SubSh(L)(f ∗よ(c)) SubSh(L)(U) SubSh(L)(f ∗よ(c)) ⊤U ⊤U jU (f∗j)c where ⊤U picks out the top element U ∈ SubSh(L)(U) and the map SubSh(L)(f ∗よ(c)) → SubSh(L)(U) is induced by pulling back subobjects along the monomorphism U \u058c f ∗(よ(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In other words, it sends a sub- object V ∈ SubSh(L)(f ∗よ(c)) to U ∧ V ∈ SubSh(L)(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, by chasing the element U ∈ SubSh(L)(f ∗よ(c)) through the diagram, we observe that U ∧ (f∗j)c(U) = jU(U) = U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, U ⩽ (f∗j)c(U) as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Conversely, given an internal nucleus k: L ∼= f∗(ΩSh(L)) → L ∼= f∗(ΩSh(L)), we define an endomorphism kf on the subobject classifier ΩSh(L), viewed as a sheaf ΩSh(L) : (C ⋊ L)op → Sets, by setting kf (c,U)(V ) as kc(V ) ∧ U, for each (c, U) ∈ C ⋊ L and V ∈ ΩSh(L)(c, U) = { V ∈ O(Lc) | V ⩽ U }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We now demonstrate that kf is an Lawvere-Tierney topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As k is an internal nucleus, it is clear that, for each (c, U) ∈ C ⋊ L, the diagrams 1(c, U) ΩSh(L)(c, U) ΩSh(L)(c, U) ΩSh(L)(c, U) ΩSh(L)(c, U), ΩSh(L)(c, U), ⊤(c,U) ⊤(c,U) kf (c,U) kf (c,U) kf (c,U) kf (c,U) 25 ΩSh(L) × ΩSh(L)(c, U) ΩSh(L)(c, U) ΩSh(L) × ΩSh(L)(c, U) ΩSh(L)(c, U) ∧ kf (c,U)×kf (c,U) kf (c,U) ∧ all commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It remains to observe that kf is natural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each arrow (c, U) g−→ (d, V ) of C ⋊ L, the diagram ΩSh(L)(d, V ) ΩSh(L)(c, g−1(V )) ΩSh(L)(c, U) ΩSh(L)(d, V ) ΩSh(L)(d, g−1(V )) ΩSh(L)(c, U) kf (d,V ) kf (c,g−1(V )) kf (c,U) commutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The left-hand square commutes since, for each W ∈ Ld with W ⩽ V , kc(g−1(W)) ∧ g−1(V ) = g−1(kd(W)) ∧ g−1(V ) = g−1(kd(W) ∧ V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Meanwhile, the right-hand square commutes since kc(W ∧ U) ∧ U = kc(W) ∧ U for each W ∈ Lc with W ⩽ g−1(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, the bijection is completed by noting that, for each c ∈ C and U, V ∈ Lc, (f∗kf)c(V ) = kf (c,⊤)(V ) = kc(V ) ∧ ⊤ = jc(V ) and (f∗j)f (c,U)(V ) = j(c,⊤)(V ) ∧ U = j(c,U)(V ), for each internal nucleus k on L and each Lawvere-Tierney topology j on ΩSh(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3 The Frame of Internal Nuclei In this final subsection, we consider the poset of internal nuclei on an internal locale, and demonstrate that it forms a frame whose frame operations can be computed ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be a locale and let N(L) denote the set of nuclei on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We can order N(L) by setting j ⩽ k if j(U) ⩽ k(U) for all U ∈ O(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall, from [10, Proposition II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] say, that so ordered N(L) is a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The set of sublocales of L, written as SubLoc(L), can also be ordered with [K \u058c L] ⩽ [K′ \u058c L] if and only if there is a factorisation K K′ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Under the bijection between nuclei and sublocales, this is precisely the order dual N(L) ∼= SubLoc(L)op, and hence SubLoc(L) is a co-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definitions 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be an internal locale of Sh(C, J) and let E be a topos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (i) By N(L) we denote the poset of internal nuclei on L ordered by j ⩽ k if and only if, for each c ∈ C and U ∈ Lc, jc(U) ⩽ kc(U) for each pair of internal nulcei on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (ii) By LT(E) we denote the poset of Lawvere-Tierney topologies for E, ordered by j ⩽ k if and only if j = j ∧ k, given two Lawvere-Tierney topologies j, k: ΩE → ΩE (this poset is denoted as Lop(E) in [12, §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' (iii) By Sub(E) we denote the poset of subtoposes of E ordered by [F′ \u058c E] ⩽ [F \u058c E] if and only if there is a factorisation of geometric morphisms F′ F E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 26 (iv) By SubLoc(Sh(C,J))(L) we denote the poset of internal sublocales of L ordered by [L′ \u058c L] ⩽ [L′′ \u058c L] if and only if there is a factorisation of internal locale morphisms L′ L′′ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Under the bijections established in Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='7, there is an isomorphism of posets: N(L) ∼= LT(Sh(L)) ∼= Sub(Sh(L))op ∼= SubLoc(Sh(C,J))(L)op (where the latter two posets are the order duals of Sub(Sh(L)) and SubLoc(Sh(C,J))(L) respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We know already, from [12, §A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] say, that Sub(Sh(L)) is a complete co-Heyting algebra, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' a co-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will give an alternative proof using internal nuclei that N(L) is a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moreover, we will show that the frame operations of N(L) can be computed ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' That is, for each subset { ji | i ∈ I } ⊆ N(L) and each object c of C, there are equalities �� i∈I ji � c = � i∈I ji c, �� i∈I ji � c = � i∈I ji c, where � i∈I ji c and � i∈I ji c are computed as in N(Lc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The first of these equalities is easily shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The meet of a subset { ji | i ∈ I } ⊆ N(L) is given by �� i∈I ji � c (U) = � i∈I ji c(U), (8) for each c ∈ C and U ∈ Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If (8) defines a valid internal nucleus on L, it must clearly be the meet of { ji | i ∈ I } ⊆ N(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [10, Proposition II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] that � i∈I ji c yields a nucleus on Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' As g−1 : O(Ld) → O(Lc) is open, for an arrow c g−→ d of C, it preserves all meets and so g−1 �� i∈I ji d(U) � = � i∈I g−1ji d(U) = � i∈I ji cg−1(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, � i∈I ji defines an internal nucleus on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will demonstrate that N(L) is a frame by generalising the notion of a pre-nucleus on a locale, recalled below, to the internal setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We give some justification as to why the frame operations can be computed ‘point-wise’ as described in Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall that the suptoposes of Sh(C, J) correspond to Grothendieck topologies J′ on C that contain J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In the case of a Grothendieck topology J on C ⋊ L that contains KL, we observe that the added data is generated by new covering families on the fibres Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Specifically, adding a new covering family { (ci, Ui) fi −→ (c, U) | i ∈ I } to KL is equivalent to requiring that the family { (c, ∃fiUi) idc −−→ (c, U) | i ∈ I } is covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Pre-nuclei of Locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' There are many proofs of the fact that, for each locale L, N(L) is a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For example, the proof found in [10, Proposition II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5] shows that N(L) is a complete Heyting algebra by defining the Heyting operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Alternative approaches using pre-nuclei are considered in [17] and [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will follow the argument of [17] when developing our internal generalisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We briefly repeat the argument for locales below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Recall from [17, §2] that a pre-nucleus on a locale L is a (necessarily monotone) map p: L → L that is inflationary and finite-meet-preserving: that is, for all U, V ∈ L, U ⩽ p(U), p(U ∧ V ) = p(U) ∧ p(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 27 Thus, a nucleus on L is simply an idempotent pre-nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Unlike nuclei, pre-nuclei are closed under composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We denote by PN(L) the poset of pre-nuclei on L ordered by p ⩽ q if p(U) ⩽ q(U) for all U ∈ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It is clear that PN(L) is a complete lattice: for each subset { pi | i ∈ I } ⊆ PN(L) and U ∈ L, �� i∈I pi � (U) = � i∈I pi(U), �� i∈I pi � (U) = � i∈I pi(U), where � i∈I pi(U) and � i∈I pi(U) are calculated as in L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' It follows by the infinite distributive law for L that PN(L) is also a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In [5, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1] it is shown that the inclusion of nuclei into pre-nuclei N(L) ֒→ PN(L) has a left adjoint (−)∞ : PN(L) → N(L), which we call the nucleation (the nuclear reflection in [5] and idempotent closure in [17]), constructed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each ordinal α and limit ordinal λ, we define inductively: p0(U) = U, pα+1(U) = p(pα(U)), pλ(U) = � α<λ pα(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' At each stage, the resultant map pκ : L → L is a pre-nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Necessarily, as L is small, there is a sufficiently large ordinal κ such that pκ is idempotent and therefore a nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We label this p∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We observe that if p ⩽ q then p∞ ⩽ q∞, that p ⩽ p∞, and if j is a nucleus then j = j∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' That is, nucleation is functorial, and has units and counits yielding the adjunction N(L) PN(L) (−)∞ ⊥ witnessing N(L) as a reflective subcategory of PN(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, N(L), in addition to the meets constructed in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='9, has all joins: for a subset { ji | i ∈ I } ⊆ N(L), the join in N(L) is given by �� i∈I ji�∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The infinite distributive law for N(L), and hence the fact that N(L) is a frame, is a consequence of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='10 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1 [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be a locale, n a nucleus on L, and let { pi | i ∈ I } be a collection of pre-nuclei on L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The infinite distributive law � n ∧ � i∈I pi �∞ = n ∧ �� i∈I pi �∞ holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will show that � n ∧ � i∈I pi�κ = n ∧ �� i∈I pi�κ, for each ordinal κ, and thereby deduce the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The base case � n ∧ � i∈I pi �0 = idL = n ∧ �� i∈I pi �0 is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Suppose that � n ∧ � i∈I pi�α = n ∧ �� i∈I pi�α, then: � n ∧ � i∈I pi �α+1 = � n ∧ � i∈I pi � � n ∧ � i∈I pi �α , = n �� n ∧ � i∈I pi �α� ∧ � i∈I pi �� n ∧ � i∈I pi �α� , = n ∧ n ��� i∈I pi �α� ∧ � i∈I pin ∧ pi ��� i∈I pi �α� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 28 Using that n ⩽ n ��� i∈I pi�α� , and n ⩽ pin, for all i, we have that: � n ∧ � i∈I pi �α+1 = n ∧ � i∈I pin ∧ pi ��� i∈I pi �α� , = � i∈I n ∧ pin ∧ pi ��� i∈I pi �α� , = � i∈I n ∧ pi ��� i∈I pi �α� , = n ∧ �� i∈I pi �α+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, if λ is a limit ordinal such that � n ∧ � i∈I pi�α = n ∧ �� i∈I pi�α for each ordinal α < λ, then: � n ∧ � i∈I pi �λ = � α<λ � n ∧ � i∈I pi �α , = � α<λ n ∧ �� i∈I pi �α , = n ∧ �� i∈I pi �λ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Internal Pre-nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We now extend the theory of pre-nuclei and nucleation to the internal context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' In doing so we will observe that N(L) is a frame for every internal locale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' An internal pre-nucleus is a natural transformation p: L → L such that, for each c ∈ C, pc: Lc → Lc is a pre-nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The set of internal pre-nuclei, denoted by PN(L), can be ordered by p ⩽ q if pc(U) ⩽ qc(U) for all c ∈ C and U ∈ Lc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The poset of internal pre-nuclei PN(L) on an internal locale L of Sh(C, J) has all meets and all joins, which are computed ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Thus, by the infinite distributivity law for Lc, for each c ∈ C, PN(L) is a frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We show that an internal nucleation can be performed ‘point-wise’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let p: L → L be an internal pre-nucleus on an internal locale L, fibred over a category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The pointwise nucleations p∞ c : L → Lc of each component pc of p are the components of an internal nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' For each object c ∈ C, the nucleation p∞ c : Lc → Lc of pc is a nucleus, so it remains only show that they are natural in c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' This is easily shown by induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We will perform the case for a limit ordinal λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let g : c → d be an arrow of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' If, for all α < λ, the square Ld Lc Ld Lc g−1 pα d pα c g−1 commutes, then we have the desired equality g−1 � � α<λ pα d � = � α<λ g−1pα d = � α<λ pα c g−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 29 As a result, we obtain a left adjoint to the inclusion N(L) ֒→ PN(L), N(L) PN(L), (−)∞ ⊥ just as we did for locales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The functor (−)∞ : PN(L) → N(L), the internal nucleation, sends internal pre-nuclei to their point-wise nucleation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The poset N(L) of internal nuclei is a frame whose frame operations can be computed ‘point-wise’ in that, for each subset { ji | i ∈ I } ⊆ N(L) and each object c of C, there are equalities �� i∈I ji � c = � i∈I ji c, �� i∈I ji � c = � i∈I ji c, (9) where � i∈I ji c and � i∈I ji c are computed as in N(Lc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' We saw in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 that N(L) has all meets and that these are computed pointwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The join of { ji | i ∈ I } ⊆ N(L) is the nucleation of the join of { ji | i ∈ I } as internal pre-nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since the nucleation of internal pre-nuclei is computed pointwise, as are joins in PN(L), the joins in N(L) are also computed pointwise in the sense of (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Finally, as N(Lc) satisfies the infinite distributivity law for each c ∈ C, we obtain the infinite distributivity law for N(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Let L: Cop → Frmopen be an internal locale of Sh(C, J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Since the frame operations of N(L) are computed ‘point-wise’, for each object c of C, the projection πc : N(L) → N(Lc) that sends an internal nucleus j : L → L to its component jc : Lc → Lc at c preserves all joins and meets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Therefore, πc : N(L) → N(Lc) is an open frame homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='15 (§A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='5 [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The poset of subtoposes of a Grothendieck topos is a co-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Every Grothendieck topos E is the topos of sheaves Sh(L) for some internal locale L (see, for example, [13, Proposition VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' The result follows as Sub(E) ∼= N(L)op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Acknowledgements I thank the support of my supervisor Olivia Caramello, and acknowledge the financial support of the Insubria- Huawei studentship into “Grothendieck toposes for information and computation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' References [1] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Caramello, Theories, sites, toposes: relating and studying mathematical theories through topos- theoretic ‘bridges’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Oxford University press, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [2] ——, “Denseness conditions, morphisms and equivalences of toposes,” 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' arXiv: 1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='08737 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='CT].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [3] ——, “Fibred sites and existential toposes,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' arXiv: 2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='11693 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='AG].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [4] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Caramello and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Zanfa, “Relative topos theory via stacks,” 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' arXiv: 2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='04417 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content='AG].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Escard´o, “Joins in the frame of nuclei,” Applied Categorical Structures, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 117–124, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Giraud, “Classifying topos,” in Toposes, Algebraic Geometry and Logic, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Lawvere, Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=', Berlin, Heidelberg: Springer Berlin Heidelberg, 1972, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 43–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Johnstone, Topos Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Academic Press, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [8] ——, “Open maps of toposes,” Manuscripta mathematica, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 31, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 217–248, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [9] ——, “Factorization theorems for geometric morphisms, I,” Cahiers de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 3–17, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 30 [10] ——, Stone Spaces, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Cambridge Studies in Advanced Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Cambridge University Press, 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [11] ——, “The point of pointless topology,” Bulletin (New Series) of the American Mathematical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 41–53, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [12] ——, Sketches of an Elephant: A topos theoretic compendium, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Oxford University Press, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Joyal and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Tierney, “An extension of the Galois theory of Grothendieck,” Memoirs of the Amer- ican Mathematical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 51, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Kock and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moerdijk, “Presentations of ´etendues,” Cahiers de Topologie et G´eom´etrie Diff´erentielle Cat´egoriques, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 145–164, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' MacLane and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Springer New York, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Picado and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Pultr, Frames and Locales: Topology without points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Springer Basel, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' [17] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' Simmons, “Near-discreteness of modules and spaces as measured by Gabriel and Cantor,” Journal of Pure and Applied Algebra, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 119–162, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} +page_content=' 31' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtAzT4oBgHgl3EQfCfq3/content/2301.00961v1.pdf'} diff --git a/xtE3T4oBgHgl3EQflwoI/content/2301.04609v1.pdf b/xtE3T4oBgHgl3EQflwoI/content/2301.04609v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..77d883a98aad43b7709a46306868a0f56b8442ea --- /dev/null +++ b/xtE3T4oBgHgl3EQflwoI/content/2301.04609v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c2c2bc699bd9889cb4c0380a3d5d59dffa9982bf46d7963f9a8aa1a6616bacb +size 334438 diff --git a/xtE3T4oBgHgl3EQflwoI/vector_store/index.faiss b/xtE3T4oBgHgl3EQflwoI/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..a8643596b66b04b278e19c9e738e0450951daf30 --- /dev/null +++ b/xtE3T4oBgHgl3EQflwoI/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9df2bdf1a5ce5ef7ec1738e8bb2aa9cbfaec02c1c91c2ac3c7431f37eb09d5b9 +size 2949165 diff --git a/xtE3T4oBgHgl3EQflwoI/vector_store/index.pkl b/xtE3T4oBgHgl3EQflwoI/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..dacafc1b05291778a03f060a6c3dcf348590d954 --- /dev/null +++ b/xtE3T4oBgHgl3EQflwoI/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e309da93287cfbf1a10bcc6ef714c7c5c57bf5568723340df964f472047a722d +size 105631 diff --git a/yNE0T4oBgHgl3EQftQGw/content/2301.02590v1.pdf b/yNE0T4oBgHgl3EQftQGw/content/2301.02590v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2ab7fe6868be056612e17205509a3029ef182984 --- /dev/null +++ b/yNE0T4oBgHgl3EQftQGw/content/2301.02590v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0c15c40e5b716d8dce5976b15299bb1c89755739835cce020b3e1a8c06a7a970 +size 614855 diff --git a/ydE1T4oBgHgl3EQf4AWL/content/2301.03496v1.pdf b/ydE1T4oBgHgl3EQf4AWL/content/2301.03496v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8954f1ed5ea7e8f2510447fad8c64cc263e73f1f --- /dev/null +++ b/ydE1T4oBgHgl3EQf4AWL/content/2301.03496v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c346bbfb8f4d0bf3435f5003faec4e2d75845e5a67cebb05a7e699090269f6ad +size 1854084 diff --git a/ydE1T4oBgHgl3EQf4AWL/vector_store/index.faiss b/ydE1T4oBgHgl3EQf4AWL/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..61fe2cbf9ea6218ba89d9a48cbf9c407615200fb --- /dev/null +++ b/ydE1T4oBgHgl3EQf4AWL/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4be983a6719595aba0a06cc37d7e17735ee318ab519a452d4f7aae2cce80d09c +size 3932205 diff --git a/ydE1T4oBgHgl3EQf4AWL/vector_store/index.pkl b/ydE1T4oBgHgl3EQf4AWL/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..0316c3806d6e3612bc6f86defc334d457e86feeb --- /dev/null +++ b/ydE1T4oBgHgl3EQf4AWL/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:92d6b49e37b0e156b95b19bd15a15302d9894039a988504ac33b5f080078e1df +size 158166 diff --git a/zNE0T4oBgHgl3EQf_AJ2/content/2301.02821v1.pdf b/zNE0T4oBgHgl3EQf_AJ2/content/2301.02821v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4b7e294eb014ce0e3444639385ed7f3890c9c3fb --- /dev/null +++ b/zNE0T4oBgHgl3EQf_AJ2/content/2301.02821v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60d6a5558236cf31793441630bdc5e73e0406087090c8df568c781fd93ff60f5 +size 998209 diff --git a/zNE0T4oBgHgl3EQf_AJ2/vector_store/index.faiss b/zNE0T4oBgHgl3EQf_AJ2/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..a7b963b87cae0fb3b0933e25b26350f0901dd83a --- /dev/null +++ b/zNE0T4oBgHgl3EQf_AJ2/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:089b4079ca57895c7fa24e96714f71099f1e6b58008151878fe56bb714910e67 +size 3801133